In
Select the correct
function
that represents
this data.
21012 x
Out
8
3
-2
-7
-12
[?]
A. f(x) = -5x - 2
B. f(x) = -5x + 7
C. f(x) = -5x + 2

Answer:

= 3y2-y2+2y+y

= 2y+3y

= 5y

Answer:

[tex] \displaystyle 0.344[/tex]

Step-by-step explanation:

we are given that a coin is tossed 6 times and we want to find the probability of getting at most 2 heads.

To solve this problem,we can consider binomial distribution, which is given by

[tex] \displaystyle P(X = r) = \binom{n}{r} {p}^{r} {q}^{n - r} [/tex]

where:

we want to figure out the probability of getting at most 2 heads out of 6 trials , The probability can therefore be found by adding up all the binomial distributions including X=2 and less than it, Thus

[tex] \displaystyle P(X \leq 2) = P(X=0)+P(X=1)+P(X=2) [/tex]

[tex] \displaystyle P(X \leq 2) = \binom{6}{0} {p}^{0} {q}^{6 - 0} + \binom{6}{1} {p}^{1} {q}^{6- 1} + \binom{6}{2} {p}^{2} {q}^{6 - 2} [/tex]

when a coin is tossed, the probability of getting both head (success) and tail (failure) are ½ which is why ,the variables, p and q are assigned to ½. therefore substitute

[tex] \rm\displaystyle P(X \leq 2) = \binom{6}{0} { \left( \frac{1}{2} \right) }^{0} { \bigg( \frac{1}{2} \bigg) }^{ 6- 0} + \binom{6}{1} { \bigg( \frac{1}{2} \bigg) }^{1} { \bigg( \frac{1}{2} \bigg) }^{6 - 1} + \binom{6}{2} { \bigg( \frac{1}{2} \bigg)}^{2} { \bigg( \frac{1}{2} \bigg) }^{6- 2} [/tex]

since p and q are the same. it won't make any difference to write all the product of p and q as (½)⁶:

[tex]\rm\displaystyle P(X \leq 2) = \binom{6}{0} { \bigg( \frac{1}{2} \bigg) }^{ 6} + \binom{6}{1} { \bigg( \frac{1}{2} \bigg) }^{6} + \binom{6}{2} { \bigg( \frac{1}{2} \bigg) }^{6}[/tex]

In the expression the term (½)⁶ is common thus factor it out:

[tex]\rm\displaystyle P(X \leq 2) = { \bigg(\frac{1}{2}\bigg) }^{ 6} \left( \binom{6}{0} + \binom{6}{1} + \binom{6}{2} \right) [/tex]

calculate the combinations:

[tex]\rm\displaystyle P(X \leq 2) = { \bigg(\frac{1}{2}\bigg) }^{ 6} \left(1+6+15\right) [/tex]

simplify addition:

[tex]\rm\displaystyle P(X \leq 2) = { \bigg(\frac{1}{2}\bigg) }^{ 6} \left(22\right) [/tex]

simplify exponent:

[tex]\rm\displaystyle P(X \leq 2) = { \bigg(\frac{1}{64}\bigg) } \left(22\right) [/tex]

simplify multiplication:

[tex]\rm\displaystyle P(X \leq 2) = \frac{22}{64} [/tex]

dividing yields:

[tex]\rm\displaystyle P(X \leq 2) = 0.34375 [/tex]

[tex]\rm\displaystyle P(X \leq 2) \approx 0.344 [/tex]

In conclusion

The answer is 0.344

Answer:

good luck

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

this is the answer

it is irrational because it cannot be expressed in a ratio of two integers

please give me brainliest .

Answer:

5,400

Step-by-step explanation:

do the exponent which is 10x10=100 then add it to 5,300

Answer:

22.5 degrees and 67.5 degrees

Step-by-step explanation:

complementary angles add up to 90°

x + 3x = 90°

4x = 90

90/4 = x

x = 22.5

The first angle is 22.5

The second angle is 3 times as much

22.5 x 3 = 67.5

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

Uhh i dont rly know sry

Step-by-step explanation:

Step-by-step explanation:

F[G(x)]=2(3x+2)-1= 6x+4-1= 6x +3

F[x]=2x-1

F[G(x)] - F(x)=6x+3-(2x-1)=6x+3-2x-1

=4x+2

answer=4x+2

Answer: A

Step-by-step explanation:

[tex]F(x)=2x-1\\G(x)=3x+2\\\\F(G(x))-F(x)=F(3x+2)-(2x-1)\\\\=2*(3x+2)-1-2x+1\\\\=6x+4-2x\\\\=4x+4\\\\\\Answer\ A[/tex]

Answer:

It is 5.83 units

Step-by-step explanation:

[tex]{ \bf{length = \sqrt{ {(x_{1} - x _{2} ) }^{2} + {(y _{1} - y_{2})}^{2} } }}[/tex]

x1 is -1

x2 is 2

y1 is 3

y2 is -1

[tex] = \sqrt{ {( - 1 - 2)}^{2} + { \{3 - ( - 2) \}}^{2} } \\ \\ = \sqrt{9 + 25} \\ = \sqrt{34} [/tex]

Here is your answer. Hope this helps you.

