I need help with question 20

Answer:

The approximate population of bacteria in the culture after 10 hours is 93,738.  

Step-by-step explanation:

BPEMDAS Order of Operations:

We are given the following Exponential Growth Function (Doubling Time Model), [tex]\displaystyle\mathsf{P_{(t)}\:=\:P_0\cdot2^{(t/d)}}[/tex] where:

Step 1: Identify the given values.

Step 2: Find value.

1. Substitute the values into the given exponential function.

  [tex]\displaystyle\mathsf{P_{(t)} = P_0\cdot2^{(t/d)}}[/tex]

  [tex]\displaystyle\mathsf{\longrightarrow P_{(10)} = 9300\cdot2^{(10/3)}}[/tex]

2. Evaluate using the BPEMDAS order of operations.

  [tex]\displaystyle\mathsf{P_{(10)} = 9300\cdot2^{(10/3)}\quad \Longrightarrow BPEMDAS:\:(Parenthesis\:\:and\:\:Division).}[/tex]

  [tex]\displaystyle\sf P_{(10)} = 9300\cdot2^{(3.333333)}\quad\Longrightarrow BPEMDAS:\:(Exponent).}[/tex]

  [tex]\displaystyle\sf P_{(10)} = 9300\cdot(10.079368399)\quad \Longrightarrow BPEMDAS:(Multiplication).}[/tex]

 [tex]\boxed{\displaystyle\mathsf{P_{(10)} \approx 93,738.13\:\:\:or\:\:93,738}}[/tex]

Hence, the population of bacteria in the culture after 10 hours is approximately 93,738.  

We can solve for the amount of time (t ) it takes for the population of bacteria to increase to 93,738.

1. Identify given:

2. Substitute the values into the given exponential function.

  [tex]\displaystyle\mathsf{P_{(t)} = P_0\cdot2^{(t/d)}}[/tex]

  [tex]\displaystyle\mathsf{\longrightarrow 93,378 = 9,300\cdot2^{(t/3)}}[/tex]

3. Divide both sides by 9,300:

  [tex]\displaystyle\mathsf{\longrightarrow \frac{93,378}{9,300} = \frac{9,300\cdot2^{(t/3)}}{9,300}}[/tex]

  [tex]\displaystyle\mathsf{\longrightarrow 10.07936840 = 2^{(t/3)}}[/tex]

4. Transform the right-hand side of the equation into logarithmic form.

  [tex]\boxed{\displaystyle\mathsf{\underbrace{ x = a^y}_{Exponential\:Form} \longrightarrow \underbrace{y = log_a x}_{Logarithmic\:Form}}}[/tex]    

  [tex]\displaystyle\mathsf{\longrightarrow 10.07936840 = \bigg[\:\frac{t}{3}\:\bigg]log(2)}[/tex]  

5. Take the log of both sides of the equation (without rounding off any digits).  

  [tex]\displaystyle\mathsf{log(10.07936840) = \bigg[\:\frac{t}{3}\:\bigg]log(2)}[/tex]

  [tex]\displaystyle\mathsf{\longrightarrow 1.003433319 = \bigg[\:\frac{t}{3}\:\bigg]\cdot(0.301029996)}[/tex]

6. Divide both sides by (0.301029996).

  [tex]\displaystyle\mathsf{\frac{1.003433319}{0.301029996} = \frac{\bigg[\:\frac{t}{3}\:\bigg]\cdot(0.301029996) }{0.301029996}}[/tex]

  [tex]\displaystyle\mathsf{\longrightarrow 3.3333333 = \frac{t}{3}}[/tex]

7. Multiply both sides of the equation by 3 to isolate "t."

  [tex]\displaystyle\mathsf{(3)\cdot(3.3333333) = \bigg[\:\frac{t}{3}\:\bigg]\cdot(3)}[/tex]

  [tex]\boxed{\displaystyle\mathsf{t\approx10}}[/tex]

Hence, it will take about 10 hours for the population of bacteria to increase to 93,378.    

__________________________________

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When Leonardo and his wife file married filing jointly in 2021, the average tax rate will be 15.63 percent

In the question above, Leonardo's taxable income = $80,000

Theresa's taxable income = $15,000

Total taxable income for both of them will be:

$ 80,000 + $ 50,000 = $ 130,000

When you make use of the Schedule Y-1,

The amount of the tax on total income shall be said as:

Tax liability = $9,086 + (($130,000 - $78,950) * 22%)

= $9,086 +($51,050 * 22%)

= $9,086 + $11,231

= $ 20,317

To get the Effective tax rate, it will be:

= tax liability / Total taxable income Effective tax rate

= [tex]\frac{20,317}{30000}[/tex]  that is also written as $20,317/ $130,000

So, the  average tax rate is = 15.63%

Therefore, the average tax rate will be = 15.63 percent

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Answer:

10 and 4; and -8 and -5.

