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Complete Question
A doctor estimates that a particular patient is losing bone density at a rate of 3% annually. The patient currently has a bone density of 1,500 kg/mg³. The doctor writes an exponential function to represent the situation. Which values should the doctor use for a and b in a function written in the form f(x) = ab^x, where f(x) represents the bone density after x years?
Answer:
a = 1500
b = 0.97
f(x) = ab^x
f(x) = 1500(0.97)^x
f(x) = 1500 × 0.97^x
Step-by-step explanation:
We are to find a and b
This question has to do with exponential decay.
This is written as
y = a(1 - r)^x
f(x) = ab^x
r = rate of exponential decay
f(x) = y
a = a
b^x = (1 - r)^x
a = current bone density of the patient = 1500kg/m³
b = (1 - r)
r = 3% = 0.03
b = (1 - 0.03)
b = 0.97
Therefore,
a = 1500
b = 0.97
Hence:
f(x) = ab^x
f(x) = 1500(0.97)^x
f(x) = 1500 × 0.97^x
Parker owns a food truck that sells tacos and burritos. He sells each taco for $3.25 and each burrito for $7. Yesterday Parker made a total of $552 in revenue from all burrito and taco sales and there were twice as many burritos sold as there were tacos sold. Write a system of equations that could be used to determine the number of tacos sold and the number of burritos sold. Define the variables that you use to write the system.
Answer:
let t= the number of tacos sold
let b= the number of burritos sold
3.25t+7b=552
b=2t
Step-by-step explanation:
Since there were twice as many burrito sold as tacos sold, there were more burritos sold, so if we multiply by 2 the number of tacos sold, we will get the number of burritos sold, meaning b=2t.
The system of equation should be considered as the 3.25t+7b=552 and the value of b should be equivalent to 2t.
Calculation of the equation:here we assume that
t= the number of tacos sold
And, b= the number of burritos sold
As per the situation, the equation be like
3.25t+7b=552
b=2t
So,
put b value in the first equation
3.25t + 14t = 552
t = 3.01
And, b = 1.51
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Each piece of paper is 910 inch long. Each ballot needs to be 310 inch long. How many ballots can be cut from one piece of paper?
Answer:
about 3 pages can be cut.
Step-by-step explanation:
910/310=2.9
Answer:
3
Step-by-step explanation:
Use this if your teacher asks you how.
By dividing 910/310 you get 2.9. notice that on the calculator it shows 2.9 then infinity but dont mind that. as said to get 3 you round 2.9 to the nearest whole number. which is 3 :)
When you can.. please answer these! THANK YOU SO MUCH WAHHH
Match the corresponding rational expressions with the letter of the correct answer.
Answer:
1-C
2-F
3-A
4-D
5-B
6-E
Step-by-step explanation:
a) The y-intercept of the line with the largest slope
is _____
b) For the two lines with a negative slope, the difference
in the value of their x-intercepts is _____
c) For the line with the y-intercept -3, its equation in
slope-intercept form is ____
d) For the line with a slope of 2, the input of _____
gives an output of 17
Answer:
a) the largest y-intercept is 1
b) 13.5
c) y=x-3
d) 8
Step-by-step explanation:
the question was worded very strangely and I will answer the way I precieved it.
for question d, I simply considered the question to be asking what is X when y is 17 and since the equation of that line is 2x-1
What is 3.258 x 105 written in standard form?
3.258 x 105=342.09
Brainliest plz!
A. Car B was 20 miles east of car A
B. Car A was 10 miles east of car B
C. Car B was 10 miles east of car A
D. Car A was 30 miles east of car B
Answer:
D
Step-by-step explanation:
Its D because If one was going 60 and then the second one went 150 on the same road. They both had to start off low and the lowest number closer to those to are 30.
PLEASE HELP MEE!!! Which ordered pair is a solution to the linear system? –4x – 5y = 12 and 6x + 5y = 2
A)
(7,7)
B)
(7,–8)
C)
(–8,–6)
D)
(–8,–7)
Answer:
The answer is negative 8 and negative 7
Carmen drew this figure to represent the dividend of a division expression.
A number line going from negative 4 to positive 12. An arrow goes from 0 to 9.
What number is represented by the arrow?
–9
0
1
9
Answer
D:9
Step-by-step explanation:
i took the test and got it right
Answer:
D- 9
Step-by-step explanation:
good luck :)
x² + 4x + 3 = 0
Can someone please help me solve this quadratic equation
Answer:
Step-by-step explanation:
x= -1 and -3
What when multiplied is +3 but when added is 4? 3 and 1. You then get (x+3)(x+1) is the first part of the answer. If you want to find x, set x+3 to 0. x+3=0. Then subtract 3 from both sides to get x by itself. x= -3. Do the same with the x+1.
