Each of four friends orders a sweatshirt from a catalog. There are 16 colors of sweatshirts, 7 of which are all cotton and 9 of which are a blend. Each one orders a different color (no repeats) at random. What is the probability that the friends order only cotton sweatshirts?

Answer:

According to steps 2 and 4. The second-order polynomial must be added by [tex]-c[/tex] and [tex]b^{2}[/tex] to create a perfect square trinomial.

Step-by-step explanation:

Let consider a second-order polynomial of the form [tex]a\cdot x^{2} + b\cdot x + c = 0[/tex], [tex]\forall \,x \in\mathbb{R}[/tex]. The procedure is presented below:

1) [tex]a\cdot x^{2} + b\cdot x + c = 0[/tex] (Given)

2) [tex]a\cdot x^{2} + b \cdot x = -c[/tex] (Compatibility with addition/Existence of additive inverse/Modulative property)

3) [tex]4\cdot a^{2}\cdot x^{2} + 4\cdot a \cdot b \cdot x = -4\cdot a \cdot c[/tex] (Compatibility with multiplication)

4) [tex]4\cdot a^{2}\cdot x^{2} + 4\cdot a \cdot b \cdot x + b^{2} = b^{2}-4\cdot a \cdot c[/tex] (Compatibility with addition/Existence of additive inverse/Modulative property)

5) [tex](2\cdot a \cdot x + b)^{2} = b^{2}-4\cdot a \cdot c[/tex] (Perfect square trinomial)

According to steps 2 and 4. The second-order polynomial must be added by [tex]-c[/tex] and [tex]b^{2}[/tex] to create a perfect square trinomial.

Answer: D

Step-by-step explanation:

EDGE 2023

Answer:

A. The graph of g(x) is vertically compressed by a factor of 3.

Step-by-step explanation:

When there is a fraction, that means that there is a veritcal dilation.

Hope this helps! Good luck!

Answer:

[tex]\displaystyle x = \frac{\pi}{3} +k\, \pi[/tex] or [tex]\displaystyle x =- \frac{\pi}{3} +2\,k\, \pi[/tex], where [tex]k[/tex] is an integer.

There are three such angles between [tex]0[/tex] and [tex]2\pi[/tex]: [tex]\displaystyle \frac{\pi}{3}[/tex], [tex]\displaystyle \frac{2\, \pi}{3}[/tex], and [tex]\displaystyle \frac{4\,\pi}{3}[/tex].

Step-by-step explanation:

By the double angle identity of sines:

[tex]\sin(2\, x) = 2\, \sin x \cdot \cos x[/tex].

Rewrite the original equation with this identity:

[tex]2\, (2\, \sin x \cdot \cos x) - 2\, \sin x + 2\sqrt{3}\, \cos x - \sqrt{3} = 0[/tex].

Note, that [tex]2\, (2\, \sin x \cdot \cos x)[/tex] and [tex](-2\, \sin x)[/tex] share the common factor [tex](2\, \sin x)[/tex]. On the other hand, [tex]2\sqrt{3}\, \cos x[/tex] and [tex](-\sqrt{3})[/tex] share the common factor [tex]\sqrt[3}[/tex]. Combine these terms pairwise using the two common factors:

[tex](2\, \sin x) \cdot (2\, \cos x - 1) + \left(\sqrt{3}\right)\, (2\, \cos x - 1) = 0[/tex].

Note the new common factor [tex](2\, \cos x - 1)[/tex]. Therefore:

[tex]\left(2\, \sin x + \sqrt{3}\right) \cdot (2\, \cos x - 1) = 0[/tex].

This equation holds as long as either [tex]\left(2\, \sin x + \sqrt{3}\right)[/tex] or [tex](2\, \cos x - 1)[/tex] is zero. Let [tex]k[/tex] be an integer. Accordingly:

Any [tex]x[/tex] that fits into at least one of these patterns will satisfy the equation. These pattern can be further combined:

Answer:

3x-4

Step-by-step explanation:

Have a good day!!

