You go to the doctor and he injects you with 13 milligrams of radioactive dye. After 12 minutes, 4.75 milligrams of dye remain in you system. To leave the doctor's office, you must pass through a radiation detector without sounding the alarm. If the detector will sound will sound the alarm whenever more than 2 milligrams of the dye are in your system, how long will your visit to the doctor take, assuming you were given the dye as soon as you arrived and the amount of dye decayse exponentially?
Answer:
Step-by-step explanation:
You need to find the model for this situation using the points given. If you are given 13 mg immediately, the coordinate point for that is (0, 13), where the x coordinate is the time in minutes and the y coordinate is the amount of dye in mg.
If after 12 minutes, 4.75 mg remain, the coordinate point for that is (12, 4.75). Just so you know, the time unit always goes in for x, never for y.
Now that we have these coordinates we are going to use them as a system and find the model. Begin with the point (0, 13) in
[tex]A=a(b)^t[/tex] where A is the amount left in the body, a is the initial amount injected, b is the rate at which it decays, and t is the time in minutes. Plug in the first set of coordinates:
[tex]13=a(b)^0[/tex] and since anything raised to the power of 0 is equal to 1, we have
13 = a. Now we can use that and write another equation with the other set of coordinates to solve for b:
[tex]4.75=13(b)^{12}[/tex] and divide both sides by 13 (don't round anything yet) to get
.3653846154 = b¹². Now take the 12th root of both sides (you need a scientific calculator for this) to get that
b = .9195228407 Yikes.
Now for the model, using the fact that a = 13 and b = .9195228407:
[tex]A=13(.9195228407)^t[/tex]
We are told that the amount that we are allowed to leave with still remaining in our system cannot be more than 2 mg, so we sub in a 2 for A:
[tex]2=13(.9195228407)^t[/tex] and begin by dividing away 13 to get
[tex].1538461538=.9195228407^t[/tex] Take the natural log of both sides, which allows us to bring the t out front:
ln(.1538461538) = t ln(.9195228407) and finally divide by ln(.9195228407) to get
t = 22.3 minutes
Need some help in this!!
Answer:
Step-by-step explanation:
<AEC = <BED Vertically opposite angles are equal.
<A = <B An angle's vertex when touching the same part of the circumference of a circle (on the same side of CD) as another angle with the same endpoints (CD) are equal
CD = DE Given
ΔAEC = ΔBED AAS
Draw the parabola's axis of symmetry.
The midpoint of a segment is ( 6, -6) and one endpoint is (13,-1). Find the coordinates of the other endpoint
PLEASE HELP!
Create an equation to model a population of cells which starts with 10 cells and doubles in size every day. How many days will it take to reach 1,000,000 cells?
Answer:
100,000 days
Step-by-step explanation:
1,000,000 / 10 = 100,000 days.
please help geometry!!
Answer:
A' (-5, 5)
B' (20, 0)
C' (5, -15)
Step-by-step explanation:
Multiply each coordinate by 5, and your result is given above.
Answer:
Step-by-step explanation:
HELPPPPPPPPP !!!!!!!!! plzzzzz
Answer:
a) its root 2
b) 2
c) 3,4,5,6 (just all x numbers)
d) inverse is just reverse of points ex: (2,1) for the first set
also what is that equation up top am i suppose to use that for something
Step-by-step explanation:
Craig wants to prove that if quadrilateral ABCD has diagnols that biscet each other then it is a parallelogram
Solution :
Consider quadrilateral ABCD is a parallelogram. The parallelogram have diagonals AC and DB.
So in the given quadrilateral ABCD, let the diagonal AC and diagonal DB intersects at a point E.
Thus in the quadrilateral ABCD we see that :
1. AC and DB are the diagonals of quadrilateral ABCD.
2. Angle DCE is congruent to angle BAE and angle CDE is congruent to angle ABE. (they are alternate interior angles)
3. Line DC is congruent to line AB. (opposites sides are congruent in a parallelogram )
4. Angle ABE is congruent to angle CDE. (Angle side angle)
5. Line AE is congruent to line EC. And line DE is congruent to line EB. (CPCTC)
Thus we see that if the diagonals of a [tex]\text{quadrilateral bisects each other}[/tex], then the quadrilateral is a parallelogram.