A new car is purchased for 24600 dollars. The value of the car depreciates at 5.5% per year. To the nearest year, how long will it be until the value of the car is 11300 dollars?
Answer:
The number of years until the value of the car is 11300 dollars is 9 years.
Step-by-step explanation:
This can be calculated using the following formula:
Value of the Car = Purchase cost - (Annual depreciation expenses * N) ........ (1)
Where;
N = Number of years until the value of the car is 11300 dollars
Purchase cost = $24,600
Annual depreciation rate = 5.5%
Annual depreciation expenses = $24,600 * 5.5% = $1,353
Value of the car = $11,300
Substituting the value into equation (1) and solve for N, we have:
$11,300 = $24,000 - ($1,353 * N)
$1,353 * N = $24,000 - $11,300
$1,353 * N = $12,700
N = $12,700 / $1,353
N = 9.38654841093865
Rounding to the nearest year as required by the question, we have:
N = 9
Therefore, the number of years until the value of the car is 11300 dollars is 9 years.
Answer:
14
Step-by-step explanation:
Which triangles must be congruent?
Answer:
It stands for "side-side-side". If two triangle both have all of their sides equal (that is, if one triangle has side lengths a, b, c, then so does the other triangle), then they must be congruent.
Which equation represents the perpendicular
bisector of AB whose endpoints are A(8,2) and
B(0,6)?
Answer:
y = ½x + 2
Step-by-step explanation:
We are given the coordinates of the endpoint as;A(8,2) and
B(0,6)
The midpoint coordinates will be;
((8 + 0)/2, (2 + 6)/2) = (4, 4)
The slope of the midpoint using gradient formula will be;
m = (6 - 2)/(0 - 8)
m = 4/-8
m = -2
Thus, slope of a line perpendicular to the midpoint is;
m_p = -1/m
m_p = -1/-2
m_p = 1/2
Thus, using slope intercept concept, the equation to represent the perpendicular bisector is;
y - 4 = ½(x - 4)
Multiply both sides by 2 to get;
2y - 8 = x - 4
Add 8 to both sides to get;
2y - 8 + 8 = x - 4 + 8
2y = x + 4
Divide through by 2 to get;
y = ½(x + 4)
y = ½x + 2
Last night, the temperature fell from 0°F to -13 1/5 in 4 2/5 hours. What was the average temperature change per hour? Solve the division problem.
-13 1/5 ÷ 4 2/5
Answer:
-16
Step-by-step explanation:
Answer:d
Step-by-step explanation:
What are the differences between a recursive
and explicit rule?
Answer:
the recursive formula gives the value of a certain term based on the previous term but the explicit formula gives the value of a specific term based on the position.
Step-by-step explanation:
Joseph recently noticed that this time next year he will be twice as old as Jasmine. I couldn't help noticing that when I am 66 at this time of the year the combined future ages of Joseph and Jasmine will also be 66. Also, 6 years from now my future age will be a multiple of the sum of Joseph and Jasmine's future ages. Of course, all ages are non-negative integers. How old. are Joseph Jasmine, and I now?
John and gary are playing a game. john spins a spinner numbered with integers from 1 to 20. gary then writes a list of all of the positive factors of the number spun except for the number itself. gary then creates a new spinner with all of the numbers on his list. john then spins this spinner, and the process continues. the game is over when the spinner has no numbers on it. if john spins a 20 on his first spin, what is the maximum number of total spins (including the one he already made) that john can make before the game is over?
Answer:
4
Step-by-step explanation:
So let's say he gets a result of 20 from the first spin. This means that the factors of 20 would be:
1, 2, 4, 5 and 10. Since 20 is not taken into account when building the next spinner.
now, the possibilities for each of the given factors are:
1: 1
2: 1, 2
4: 1, 2, 4
5: 1, 5
10: 1, 2, 5, 10
So let's take the one with the biggest amount of possible factors, in this case it would be the 10. So let's say that on the second spin, he gets a 10.
So our possible factors for 10 would be:
1, 2, 5 since we don't take 10 itself into account.
So let's see the possible factors for 1, 2 and 5
1: 1
2: 1, 2
5: 1, 5
For the third spin, you could either get a 2 or a 5, it doesn't matter which result you get since for theh last spinner, it would only have a result of 1.
so for the fourth spin, you would get a 1 as an answer and the game ends there with a total of four spins.
Answer:
4
Step-by-step explanation:
If John spins a 20, then Gary's list contains the numbers 1, 2, 4, 5, 10. Thus, these are the numbers on the second spinner.