Answer:

3x-4

Step-by-step explanation:

Answer:

Step-by-step explanation:

Solution,

Use the BODMAS Rule:

B = Bracket

O = Of

D = Division

M= Multiplication

A = Addition

S = Subtraction

Now,

Let's solve,

[tex]2 + 8 \div 2 \times 3[/tex]

First we have to divide 8 by 2

[tex] = 2 + 4 \times 3[/tex]

Calculate the product

[tex] = 2 + 12[/tex]

Calculate the sum

[tex] = 14[/tex]

Hope this helps...

Good luck on your assignment..

Answer:

14

Step-by-step explanation:

2 + 8 ÷ 2 x 3 =

There is an addition, a division, and a multiplication. According to the correct order of operations, we do first the multiplications and divisions in the order they appear from left to right.

= 2 + 4 x 3

= 2 + 12

Now we do the addition.

= 14

Answer:

625.

Step-by-step explanation:

(5+5×5÷5-5)⁵/5

=[ ( 5 + 25 / 5 - 5)^5] /  5

= [(5 + 5 - 5)^5] /  5

= [ (10 - 5)^5] /  5

= 5^5 / 5

= 5^4

= 625.

Answer:

625

Step-by-step explanation:

The rule is to do Parentheses/Brackets, then Exponents/Orders, followed by doing Multiplication and Division from left to right, and finally Addition and Subtraction from left to right. The answer is 625

Answer:

48 wings

Step-by-step explanation:

12:3 is the ratio. So multiply both of it by 4. Then it would be 48:12

Answer:

48 chicken wings

Step-by-step explanation:

If Bao can eat 12 chicken wings in 3 minutes and 12 minutes is 3 minutes times 4, then the answer would be 12 chicken wings times 4, so 12 times 4, which is 48, so the answer would be 48 chicken wings.

Step-by-step explanation:

in each equation once substitute the value of x as 0 and again y as zero by this way you will get two values of X and y .

then again find the slope for each equation by the formula

slope= -coefficient of x / coefficient of y

for example,

X+y is greater or equals to 5

or, X+y= 5

or, X=5-y

or, when y is equals to zero

X= 5

and when X is equals to zero

y= 5

then plot the above point in the graph with respect to its slope and the shaded part is the solution

Answer:

3 [tex]\pm[/tex] [tex]\sqrt{5}[/tex].

Step-by-step explanation:

x^2 = 6x - 4

x^2 - 6x + 4 = 0

Now, we can use the quadratic formula to solve.

[tex]\frac{-b\pm\sqrt{b^2 - 4ac} }{2a}[/tex], where a = 1, b = -6, and c = 4.

[tex]\frac{-(-6)\pm\sqrt{(-6)^2 - 4 * 1 * 4} }{2 * 1}[/tex]

= [tex]\frac{6\pm\sqrt{36 - 4 * 4} }{2}[/tex]

= [tex]\frac{6\pm\sqrt{36 - 16} }{2}[/tex]

= [tex]\frac{6\pm\sqrt{20} }{2}[/tex]

= [tex]\frac{6\pm2\sqrt{5} }{2}[/tex]

= 3 [tex]\pm[/tex] [tex]\sqrt{5}[/tex]

x = 3 [tex]\pm[/tex] [tex]\sqrt{5}[/tex].

Hope this helps!

Answer:

the answer would be x is less than 6.

Step-by-step explanation:

the reason why it would not be x is less than or equal to 6 is that the circle is not filled in.

Answer:

B

Step-by-step explanation:

x≤6

We can see from the graph that it starts from 6 and goes to 5, 4, 3, 2.

Hope this helps ;) ❤❤❤

Answer:

Jordon's brother got $40

Step-by-step explanation:

We can set up a system of equations to solve this.

Let's say that Jordon got x dollars.

