In a particular library, 18% of the books are children's books, 53% of the books are adult fiction, and the rest are adult nonfiction. You select 3 books at random; what is the probability That none of them are children's books?

Answer:

The solutions I found to this system of equations are (1, 0) and (⁸/₁₅, -7).  

I keep second guessing and recalculating the second point there, so I'd suggest double-checking it by going through the work yourself.  The first one checks out though.

Step-by-step explanation:

Let's solve this by substitution, where one equation is solved for one variable and substituted in to the other.  As the latter equation is already solved for y, we can simply substitute it into the other:

given:

   y = 3x² - 4x + 1

   3x - 5y = 3

then:

  3x - 5(3x² - 4x + 1) = 3

Which we can then simplify and solve:

3x - 15x² + 20x - 5 = 3

-3x + 15x² - 20x + 5 = -3

15x² - 23x = -8

Now we can find find the solution by completing the square:

15(15x² - 23x) = 15(-8)

225x² - 345x = -120

225x² - 345x  + (23/2)² = -120 + (23/2)²

225x² - 345x  + 529/4 = -120 + 529/4

(15x - 11.5)² = -120 + 132.25

(15x - 11.5)² = 12.25

15x - 11.5 = ± √12.25

15x - 11.5 = ± 3.5

15x = 11.5 ± 3.5

x = (11.5 ± 3.5) / 15

x = 15 / 15, and 8 / 15

x = 1, and 0.5333...

Now that we have x, we can solve for y.

given: 3x - 5y = 3

for x = 1:

3 - 5y = 3

y = 0

for x = ⁸/₁₅:

3(⁸/₁₅) - 5y = 3

5y = 3(⁸/₁₅) - 3

5y = ²⁴/₁₅ - ⁴⁵/₁₅

5y = -²¹/₁₅

y = -²¹/₃

y = -7

So the solutions to this system of equations are (1, 0) and (⁸/₁₅, -7).

Answer:

B

Step-by-step explanation:

Both triangles are similar. The similarity ratio between AB and EF is 4, which must mean that FG is BC (60)/4. The area of a rectangle is base x height -> 6.25 x 15 = 93.75 square cm

Hope this helps!

Answer:

equivalent of √6 . ✓3 is option a. 3√2

√6×3 = √18 = √9. √2 = 3√2

Answer:

Step-by-step explanation:

area = (3x³y)(2xy + x⁵)

= 3x³y·2xy + 3x³y·x⁵

= 6x⁴y² + 3x⁸y

Answer:

skewed left

Step-by-step explanation:

Answer is in the file below

tinyurl.com/wpazsebu

Answer:

no its not 3.5

Answer:

undefined

Step-by-step explanation:

The slope of a vertical line is undefined, and can't be found. This is because the denominator of the rise over run fraction is always 0.

Answer:

362+3x=500

Step-by-step explanation:

x is the varible and it represents how many chairs you need.

Answer:

The 4th option, 10g + 24 = t

Step-by-step explanation:

It costs 24 dollars per month no matter what.

$10 * the amount of GB you want

Add those two values to get the total cost per month.

In this case you want 5 GB, so substitute the g in the equation for 5. You will get:

10 * 5 +24 = t

50 + 24 = t

74 = t

So it costs 74 dollars per month to get 5 GB.

Answer:

1.13

Step-by-step explanation:

Edge 2021 hope this helps

Answer:

C. y= 1.5x

Step-by-step explanation:

Everytime multiply the first number 1.5 (y) by the X variables it gives you another Y variable. For example, 1.5 times 2 = 3. 1.5 times 3 = 4.5. And 1.5 times 4 = 6!

Answer (assuming it can be in slope-intercept form):

[tex]y = -2x +10[/tex]    

Step-by-step explanation:

1) First, we need to find the slope of the given equation. To do that easily, convert it to slope-intercept form, represented by the formula  [tex]y = mx + b[/tex]. Isolate y:

[tex]2x + y = 3\\y = -2x + 3[/tex]

The number in place of [tex]m[/tex], or the coefficient of the x-term, represents the slope of the equation. So, the slope of the given equation is -2.

Lines that are parallel share the same slope. So, the slope of the new equation will be -2 as well.  