If John spins a 1, then Gary's list will be empty because there are no positive factors of 1 besides itself. Thus, the game will be over. This yields a maximum of 1 additional spin.
If John spins a 2, then Gary's list will only contain the number 1. Then on John's next spin, we will have the same scenario as above. This yields a maximum of 2 additional spins.
If John spins a 4, then Gary's list will contain the numbers 1 and 2. As we have already found above, spinning a 2 yields more additional spins than a 1, so the maximum additional spins in this case is 3 spins.
If John spins a 5, then Gary's list will only contain the number 1. As above, this will yield a maximum of 2 additional spins.
Finally, if John spins a 10, then Gary's list will contain the numbers 1, 2, and 5. Of these numbers, 2 and 5 have the highest maximum number of additional spins, so this case has a maximum of 3 additional spins.
Thus, of all of the possibilities, spinning a 4 or 10 next could result in 3 additional spins, so the maximum total number of spins is [tex]$\boxed{4}$[/tex]. These would be achieved by spinning 20, 10, 2, 1 or 20, 10, 5, 1 or 20, 4, 2, 1.
Someone help me with this please!!
Answer:
1
Step-by-step explanation:
Three years ago , Ahmed was one third of his sister's age. In a years time ,Ahmed's age doubled will match his sisters age. How old is Ahmed now.
Help the due is tomorrow
The x-intercept shows that you can buy short-sleeve shirts and long-sleeve shirts. The y-intercept shows that you can buy long-sleeve shirts and short-sleeve shirts.
Question:
You are ordering short-sleeve shirts (x) for $10 and long-sleeve shirts (y) for $15. Your budget is $300. Write the equation and find the intercepts.
Interpret their meaning.
Answer:
The x-intercept shows that you can buy 30 short-sleeve shirts and 0 long-sleeve shirts.
The y-intercept shows that you can buy 20 long-sleeve shirts and 0 short-sleeve shirts.
Step-by-step explanation:
Given
$10 per short sleeve
$15 per long sleeve
Budget = $300
The above can be represented as:
Total Cost of Short Sleeve + Total Cost of Long Sleeve = Budget
i.e.
[tex]10 * x + 15 * y =300[/tex]
[tex]10x + 15y =300[/tex]
To solve for the y intercept, we set x to 0
[tex]10 * 0 + 15y =300[/tex]
[tex]15y =300[/tex]
Divide through by 15
[tex]y = 20[/tex]
This implies that, you can buy 0 short sleeves and 20 long sleeves
To solve for the x intercept, we set y to 0
[tex]10x + 15 * 0 = 300[/tex]
[tex]10x = 300[/tex]
Divide through by 10
[tex]x = 30[/tex]
This implies that, you can buy 0 long sleeves and 30 short sleeves
Pls Help!!! Worth 99 Pts!!
Explain how to sketch a graph of the function f(x) = x3 + 2x2 – 8x. Be sure to include end-behavior, zeroes, and intervals where the function is positive and negative.
Answer:
First, for end behavior, the highest power of x is x^3 and it is positive. So towards infinity, the graph will be positive, and towards negative infinity the graph will be negative (because this is a cubic graph)
To find the zeros, you set the equation equal to 0 and solve for x
x^3+2x^2-8x=0
x(x^2+2x-8)=0
x(x+4)(x-2)=0
x=0 x=-4 x=2
So the zeros are at 0, -4, and 2. Therefore, you can plot the points (0,0), (-4,0) and (2,0)
And we can plug values into the original that are between each of the zeros to see which intervals are positive or negative.
Plugging in a -5 gets us -35
-1 gets us 9
1 gets us -5
3 gets us 21
So now you know end behavior, zeroes, and signs of intervals
Hope this helps
Answer:
The degree of the function is odd and the leading coefficient is positive – so the function goes to negative infinity as x goes to negative infinity and to positive infinity as x goes to positive infinity. The zeroes are –4, 0, and 2, all with multiplicity 1. The function is negative from negative infinity to –4 and from 0 to 2. The function is positive from –4 to 0 and from 2 to infinity.
Step-by-step explanation:
sample response on edge 2022
parts of complex numbers
z = 4- 2i
Step-by-step explanation:
This is the trigonometric form of a complex number where
|
z
|
is the modulus and
θ
is the angle created on the complex plane.
z
=
a
+
b
i
=
|
z
|
(
cos
(
θ
)
+
i
sin
(
θ
)
)
The modulus of a complex number is the distance from the origin on the complex plane.
|
z
|
=
√
a
2
+
b
2
where
z
=
a
+
b
i
Substitute the actual values of
a
=
4
and
b
=
−
2
.
|
z
|
=
√
(
−
2
)
2
+
4
2
Find
|
z
|
.
|
z
|
=
2
√
5
The angle of the point on the complex plane is the inverse tangent of the complex portion over the real portion.