His brother got y dollars.

x+y=100 since they are dividing the 100 dollars

1/3x=1/2y (the same indicates that they are equal)

Multiply the entire second equation by 3.

x=1.5y

Now we can substitute 1.5y in for x in the first equation.

x+y=100

1.5y+y=100

2.5y=100

Divide both sides by 2.5

y=40

Jordon's brother got $40.

Plug that in to find how much Jordon got.

x+y=100

x+40=100

Subtract 40 from both sides

x=60

Jordon got 60.

Answer:

here you go :)

Step-by-step explanation:

You would take 20% of $22.50 (22.5 multiplied by .2). You would get $4.50 off of the book with the discount. So you would subtract 4.5 from 22.5 and get $18. Then you would take 10% of $18 for the sales tax. (18 multiplied by .1). You would get $1.80 towards sales tax. you would then add $1.80 to $18 and get $19.80.

Answer:

The correct answer is 50.6195

Step-by-step explanation:

The probability that only girls bought lunches is given as D. 50%

To find the probability that only girls bought lunches, we solve:

We can see that the total number of girls is 30 and the total number of both boys and girls is 60

So, to solve, it becomes:

30/60= 50%

Probability is a mathematical concept used to measure the likelihood of an event occurring, ranging from 0 (impossible) to 1 (certain), and is calculated using ratios, frequencies, or subjective judgments.

Read more about probability here:

https://brainly.com/question/23417919

#SPJ2

Answer:

Option D.

Step-by-step explanation:

The given points are (-2,0), (0,1), (0,-4) and (3,0).

In each ordered pair first element is x-coordinate and second is y-coordinate.

For 4 points, the table must have 2 columns and 4 rows.

So, the required table of values is

x         y

-2        0

0       -4

0        1

3        0

Therefore, the correct option is D.

The graph of y=2x^2-8x+15 has no x-intercepts.

Answer: <CED is the right angle, which measures 90 degrees. Since the measure of a straight angle is 180 degrees. <CEA must also be 90 degrees by the Definition of Right Angle. A bisector cuts the angle measure in half. m<AEB is 45 degrees.

Answer:

  (-8,10)

Step-by-step explanation:

hope i helped!

u can substitute if u want to recheck

can i get brainliest pls?

-Zylynn

Answer:

5 is the answer..

Step-by-step explanation:

simply by calculating

Answer:

.0000416

Step-by-step explanation:

Since 10 is squared by a negative number, the number (4.16) will be smaller. To find the answer, move the decimal 5 places to the left

Answer:

0.0000416.

Step-by-step explanation:

When 10 is raised to a negative power, that means that the decimal point will be moved to the left a certain number of units.

In this case, it is 10^-5, so the decimal point will move to the left by 5 units.

4.16 * 10^-5 = 000004.16 * 10^-5 = 0.0000416.

Hope this helps!

Answer:

5x² and 7x² are like terms because they contain x².

3x and 8x are like terms because they contain x.

10 and 11 are like terms because they are constants.

Step-by-step explanation:

Let's recall that the definition of like terms is that they are terms that contain the same variables raised to the same power and only like terms can be combined.

Upon saying that, we have:

5x² and 7x² are like terms because they contain x²

3x and 8x are like terms because they contain x

10 and 11 are like terms because they are constants.

Answer:

[tex]\frac{4}{3}[/tex]

Step-by-step explanation:

The area of a regular octahedron is given by:

area = [tex]2\sqrt{3}\ *edge^2[/tex]. Let a is the length of the edge (diagonal).

area = [tex]2\sqrt{3}\ *a^2[/tex]

Given that the diagonal of the octahedron is equal to height (h) of the tetrahedron i.e.

a = h, where h is the height of the tetrahedron and a is the diagonal of the octahedron. Let the edge of the tetrrahedron be e. To find the edge of the tetrahedron, we use:

[tex]h=\sqrt{\frac{2}{3} } e\\but\ h=a\\a=\sqrt{\frac{2}{3} } e\\e=\sqrt{\frac{3}{2} }a[/tex]

