A bacteria culture begins with 4 bacteria which double in size every hour. How many bacteria exist in the culture after 8 hours.

Answer:

-2

Step-by-step explanation:

I believe its -2 :) :3

[tex]x+2[/tex] is a factor of [tex]x^5+32[/tex] because (by the remainder theorem) the remainder upon dividing [tex]x^5+32[/tex] by [tex]x+2[/tex] is [tex](-2)^5+32=0[/tex].

There's also the sum of fifth powers formula,

[tex]a^5+b^5=(a+b)(a^4-a^3b+a^2b^2-ab^3+b^4)[/tex]

ANSWER

The correct answer is A

EXPLANATION

The given polynomial is

[tex]p(x) = {x}^{5} + 32[/tex]

According to the remainder theorem, if p(x) is divided by x+2 the remainder is p(-2).

If the remainder is zero then x+2 is a factor of f(x).

We plug in x=-2 into the function to obtain;

[tex]p( - 2) = { (- 2)}^{5} + 32[/tex]

[tex]p( - 2) = - 32 + 32[/tex]

[tex]p( - 2) = 0[/tex]

Since the remainder is zero, x+2 is a factor.

The correct answer is A

Answer:

3 lawns per hour

Step-by-step explanation:

Divide the lawns by the time: 6/2=3

6/2 = 3

So, Mia mowed 3 lawns in an hour.

Answer: 6 divided by 2 equals 3

Answer:

[tex]\large\boxed{x^2+10x+5=\left(x+5+2\sqrt5\right)\left(x+5-2\sqrt5\right)}[/tex]

Step-by-step explanation:

[tex]\text{Use the quadratic formula:}\\\\ax^2+bx+c=a\left(x-\dfrac{-b-\sqrt{b^2-4a}}{2a}\right)\left(x-\dfrac{-b+\sqrt{b^2-4ac}}{2a}\right)\\======================================[/tex]

[tex]\text{We have:}\ x^2+10x+5\to a=1,\ b=10\ \text{and}\ c=5\\\\\text{Substitute}\\\\b^2-4ac=10^2-4(1)(5)=100-20=80\\\sqrt{b^2-4ac}=\sqrt{80}=\sqrt{16\cdot5}=\sqrt{16}\cdot\sqrt5=4\sqrt5\\\\x_1=\dfrac{-10-4\sqrt5}{2(1)}=-5-2\sqrt5\\\\x_2=\dfrac{-10+4\sqrt5}{2(1)}=-5+2\sqrt5\\\\\bigg(x-\left(-5-2\sqrt5\right)\bigg)=\left(x+5+2\sqrt5\right)\\\\\bigg(x-\left(-5+2\sqrt5\right)\bigg)=\left(x+5-2\sqrt5\right)[/tex]

Answer:

5 carrots

Step-by-step explanation:

Since there are 6 friends, find the factor closest to 47. The closest one would be 6*7=42. Thus, the answer is 5 because every friend gets 7 carrots.

Answer:

77.79 yard

Step-by-step explanation:

Given in the question that,

falcon flying at a height of 200 yards

sparrow flying at a height of 150 yards

Suppose, distance between Falcon and Sparrow = x yards

Step 1

Difference between the height of falcon and sparrow = 200-150 = 50 yards

Step 2

We will use Trigonometry Identity to find the distance between Falcon and Sparrow

SinФ = opposite / hypotenuse

Sin(40) = 50 / x

x = 50 / Sin(40)

x = 77.79 yard

Answer:

78

Step-by-step explanation:

Answer:

D) 6 in

Step-by-step explanation:

The length is 24 feet. The blueprint scales 1 ft : ¹/₄ in.

So, we can set up a proportion: 1 ft / ¹/₄ in = 24 ft / x in

Cross-multiply: 24 * ¹/₄ = x

Multiply: x = 6 in

Answer:

See below

Step-by-step explanation:

Givens

Jenny's Stats

t = m - 2

d = 60 miles

r = r1 + 10

Maureen's stats

d = 50 miles

t = m

r = r1

=======

60 = (r1 + 10) * (m - 2)

50 = r1 * m

m = 50/r1

60 = (r1 + 10)* (50/r1 - 2)  

60 = 50 + 500/r1 - 2r1 - 20

60 = 30 + 500/r1 - 2r1

60r1 = 30r1 + 500 - 2*r1^2

30r1 = 500 - 2r1^2

2r1^2 + 30r1 - 500

This quadratic factors into

2 (r1 - 10)(r1 + 25)

r1 = 10 mph             The 25 has no meaning.

m = 50/r1

m = 50/10

m = 5 hours

m - 2 = 3 hours.