θ
=
arctan
(
−
2
4
)
Since inverse tangent of
−
2
4
produces an angle in the fourth quadrant, the value of the angle is
−
0.4636476
.
θ
=
−
0.4636476
Substitute the values of
θ
=
−
0.4636476
and
|
z
|
=
2
√
5
.
2
√
5
(
cos
(
−
0.4636476
)
+
i
sin
(
−
0.4636476
)
)
Replace the right side of the equation with the trigonometric form.
z
=
2
√
5
(
cos
(
−
0.4636476
)
+
i
sin
(
−
0.4636476
)
)
19-5/2x = 34 Solve for X
Answer: -6
Step-by-step explanation:
The solution is: solve of the equation 19-5/2x = 34 is: x = -6.
Here, we have,
given that,
the equation is: 19-5/2x = 34
now, we have to solve this.
so, we have,
19-5/2x = 34
isolating the like terms, we get,
5/2 x = 19- 34
or, 5/2 x = - 15
dividing both side by 5 we get,,
x/2 = -3
cross-multiplying, we get,
x = -6
Hence, The solution is: solve of the equation 19-5/2x = 34 is: x = -6.
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Here's a screenshot of my problem does someone mind helping me
Answer:
B. Find the ratio of minutes to miles, 4:1. Multiply 7.5 by 4.
Step-by-step explanation:
Look for a pattern within the table.
10 : 2.5
16 : 4
? : 7.5
48 : 12
10/2.5 = 4
16/4 = 4
14/12 = 4
this means that if we multiply 7.5 by 4 we will be able to find the missing number!
Therefore, the answer is B.
Hope this helps! :)
please someone answer no trolls please this is very serious will give brainliest
Answer:
Required equation of line in point-slope form is:
[tex]y-5 = -\frac{3}{5}(x+5)[/tex]
Step-by-step explanation:
Given equation of line is:
[tex]y = \frac{5}{3}x+2[/tex]
The slope-intercept form of line is:
[tex]y = mx+b[/tex]
Comparing both we get
m = 5/3
We have to find the equation of a line that is perpendicular to given line and passes though (-5,5)
The product of slopes of two perpendicular lines is -1
Let m1 be the slope of line perpendicular to given line then
[tex]m.m_1 = -1\\\frac{5}{3} . m_1 = -1\\m_1 =-\frac{3}{5}[/tex]
Point-slope form is given by:
[tex]y-y_1 =m_1(x-x_1)\\[/tex]
Putting m = -3/5 and (x1,y1) = (-5,5)
[tex]y-5 =-\frac{3}{5}(x-(-5))\\y-5 = -\frac{3}{5}(x+5)[/tex]
Hence,
Required equation of line in point-slope form is:
[tex]y-5 = -\frac{3}{5}(x+5)[/tex]
A kangaroo can jump at a speed of 40 miles per hour. Which representation shows the distance a kangaroo can jump at this rate?
Answer:
y=40x
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
x - 5 (x-1) = x - (2x - 3)
Answer:
x=2/3
Step-by-step explanation:
hope this helps :)
The solution to the equation is x = 2/3.
We have,
To solve the equation x - 5(x - 1) = x - (2x - 3), follow these steps:
- Distribute the -5 to the terms inside the parentheses:
x - 5x + 5 = x - 2x + 3
- Simplify the terms on both sides of the equation:
-4x + 5 = -x + 3
- Add -x from both sides of the equation:
-4x + x + 5 = -x + 3 + x
-3x + 5 = 3
-3x = 3 - 5
-3x = -2
x = 2/3
Therefore,
The solution to the equation is x = 2/3.
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PLEASE HELP
ONLY ANSWER IF YOU KNOW
I WILL REPORT IF IT HAS NOTHING TO DO WITH THE TOPIC
Answer:
One would be -3 and the other would be 0.
Step-by-step explanation:
first would be 0 because it's already an answer
second, we take -3 from the left side and subtract it from 0 from the other side which is -3
Answer:
x=3
Step-by-step explanation:
x−3=0
2) Add 3 to both sides.
x=3
The length of a rectangle is 3cm longer than its width.
If the perimeter of the rectangle is 70cm, find its length and width.
Answer:
width=8cm
lenth=11
Step-by-step explanation:
NEED ASAP . Plz help
What is the value of y? Enter your answer in the box