Using an exponential function, it is found that 4 mg of the substance would still be left after 32 days.
What is an exponential function?A decaying exponential function is modeled by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
In which:
A(0) is the initial value.r is the decay rate, as a decimal.In this problem, considering that the initial amount if of 64 mg, and we are working with half-lifes, the equation is given by:
[tex]A(t) = 64(0.5)^t[/tex]
32 days is 32/8 = 4 half-lifes, hence the amount remaining in mg is given by:
[tex]A(4) = 64(0.5)^4 = 4[/tex]
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Jasmyn and Samantha go to the mall to go shopping. Jasmyn buys a new t-shirt that is $24.99 and Samantha buys a new pair of pants that are $48.99. If sales tax is 6%, how much will they have to pay total for the t-shirt and pants including tax?
The total cost of both items is $ ____
Answer:
78.42
Step-by-step explanation:
[tex]1.06(24.99 + 48.99)[/tex]
[tex]1.06 \times 73.98 = 78.42[/tex]
Suppose that the objective function coefficient for product C increases by $8. What impact will this have on the current values of the optimal solution
When the objective function coefficient for the product increases by $8, the impact on the current values of the optimal solution is that the current solution will change.
What is an objective function?An objective function simply means the function whose value is to be either maximized or minimized over the alternatives.
In this case, when the objective function coefficient for the product increases by $8, the impact on the current values of the optimal solution is that the current solution will change. The change is due to the varied objectives.
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Find the measure of the missing angle
Answer:
g=118 degrees h=62 degrees
Step-by-step explanation:
So we can use some angle rules that I forget the name of to solve this.
Let's look at angle g first. We know that the opposite angle is 118 degrees. So that also means that g is going to be 118 degrees.
Since g is 118 degrees we can find h. The angle of a line is 180 degrees. This means that we can do 180-118 to find h. h=62 degrees.
We can do the same thing for k and m. Try doing what I did for g and h for those two. Comment if you need help.
Write down a number which is •a multiple of 4. •a factor of 400. •not 4 or 400
Answer:
200
Step-by-step explanation:
4 multiplied by 50 = 200
400 divided by 200 = 2
so it is both a factor of 400, a multiple of 4, and it's neither 4 nor 400 :)
In a regular polygon the line from the center to the mid-point of an outer side is a(n)
Answer:
The apothem (sometimes abbreviated as apo) of a regular polygon is a line segment from the center to the midpoint of one of its sides. Equivalently, it is the line drawn from the center of the polygon that is perpendicular to one of its sides.
Step-by-step explanation:
Apothem In a regular polygon the line from the center to the mid-point of an outer side is a(n).
What is a cube?It is a polygon having six faces.
The volume of a cube is a side cube.
We have,
The apothem of a regular polygon is a line segment from the center to the midpoint of any one of its sides.
Thus,
The line from the center to the mid-point of an outer side is a(n) is Apothem.
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17. Kayden creates a linear function where x is the input, y, is the output, and
m and b are constants.
A. Which equation could represent Kayden's function?
y=1/x+ mb
y = mx + b
© x = my • by
.
B.
Which statement about the graph of Kayden's function is true for all
values of m and b?
~ The graph is increasing.
® The graph is decreasing.
© The graph goes through the origin.
The graph has a constant rate of change.
Answer:
see explanation
Step-by-step explanation:
A linear function has the form
y = mx + b ( m is the slope and b the y- intercept )
B
the graph has a constant rate of change , measured by the slope m of the linear function.
Suppose that 16 inches of wire costs 48 cents at the same rate ,how many inches of wire can be bought for 39 cents?
Find the values of x and y
x=
and
y=
Answer:
x=145 and y=35
Step-by-step explanation:
the hole line equals 180 so do 35-180 which equals 145 and y would equal 35
Geena can rent an apartment for $850 per month or she can buy a house for $175,000 at 3.875% interest for 30 years. How much will each housing choice cost for one year?
A. Price of Renting:
B. Price of Buying:
Using simple interest, it is found that the prices are as follows:
A. $10,200.
B. $12,614.58.
Simple InterestSimple interest is used when there is a single compounding per time period.
The amount of money after t years in is modeled by:
[tex]A(t) = A(0)(1 + rt)[/tex]
In which:
A(0) is the initial amount.r is the interest rate, as a decimal.Item a:
$850 for 12 months, hence the yearly cost is:
P = 850 x 12 = $10,200.
Item b:
The total cost is found using simple interest with A(0) = 175000, t = 30, r = 0.03875, hence:
A(t) = A(0)(1 + rt)
A(30) = 175000[1 + 0.03875(30)]
A(30) = 378437.5.