Answer:
△ABE and△CDE by side-angle-side
9. Find the zero of the polynomial in each of the following
i)f(x) = 3x- 5
Answer:
[tex]f(x) = 3x - 5[/tex]
For a zero, f(x) = 0:
[tex]{ \tt{0 = 3x - 5}} \\ { \tt{x = \frac{5}{3} }}[/tex]
"The mean age of all students at the University has a 95% chance of falling between 21.3 and 24.6 years of age." This statement represents:
Answer:
Confidence interval of the population mean
Step-by-step explanation:
The statement above is a report of the estimated confidence interval value which is used to obtain the estimate if the population mean from a given sample.
The statement above gives the confidence interval at α = 95%
căn bậc 2 của 5 là bao nhiêu
Answer:5
Step-by-step explanat[tex]\sqrt{5} = 5[/tex]
[tex]\sqrt{5}[/tex] = 2.23
\sqrt{10(x-3)} =\sqrt{26\\
Step-by-step explanation:
[tex]\sqrt{10(x-3)} =\sqrt{26}[/tex]
[tex]\sqrt{10x-30} = \sqrt{26} \\\10x-30 = (\sqrt{26} )^2\\10x - 30 = 26\\10x = 56\\x = 56/10\\so, x = 28/5[/tex]
What is the value of x in the equation
3x - y = 30, when y = 15?
Answer:
x = 15
Step-by-step explanation:
3x - y = 30
Given;
y = 15
To find;
value of 'x'
Putting the value of y in the given equation;
3x - 15 = 30
3x = 30 + 15
3x = 45
x = 45/3
x = 15
Answer:
x = 15Step-by-step explanation:
3x - y = 30let y = 153x - 15 = 303x = 30 + 153x = 45x = 45/3x = 15Let's check:3x - y = 303(15) - 15 = 3045 - 15 = 3030 = 30[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]
An article in Fortune (September 21, 1992) claimed that nearly one-half of all engineers continue academic studies beyond the B.S. degree, ultimately receiving either an M.S. or a Ph.D. degree. Data from an article in Engineering Horizons (Spring 1990) indicated that 117 of 484 new engineering graduates were planning graduate study. Are the data from Engineering Horizons consistent with the claim reported by Fortune
Answer:
unless this is a stats question and you are suggesting that you have bad sampling techniques being used
117/484 is about 24% that is 100% under the "about 50%" stated in the article
Step-by-step explanation:
(2x2 + 1) + 3/2x2=1=4
Answer:
3(2×2+1)+3×(2×2)/3=1×3=4×3
36+3+4=3=12
36+3+4-3-12
43-15
28
Drag each label to the correct image. Each label can be used more than once, but not all labels will be used. A cube is a rectangular prism whose faces are all squares with sides of the same length. Match each cross section of the cube to its correct image.
Answer:
From left to right it's square square rectangle.
Becky bikes 6 miles in 24 minutes. At the same rate, how many miles would she bike in 60
minutes?
Answer:
10 miles
Step-by-step explanation:
6 in 24 min 6÷24=4
60÷6 =10
=======================================================
Here's one approach:
(6 miles)/(24 minutes) = (x miles)/(60 minutes)
6/24 = x/60
6*60 = 24*x
360 = 24x
24x = 360
x = 360/24
x = 15
She travels 15 miles in 60 minutes (aka 1 hour). So we can say her speed is 15 mph.
-----------------------------
Here's another approach:
If she travels 6 miles in 24 minutes, then her unit rate is distance/time = 6/24 = 1/4 = 0.25 miles per minute.
So if she travels for 60 minutes, then she'll cover a distance of 60*0.25 = 15 miles
Please answer I'll mark u the brialintest
1) 3 × --- = (-12)
8) 2/5 × 4 is equal to ------
Answer:
1. -4
2. 8/ 5 - 1. 6
Step-by-step explanation:
1 . 3 × -4
= (-12)
2. 2/5 × 4
= 8 / 5
= 1.6
Hope this answer helps you :)
Have a great day
Mark brainliest
The lines shown below are perpendioular. If the green line has a slope of
-2/3 what is the slope of the red line PLEASE HELP ASAP
Answer:
C)3/2
Step-by-step explanation:
Perpendicular lines have a negative reciprocal slopes.