Answer:

Step-by-step expiation : 5575.3

The sequence is an arithmetic sequence and the expression used to find the nth term would be 3n option fourth I and II is correct.

It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

We have a sequence:

3, 6, 9, 12…

First term a  = 3

Common difference d = 6 - 3 = 3

This is an arithmetic sequence.

nth term of the arithmetic sequence:

a(n) = 3 + (n-1)(3)

a(n) = 3n

Plug n = 5

a(5) = 3(5) = 15

Thus, the sequence is an arithmetic sequence and the expression used to find the nth term would be 3n option fourth I and II is correct.

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Answer:

103.9

Step-by-step explanation:

yes

Answer:

1.64

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2+b^2 = c^2  where a and b are the legs and c is the hypotenuse

6.6^2 + x^2 = 6.8^2

43.56+x^2=46.24

Subtract 43.56 from each side

x^2 = 46.24-43.56

x^2 =2.68

Take the square root of each side

sqrt(x^2) = sqrt(2.68)

x =1.637080554

To 3 significant digits

x = 1.64

Answer:

Step-by-step explanation:

       x = 1.637 mm

        We can use Pythagorean theorem, to find the unknown side for a right angled triangle.

The side opposite to 90 is the longest side and it is the hypotenuse.

Base² + altitude² = hypotenuse²

 x²     + 6.6²        = 6.8²

      x²  +  43.56  = 46.24

                     x²   = 46.24 - 43.56

                    x²    = 2.68

                      x   = √2.68

                      [tex]\sf \boxed{\bf x = 1.637 \ mm }[/tex]

Mean measure of central tendency is the most affected by outliers. Then the correct option is B.

The mean is the straightforward meaning of the normal of a lot of numbers. In measurements, one of the markers of focal propensity is the mean. The normal is alluded to as the number-crunching mean. It's the proportion of the number of genuine perceptions to the absolute number of perceptions.

Mean measure of central tendency is the most affected by outliers.

Then the correct option is B.

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Answer + Step-by-step explanation:

CE bisects AB

CE ⊥ AB

Then

CE is the perpendicular bisector of AB.

Therefore

CA = CB and DA = DB

…………………………………

we have :

CA = CB

DA = DB

CD is a common side of the two triangles ACD and BCD

Hence , ΔACD ≅ ΔBCD

⇒ ∠CAD ≅ ∠CBD.

Answer:

it is b

Step-by-step explanation:

The solution is Option A.

The coordinates of the vertex A before the reflection across the line y = x is given by A = A ( 10 , -2 )

Reflection is a type of transformation that flips a shape along a line of reflection, also known as a mirror line, such that each point is at the same distance from the mirror line as its mirrored point. The line of reflection is the line that a figure is reflected over. If a point is on the line of reflection then the image is the same as the pre-image. Images are always congruent to pre-images.

The reflection of point (x, y) across the x-axis is (x, -y). When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).

Given data ,

Let the coordinates of the point A be A ( x , y )

Now , the vertex A is reflected over the line y = x

When you reflect a point across the y = x , the y-coordinate gets interchanged with x-coordinate. The reflection of point (x, y) across the line y = xis ( y , x )

So , the coordinates of the point A' ( -2 , 10 )

Now , the coordinates of the point A will be

A ( x , y ) = A ( 10 , -2 )

Therefore , the value of A is A ( 10 , -2 )

Hence , the coordinates of the point before reflection is A ( 10 , -2 )

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Answer:

g(x) = 1/3 • |x|

Step-by-step explanation:

To stretch a parent function, you multiply by whatever you want to stretch it with. If you multiplied by 3, it would be a vertical stretch... if you multiplied by 1/3, it makes it horizontal.

Hope this helps!

Answer:

97

Step-by-step explanation:

Number of adult tickets = a.

Number of student tickets = s.

"A total of 388 tickets were sold"

a + s = 388

"the number of student tickets sold was three times the number of adult tickets sold"

s = 3a

a + s = 388

s = 3a

Substitute s in the first equation with 3a.

a + 3a = 388

4a = 388

a = 97

Answer: 97 tickets

im not in collage but I'll try ok so its most likely

Factor then solve to find the complex solutions.

x=2πn, for any integer n

if i was right could i get brainly?

Translating the given phrase into a variable expression is equal to k - 2.

A variable expression refers to a mathematical equation which can be used to show the relationship that exist between a numerical quantity and a variable.