The yearly cost is given by:
378437.5/30 = $12,614.58.
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Solve for x -3/4x + 8=23
One number is two times greater than another number. if the greater number is x what is the other number?
Answer:
[tex]\frac{1}{2}x[/tex]
Step-by-step explanation:
If the greater number is x and it is two times greater than the other number then the other number is half as big. This is true because 2*[tex]\frac{1}{2}[/tex]x = x
The other number is equal to x/2.
What is a Fraction?A fraction in mathematics represents a portion or element of the whole. It represents the appropriate parts of the totality. A fraction is made up of two parts: the numerator and the denominator.
As per the given data:
We are given the relationship between 2 numbers, It's given that One number is two times greater than another number.
The greater number = x
Let's assume that the smaller number is y.
From the given data in the question:
One number is two times greater than another number
= x = 2y ...(i)
The other number that is the smaller number is given by:
By dividing eq (i) by 2 from both sides.
y = x/2
The other number is equal to x/2
Hence, The other number is equal to x/2
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m(m − n)
for m = 3 and n = 1
The three sides of a triangle of lengths 4, 5, and 7. The triangle is obtuce
Answer:
Let's check this!
Obtuse triangle formula:
c² < b² + a²
Next fill in the formula:
7² < 5² + 4²
Then simplify:
49 < 25 + 16
Then add:
49 < 41
^^49 is not greater than 41 so therefore the triangle is not obtuse.
When the hypotenuse is bigger than the legs of the triangle it is an acute triangle.
Acute triangle formula:
c² > b² + a²
7² > 5² + 4²
49 > 25 + 16
49 > 41 ✔
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The three sides of a triangle of lengths 4, 5, and 7 are not obtuse triangles.
What is the obtuse triangle?The triangle is an obtuse triangle if the sum of the squares of the smaller sides is less than the square of the largest side.
The three sides of a triangle of lengths 4, 5, and 7.
An obtuse triangle is a triangle in which one of the interior angles is greater than 90°.
The sides of a triangle are not an obtuse triangle as determined in the fooling step given below.
Obtuse triangle formula:
c² < b² + a²
7² < 5² + 4²
49 < 25 + 16
49 < 41
Here; 49 is not greater than 41 so therefore the triangle is not obtuse.
Hence, the three sides of a triangle of lengths 4, 5, and 7 are not obtuse triangles.
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If you read 84 pages in 156. At this rate how long will it take you to read 21 pages?
Answer:
39
Step-by-step explanation:
you can set a proportion
84/156 = 21/x
when u solve for x u get 39
In the parallelogram shown, find the measure of ∠A.
Answer: 40 degrees
Step-by-step explanation:
Study the figure to answer the question.
Triangle A B C. The coordinates of the vertices of triangle A B C are A (0, 4), B (4, 0), and C (0, 0).
Which best describes the three-dimensional figure obtained from rotating the figure around the y-axis?
a triangular prism with a base length of 4 units
a cone with a radius of 2 units
a cylinder with a radius of 4 units
a cone with a radius of 4 units
Answer:
a cone with a radius of 4 units
Step-by-step explanation:
when rotating something, this involves a circle. so, the result will always be round and never edgy. therefrom the first option is wrong.
and we are rotating a triangle. the result will have a wide base and a pointed tip. so, the third option is wrong.
the rotation does not make the basic shape smaller. so, the second option is wrong.
yes, the fourth option is correct.
please help??????????????????????????????? so confused
8s-11s+6s
Answer: = 3 seconds
Step-by-step explanation: combine the like terms Hope it helps !!
To simplify: 8s - 11s + 6s. Simplify the like terms by combining them
Simplifying 8s - 11s + 6s will give 3s.
Given,
8s - 11s + 6s
Now,
Expression : 8s-11s+6s
To simplify the expression combine like terms. So, all the terms consists of variable s.
Combine all terms having same sign,
So,
Firstly apply addition
8s + 6s
= 14s
Now,
Apply subtraction,
14s - 11s
= 3s
Therefore the simplified version is 3s.
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divide, need help again ppl, thanks!