Therefore C)3/2
Take a factor out of the square root: 48x^2 , where x≤0
Answer:
[tex]-4x\sqrt{3}[/tex]
Step-by-step explanation:
One is given the following expression:
[tex]\sqrt{48x^2}[/tex]
Factor out the expression. Rewrite the expression as the product of a number times itself times another number. This will allow one to take factors out of the radical. Remember, the square root operation indicates that a number times itself equals the number under the radical. Bear in mind, the result of the square root operation must always be positive. Since (x) is negative, one has to multiply the result of the operation by (-1) to compensate for the fact that (x) is negative. Rewrite the value under the radical:
[tex]\sqrt{4*4*3*x^2}[/tex]
Take out the factors,
[tex]=-4x\sqrt{3}[/tex]
write an inequality and show on a number line all numbers greater (-3) but less than equal to3
Answer:
-3<x<_3
You plot this on a number line by writing and open circle on -3 and drawing and arrow from that open circle all the way until 3 and them draw a closed circle on 3.
Step-by-step explanation:
Mrs brown designed a rug if it cost $22 per square foot to make how much will Mrs brown pay if the square feet is 31.25
Answer:
$687.5
Step-by-step explanation:
Cost of the rug per square foot = $22
Length of the rug = 31.25 feet
Total amount Mrs brown will pay = Cost of the rug per square foot × Length of the rug
= 31.25 × 22
= $687.5
Total amount Mrs brown will pay = $687.5
A grocery store offers 2 free flashlights with any purchase. Rita can spend $100. The number of items that she can buy is given by
y = 100/x +2
where x is the average price per item. Identify the reasonable domain and range values.
D: x < 0
R: natural numbers > 2
D: x < 0
R: natural numbers < 2.
D: x > 0
R: natural numbers > 2
D: x > 0
R: natural numbers < 2
Answer:
The answer is D: x > 0
R: natural numbers > 2
Step-by-step explanation:
I got 100 on the quiz good luck bro
I really really need help with this
Answer:
c) 21
Step-by-step explanation:
[tex] \sqrt{169} + \sqrt{64} [/tex]
13+8
answer is 21
Find the value of y.
Tatia, Mary, and Erica were partners in business. Tatia received twice as much of the profit as Erica received. Mary received 2/3 of the amount Tatia received. If the total profit was $52,000, how much did Mary recieve
Answer:
$16000
Step-by-step explanation:
let Amount Erica received be 'x'
Tatia received = 2x
Mary received = 2/3(2x) = 4x/3
x + 2x + 4/3(x) = 52000
3x + 4x/3 = 52000
(9x+4x)/3 = 52000
13x/3 = 52000
x = (52000 x 3) / 13
x = 4000 x 3
x = 12000
Mary Received = 4x/3 = 4(12000)/3 = 16000
Answer:
$16000
Step-by-step explanation:
erica would get -n
tatia gets -2n
Mary gets -2/3 of 2n
2n +( 2/3 of 2 n ) + n =$52000
2n + 4/3n+ n=$52000
3 4/3 n=$52000
13/3 n= $52000
n= $16000
Defenation of time, distance and speed
Which function is increasing?
Answer:
A, it's the only one with a number greater then 1
Which polynomial is prime?
Answer:
4x^(3)+2x^(2)+6x+3
Step-by-step explanation:
A polynomial is a combination of terms separated by + or − signs. A polynomial does not contain variables raised to negative or fractional exponents, variables in the denominator or under a radical, or any special features such as trigonometric functions, or logarithms. Polynomial
help please coordinates for math
Answer: Slope = c / a + b
Concept:
Here, we need to know the idea of a slope.
In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.
Slope = Rise / Run = Δy / Δx = (y₂ - y₁) / (x₂ - x₁)
Solve:
STEP ONE: Identify the points
A (0, 0)
C (a + b, c)
STEP TWO: Apply the formula
Slope = (y₂ - y₁) / (x₂ - x₁)
Slope = (c - 0) / (a + b - 0)
Slope = c / a + b
Hope this helps!! :)
Please let me know if you have any questions