Answer:

51

Step-by-step explanation:

15= a/3 -2

17= a/3

51=a

Answer:

Step-by-step explanation:

[tex](x+2)(x-1)= x^2+2x-x-2= x^2 +x -2\\\\( x + 2 ) ( x - 1 ) - x ^ { 2 } + 1 =x^2+x-2-x^2+1=x-1\\\\- 3 [ ( x + 2 ) ( x - 1 ) - x ^ { 2 } + 1 ] =-3(x-1)=-3x+3\\\\- 3 [ ( x + 2 ) ( x - 1 ) - x ^ { 2 } + 1 ] + 3 ( x - 1 ) =-3x+3+3x-3=6x\\[/tex]

Answer:

13, 24, and 34

Step-by-step explanation:

0, 1, 1, 2, 3, 5, 8, 13, 24, 34, . . .

0+ 1 = 1

1+ 1 = 2

2+ 1 = 3

3+ 2 = 5

5+ 3 = 8

8+ 5 = 13

13+ 8 = 24

24+ 13 = 34

start at 1, then add the number behind it to move forward one space. repeat process.

Answer:

Surface area of sphere = 4 π r²

154 = 4 × 22/7 × r²

154 = 88/7 × r²

154 × 7/88 = r²

12.25 = r²

3.5 = r

Now

Volume of sphere = 4/3 × π r³

Volume = 4/3 × 22/7 × (3.5)³

Volume = 88/21 × 42.875

Volume = 154 cm³

Volume of sphere = Volume of cube

Volume of cube = 154 cm³

Answer:

$7.10

Step-by-step explanation:

Step 1: We make the assumption that 35.5 is 100% since it is our output value.

Step 2: We next represent the value we seek with $x$.

Step 3: From step 1, it follows that $100\%=35.5$.

Step 4: In the same vein, $x\%=20$.

Step 5: This gives us a pair of simple equations:

$100\%=35.5(1)$.

$x\%=20(2)$.

Step 6: By simply dividing equation 1 by equation 2 and taking note of the fact that both the LHS

(left hand side) of both equations have the same unit (%); we have

Step 7: Taking the inverse (or reciprocal) of both sides yields

Hope this helps <3

Answer:

Step-by-step explanation:

[tex][(\sqrt[4]{x^{\dfrac{3}{4}}})^{\dfrac{-4}{3}} ]^{4}[/tex]

[tex]= [(x^{\frac{3}{4}*\frac{1}{4}})^{\frac{-4}{3}}]^{4}\\\\\\= [(x^{\frac{3}{16} ) ^{\frac{-4}{3}}}]^{4}\\\\=[ x^{\frac{3}{16}*\frac{-4}{3}}]^{4}\\\\=[x^{\frac{-1}{4}}]^{4}\\\\=x^{\frac{-1}{4}*4}\\\\=x^{-1}\\\\=\dfrac{1}{x}[/tex]

Hint:

[tex](a^{m})^{n}=a^{m*n}[/tex]

Answer:

[tex]1/x[/tex]

Step-by-step explanation:

To simplify, work from the inside out.

We start with

[tex]\sqrt[4]{x^{3/4}}[/tex]

on the inside. And we can change the fourth root into a fractional exponent -- 1/4:

[tex](x^{\frac{3}{4})^{1/4}[/tex]

A power of a power means multiply the exponents, giving

[tex]x^{\frac{3}{4} * \frac{1}{4}} = x^{3/16}[/tex]

So now we have

[tex][(x^{3/16})^{-4/3}]^4[/tex]

From here, apply the "power of a power rule" again, working from the inside out.

[tex](x^{-12/48})^4[/tex]

[tex]x^{-48/48}[/tex]

[tex]x^{-1}[/tex]

or

[tex]1/x[/tex]

Answer:

-12

Step-by-step explanation:

18 plus 13 is 41 29 subtracted from 41 is -12

Answer:

- $2

Step-by-step explanation:

Alex withdrew money twice, or he subtracted those amounts from the total that he had.

In this case, he withdrew $13 first, and then $18, or:

13 + 18 = 31

$31 dollars in all.

Alex had $29. Subtract the total that he withdrew from the amount he had:

29 - 31 = -2

Alex has - $2, or he owes the bank $2 with interest.

~

Answer:

1.079.

Step-by-step explanation:

Use ur calculator.

Hi ;-)

[tex]s=zh-2zt^3\\\\z(h-2t^3)=s \ \ /:(h-2t^3)\\\\z=\dfrac{s}{h-2t^3}[/tex]

Answer:

z = [tex]\frac{s}{h-2t^3}[/tex]

Step-by-step explanation:

Given

s = zh - 2zt³ ← factor out z from each term

s = z(h - 2t³ ) ← divide both sides by h - 2t³

[tex]\frac{s}{h-2t^3}[/tex] = z

Answer:

4570 species of the type A and 1540 species of the type B.