Answers:
5.) [tex]\displaystyle \pm{1\frac{2}{3}}[/tex]
4.) [tex]\displaystyle 2[/tex]
3.) [tex]\displaystyle \pm{1\frac{2}{3}}[/tex]
2.) [tex]\displaystyle 2[/tex]
1.) [tex]\displaystyle \pm{2}[/tex]
Step-by-step explanations:
5.) [tex]\displaystyle \frac{\sqrt{75}}{\sqrt{27}} \hookrightarrow \sqrt{2\frac{7}{9}} \hookrightarrow \frac{\pm{5\sqrt{3}}}{\pm{3\sqrt{3}}} \\ \\ \boxed{\pm{1\frac{2}{3}}}[/tex]
4.) [tex]\displaystyle \frac{\sqrt[5]{96}}{\sqrt[5]{3}} \hookrightarrow \sqrt[5]{32} \hookrightarrow \frac{2\sqrt[5]{3}}{\sqrt[5]{3}} \\ \\ \boxed{2}[/tex]
3.) [tex]\displaystyle \frac{\sqrt{125}}{\sqrt{45}} \hookrightarrow \sqrt{2\frac{7}{9}} \hookrightarrow \frac{\pm{5\sqrt{5}}}{\pm{3\sqrt{5}}} \\ \\ \boxed{\pm{1\frac{2}{3}}}[/tex]
2.) [tex]\displaystyle \frac{\sqrt[3]{24}}{\sqrt[3]{3}} \hookrightarrow \sqrt[3]{8} \hookrightarrow \frac{2\sqrt[3]{3}}{\sqrt[3]{3}} \\ \\ \boxed{2}[/tex]
1.) [tex]\displaystyle \frac{\sqrt{8}}{\sqrt{2}} \hookrightarrow \sqrt{4} \hookrightarrow \frac{\pm{2\sqrt{2}}}{\pm{\sqrt{2}}} \\ \\ \boxed{\pm{2}}[/tex]
I am joyous to assist you at any time.
Name the postulate that proves these two triangles congruent.
Answer:
the postulate that proves these two triangles congruent is AAA or angle angle angle.
Please Help! Will Give Brainlest!
Answer:
y = 0
Step-by-step explanation:
Midline = the horizontal center line
HELP WILL MARK BRAINLIST AND 5 STARS
Answer:
10 ft
Step-by-step explanation:
5 1/6 + 4 5/6 = 10
5 + 4 = 9
1/6 + 5/6 = 6/6 = 1
9 + 1 = 10
Answer:
10 feet
Step-by-step explanation:
We are trying to find Madison's height plus Jade's height...
Turn the fractions into improper fractions
So,
5 1/6 = 31/6
4 5/6 = 29/6
31/6 + 29/6 = 10 feet
or
5+4= 10 and 1/6+5/6 = 1
so the answer is 10 feet
PLEASE RATE!! I hope this helps!!!
If you have any questions comment below
Lol pla helllllllllp
Answer:
66x
Step-by-step explanation:
Rect = bh
Rect = 15 x 4x
Rect = 60x
Triangle = (bh) / 2
B = 7x - 4x
B = 3x
A = 15 - 11
A = 4
Tri = (4 x 3x) / 2
Tri = 12x / 2
Tri = 6x
All = Rect + Tri
All = 6x + 60x
All = 66x
(I promise it's right this time)
Answer:
66x
Step-by-step explanation:
Separate the shape into a rectangle and a triangle.
Dimension of the rectangle:
length = 15width = 4xDimension of the triangle:
base = (15 - 11) = 4height = (7x - 4x) = 3xArea of a rectangle = length × width
Area of a triangle = 1/2 × base × width
Total area = area of rectangle + area of triangle
= (15 × 4x) + (1/2 × 4 × 3x)
= 60x + 6x
= 66x
2x+2y=6 3x-y=5 equivalent equation
Answer:
x = 2, y = 1
Step-by-step explanation:
Given:
[tex]\begin{bmatrix}2x+2y=6\\ 3x-y=5\end{bmatrix}[/tex]
Solve:
[tex]\mathrm{Isolate\;x\;for\;2x+2y=6:x=3-y}[/tex]
[tex]\mathrm{Substitute\:}[/tex]
[tex]\begin{bmatrix}3\left(3-y\right)-y=5\end{bmatrix}[/tex]
[tex]\mathrm{Simplfy}[/tex]
[tex]\begin{bmatrix}9-4y=5\end{bmatrix}[/tex]
[tex]\mathrm{Isolate\;y\;for\;9-4y=5:y=1}[/tex]
[tex]\mathrm{For\:}x=3-y\;\mathrm{Substitute\:}y=1[/tex]
[tex]x=3-1[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]x=2[/tex]
[tex]\mathrm{The\:Answers\:to\:the\:system\:of\:equations\:are:}[/tex]
[tex]x=2,\:y=1[/tex]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Check Answer:
Since [tex]x =2 , y =1[/tex]
[tex]2(2)+2(1)[/tex]
[tex]4 + 2[/tex]
[tex]= 6[/tex]
True
[tex]3(2) - (1)[/tex]
[tex]6 -1[/tex]
[tex]5[/tex]
True
Hence, [tex]x = 2, y = 1[/tex]
~Lenvy~
What is the next term of the geometric sequence? 40/27, 20/9, 10/3, ??