Next, we would translate the given phrase into a variable expression as follows:

Let the number of keys on the keyring be k.

Therefore, the variable expression is equal to k - 2.

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Complete Question:

Translate the phrase into a variable expression. Use the letter k to name the variable. If necessary, use the asterisk (*) for multiplication and the slash (/) for division.

The number of keys on the keyring minus 2?

Answer: B 3.0

Step-by-step explanation:

[tex]\begin{cases} u=6i-2j\\\\ v=-3i+7j \end{cases}\qquad \begin{cases} < 6~~,~~-2 > \\\\ < -3~~,~~7 > \end{cases} \\\\[-0.35em] ~\dotfill\\\\ u-v\implies < 6~~,~~-2 > ~~ - ~~ < -3~~,~~7 > \\\\\\ < 6-(-3)~~,~~-2-7 > \implies < 6+3,-9 > \implies < 9,-9 > \implies 9i-9j[/tex]

The graphed cosine function can either be:

cos(x + pi) or cos(x - pi).

We know that this function is a cosine function with a phase shift, so the general form is:

f(x) = cos(x + P).

Where P is the phase shift.

In the graph we can see that when x = 0, f(0) = -1

And we know that cos(pi) = -1 = cos(-pi)

Then we must have that:

f(0) = cos(P) = -1

By what we wrote above, we know that P can be either -pi or pi (because of the parity of the cosine). Let's say that P = pi, then the cosine function is:

f(x) = cos(x + pi).

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The graph that could represent the motion of the apple is graph B.

A graph is a diagram showing the relation between variable quantities, typically of two variables, each measured along with one of a pair of axes at right angles.

Here, the speed of apple at time t is given by v=0 + at which is a straight line of slope a that passes through origin because constant is zero. At time t=0 its initial speed is 0 and it will increase constantly with time. Therefore, graph (B) is correct

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Answer:

f(-3) = -6

Step-by-step explanation:

f(x) = x^2 + 4x - 3

f(-3) means to put -3 in place of x and then do the calculation.

f(-3)

= (-3)^2 + 4(-3) - 3

= 9 - 12 - 3

= -3 - 3

= -6

First square -3, its 9. Then multiply -3 and 4, that's -12. Then add everything.

f(-3) = -6

Answer: 9

Step-by-step explanation:

By the geometric mean theorem, [tex]\frac{x}[6} =\frac{6}{4} \longrightarrow x=\left(\frac{6}{4} \right)(6)=\boxed{9}[/tex]

The amount of the interest with simple interest of 6.9% will be $ 10.35.

Simple interest is the concept that is used in many companies such as banking, finance, automobile, and so on.

Miguel Rodriguez borrowed ​$300 from his brother Julio to pay for books and tuition.

He agreed to pay Julio in 6 months with simple annual interest at ​6.9%

Then the amount of the interest will be

Amount = P x R x T / 100

We have

P = $ 300

R = 6.9%

T = 6 months = 0.5 years

Then we have

P = (300 x 6.9 x 0.5) / 100

P = $ 10.35

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Answer:

C

Step-by-step explanation:

The answer would have to be C cus it can't be A or D

Answer:

x = 3 or x = 1

y = 3 or y = -1

(x, y) = (3, 3)

(x, y) = (1, -1)

Step-by-step explanation:

Step-by-step explanation:

x = earnings from the store

y = earnings from the college

x + y = 67,250

x = 3y + 1,250

now we use the identity of the second equation in the first equation :

(3y + 1,250) + y = 67,250

4y = 66,000

y = $16,500

x = 3y + 1,250 = 3×16,500 + 1,250 = 49,500 + 1,250 =

= $50,750

Hello there!

I will only explain the ones that do not appear correct to me. If you require further explanation, please let me know.

1] vertical

2] corresponding

   -> These two angles are in corresponding places on points of the lines, so they are corresponding angles.

3] alternate interior

4] alternate exterior

   -> These angles are on the "outside" of the parallel lines, and on "opposite" sides of the transversal. With this in mind, they are alternate exterior angles

5] same side interior

6] same side exterior

   -> These angles are on the "outside" of the parallel lines, and on the same side of the transversal. With this in mind, they are same-side exterior angles

Answer: B

Step-by-step explanation:

The angles add to 90 degrees if they are complementary, so:

[tex]x-2+2x+5=90\\3x+3=90\\3x=87\\x=29[/tex]

So, the angles measure 29-2=27 degrees and 2(29)+5=63 degrees.

Answer:

she will need 728 pounds to buy 28 cans but she only has 10 pounds so she doesn't even have enough for 1 can of soda