2) Now, remember that the slope-intercept form is represented by the formula [tex]y = mx + b[/tex]. In order to write an equation of a line using that formula, we need to substitute values for [tex]m[/tex] and [tex]b[/tex]. We know [tex]m[/tex] is the slope, so we already know what that equals. Now, we just need to find [tex]b[/tex].

To do that, substitute -2 for [tex]m[/tex] in the slope-intercept formula. Additionally, substitute the x and y values of the point (2,6) for the x and y in the formula as well. This sets up the equation so that we can isolate [tex]b[/tex] and find its values:  

[tex]y = mx +b\\6 = (-2)(2)+b\\6 = -4 + b\\10 = b[/tex]

So, [tex]b[/tex] = 10.

3) Substitute values for [tex]b[/tex] and [tex]m[/tex] into the slope-intercept formula to write the slope-intercept form of the line:

[tex]y = -2x +10[/tex]

Equation of a line parallel to the line 2x + y = 3 that passes through the point (2,6) is y+2x=10

Lines which does not intersect each other at any point is said to be Parallel.

Here given equation of line is 2x+y=3

first we will write this equation in y=mx+c form

So y=3-2x

y= -2x+3

We know that slope of parallel lines is same

So equation of parallel line will be

y=-2x+a

Now we know that line is passing through (2,6)

So

[tex]6=-2(2)+a\\\\6+4=a\\\\a=10[/tex]

Hence equation of parallel line is y=-2x+10

or we can write it as y+2x=10

Equation of a line parallel to the line 2x + y = 3 that passes through the point (2,6) is y+2x=10

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Answer:

No, AB is not tangent to C.

If it were tangent, it would form a right angle with the radius, and we could use Pythagorean's Theorem.

3²+6²=7²

9+36=49

45=49  Since this is false, it's not a right angle, and AB is not tangent.

Step-by-step explanation:

No, AB is not tangent to C.

If it were tangent, it would form a right angle with the radius, and we could use Pythagorean's Theorem.

3²+6²=7²

9+36=49

45=49  Since this is false, it's not a right angle, and AB is not tangent.

The line segment AB is not a tangent to C since it is not perpendicular to BC.

The tangent is perpendicular to the radius of the circle joined from the center to the point at which the tangent touches the circle.

The Pythagorean theorem states that in a right-angled triangle, the sum of the squares of the sides is equal to the square of the hypotenuse.

z² = x² + y²

The line segment AB would be a tangent if the triangle ABC is a right-angled triangle. We can use the Pythagorean theorem.

7² = 3² + 6²

49 = 9 +36

49 = 45

This is incorrect.

49 ≠ 45

This means that the triangle is not a right-angled triangle. This in turn means that AB is not a tangent to C.

We have determined that AB is not a tangent to C as it is not perpendicular to BC.

Learn more about tangents here-https://brainly.com/question/16507124

#SPJ2

Answer:

C

Step-by-step explanation:

We want to evaluate the definite integral:

[tex]\displaystyle \int_0^1 (x+2)(3x^2+12x+1)^{1/2}\, dx[/tex]

Again, notice that the radicand is quite similar to the outside factor. So, we can use u-substitution again. We will let:

[tex]\displaystyle u=3x^2+12x+1[/tex]

Then:

[tex]\displaystyle \frac{du}{dx}=6x+12[/tex]

Hence:

[tex]\displaystyle du=6x+12 \, dx[/tex]

And we can divide both sides by 6:

[tex]\displaystyle \frac{1}{6}\, du=x+2\, dx[/tex]

Note that the limits of integration of our original integral (from x = 0 to x = 1) is in the domain of x. Since we changed variables, we should also change the limits of integration to u. So:

[tex]u(0)=3(0)^2+12(0)+1=1[/tex]

And:

[tex]u(1)=3(1)^2+12(1)+1=16[/tex]

Hence, our new limits of integration is from u = 1 to u = 16.

Perform the substitution:

[tex]\displaystyle =\int_{1}^{16} u^{1/2}\Big(\frac{1}{6}\, du\Big)[/tex]

Simplify:

[tex]\displaystyle =\frac{1}{6}\int_1^{16}u^{1/2}\, du[/tex]

Integrate:

[tex]\displaystyle =\frac{1}{6}\Big(\frac{2}{3}u^{3/2}\Big)\Big|_{1}^{16}[/tex]

Simplify:

[tex]=\displaystyle \frac{1}{9}\Big(u^{3/2}\Big|_1^{16}\Big)[/tex]

Evaluate:

[tex]\displaystyle =\frac{1}{9}\Big(16^{3/2}-1^{3/2}\Big)=\frac{1}{9}(64-1)=7[/tex]

The answer is C.