Answer:

17%

Step-by-step explanation:

4/24=1.6666666667 rounded up is 17%

The probability that the next tee shot ends up on green is 1 / 6.

It's a field of mathematics that studies the probability of a random event occurring. From 0 to 1, the value is expressed.

P(Event) = Favourable outcomes / Total no. of outcomes

Total no. of shots taken = 4 + 5 + 7 + 3 + 5 = 24

Shots that landed on Green = 4

P( Shot will land on green) = 4 / 24 = 1 / 6

Hence, the probability that the next show will land on green is 1/6.

Learn more about probability on:

https://brainly.com/question/24756209

#SPJ2

First you must combine like terms (x and x)

2y + 2 + (x + x)

2y + 2 + 2x

^^^All have the number two in common so we can take a two out like so...

2 (y + 1 + x)

or

2(x + y + 1)

There fore the answer is A!

Hope this helped!

~Just a girl in love with Shawn Mendes

class b median is 80

class a median is 77

the comparison tells me in terms of the situation the data represents is that class b did better than class a

Answer:

46

Step-by-step explanation:

There is an open + in the middle. It does not have any brackets around it. Therefore you do it at the very last.

Left side of the plus sign.

[16 ÷ (2 + 3*2)] Do the multiplication inside the parenthesis ( 2*3) first.

= [16 ÷ (2 + 6)] Add inside the parenthesis.

= [16 ÷ 8 ]         Do the division

= 2

Right side of the open plus sign

[4 * (36 - 25)]   Do the subtraction first.

[4 * 11 ]             Do the multiplication

44

Now combine both right and left side.

2 + 44

46

The answer is 46.

46

I don’t think I helped

Answer:

204q+228

Step-by-step explanation:

ANSWER

[tex]12(17q + 19) = 204q + 228[/tex]

EXPLANATION

The given expression is:

[tex]12(17q + 19)[/tex]

Recall the distributive property,

If a, b, and c are real numbers, then

a(b+c)=ab+ac

We apply this property to expand the parenthesis and obtain:

[tex]12(17q + 19) = 12 \times 17q + 12 \times 19[/tex]

[tex]12(17q + 19) = 204q + 228[/tex]

Answer: Option A and Option B.

Step-by-step explanation:

You need to remember the logarithms properties:

[tex]log(a)+log(b)=log(ab)\\\\log(a)-log(b)=log(\frac{a}{b})\\\\log(a)^b=b*log(a)[/tex]

You can observe in Option A:

[tex]logM^p=p*logM[/tex] (This is true)

You can observe in Option B:

[tex]logM+logN=log(MN)[/tex] (This is true)

You can observe in Option C:

[tex]logM-logN=log(M-N)[/tex] (This is not true)

You can observe in Option D:

[tex](logM)^p=p*logM[/tex] (This is not true)

OK so first you find the square root of 363 which is 19.05255888325765 then you find the square root of 27 which is 5.196252422706632 then times that by 3 you get 15.5884572681199 so then you have 19.05255888325765 subtract 15.5884572681199 which equals 3.46410161513775

Hope this helped!

Answer:

[tex]a_n=3(3)^{n-1}[/tex]

Step-by-step explanation:

We have the following sequence

3,9,27,81,243

Note that if you divide each term of the sequence between the previous term you get:

[tex]\frac{9}{3} = 3\\\\\frac{27}{9} = 3\\\\\frac{81}{27} = 3[/tex]

then the radius of convergence of the series is r.

therefore this is a geometrical series.

The formula to find the general term [tex]a_n[/tex] of the geometric sequence is:

[tex]a_n=a_1(r)^{n-1}[/tex]

Where

[tex]a_1[/tex] is the first term of the sequence

Then the general term for this sequence is:

[tex]a_n=3(3)^{n-1}[/tex]

The answers are:

B. Before practice, there are 648 ounces of sports drink in the cooler.

C. Each plater drinks approximately 24 ounces of sports drink at practice.

E. For each additional player that takes a drink, there will be approximately  24 fewer ounces of sporks drink remaining after the practice.

