Suppose a group of 12 students consists of five freshmen and seven sophomores. How many six-student teams can be chosen that consist of three freshmen and three sophomores? Give your answer as an integer.

Answer:

Step-by-step explanation:

If the roots are 7 and 3, then x = 7 and x = 3 are solutions. In factor form, x = 7 is (x - 7); in factor form, x = 3 is (x - 3). We FOIL these together to get

[tex]x^2-3x-7x+21[/tex] which simplifies to

[tex]x^2-10x+21[/tex] and we distribute in the 4:

[tex]4(x^2-10x+21)[/tex] to get

[tex]4x^2-40x+84[/tex] which is another way to write the last choice you're given.

Answer:

[tex] \sqrt{113} [/tex]

Step-by-step explanation:

To find the distance between the two points, apply the distance formula given as:

[tex] d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]

Where,

[tex] (-4, -5) = (x_1, y_1) [/tex]

[tex] (4, 2) = (x_2, y_2) [/tex]

Plug in the values

[tex] d = \sqrt{(4 -(-4))^2 + (2 -(-5))^2} [/tex]

[tex] d = \sqrt{(8)^2 + (7)^2} [/tex]

[tex] d = \sqrt{64 + 49} [/tex]

[tex] d = \sqrt{113} [/tex]

The formula in finding the distance between two points is given below:

Now, you know the distance formula. So, let us try solving the given problem using the distance formula.

Problem: Determine the distance between (-4, -5) and (4, 2).

From inspection on the given problem:

Substitute the given values into the distance formula and solve for d:

Therefore, the distance between two points is [tex]\sqrt{113}[/tex] or 10.6 units.

[tex]\\[/tex]

Now, wasn't that easy? Try this sample problem:

From the sample problem above, you may solve it on your own to enhance your skill on calculating the distance.

For more information about the Distance Formula, just visit this link: https://brainly.com/question/18156437

Answer:

2/9

Step-by-step explanation:

7/9×18/63

Rewriting

7/63  * 18/9

1/9 * 2/1

2/9

[tex]\longrightarrow{\green{ \frac{2}{9}}}[/tex] 

[tex]\sf \bf {\boxed {\mathbb {Step-by-step\:explanation:}}}[/tex]

✒[tex] \: \frac{7}{9 } \times \frac{18}{63} [/tex]

✒[tex] \: \frac{2}{9} [/tex]

[tex]\bold{ \green{ \star{ \orange{Mystique35}}}}⋆[/tex]

Answer:

(w² + 6)(w² - 6)

Step-by-step explanation:

difference of squares

w⁴ - 36 = (w² + 6)(w² - 6)

Step-by-step explanation:

x⁴(4x+1)

4x⁵+x⁴

degree is 5

Answer: Assuming pi is rounded off to 3.14, it is 219.8 feet; if not it is 70π feet

Circumference=one revoloution

Circumference=Diameter times pi

C=Dπ

C=3.14*70

=219.8

219.8 feet

Answer:

The line has a slope of -1.

Step-by-step explanation:

To solve for the slope of the line, use the rise over run formula. The rise over run formula is a measure of how much something changes vertically compared to how much it changes in the horizontal direction. The rise over run formula calculates the difference between the two points in the vertical direction (rise) and then divide it by the difference in the horizontal direction (run). The formula looks like [tex]\frac{rise}{run}[/tex], but in terms of finding a slope, it looks like [tex]\frac{y_{2 }-y_{1} }{x_{2} -x_{1} }[/tex].

For finding the slope of this line with the points (-3,5) and (5,-3), start by writing down the information given from the question.

[tex]y_{2}=-3[/tex]

[tex]y_{1}= 5[/tex]

[tex]x_{2}=5[/tex]

[tex]x_{1} =-3[/tex]

Next, plug in the information given from the question into the formula, and the formula will look like [tex]\frac{-3-(5)}{5-(-3)}[/tex]. Then, simplify the equation, which will look like  [tex]\frac{-8}{8}=-1[/tex]. The final answer will be -1.

Answer:

Time plot

Step-by-step explanation:

The data from which a plot or graph is to be generated will have only one variable, which is the rain acidity, that is acidity level of Rainfall over a certain period. However, the data gbwre is time dependent, hence, it is a time series plot. Hence, this is a two dimensional univariate plot, with the acidity label of Rainfall on one axis and time on the other. Therefore, the graph which is best to display such information is the time series plot.

Answer:

you have to solve for z, z = 6\root(5)(i), this to the power of 5 equals 77761

Step-by-step explanation:

Answer:

(26.2252 ; 27.3748)

Step-by-step explanation:

The confidence interval is given by :

x ± Margin of error

The margin of error = Zcritical * (σ/√(n))

σ = 7.5 ; n = 654

Zcritical = Zα/2 = 1.96

The margin of error = 1.96 * (7.5/√654) = 0.5748

The confidence interval :

Upper boundary = 26.8 + 0.5748 = 27.3748

Lower boundary = 26.8 - 0.5748 = 26.2252

(26.2252 ; 27.3748)

We are 95% confident that the mean BMI of the entire population will fall in between (26.2252 ; 27.3748)

While

Step-by-step explanation:

my answer is in the image above

9514 1404 393

Answer:

  (b)  y=2x^3

Step-by-step explanation:

The function y=2x^3 is an example of the parent function y=x^3 being vertically scaled by a factor of 2. As such, it is not the parent function.

_____

Additional comment

A parent function is one that has not been translated or scaled in any way. One could argue that the parent function of the form y=constant is y=1, so that the function y=1/2 has been scaled by a factor of 1/2. In this problem, we recognize the parent function y=x^3 has clearly been scaled to get y=2x^3, so the latter is not an example of a parent function.