The area of a tetrahedron is given by:

area = [tex]\sqrt{3}\ *edge^2[/tex] = [tex]\sqrt{3} *(\sqrt{\frac{3}{2} }a)^2=\frac{3}{2}\sqrt{3} *a^2[/tex]

The ratio of area of regular octahedron to area tetrahedron regular is given as:

Ratio = [tex]\frac{2\sqrt{3}\ *a^2}{\frac{3}{2} \sqrt{3}*a^2} =\frac{4}{3}[/tex]

Answer:

Step-by-step explanation:

please include a picture of the question! :)

Answer:

[tex]2ab - 6a + 5b - 15[/tex]

Step-by-step explanation:

Given

[tex]2ab - 6a + 5b + \_[/tex]

Required

Fill in the gap to produce the product of linear expressions

[tex]2ab - 6a + 5b + \_[/tex]

Split to 2

[tex](2ab - 6a) + (5b + \_)[/tex]

Factorize the first bracket

[tex]2a(b - 3) + (5b + \_)[/tex]

Represent the _ with X

[tex]2a(b - 3) + (5b + X)[/tex]

Factorize the second bracket

[tex]2a(b - 3) + 5(b + \frac{X}{5})[/tex]

To result in a linear expression, then the following condition must be satisfied;

[tex]b - 3 = b + \frac{X}{5}[/tex]

Subtract b from both sides

[tex]b - b- 3 = b - b+ \frac{X}{5}[/tex]

[tex]- 3 = \frac{X}{5}[/tex]

Multiply both sides by 5

[tex]- 3 * 5 = \frac{X}{5} * 5[/tex]

[tex]X = -15[/tex]

Substitute -15 for X in [tex]2a(b - 3) + 5(b + \frac{X}{5})[/tex]

[tex]2a(b - 3) + 5(b + \frac{-15}{5})[/tex]

[tex]2a(b - 3) + 5(b - \frac{15}{5})[/tex]

[tex]2a(b - 3) + 5(b - 3)[/tex]

[tex](2a + 5)(b - 3)[/tex]

The two linear expressions are [tex](2a+ 5)[/tex] and [tex](b - 3)[/tex]

Their product will result in [tex]2ab - 6a + 5b - 15[/tex]

Hence, the constant is -15

Answer:

The function has two real roots and crosses the x-axis in two places.

The solutions of the given function are

x = (-0.4495, 4.4495)

Step-by-step explanation:

The given quadratic equation is

[tex]G(x) = -x^2 + 4x + 2[/tex]

A quadratic equation has always 2 solutions (roots) but the nature of solutions might be different depending upon the equation.

Recall that the general form of a quadratic equation is given by

[tex]a^2 + bx + c[/tex]

Comparing the general form with the given quadratic equation, we get

[tex]a = -1 \\\\b = 4\\\\c = 2[/tex]

The nature of the solutions can be found using

If [tex]b^2- 4ac = 0[/tex] then we get two real and equal solutions

If [tex]b^2- 4ac > 0[/tex] then we get two real and different solutions

If [tex]b^2- 4ac < 0[/tex] then we get two imaginary solutions

For the given case,

[tex]b^2- 4ac \\\\(4)^2- 4(-1)(2) \\\\16 - (-8) \\\\16 + 8 \\\\24 \\\\[/tex]

Since 24 > 0

we got two real and different solutions which means that the function crosses the x-axis at two different places.

Therefore, the correct option is the last one.

The function has two real roots and crosses the x-axis in two places.

The solutions (roots) of the equation may be found by using the quadratic formula

[tex]$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$[/tex]

[tex]x=\frac{-(4)\pm\sqrt{(4)^2-4(-1)(2)}}{2(-1)} \\\\x=\frac{-4\pm\sqrt{(16 - (-8)}}{-2} \\\\x=\frac{-4\pm\sqrt{(24}}{-2} \\\\x=\frac{-4\pm 4.899}{-2} \\\\x=\frac{-4 + 4.899}{-2} \: and \: x=\frac{-4 - 4.899}{-2}\\\\x= -0.4495 \: and \: x = 4.4495 \\\\[/tex]

Therefore, the solutions of the given function are

x = (-0.4495, 4.4495)

A graph of the given function is also attached where you can see that the function crosses the x-axis at these two points.

Answer:

Step-by-step explanation:

Berto’s train was 34 miles past the egg farm .

Eduardo’s train had 12 miles to go before it reached the egg farm.

Distance between two trains = 34 + 12 = 46 miles

This distance has to be reduced to zero for their crossing each other .

Rate at which this distance is reduced  = their relative velocity

= 110 - 85

= 25 miles / h       [ They are moving in the same direction ]

So, time taken for them to meet each other

= 46 / relative velocity

= 46 / 25

= 1.84 hours .

Answer:

The answer is D or 1.84 hours.

Step-by-step explanation:

I got 100% on this quiz.

Answer:

(-4, 6), (0, 2), (4, -2)

Step-by-step explanation:

You just need to guess and check.

(-4,6) → -4 + 6 = 2 ✔

(0,2) → 0+2 = 2 ✔

(4,2) → 4 + 2 = 6

(4, -2) → 4 - 2 = 2 ✔

(-4,-6) → -4 - 6 = -10

The correct answer is the second list (-4, 6), (0, 2), (4, -2)

Answer:

46 minutes.

Step-by-step explanation:

2 km in 13 minutes would equal to 6 minutes and 30 seconds per km.

minutes: 6 x 7 = 42

seconds: 30 x 7 = 210

seconds pt 2: 210/60 = 3 minutes 30 seconds

adding altogether: 42 minutes + 3 minutes 30 seconds + 45 minutes 30 seconds, rounded would equal to 46 minutes

Answer:

The surface area of the pyramid is 80.9 cm²

Step-by-step explanation:

The side length, s of the cube is given as 5 cm

Therefore, the largest pyramid that can fit into the cube will have a base side length, s = The side length of the cube = 5 cm

The height, h of the largest pyramid = The height of the cube = 5 cm.

The surface area of a pyramid =  Area of base, A + 1/2 × Perimeter of base, P × Slant height, S

The slant height of the pyramid = √(h² + (s/2)²) = √(5² + (5/2)²) = (5/2)×√5

The perimeter of the base = 4×5 = 20 cm

The area of the base = 5×5 = 25 cm²

The surface area of a pyramid = 25 + 1/2×20×(5/2)×√5 = 80.9 cm².

The surface area of a pyramid =  80.9 cm².

Answer:

The answer is 12

Step-by-step explanation:

Trust me, kay? Please mark Brainliest!!!!

Answer:

12.8

Step-by-step explanation:

16% of 80

[tex]\frac{16}{100}[/tex] × 80

[tex]\frac{16}{10}[/tex] × 8

[tex]\frac{16}{5}[/tex] × [tex]\frac{4}{1}[/tex]

16 × 4

5

12[tex]\frac{4}{5}[/tex] = 12.8

Answer:

B

Step-by-step explanation:

Here, we have a grain silo having 2 shapes fused together to make it.

A cylinder and then a hemisphere ( half sphere)

Now, we want to calculate the volume of grain that could completely fill the silo.

Mathematically, to do that, we will need to add the volume of the cylinder to the volume of the hemisphere.

Mathematically,

Volume of cylinder is;

pi * r^2 * h

From the question, r = 6 ft and h = 168 with pi = 22/7

Substituting these values, we have

Volume of cylinder= pi * 6^2 * 168 = 6,048 pi

The volume of the sphere will be;

4/3* pi * r^3= 4/3 * pi * 6^3 = 288 pi

So the total volume of the silo will be;

288 pi + 6,048 pi = 6336 pi

So to have the final result, let’s multiply by value of pi

6336 * 22/7 = 19,193 ft^3

The closest answer here probably due to previous approximations is 19,008 ft^3