We are given the equation:

[tex]y=f(x)=648-24x[/tex]

Let's discard each of the given options in order to find the three correct options.

A. The cooler is meant to be used only by 24 players: False.

If we want to calculate how many players can use the cooler, we need to isolate "x" (rate of change) from the given equation, so, isolating we have:

[tex]f(x)=648-24x[/tex]

[tex]0=648-24x[/tex]

[tex]648=24x\\\\24x=648\\\\x=\frac{648}{24}=27[/tex]

We have that the cooler can be used by 27 players, so, the first option that states that "The cooler is meant to be used only by 24 players" is false.

B. Before practice, there are 648 ounces of sports drink in the cooler: True.

We have that before the practice when the cooler is not being used by any player (or there is no any player) has 648 ounces (full), we can calculate it making the variable "x" equal to 0, so, calculating we have:

[tex]f(x)=648-24x[/tex]

[tex]f(0)=648-24*(0)=648[/tex]

Therefore, we have that the statement "Before practice, there are 648 ounces of sports drink in the cooler." is true.

C. Each plater drinks approximately 24 ounces of sports drink at practice: True.

From the statement, we know that the rate of change is equal to (-24), and it's equal to the number of ounces that each player drinks.

Hence, we have that the statement  "Each plater drinks approximately 24 ounces of sports drink at practice." is true.

D. If  24 players get drinks from the cooler, they will drink a total of 648 ounces of sports drink: False.

If we want to calculate the number of ounces that 24 players will drink, we need to use the slope value. If we know that each player drinks 24 ounces, so, to calculate how many ounces of sports drink will 24 players drink, we need to use the following equation:

[tex]DrankOunces=24oz*Players\\\\DrankOunces=24oz*24=576oz[/tex]

We have that 24 players will drink a total of 576 ounces, so, the statement "If  24 players get drinks from the cooler, they will drink a total of 648 ounces of sports drink." is false.

E. For each additional player that takes a drink, there will be approximately 24 fewer ounces of sporks drink remaining after the practice: True.

From the statement and the equation, we know that the slope (rate of change) is negative, meaning that for each player (x) it will be 24 fewer ounces of sports drink after practice, for example, calculating for 1 and 2 players, we have:

[tex]f(1)=648-24*1=624[/tex]

[tex]f(x)=648-24*2=600[/tex]

We can see that for each player, it will be 24 fewer ounces of sports drink after practice.

Hence, we have that the statement "For each additional player that takes a drink, there will be approximately  24 fewer ounces of sporks drink remaining after the practice." is true.

Therefore, the correct options are:

B. Before practice, there are 648 ounces of sports drink in the cooler.

C. Each plater drinks approximately 24 ounces of sports drink at practice.

E. For each additional player that takes a drink, there will be approximately  24 fewer ounces of sporks drink remaining after the practice.

Have a nice day!

Answer:

C) 6.6 gallons

Step-by-step explanation:

10oz * 85 = 850oz

There are 128 ounces in a gallon.

850/128 = 6.64

Answer:  Option 'c' is correct.

Step-by-step explanation:

Since we have given that

Number of servings = 85

Number of ounces per serving = 10 ounce

Total number of ounces would be

[tex]85\times 10\\\\=850[/tex]

As we know that

1 gallon = 128 ounces

So, Number of gallons of the soup were sold on Monday would be \

[tex]\dfrac{850}{128}\\\\=6.64\\\\\approx 6.6 \ gallons[/tex]

Hence, Option 'c' is correct.

Answer:

slope = 0

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (1, - 3) and (x₂, y₂ ) = (- 1, - 3)

m = [tex]\frac{-3+3}{-1-1}[/tex] = [tex]\frac{0}{-2}[/tex] = 0

Answer:

The 2.50a is the constant. He's getting paid 2.50 dollars weekly

Step-by-step explanation:

When theres a variable next to a number, that means that's the constant.

Answer:

no. Hes getting paid 290, guaranteed.

Step-by-step explanation:

...