If this is a "check all that apply" question, then y=1/2 is another reasonable answer.

Answer:(b)  y=2x^3

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex] \frac{3}{2} \div 5[/tex]

[tex] = \frac{3}{2} \times \frac{1}{5} [/tex]

[tex] = \frac{3}{10} [/tex]

= 0.3 (Ans)

Answer:

3/10

Step-by-step explanation:

3/2÷5

3/2÷5/1

3/2÷10/2 ( LCM of denominators)

3/2×2/10 ( Reciprocal of 10/2)

3/10 (Cancelling 2 by 2)

Answer:

option D

Step-by-step explanation:

[tex]9x^2 + 6x - 17 = 0 , \ where \ a = 9 \ , \ b = 6 \ , c = - 17[/tex]

[tex]x = \frac{ - b \ \pm \sqrt{b^2 - 4ac}}{2a} \\\\x = \frac{-6 \pm \sqrt{36 - (4 \times 9 \times -17)}}{2 \times 9}\\\\x = \frac{-6 \pm \sqrt{ 36 + 612}}{18}\\\\x = \frac{-6 \pm \sqrt{ 648}}{18}\\\\x = \frac{-6 \pm \sqrt{ 2^3 \times 3^4}}{18}\\\\x = \frac{-6 \pm \sqrt{2 \times 2^2 \times 3^ 4 }}{18}\\\\x = \frac{-6 \pm ( 2 \times 9 )\sqrt{ 2}}{18}\\\\x = \frac{-6 \pm 18\sqrt{2}}{18}\\\\x = \frac{-1 \pm 3 \sqrt{ 2}}{3}[/tex]

Answer:

Reason 5

Step-by-step explanation:

Reason 1 and 2 are Given

Reason 3 is Reflexive

Reason 4 is Side-Side-Side congruency

Answer:

Reason 5

Step-by-step explanation:

It helps to know what CPCTC means and how it's used.

CPCTC means "corresponding parts of congruent triangles are congruent."

To use it, you must first either prove two triangles to be congruent or be given that two triangles are congruent.

Once you have the congruent triangles, then you state that two corresponding parts of those triangles are congruent, and you use CPCTC as the reason.

In step 4, the triangles are proven congruent by SSS.

Then CPCTC can be used as reason 5 for stating that the corresponding angles A and C are congruent.

Answer:

1 oz = $25

Step-by-step explanation:

Answer:

1 OZ= 25 cents.................. this is correct

Step-by-step explanation:

you multiple 16 times .25 which gets 4.00

Area of a circle is pi x radius^2

Area = pi x 22 ^2

Area = pi x 484

Area = 1,519.8 mm^2

Answer:

1520.5mm²

Step-by-step explanation:

Area of a circle=πr²

π(22mm)²

π484mm²

1520.5308443374599mm²

to one decimal place

1520.5mm²

Answer:

Pythagorean Theorem

Question Answer

Find the width of a triangle that has a 15cm height and a hypotenuse of 19cm. 11.7cm

A helicopter rises straight up 300m then flies west 400m. How far is it from the beginning (if it travels in a straight line back)?

Answer:

m=16x+8y

Step-by-step explanation:

let the amount of money she spend be 'm'

m=16x+8y

Answer:

a=16x+8y

Step-by-step explanation:

Let the amt of money she spends be a.

hope it helps!!!

Answer:

Step-by-step explanation:

Answer:

Olivia will make 209 cookies on 11 hours

Step-by-step explanation:

if she makes 95 per 5 hours

we can make

5 + 5 = 10

this is the same as doing

95 + 95 = 190

now, for the 1 hour

95 : 5 = 19

now to verify it

19 x 5 = 95

now you make

95 + 95 + 15 = 209

Oops, srry my bad, i fixed the thing i did wrong

Answer:

20 units

Step-by-step explanation:

We can see that triangle QRS and triangle VWS are similar triangles.

Similar triangles are triangles in which the ratio of their corresponding sides are in the same proportion.

V is the midpoint of QS.

VS = 2a, QS = 2 * VS = 2(2a) = 4a

Since both triangles are similar triangles, hence:

\begin{gathered}\frac{VS}{QS}=\frac{VW}{QR}\\\\\frac{2a}{4a} =\frac{2a-2}{3a+6} \\\\\frac{2a-2}{3a+6} =\frac{1}{2} \\\\2(2a-2)=3a+6\\\\4a-4=3a+6\\\\a=10\ units\\\\VS=2a=2(10)=20\ units\end{gathered}

QS

VS

=

QR

VW

4a

2a

=

3a+6

2a−2

3a+6

2a−2

=

2

1

2(2a−2)=3a+6

4a−4=3a+6

a=10 units

VS=2a=2(10)=20 units

ur wlcm♥️♥️

Answer:

20 UNITS

Step-by-step explanation:

EDG 2020

Answer:

b) 0.5

c) 0.633

Step-by-step explanation:

a) Please find the attached image - tree diagram

b) b) The probability that A is in charge of the selected campaign and that it produces satisfactory results  = 2/3 * 3/4 = 1/2 = 0.5

c) P (selected campaign is satisfactory)

         = P(A's campaign and satisfactory) + P(B's campaign and satisfactory)

         = 2/3*3/4 + 1/3*2/5

         = 0.6333

Step-by-step explanation:

[tex] {7}^{2n + 1} \div 49 = {7}^{3} [/tex]

[tex] {7}^{2n + 1} \div {7}^{2} = {7}^{3} [/tex]