What is the equivalent to 178 and 739

4. A rectangle has a diagonal of 8 cm. The diagonal creates a 60° angle at the base of the rectangle.

tamaranim1 [39]

9514 1404 393

Answer:

a) see attachment

b) base: 4, height: 4√3

c) area: 16√3

Step-by-step explanation:

a) The figure is drawn in the attachment

__

b) The side lengths of a 30-60-90 right triangle have the ratio ...

1 : √3 : 2

Multiplying these by 4 gives the side lengths of each triangle created by the diagonal. The base (short leg) is 4 units; the height (long leg) is 4√3 units.

__

c) The area is the product of base and height:

A = bh

A = 4(4√3) = 16√3 . . . . square units

7 0

3 years ago

A new car battery is sold with a two-year warranty whereby the owner gets the battery replaced free of cost if it breaks down du

Mariana [72]

Answer:

4.01% probability that the battery will break down during the warranty period

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

$\mu = 45, \sigma = 12$

a. What is the probability that the battery will break down during the warranty period

Warranty of 2 years = 24 months. So this is the pvalue of Z when X = 24.

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{24 - 45}{12}$

$Z = -1.75$

$Z = -1.75$ has a pvalue of 0.0401

4.01% probability that the battery will break down during the warranty period

7 0

3 years ago

For the system below identify the parameters as growth rates, carrying capacities, and measure of interactions between species.

babunello [35]

Answer:

2 and 3 are the the growth rates parameter for x and y respectively
16 and 20 are the carrying capacities for x and y respectively
2 and 7 measures the benefit to x and y of the interaction of the two species.

The species compete each other.

Step-by-step explanation:

When we have a population model for two species as we have here, the differential equations looks like this:

$\frac{dx}{dt}=a*x+b\frac{x^{2}}{N}+c*xy$

$\frac{dy}{dt}=d*x+e\frac{y^{2}}{M}+f*xy)$

Here:

a and d are the the growth rates parameter for x and y respectively

N and M are the carrying capacities for x and y respectively

c and f measures the benefit to x and y of the interaction of the two species.

So in our case we have:

$\frac{dx}{dt}=2*x+\frac{x^{2}}{16}+2*xy$

$\frac{dy}{dt}=3*x-\frac{x^{2}}{20}-7*xy$

Therefore:

2 and 3 are the the growth rates parameter for x and y respectively
16 and 20 are the carrying capacities for x and y respectively
2 and 7 measures the benefit to x and y of the interaction of the two species.

The term xy determine the if the species are cooperating of competing, so in this case have negative xy term in the second equation, it means the presence of either species decreases the rate of change of the other, so the species compete each other.

I hope it helps you!

3 0

3 years ago

Which of the following lists the three named stars in order of increasing mass (lowest mass first)?

Helga [31]

Answer:

Option (A)

Step-by-step explanation:

The Barnard's Star is usually considered to be a red dwarf, that is approximately six light-years away from the location of earth. It is present in the Ophiuchus constellation and forms the 4th proximate star to the sun.

Altair refers to the bright shining star present in the Aquila constellation. It forms the 12th brightest star that occurs in the night sky.

Spica is one of the proximate stars to the earth and that is extremely large having a mass of almost ten times the mass of the sun.

The mass of Barnard's star is= 2.864 × 10^29 kg

The mass of the Altair is= 3.56 × 10^30 kg

The mass of the Spica= 19.89 × 10^30 kg

The arrangement of these given stars in the increasing order are as follows-

Barnard's star (minimum) < Altair star < Spica star (maximum)

Hence, the correct answer is option (A).

3 0

3 years ago

Use compatibale numbers to find two estimates for 478 divided by 2

iogann1982 [59]

Hi on this question I got 239

4 0

3 years ago