For this case we must solve the following quadratic equation:

[tex]-3x ^ 2 + 1467x-86940 = 0[/tex]

If we divide both sides of the equation by 3 we have:

[tex]-x ^ 2 + 489-28980 = 0[/tex]

The solutions will come from:

[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2 (a)}[/tex]

Where:

[tex]a = -1\\b = 489\\c = -28980[/tex]

Substituting:

[tex]x = \frac {-489 \pm \sqrt {(489) ^ 2-4 (-1) (- 28980)}} {2 (-1)}\\x = \frac {-489 \pm \sqrt {239121-115920}} {- 2}\\x = \frac {-489 \pm \sqrt {123201}} {- 2}\\x = \frac {-489 \pm351} {- 2}[/tex]

The roots are:

[tex]x_ {1} = \frac {-489 + 351} {- 2} = \frac {-138} {- 2} = 69\\x_ {2} = \frac {-489-351} {- 2} = \frac {-840} {- 2} = 420[/tex]

ANswer:

[tex]x_ {1} = 69\\x_ {2} = 420[/tex]

That is very true.

In mathematics, an inverse operation is an operation that undoes what was done by the previous operation. The four main mathematical operations are addition, subtraction, multiplication, division. The inverse of addition is subtraction and vice versa. The inverse of multiplication is division and vice versa.

Addition and subtraction are indeed inverse operations. They are algebraic operations that do the opposite of one another and can thus 'undo' each other's effects.

The statement that Addition and subtraction are inverse operations is indeed true. In mathematics, an inverse operation is an operation that undoes what was done by the previous operation. In the case of addition and subtraction, they do exactly that. For instance, if you were to add 3 and 4 to get 7, you can undo this operation by subtracting 3 or 4 from 7 which will give back the other original number. Hence, addition and subtraction are deemed as inverse operations.

https://brainly.com/question/17776628

#SPJ11

Answer:

 The measure of G = 9.2°

Step-by-step explanation:

From the figure we can write,

The measure of <G is half the  the measure of arc AD

To find the value of x

We have  AD = (6x - 80)° and 2G = (x + 2)°

6x - 80 = (x + 2)

6x - 80 = x + 2

6x - x = 82

5x = 82

x = 82/5 = 16.4

To find the measure of <gG

m<G = (x + 2 )/2

 = (16.4 + 2)/2 = 18.4 = 9.2

Therefore the measure of <G =  9.2°

Answer:

3

Step-by-step explanation:

Given a polynomial with zeros x = a, x = b, x = c

Then the factors are (x - a), (x - b) and (x - c)

and the polynomial is the product of the factors

f(x) = k(x - a)(x - b)(x - c) ← k is a multiplier

here the zeros are x = - 3, x = 0, x = 4, thus the factors are

(x - (- 3)), (x - 0) and (x - 4), that is

(x + 3), x and (x - 4)

let k = 1, then

f(x) = x(x + 3)(x - 4) → 3

Answer:

F(x) = x(x + 3)(x – 4)

Step-by-step explanation:

The polynomial function has zeros at -3, 0, and 4  is F(x) = x(x + 3)(x – 4)

x(x + 3)(x – 4), set each part = 0 to find the solutions

x(x + 3)(x – 4) = 0

x = 0

x + 3 = 0; x = -3

x - 4 = 0; x = 4

Answer: [tex]x(11-x)=0[/tex]

Step-by-step explanation:

Given the quadratic equation [tex]11x-x^2=0[/tex], you need to factor it.

In order to find the form asked of the given equation, you need to factor out the common factor of the terms.

You can observe that the common factor of the terms of the equation is: [tex]x[/tex]

Now, knowing this, you must factor out [tex]x[/tex]. Then you get the following form:

[tex]x(11-x)=0[/tex]

Therefore, the factored fom of the equation  [tex]11x-x^2=0[/tex] is:

 [tex]x(11-x)=0[/tex]

The volume of Zara's sandwich formed as a rectangular prism, is 421.2 cm³, calculated by multiplying the sandwich's length, width, and height. The surface area is 561.6 cm² which is calculated by adding the areas of each face of the prism. When the sandwich is cut and stacked, the volume remains the same, but the surface area increases.

