All categories

3 years ago

Need help with a math question

Mathematics

2 answers:

sveta [45]3 years ago

7 0

Answer:

75%

Step-by-step explanation:

Thee are 8 juniors... from this 6 are female.

So the probability of the student is female given its junior)=6/8=3/4=.75=75%

OleMash [197]3 years ago

5 0

Answer:

20 percent

Step-by-step explanation:

6/30

6÷30=.2

You might be interested in

Need help with trig problem in pic

Sidana [21]

Answer:

a) $cos(\alpha)=-\frac{3}{5}\\$

b) $\sin(\beta)= \frac{\sqrt{3} }{2}$

c) $\frac{4+3\sqrt{3} }{10}\\$

d) $\alpha\approx 53.1^o$

Step-by-step explanation:

a) The problem tells us that angle $\alpha$ is in the second quadrant. We know that in that quadrant the cosine is negative.

We can use the Pythagorean identity:

$tan^2(\alpha)+1=sec^2(\alpha)\\(-\frac{4}{3})^2 +1=sec^2(\alpha)\\sec^2(\alpha)=\frac{16}{9} +1\\sec^2(\alpha)=\frac{25}{9} \\sec(\alpha) =+/- \frac{5}{3}\\cos(\alpha)=+/- \frac{3}{5}$

Where we have used that the secant of an angle is the reciprocal of the cos of the angle.

Since we know that the cosine must be negative because the angle is in the second quadrant, then we take the negative answer:

$cos(\alpha)=-\frac{3}{5}$

b) This angle is in the first quadrant (where the sine function is positive. They give us the value of the cosine of the angle, so we can use the Pythagorean identity to find the value of the sine of that angle:

$cos (\beta)=\frac{1}{2} \\\\sin^2(\beta)=1-cos^2(\beta)\\sin^2(\beta)=1-\frac{1}{4} \\\\sin^2(\beta)=\frac{3}{4} \\sin(\beta)=+/- \frac{\sqrt{3} }{2} \\sin(\beta)= \frac{\sqrt{3} }{2}$

where we took the positive value, since we know that the angle is in the first quadrant.

c) We can now find $sin(\alpha -\beta)$ by using the identity:

$sin(\alpha -\beta)=sin(\alpha)\,cos(\beta)-cos(\alpha)\,sin(\beta)\\$

Notice that we need to find $sin(\alpha)$ , which we do via the Pythagorean identity and knowing the value of the cosine found in part a) above:

$sin(\alpha)=\sqrt{1-cos^2(\alpha)} \\sin(\alpha)=\sqrt{1-\frac{9}{25} )} \\sin(\alpha)=\sqrt{\frac{16}{25} )} \\sin(\alpha)=\frac{4}{5}$

Then:

$sin(\alpha -\beta)=\frac{4}{5}\,\frac{1}{2} -(-\frac{3}{5}) \,\frac{\sqrt{3} }{2} \\sin(\alpha -\beta)=\frac{2}{5}+\frac{3\sqrt{3} }{10}=\frac{4+3\sqrt{3} }{10}$

Since $sin(\alpha)=\frac{4}{5}$

then $\alpha=arcsin(\frac{4}{5} )\approx 53.1^o$

4 0

3 years ago

A rectangular parking lot has an area of 315 square yards. The width of the parking lot is 5 yards longer than the length of the

Blababa [14]

Answer:

Dimension of parking lot is approximately 15.425 × 20.425 yards.

Step-by-step explanation:

Given:

Area of the parking lot = $315 \ yd^2$

Let the length of the parking lot be $'l'$

Also Given:

The width of the parking lot is 5 yards longer than the length of the parking lot.

so we can say that;

width of the parking lot, $w=5+l$

We need to find the dimension of parking lot.

Solution:

Now we can say that;

Area of rectangle is equal to length times width.

framing in equation form we get;

$lw=315$

Now substituting the value of w in above equation we get;

$l(l+5)=315\\\\l^2+5l=315\\\\l^2+5l-315=0$

Now we will find the roots using quadratic equation.

$ax^2+bx+c =0$

a = 1

b=5

c=-315

Formula for quadratic equation is;

$l =\frac{-b\±\sqrt{b^2-4ac}}{2a}$

First we will find;

$\sqrt{b^2-4ac} = \sqrt{5^2-4\times1\times-315} =\sqrt{25+1260}=\sqrt{1285} \approx35.85$

Now we will substitute the value we get;

$l =\frac{-5\±35.85}{2\times1}= \frac{-5\±35.85}{2}$

Now we will find 2 roots we get;

$l= \frac{-5+35.85}{2}= \frac{30.85}{2}\approx15.425\\\\OR\\\\l =\frac{-5-35.85}{2}= \frac{-40.85}{2} \approx -20.425$

Now we get 2 values of length one is positive and other is negative.

But length of parking lot cannot be negative hence we will discard the negative value.

Hence the length of the parking lot = 15.425 yards

Width of the rectangular parking lot = $l+5=15.425+5 =20.425$

Hence we can say that dimension of parking lot is approximately 15.425 × 20.425 yards.

3 0

3 years ago

Must show work to get brainly.

ale4655 [162]

Answer:

D. 32, 8, 256

Step-by-step explanation:

You want to get the same base numbers so you can add exponents

sqrt(2)^(4x+1) = 2^(2x+1/2)

16^x = 2^4x

4^(8x-6) = 2^(16x-12)

Now you can drop the bases and do the following equation

2x+1/2 + 4x = 16x-12

Solve for x, which is 1.25

Plug 1.25 back into the original numbers and you get the answers for the dimensions and area.

8 0

3 years ago

During the fall semester, Marvin, Latoya, and Abdulla each read three sevenths of the library books in the classroom. If Latoya

Romashka-Z-Leto [24]

Answer:

There are 45 library books in the classroom.

Step-by-step explanation:

The problem says that Marvin, Latoya and Abdulla each read 3/7 of the library books in the classroom. If Latoya read 3/7 of the books, we can form a proportion to determine the number of total library books in the classroom.

$\frac{3}{7} =\frac{15}{x}$

To solve for 'x', we can either cross-multiply and divide, or we can multiply the denominator by the same factor as the numerator to get a product of 15. In this case, the same factor would be 5, so 7 x 5 = 35. If we cross-multiply:

3x = (15)(7) or x = 35.

7 0

4 years ago

Write the equation of a line that is parallel to y=9 and that passes through the point (3,-8)

Nitella [24]

Answer:

y = - 8

Step-by-step explanation:

You would use the Y value

6 0

3 years ago