how do you solve this question

Using exponential functions, it is found that:

a) Since the amount of caffeine will be less than 50 mg, the patient will be ready for the blood test by 6 a.m.

b) The patient could have ingest 231 milligrams of caffeine.

A decaying exponential function is modeled by:

[tex]A(t) = A(0)(1 - r)^t[/tex]

In which:

In this problem:

Then:

[tex]A(t) = A(0)(1 - r)^t[/tex]

[tex]A(t) = A(0)(1 - 0.13)^t[/tex]

[tex]A(t) = A(0)(0.87)^t[/tex]

Item a:

The coffee cup contains 150 milligrams of caffeine, hence [tex]A(0) = 150[/tex].

At 6 a.m., it is 8 hours after drinking the coffee, hence we have to find A(8).

[tex]A(t) = A(0)(0.87)^t[/tex]

[tex]A(8) = 150(0.87)^8[/tex]

[tex]A(8) = 49.2[/tex]

Since the amount of caffeine will be less than 50 mg, the patient will be ready for the blood test by 6 a.m.

Item b:

This A(0), considering A(11) = 50, hence:

[tex]50 = A(0)(0.87)^{11}[/tex]

[tex]A(0) = \frac{50}{(0.87)^{11}}[/tex]

[tex]A(0) = 231[/tex]

The patient could have ingest 231 milligrams of caffeine.

A similar problem is given at https://brainly.com/question/25537936

Answer:

C

Step-by-step explanation:

Answer: C

Step-by-step explanation:

An advantage of using graphics is to present information briefly.

Answer:

-4y²- 16y

Step-by-step explanation:

   2y(-2y - 8)

   2y (-2y) + 2y (-8)  Distributive

      -4y² - 16y                Multiply (+)(-) = -   and (y)(y) = y²

Answer:

Step-by-step explanation: All we are doing here is inserting 2 in place of all the x variables. So that is written as 12(2)-3(3(2)-5)+24. Next, we follow the order of operations to solve

1) Multiply 3 by 2 and subtract by 5 inside the parenthesis = 12(2)-3-1+24

2) Multiply 12 by = 24-3+1+24

3) subtract 3 from 24 = 21+24

4) Add the final two terms = 45

MARK BRAINLIEST

ANSWER: [tex]y=-\frac{3}{4} x +6 <=>3x=24-4y[/tex]

Ok done. Thank to me :>

Answer:

I NEEEEEEEED TO SEEEE GRAPHHHHHHHHHHHH

Step-by-step explanation:

Answer:

1/3 OR -1/3

Step-by-step explanation:

1/2 - 1/6 = ?

3/6 - 1/6 = 2/6

2/6 = 1/3

OR

1/6 -1/2 =?

1/6 - 3/6 = -2/6

-2/6 = -1/3

Answer:

$7,507

Step-by-step explanation:

Answer:

[tex]y = -\frac{1}{6}x - 3[/tex]

Step-by-step explanation:

Slope Intercept Form :   [tex]y = mx + b[/tex]

Using our slope, -1/6, input it for m, then plug the point (-6, -2) for x and y

[tex]y = mx+b\\\\-2 = (-1/6)(-6) + b\\\\-2 = 1 + b\\\\b = -3[/tex]

Equation : [tex]y = -\frac{1}{6}x - 3[/tex]

-Chetan K

4.3-3(4r-3(=0.7(6r-10

We move all terms to the left:

4.3-3(4r-3(-(0.7(6r-10)=0

Answer:

Step-by-step explanation:

B

Answer:

10

Step-by-step explanation:

Answer:

1) g = -8 (one solution)

2) b = 0 (infinitely many solutions)

3) w = 5/6 (one solution)

4) c = 0 (infinitely many solutions)

Step-by-step explanation:

1) 1/2g -4 = 2g - 1/2g + 4

1/2g -2g +1/2 g = 8

-g = 8

2) 5.3-5.3 = 2.1b + b - 3.1b

0=0

3) 3/4w+ 3/4w = 10/4 - 5/4

3/2w = 5/4

w = (5/4) / (3/2)

w = 5/6

4) 5.7c + 3.2c - 7.8c - 1.1c = 1.5 - 1.5

0 = 0

Answer:

6

Step-by-step explanation:

Since the range of a set is the difference between the highest and the lowest value in that set, the range here is:

9 - 3 = 6

Answer:

since opp. angles of a parallelogram is equal.

therefore,

let the angle be x

thus,

x+x=140

2x=140

x=70°

co interior angles are supplimentary,

thus,

x+y=180

y=180-70

y=110°

opp. angles are equal thus,

fourth angle =110°

1st angle=70

2nd angle=70

3rd angle =110°

Step-by-step explanation:

Answer:  [tex]\boldsymbol{4\sqrt{11}}\\\\[/tex]

Work Shown:

[tex]\sqrt{176}\\\\\sqrt{4*44}\\\\\sqrt{4}*\sqrt{44}\\\\2*\sqrt{4*11}\\\\2*\sqrt{4}*\sqrt{11}\\\\2*2*\sqrt{11}\\\\\boldsymbol{4\sqrt{11}}\\\\[/tex]

The idea is to factor the number such that we pull out perfect square factors. We use the rule that [tex]\sqrt{x*y} = \sqrt{x}*\sqrt{y}[/tex] to help break up the root. We also use the idea that [tex]\sqrt{x^2} = x[/tex] when x is nonnegative.

Answer:

y=(-1/2)(x)-8

Step-by-step explanation:

Since they give the slope and y intercept, you can literally plug it into the equation:

y=mx+b

where m is slope and b is y interecept.

Therefore, we get

y=(-1/2)(x)-8

Answer:

y=5x-8

Step-by-step explanation:

Slope=m=(7-3)/(3-2)

y=5x+b=>2=5*2+c=>c=-8

So y=5x-8

[tex]\text{Given that,}\\\\(x_1,y_1) = (2,2), ~ \text{and}~ (x_2,y_2) = (3,7)\\\\\text{Slope, m =} \dfrac{y_2-y_1}{x_2-x_1} = \dfrac{7-2}{3-2} = \dfrac 51 = 5\\\\\text{Equation with given points,}\\\\y-y_1 = m(x-x_1)\\\\\implies y-2= 5(x-2)\\\\\implies y -2 = 5x-10\\\\\implies y = 5x -10 +2\\\\\implies y = 5x -8\\\\\\\text{It is now in a form of y = mx +c}[/tex]

espaneool

Step-by-step explanation:

Answer:

(1, 4)

Step-by-step explanation:

im assuming that the point is h(1) = 4

this point is basically just h(x) = y

1 is your x

4 is your y

you plot it at the point (1, 4)

[tex] \: \: \: \: \: \: [/tex]

[tex] = \frac{1}{9} \\ \\ or \: \: in \: \: alternate \: form \: \: \\ \\ 0.1, {3}^{ - 2} [/tex]

Step-by-step explanation:

[tex] \frac{5}{9} \div 5[/tex]

[tex] \frac{5}{9} \times \frac{1}{5} [/tex]

[tex] = \frac{1}{9} \: \: \\ \\ or \: \: in \: \: alternate \: \: form \\ \\ 0.1, {3}^{ - 2} [/tex]

Answer:

The Slope is -2

Step-by-step explanation:

The entered points belong to a decreasing, linear function.

Equation: y = -2x + 5.

Answer:

Slope = -2

Step-by-step explanation:

[tex]\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\\\\left(x_1,\:y_1\right)=\left(-4,\:13\right),\:\left(x_2,\:y_2\right)=\left(8,\:-11\right)\\m=\frac{-11-13}{8-\left(-4\right)}\\\mathrm{Refine}\\m=-2[/tex]

In order to use the Pythagorean Theorem to find out if a triangle has a right angle, you have to determine If the squares of the two shorter sides add up to the square of the hypotenuse, then you know the triangle contains a right angle.

Answer:

24

Step-by-step explanation:

If Matilda earns $48 in 4 hours, then she must earn 48/4 (12) dollars per hour. We know she earns $12 per hour, and that she made $288, so we divide the total amount earned (288) by her hourly wage ($12) to find she worked 288/12 or 24 hours.

Matilda will earn $288 in 24 hours.

A word problem is a few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.

Given is that Matilda earns $48 in 4 hours.

Let us assume that it will take her {x} hours to earn $288.

Then, we can write -

there is earning of $48 in 4 hours.

so, there will be earning of $1 ins (4/48) or (1/12) hours.

hence, she will earn $288 in (1/12 x 288) or 24 hours.

Therefore, Matilda will earn $288 in 24 hours.

To solve more questions on equation modelling, visit the link below -

brainly.com/question/29299318

#SPJ2

Answer:

a=√2, c=4√3

Step-by-step explanation:

Recall that in a 45-45-90 triangle, the side lengths are the same but the hypotenuse is the side length times the square root of 2. Therefore, a=2/√2=√2.

Recall that in a 30-60-90 triangle, the shorter side length is x, the longer side is x√3, and the hypotenuse is 2x. Therefore, c=4√3

Answer:

  10

Step-by-step explanation:

The restriction m < 0 means we can multiply by -7m/2 without changing the direction of the inequality symbol

  [tex]\dfrac{3}{m}\le-\dfrac27\\\\-\dfrac{21}{2}\le m\qquad m<0}[/tex]

Then the solution is the number of negative integer values between -10.5 and 0. There are 10 negative integer values of m that satisfy the inequality.

Answer:

Step-by-step explanation:

I dont really know how to find out the variables but what i assume to do is this:

Find the square root of n and add it to m. The sum of both you divide by p. then when you figure that out, you distribute the x value into the parenthesis. This might be obvious but i looked at this question for 10 minutes and couldnt  find the value sorry :(

For the 1st equation,

Answer:

A. 2x + y = 20

Hope you could get an idea from here.

Doubt clarification - use comment section.

The solutions to the equation [tex]3-k=\sqrt{3k+1}[/tex] are k = 1 and 8

The given equation is:

[tex]3-k=\sqrt{3k+1}[/tex]

Square both sides of the equation

[tex](3-k)^2=3k+1[/tex]

Expand the left side of the equation above

[tex](3-k)^2=3k+1\\\\(3-k)(3-k)=3k+1\\\\3^2-3k-3k+k^2=3k+1\\\\9-6k+k^2=3k+1[/tex]

Write the quadratic equation in standard form

[tex]k^2-6k-3k+9-1=0\\\\k^2-9k+8=0\\\\[/tex]

Factor the quadratic equation

[tex](k-8)(k-1)=0[/tex]

Use the zero product property

k - 8 = 0

k = 8

k - 1 = 0

k = 1

The solutions to the equation [tex]3-k=\sqrt{3k+1}[/tex] are k = 1 and 8

Learn more here: https://brainly.com/question/25840704

answer

first one: 8 and 1

second one: is 1

Step-by-step explanation:

slay