A. To find the volume of a prism (such as Zara's sandwich), we multiply the length by the width by the height. So, for Zara's sandwich, we would calculate the volume as follows (in cubic centimeters): 13cm × 10.8cm × 3cm = 421.2 cm³.

B. The surface area of a rectangular prism is calculated by 2lw + 2lh + 2wh (where l is the length, w is the width, and h is the height. Plugging in the dimensions Zara measured, we find the surface area to be: 2(13cm × 10.8cm) + 2(13cm × 3cm) + 2(10.8cm × 3cm) = 561.6 cm².

C. When Zara cuts her sandwich in half and stacks one half on top of the other, she is effectively doubling the height while keeping the length and width the same. However, since neither the volume nor surface area formulas have a square or cube factor in the height, the volume will be the same. As for the surface area, because the height is now equivalent to two sandwich halves, and the 'length' is not shared between the two halves, the surface area increases. So, Zara's conclusions are incorrect. The volume stays the same, while the surface area increases.

https://brainly.com/question/31408211

#SPJ12

a. The volume of Zara's sandwich is 421.2 cm³.

b. The surface area of Zara's sandwich is 561.6 cm².

c. Zara's conclusions are incorrect. The volume stays the same, while the surface area increases.

A. To calculate the volume of a prism (such as Zara's sandwich), multiply its length by breadth by height. So, for Zara's sandwich, the volume would be calculated as follows (in cubic centimeters): 13cm 10.8cm 3cm = 421.2 cm³.

B. A rectangular prism's surface area is computed as 2lw + 2lh + 2wh (where l is the length, w is the width, and h is the height). Using Zara's measurements, we calculate the surface area to be: 2(13cm 10.8cm) + 2(13cm 3cm) + 2(10.8cm 3cm) = 561.6 cm².

C. By cutting her sandwich in half and stacking one half on top of the other, Zara essentially doubles the height while maintaining the length and width. The volume, however, will be the same because neither the volume nor surface area formulae include a square or cube element in the height. The surface area grows since the height is now equivalent to two sandwich half and the 'length' is not split between the two halves. Zara's conclusions are thus wrong. The volume remains constant while the surface area grows.

Answer: [tex]A = 108.80\ units^2[/tex]

Step-by-step explanation:

The surface  area of right cone is calculated by the following formula

[tex]A = \pi r *\sqrt{r^2 +h^2}+\pi r^2[/tex]

Where r is the radius of the cone and h is the height

In this case we know that the diameter d of the base is:

[tex]d=2r[/tex]

So the radius is:

[tex]r=\frac{d}{2}\\\\r=\frac{6}{2}\\\\r=3\ units[/tex]

and

[tex]h=8\ units[/tex]

So the area is:

[tex]A = \pi*3 *\sqrt{3^2 +8^2}+\pi(3)^2[/tex]

[tex]A = 108.80\ units^2[/tex]

Answer:

[tex]SA=108.8 units^2[/tex]

Step-by-step explanation:

The surface area of a right cone is given by

[tex]S.A=\pi r^2+\pi rl[/tex]

The relation between the slant height l, the radius r, and the height h, is

[tex]l^2=r^2+h^2[/tex]

[tex]l^2=3^2+8^2[/tex]

[tex]l^2=9+64[/tex]

[tex]l^2=73[/tex]

[tex]l=\sqrt{73}[/tex]

[tex]S.A=\pi \times 3^2+\pi \times3\times\sqrt{73}[/tex]

[tex]S.A=\pi \times 3^2+\pi \times3\times\sqrt{73}[/tex]

[tex]SA=108.8 units^2[/tex]

The answer is D, 36 days. In 36 days, Jane can make 6 dream catchers and Zena can make 9. 9+6=15

Answer:The correct answer is 36 days

Step-by-step explanation: Jane-1 in 6 days or 2 in 12 days..Zena-1 in 4 days or 3 in 12 days. So in 12 days together the girls can make 5 dream catchers. In 24 days they would have 10, and in 36 days they would have 15.

Answer:

x=6

Hope This Helps!   Have A Nice Day!!

Answer:

x=6

Step-by-step explanation:

[tex]48+54=x(8+9)\\\\102=8x+9x\\\\102=17x\\\\6=x[/tex]