Answer:
3/1
Step-by-step explanation:
Just number 1 please and explain
tanS = 5/12
tanR = 12/5
ur welcome norissa
WILL GIVE BRAINLIEST
pls if you can pls include step by step explanation
Answer:
A. 0.125 foot per square feet
Step-by-step explanation:
When finding average rate of change, use the formula
ΔY/ΔX
The ΔY, or Y final - Y initial would be 1.5-1.0, which is equal to 0.5.
The ΔX, or X final - X initial would be 7-3, which is equal to 4.
Plug these values into the equation ΔY/ΔX to get 0.5/4.
This will give you 0.125.
PLEASEE HELPP!!!
What is the mistake in setting up the quadratic formula?
Answer:
First, we bring the equation to the form ax²+bx+c=0, where a, b, and c are coefficients. Then, we plug these coefficients in the formula: (-b±√(b²-4ac))/(2a) . See examples of using the formula to solve a variety of equations.
That 6 should be -6
Let me solve it for you
[tex]\\ \rm\rightarrowtail 2x-x-6=0[/tex]
So
[tex]\\ \rm\rightarrowtail x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]\\ \rm\rightarrowtail x=\dfrac{-(-1)\pm\sqrt{(-1)^2-4(2)(-6)}}{2(2)}[/tex]
[tex]\\ \rm\rightarrowtail x=\dfrac{1\pm \sqrt{1+48}}{4}[/tex]
[tex]\\ \rm\rightarrowtail x=\dfrac{1\pm 7}{4}[/tex]
[tex]\\ \rm\rightarrowtail x=\dfrac{8}{4}\:or\:\dfrac{-6}{4}[/tex]
[tex]\\ \rm\rightarrowtail x=2\:or\:\dfrac{-3}{2}[/tex]
Calculate the average daily balance, finance charge, and new balance using the average daily balance method. Round all dollar amounts to the nearest cent. If applicable, include a thousands comma. Monthly rate: 1.75% Date Payments Purchases Balance Number of Days Product 9/1-9/5 $387.525 1,937.60 976 $50.00 $337.521 337.52 977 - 9/18 A В С 9/19 $62.66 $400.181 400.18 9/20-9/30 D E F Total 30 G A= $ BE C= $ D=$ E= F=$ G=$ Average daily balance : 30 = $ Finance charge = monthly rate x average daily balance = $ New balance = previous balance payment/credits + finance charge + new purchases = $
Answer:
Step-by-step explanation:
Credit should go to the previous helper here:
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I have not cross-checked but the previous answers were:
"
For average daily balance:
Form date 9/1 to date 9/5 :
Balance x number of the days = $ 387.52 x 5 days = $ 1937.6
As on date 9/6 :
($ 387.52 - $ 50.00) x 1 day = $ 337.52
From date 9/7 to date 9/18 :
Balance = $ 337.50
Number of days = 12 days
Therefore, product = 12 days x $ 337.52
= $ 4050.24
As on 9/19 :
($ 337.52 + $ 62.66) x 1 day = $ 400.18
From date 9/20 to date 9/30
Balance :$ 400.18
Number of days = 11 days
Therefore, product = 11 days x $ 400.18
= $ 4401.98
Average daily balance
= ($ 1937.6 + $ 337.50 + $ 4050.24 + $ 400.18 + $ 4401.98) / 30
= $ 370.91
Finance charge = $ 370.91 x 1.75 %
= $ 6.49
New balance = $ 370.91 + $ 6.49
= $ 377.4
"
The perimeter of a rectangular field is 322 m.
If the width of the field is 67 m, what is its length?
Answer:
75
Step-by-step explanation:
322 = 2(86) + 2w
322 = 172 + 2w
322-172 = 172 +2w -172
150 = 2w
150/2 = 2w/2
w=75
A roof rises 24 feet vertically and 14 feet horizontally. What is the slope of the roof?
Answer:
1.714 feet
Step-by-step explanation:
slope is rise over run.
rise would be the vertical measurement and run would be the horizontal measurement.
24/14 = 12/7
12/7 = 1.714