So everything you have now is right so far:

[tex]\cos(24) = \frac{z}{118}[/tex]

Multiply 118 to the left side to isolate z

[tex]118\cdot\cos(24) = z[/tex]

z = 50.05

Hope this helps

Answer:

your answer will be Option C.256

Step-by-step explanation:

hope it helps

Answer:

105

Step-by-step explanation:

Answer:

I think 105 and it is this because it is correct try the answer. ✅

Adding K shifts the graph up that many units.

The vertex of f(x) is at y = -3

The vertex of g(x) is at y = 1

This as a 4 unit shift upwards.

K = 4

Answer:

0.0392 = 3.92% probability that the test result is positive.

Step-by-step explanation:

Probability of a positive test:

95% of 1%(person has the disease)

100 - 97 = 3% of 100 - 1 = 99%(person does not have the disease).

What is the probability that the test result is positive?

[tex]p = 0.95*0.01 + 0.03*0.99 = 0.0392[/tex]

0.0392 = 3.92% probability that the test result is positive.

Answer:

Step-by-step explanation:

Vertex: ( -2, -25)

Axis of symmetry: -2

Answer:

B

Step-by-step explanation:

Answer:

The ratio of a 45-45-90 traingle is 1:1:[tex]\sqrt{2}[/tex].

Answer:

0.48

Step-by-step explanation:

2.88/6=0.48

Answer:

2.88 / 6 = 0.48

Explanation:

Answer:

The principal for the account is $375.

Step-by-step explanation:

This is a simple interest problem.

The simple interest formula is given by:

[tex]E = P*I*t[/tex]

In which E is the amount of interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.

The interest earned after 1 year is $12 .If the interest rate is 3.2% for account (A).

This means, respectively, that [tex]t = 1, E = 12, I = 0.032[/tex]

We want to find P.

[tex]E = P*I*t[/tex]

[tex]12 = P*0.032*1[/tex]

[tex]P = \frac{12}{0.032}[/tex]

[tex]P = 375[/tex]

The principal for the account is $375.

Answer: I helped you now I helped me

Step-by-step explanation:

Would you shoutout me if I poured shamrock shake on my headYou

Answer:

its C aka none of the above

Step-by-step explanation:

Have a good day:))

Answer:

its D

Step-by-step explanation:

The right angle triangle with 30-60-90 degrees is the special triangle in which these angle will have the side ratio of 1, [tex]\sqrt{3} [/tex] and  2. The value of the [tex] \cos\dfrac{(-2\pi)}{3} [/tex] which Omar wants to determine is -1/2.

Omar wants to determine the  value of

[tex] \cos\dfrac{(-2\pi)}{3} [/tex]

As the degree is in the pi form. Use the conversion rate [tex]\dfrac{180}{\pi} [/tex] to convert the degree,

[tex]=\dfrac{(-2\pi)}{3} \times\dfrac{180}{\pi} [/tex]

[tex]=-120[/tex]

As the angle -120 degrees is in the third quadrant hence the reference angle is 60 degrees(by calculating as (180-theta).

Now the right angle triangle with 30-60-90 degrees measure angle. Such angle will have the side ratio of 1, [tex]\sqrt{3} [/tex] and  2.

Here 2 is the hypotenuse of the right triangle. The side opposite to the angle measure [tex]\sqrt{3} [/tex] and the side adjacent to the angle measures 1 in ratio.

Now the cos theta is the ratio of the adjacent side and hypotenuse thus,

[tex] \cos\dfrac{(-2\pi)}{3} =-\dfrac{1}{2} [/tex]

Negative sign is used for the third quadrant where x axis is negative.

[tex] \cos\dfrac{(-2\pi)}{3} =-\dfrac{1}{2} [/tex]

Thus the value of the [tex] \cos\dfrac{(-2\pi)}{3} [/tex] which Omar wants to determine is -1/2.

Learn more about the trigonometry here;

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