Step-by-step explanation:

A:

1st: 4 units

2nd: 5 units

B:

1st: 1 unit

2nd: 6 units

A=x, B=y

4x + 1y = 19820  units of the first nutrient

5x + 6y = 32090  units of the second nutrient

5x + 6*(19820-4x) = 32090.

       32090 - 6(19820-4x)

x= ------------------------------------- = 4570

                     5-24

y = 19820 - 4*4570 = 19820 - 18280 = 1540.

ANSWER:  4570 species of the type A and 1540 species of the type B.

Hopes this solves it.

The populations of each species can coexist in the environment so that all the nutrients are consumed each day are 4530 and 10600

In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Given;

Each day the environment is supplied with 19,660 units of the first nutrient and 31,890 units of the second nutrient

2 Nutrient Requirements of both species of Bacteria A and B , Total Nutrients available

Now,

Let the number of bacteria of Specie A and Specie B be x and y respectively;

To find : Number of Bacteria 1 and Bacteria 2

Nutrient 1 Constraint Equation : 4x + y = 19660

Nutrient 2 Constraint Equation : 5x + 6y = 31890

Putting the value of y from 1st equation in 2nd equation;

5x + 6 (19660 - 4x) = 31890

5x + 117960 - 24x = 31890

117960 - 31890 = 19x

19x = 86070

x = 86070 / 19 = 4530 { Bacteria A}

Putting the value of x in 1st equation;

2 (4530) + y = 19660

9060 + y = 19660

y = 19660 - 9060= 10600{Bacteria B}

Therefore, the solution of equations will be 4530 and 10600

To learn more about simultaneous equations :

brainly.com/question/16763389

#SPJ2

Answer:

Sqrt(-108)=6i*sqrt(3)

Step-by-step explanation:

-108=3*6*6*(-1). Sqrt(-108)=6i*sqrt(3) where i is iota

Answer:

6 cm

Step-by-step explanation:

Let each side of the equilateral triangle be a.

Given, area of an equilateral triangle = 9√3 cm2

Area of an equilateral triangle = (√3)/4 × (Side)²

=> (√3)/4 × a² = 9√3

[tex] {a}^{2} = \frac{9 \sqrt{3} }{ \frac{ \sqrt{3} }{4} } = \frac{9 \sqrt{3} }{ \sqrt{3} } \times 4 = 9 \times 4[/tex]

=> a² = 36

[tex] \sqrt{ {a}^{2} } = \sqrt{36} \\ a = (+ - )6[/tex]

∴ Side = 6 cm  [taking positive square root because side is always positive]

Use the co‐interior rule, corresponding angle rule, alternate angle rule and vertical opposite angle rule to solve the question above.

angle G5 = angle K1 reason : corresponding angles

angle J1 = angle H3 reason: vertical opposite angles

angle J2 = angle K4 reason: vertical opposite angles

angle G5 = angle K4 reason: co‐ interior angles

angle F6 = angle K4 reason: alternate angle

Answer:

452 + 100 × 10 = 1452

Step-by-step explanation:

There are many possible solutions. This is one of them.

Answer:

1_ 129 , 51

2_ b

3_ 40

Step-by-step explanation:

1_ we can represent the bigger angle with x and smaller one with y

and as given, y is smaller than x by 78

so y = x - 78 (1)

as x + y = 180

we put y as we did in (1)

x + x - 78 = 180

so 2x = 258

so x = 129

and y will be 51

2_ from the figure we find the two angles form one angle = 90 degree

3_ from the defenition of complementary angles

m(c) + m(d) = 90

7r + 5 + 8r + 10 = 90

15r + 15 = 90

r = 5

so m(c) will be equal 7*5 + 5 = 40

Answer:

-1/2

Step-by-step explanation:

3/2 x 5/3 ÷ (-2+7)

=> 3/2 x 5/3 ÷ (-5)

=> 3/2 x 5/3 x (-1/5)

=> -1/2

Answer:

linked below

Step-by-step explanation:

If you use desmos, it show this which is the correct graph :)

Answer:  5.6g - 2h + 9

Explanation:

Flip the sign of each term inside the parenthesis.

These sign flips occur because of the negative out front the parenthesis. It's the same as having -1 outside, and we distribute the -1 through.

Answer:

-3π/4

Step-by-step explanation:

-135° = (-135) × π/180= -3π/4

Step-by-step explanation:

I can't understand it so plz don't mind or else I will mind

Answer:

93.75%

This type of problem you have to REVERSE the question...

"at least one tail" is all possibilities EXCEPT "all heads"...

so your answer is 100% - P(4 heads)

P(4 heads) = (1/2)^4 = .0625

1 - .0625 = .9375

Step-by-step explanation: