Answer: 0.045 is the growth rate.
Step-by-step explanation:
A generic exponential growth function can be written as:
f(t) = A*(1 + r)^t
where A is the initial amount.
t is the unit of time.
r is the rate of growth.
For example if we have an increase of 10% per year, with an initial population of 100 we have that:
A = 100, r = 10%/100% = 0.10, t = number of years.
the equation will be:
f(t) = 100*(1 + 0.10)^t
Now, in this case the equation is:
S(t) = 152*(1.045)^t
We can write this as:
S(t) = 152*(1 + 0.045)^t
Then 152 is the initial amount and 0.045 is the growth rate.
Susan and Mark are given the same amount of money. Mark spends $5 and susan spends $20. If Mark now has twice as much money as Susan , how many dollars did they each have originally ?
so amnt of money is x
x - 5 is Mark's remaining amnt
x - 20 is Susan's remaining amount
x - 5 = 2( x - 20) as he has twice the amnt of Susan
x - 5 = 2x - 40
40 - 5 = 2x - x
35 = x
the original amnt is $35
What is the horizontal distance from the end of the ramp to the back of the truck?
Answer:
134.4 centimetersStep-by-step explanation:
Given,
Hypotenuse ( h ) = 158 cm
Perpendicular ( p ) = 83
Base ( b ) = ?
Now, Using Pythagoras theorem:
[tex] {h}^{2} = {p}^{2} + {b}^{2} [/tex]
[tex] {b}^{2} = {h}^{2} - {p}^{2} [/tex]
Plug the values
[tex] {b}^{2} = {158}^{2} - {83}^{2} [/tex]
Evaluate the power
[tex] {b}^{2} = 24964 - 6889[/tex]
Calculate the difference
[tex] {b}^{2} = 18075[/tex]
[tex]b = \sqrt{18075} [/tex]
Calculate
[tex]b = 134.4 \: cm[/tex]
Hope this helps..
Best regards!!
Solve x2 – 3x = –8 using the quadratic formula.
Here is the step by step answer. hope it helps!
The solution to the quadratic equation x² - 3x + 8 = 0 is given by
x = ( 3/2 ) ± i ( √23/2 )
What is Quadratic Equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
where ( b² - 4ac ) is the discriminant
when ( b² - 4ac ) is positive, we get two real solutions
when discriminant is zero we get just one real solution (both answers are the same)
when discriminant is negative we get a pair of complex solutions
Given data ,
Let the quadratic equation be represented as A
Now , the value of A is
x² - 3x = -8
Adding 8 on both sides of the equation , we get
x² - 3x + 8 = 0 be equation (1)
Now , on simplifying the equation , we get
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
Substituting the values in the equation , we get
x = [ - ( -3 ) ± √ ( -3 )² - ( 4 ) ( 1 ) ( 8 ) ] / 2
On simplifying the equation , we get
x = [ 3 ± √ ( 9 - 32 ) ] / 2
x = ( 3/2 ) ± √ ( -23 ) / 2
x = ( 3/2 ) ± i ( √23/2 )
where i² = -1
Therefore , the value of x is x = ( 3/2 ) + i ( √23/2 ) , x = ( 3/2 ) - i ( √23/2 )
Hence , the solution to the equation is x = ( 3/2 ) ± i ( √23/2 )
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The price of a boat that Arthur wants is $29,450. Arthur finances this by paying $6000 down and monthly payment of $792.22 for 36 months.
a. Determine the amount to be financed.15a. _______________
b. Determine the installment price.b. _________________
c. Determine the finance charge.c. _________________
Answer:
see details below
Step-by-step explanation:
The price of a boat that Arthur wants is $29,450. Arthur finances this by paying $6000 down and monthly payment of $792.22 for 36 months.
a. Determine the amount to be financed.15a. ___$23450____________
29450 - 6000 = 23450
b. Determine the installment price.b. ___$792,22______________
"monthly payment of $792.22"
c. Determine the finance charge.c. __$5069.92_______________
A = 792.22
n = 36
finance charge = total paid - amount to be financed
= 36*792.22 - 23450
= 5069.92
PLEASE HELP ASAP!!!!Write the ratio as a fraction in lowest terms. 9 pounds to 36 pounds.(50 points!!)
Answer:
1/4
Step-by-step explanation:
9 lbs
---------
36 lbs
We can write this because the units are the same
Divide the top and bottom by 9
9/9
----------
36 /9
1/4
Answer:
1/4
Step-by-step explanation:
9 pounds
36 pounds
Ratios are written as x:y, fractions are written as x/y.
9:36 as a fraction will be 9/36
Simplify the fraction.
1/4
One leg in a right triangle is 11 m, and the hypotenuse measures 11√2 m. Find the length of the other leg.
Answer:
[tex]\boxed{11m}[/tex]
Step-by-step explanation:
Method #1: 45-45-90 Triangle
You can use the rules for a 45-45-90 triangle. These are:
→ Each 45-45-90 triangle is a right triangle with two additional 45° angles.
→ The triangle will have 2 legs, x, and one hypotenuse, x√2.
Therefore, because the problem gives values for one leg and the hypotenuse, the value for the one leg is equal to the value for the unsolved leg.
Method #2: Pythagorean Theorem
You can use the Pythagorean Theorem to solve for a missing side in a triangle. Please note, however, that the Pythagorean Theorem only works on right triangles.
The Pythagorean Theorem is defined as [tex]a^{2} + b^{2} = c^{2},[/tex] where a and b are both legs of the triangle and c is the hypotenuse.
Therefore, substitute the known value for a, 11, and the known value for c, 11√2. Then, evaluate each value to its power (except for b - it is unsolved) and simplify the equation with basic algebraic methods. Once your equation is down to [tex]b^{2}= ?[/tex], you should take the square root of both sides of the equation to get the value for b.
[tex]11^{2} +b^{2} =(11\sqrt{2} )^{2}\\121 + b^{2} = 242\\b^{2}=121\\b=11[/tex]
Please help me!! Need help with geometry! Thank you so much!!
Answer:
b
Step-by-step explanation:
A, b, c, and d are all points. the line segements are: ab, bc, cd, da, and ac
The half-life of radioactive iodine is 60 days. How much of a 50-mg sample will be left in 40 days? Round your answer to the nearest tenth.
Answer:
Remaining amount of the element = 31.5 mg
Step-by-step explanation:
Half life of radioactive Iodine is [tex](T_{\frac{1}{2}})[/tex] = 60 days
Formula to get the remaining element after t days is,
[tex]N=N_0(e)^{\lambda.t}[/tex]
Where [tex]\lambda[/tex] = decay constant of the radioactive element
t = duration of the decay (in days)
[tex]N_0[/tex] = Initial amount of the element
N = final amount after decay
For half life period 't' = 60 days
[tex]\frac{N_0}{2}=N_0(e)^{\lambda\times 60}[/tex]
[tex]e^{60\lambda}=0.5[/tex]
[tex]ln(e^{60\lambda})=ln(0.5)[/tex]
[tex]60\lambda =-0.069315[/tex]
[tex]\lambda=-0.0115524[/tex]
Remaining amount of the element after 40 hours,
N = [tex]50(e^{40\lambda} )[/tex]
= [tex]50(e)^{-(0.0115524)\times 40}[/tex]
= 50(0.62996)
= 31.49
≈ 31.5 mg
Therefore, remaining amount of the element after 40 days is 31.5 mg.
Answer:
In 40 days, there would be approximately 31.5 mg remaining.
Step-by-step explanation:
Please help me with this
I would really appreciate it
thank you
Answer:
1) x=58, y=109
2) x=72, y=36
3) x=60, y=48
Step-by-step explanation:
1) 58 and x are so-called "F-angles" (a.k.a "corresponding angles), so x=58°
The angle on the other side of the 58 is 180-58 = 122 because they are supplementary. We need this one to calculate y.
The sum of angles in a quadrilateral is 360°, so 71 + 58 + 122 + y = 360, so y = 109
2) There are two isosceles triangles. Due to the symmetry, the bottom left angle is also 72, leaving 180-72-72 = 36 for y. The top triangle is the same triangle rotated, so x = 72.
3) Due to the parallel lines, the left angle of the top triangle is also 72, making the supplementary angle below it 180-72=108. The sum in the quadrilateral must be 360, so 72+108+2x+x=360, so 3x=180, x=60.
The sum in the outer triangle must be 180, so 72+y+x = 180, leaving y = 180-72-60 = 48
Look at this triangle work out length AB
Answer:
2√137
Step-by-step explanation:
To find AB, we can use the Pythagorean Theorem (a² + b² = c²). In this case, a = 22, b = 8 and we're solving for c, therefore:
22² + 8² = c²
484 + 64 = c²
548 = c²
c = ± √548 = ± 2√137
c = -2√137 is an extraneous solution because the length of a side of a triangle cannot be negative, therefore, the answer is 2√137.
During a quality assurance check, the actual contents (in grams) of six containers of protein powder were recorded as 1530, 1532, 1495, 1508, 1528, and 1511. (a) Find the mean and the median of the contents. (b) The third value was incorrectly measured and is actually 1515. Find the mean and the median of the contents again. (c) Which measure of central tendency, the mean or the median, was affected more by the data entry error?
Answer:
Step-by-step explanation:
Given the values of the actual content of protein powder recorded as shown:
1530, 1532, 1495, 1508, 1528, and 1511
a) We are to find the mean and median of the contents.
Mean is the average sum of the numbers. It is expressed mathematically as xbar = ΣXi/N
Xi are individual values
N is the total number of values present.
N = 6
xbar = (1,530+1,532+1,495 +1,508+1,528+1,511)/6
xbar = 9104/6
xbar = 1517.33
Median of the data is the value at the middle after rearrangement. On rearranging from lowest to highest:
1,495, 1508, 1511, 1528, 1530, 1532
The two values at the centre are 1511 and 1528.
Median = 1511+1528/2
Median = 1519.5
b) If the third value was incorrectly measured and is actually 1515, then our new data will become.
1530, 1532, 1515, 1508, 1528, and 1511
xbar = (1,530+1,532+1,515 +1,508+1,528+1,511)/6
xbar = 9124/6
xbar = 1520.67
For median:
We arrange first
1508, 1511, 1515, 1528, 1530, 1532
The two values at the centre are 1515 and 1528.
Median = 1515+1528/2
Median = 1521.5
c) To know the measure of central tendency that was most affected, we will look at the difference in the values gotten for both mean and median.
∆Mean = 1520.67-1517.33
∆Mean = 3.34
∆Median = 1521.5 - 1519.5
∆Median = 2.0
It can be seen that the measure of central tendency with greater deviation is the mean. Therefore, the mean is more affected by the data entry error.
Find the area of this shape
Answer:
12.5
Step-by-step explanation:
(7.5+2.5)x2.5/2
Answer:
12.5 units ^2
Step-by-step explanation:
This figure is a trapezoid
The area of a trapezoid is given by
A = 1/2 (b1+b2) *h
where b1 and b2 are the lengths of the bases and h is the height
A = 1/2 ( 2.5+ 7.5) *2.5
= 1/2 ( 10) * 2.5
=12.5 units ^2
Lines m and n are parallel. Which of the other 5 named angles have a measure of 110°?
Press the hotspot for all that apply.
Answer:
2 and angle that is left of 5
Step-by-step explanation:
Angle 2 is vertical from 110, and vertical angles are congruent. From this, we can figure out that 2 and 3 (they're supplementary) are 70. Angles 5 and 3 are Alternate Interior Angles, and therefore must be congruent. The one to the left of 5 is supplementary to it, and therefore must be 110. Your answers are angle 2 and the angle that is left of 5.
This Question: 1 pt
Solve the system of equations by the substitution method.
12x + 3y = 22
- 4x = y + 8
Soloct the correct choice helow and if necessary fill in the answer box to complete your choice
Answer:
no solution
Step-by-step explanation:
use the second equation because y is already by itself
-4 x = y + 8
y = -4x - 8
substitute:
12x + 3(-4x - 8) = 22
distribute the 3:
12x -12x - 24 = 22
0 - 24 = 22
-24 ≠ 22
A rectangular prism has a length of 9 cm, a width of 5 cm, and its volume is 180 cubic centimeters. What is the height of the prism?
Answer:
Right rectangular prism
Solve for height
h=4cm
l Length
9
cm
w Width
5
cm
V Volume
180
cm³
Answer:
Step-by-step explanation:
volume of rectangular prism=l×w×h
9×5×h=180
h=4 cm
where h is the height of prism.
WILL MARK BRAINLIST----- A particular map shows a scale of 1 cm:5 km. What would the map distance be (in cm) if the actual distance to be represented is 14 km?
Answer:
The map distance would be 2.8 cm
Step-by-step explanation:
Use the proportion given by the following relationship, where you use "x" as the unknown value in cm:
[tex]\frac{1\,\,cm}{5\,\,km} =\frac{x}{14\,\,km} \\\frac{1\,\,cm\.\,(14\,\,km)}{5\,\,km} =x\\x=2.8\,\,cm[/tex]
If two points are given, then exactly one line can be drawn through those two points. Which geometry term does the statement represent?
Answer:
its a postulate
Step-by-step explanation:
The statement represents a geometric postulate.
A postulate is one of the basic concepts of geography, and indicates an assumption that is accepted as true in the given theory.
In this way, the main characteristic of the postulate is its general acceptance by the spectrum that studies it, that is, by the totality or vast majority of the scientists who are dedicated to its analysis.
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The equation of a line is y = 1.5x_2. What are it’s slope and y- intercet
Answer: the slope is 1.5 and the y-intercept is -2.
Step-by-step explanation:
Assuming you meant 1.5x-2 and accidentally pressed shift to turn - into _.
This equation is in slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.
Thus, the slope is 1.5 and the y-intercept is -2.
Hope it helps <3
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▹ Answer
[tex]Slope = 1.5\\\\Y-intercept = -2[/tex]
▹ Step-by-Step Explanation
(I'm assuming the underscore was meant as a minus sign)
[tex]Slope \\equation \\\\ y = mx + b\\\\[/tex]
mx represents the slope and b represents the y-intercept.
Therefore:
1.5 is the slope, and -2 is the y-intercept.
Hope this helps!
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what is 1 plus 90876543579645968765443223456789009876543212345678909876543
Answer: 9.0876544e+58
Step-by-step explanation:
Answer:
90876543579645968765443223456789009876543212345678909876544
Step-by-step explanation:
90876543579645968765443223456789009876543212345678909876543
+
1
=
90876543579645968765443223456789009876543212345678909876544
A triangle is placed in a semicircle with a radius of 4 mm, as shown below. Find the area of the shaded region.
Use the value 3.14 for it, and do not round your answer. Be sure to include the correct unit in your answer.
Answer:
34.26 mm²
Step-by-step explanation:
To find the shaded region we must find the total area of the half-circle and then substract from it the area of the triangle
Step 1: Find the area of the half circleLet A be the area of the half circle
A = r²*π where r is the radius
A = 4²π = 16π mm²
Step2: Find the area of the triangleLet A' be the area of the triangle
A' = (b*h)/2 where b and h are respectively the base and the the height
A'= (8*4)/2 = 16
Step3: Find the area of the shaded regionLet A" be the area of the shaded region
A" = A-A'
A" = 16π -16 = 34.26 mm²
Which of the these angles is congruent to <5? Yes or no
Hello!
Answer:
A) Yes.
B) No.
C) Yes.
D) Yes.
Step-by-step explanation:
To find the correct solutions to this question, we can go through each choice and check for their congruency:
A) Yes. ∠8 is congruent to ∠5 because ∠5 and ∠8 are vertical angles.
B) No. ∠5 is not congruent to ∠6 because ∠5 and ∠6 are supplementary to each other.
C) Yes. ∠5 is congruent to ∠1 because corresponding angles are congruent.
D) Yes. ∠5 is congruent to ∠4 because alternate exterior angles are congruent.
A) The angle 8 should be congruent so it should be Yes.
B) The angle 6 should be congruent so it should be No.
C) The angle 1 should be congruent so it should be Yes.
D) The angle 4 should be congruent so it should be Yes.
What are congruent angles?The congruent angles are those angles in which the corresponding sides and angles should be of equal measure.
A) Yes. ∠8 is congruent to ∠5 since ∠5 and ∠8 are vertical angles.
B) No. ∠5 is not congruent to ∠6 since ∠5 and ∠6 are supplementary to each other.
C) Yes. ∠5 is congruent to ∠1 since corresponding angles are congruent.
D) Yes. ∠5 is congruent to ∠4 since alternate exterior angles are congruent.
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Is (4,2) a solution of the system?
Answer:
No.
Step-by-step explanation:
Substitute 4 (as x) and 2 (as y) into the 2 equations to see if they fit.
y = x - 2
2 = 4 - 2
2 = 2
The first equation is true for (4,2).
Now try the 2nd one.
y = 3x + 4
2 = 3(4) + 4
2 ≠ 16
So the 2nd equation is not true for (4,2).
Either one not true makes the solution incorrect.
No, (4, 2) is not the solution for system of Equation.
What is Solution to a Equation?An assignment of values to the unknown variables that establishes the equality in the equation is referred to as a solution.
To put it another way, a solution is a value or set of values (one for each unknown) that, when used to replace the unknowns, cause the equation to equal itself.
Given:
Equations:
y= x-2 ............(1)
y= 3x+ 4.................(2)
Put the value of y from equation 1 to equation (2), we get
x- 2 = 3x+ 4
x- 3x = 4+ 2
-2x = 6
x= -3
and, y= -3 -2 = -5
So, the solution to the system is (-3, -5)
and, (4, 2) can only satisfy the Equation y= x-2 but does not satisfy y= 3x+ 4.
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what is the vertex of f(x)=-3(x+2)^2+4
Answer:
vertex(-2,4)
Step-by-step explanation:
f(x)=-3(x+2)^2+4
f(x)=-3(x²+4x+4)+4
f(x)=-3x²-12x-12+4
= -3x²-12x-8
v(h,k)
h=-b/2a=-(12/-6)==2
substitute for x=-2
k=-3(2)²-12(-2)-8=-12+24-8=4
Graph f(x) = \xi.
Click on the graph until the graph of f(x) = \xi appears.
Answer:
The graph of IxI is:
y = x for values of x ≥ 0
y = -x for values of x ≤ 0
Then you will see a "V", with the arms pointing up and the vertex in the point (0, 0)
(Something like in the image, but with the arms pointing upside instead of downside)
The actual graph is:
find the zeros of the function. enter the solutions from least to greatest f(x)=(x+3)^2-4
Answer:
x= -5, -1
Step-by-step explanation:
To find the zeroes of a function,
First expand the terms to get the form [tex]ax^{2} + bx +c[/tex] where 'a, b, and c' are constants
[tex]f(x)= (x+3)^{2} -4[/tex]
[tex]f(x)= x^{2}+6x+9-4[/tex]
[tex]f(x)= x^{2} +6x +5[/tex]
Now, factor the equation
This can be done using the quadratic formula or other methods
One simple method is to find the two values that would get:
A sum that's equal to the 'b' value and,A product that's equal to the 'c' valueA good way to verify is to expand the terms and make sure the function looks the same
In this case, the equation can broken into
f(x)= (x+1)*(x+5)
Now, look at each term individually and set each of them to equal 0
x+1 =0
x+5=0
Solve for x in each case
x= -1
x= -5
Now, ordering them from least to greatest would be: x= -5, -1
Find the critical point of the given function and then determine whether it is a local maximum, local minimum, or saddle point.
Answer:
critical point of the given function f(x,y) = x²+y²+2xy is from line y = -x is the critical point of the function f(x0,y0) = 0
and it local minimum.
Step-by-step explanation:
Let the given function be;
f(x,y) = x²+y²+2xy
From above function, we can locate relative minima, maxima and the saddle point
f(x,y) = x²+y²+2xy = (x+y)²
df/dx = 2x+2y = 0 ---- (1)
df/dy =2y+2x = 0 ---- (2)
From eqn 1 and 2 above,
The arbitrary point (x0,y0) from line y = -x is the critical point of the function f(x0,y0) = 0
Then, from f(x,y) >= 0 for arbitrary (x,y) € R^n, the arbitrary point from the line x = -y is local minima of the function f.
The side length of the cube is s. Find the domain of the volume of the cube.
Answer:
-∞<x<∞
Step-by-step explanation:
volume of a cube=s^3
the domain is (-∞,∞) the domain is all the real number of s
The selling price of a car is $15,000. Each year, it loses 12% of its value.
Which function gives the value of the cart years after its purchase?
Select the correct answer below:
f(t) = 15,000(0.12)
f(t) = 15,000(1.12)
f(t) = 15,000(1.88)
f(t) = 15,000(0.88)
f(t) = 15,000 – (0.12)
Answer:
f(t) = 15,000(0.88)Step-by-step explanation:
Applying the formula for the car deprecation we have
[tex]f(t)=P(1-\frac{r}{100} )^n[/tex]
Where,
A is the value of the car after n years,
P is the purchase amount,
R is the percentage rate of depreciation per annum,
n is the number of years after the purchase.
1. The depreciated value of the car after 1 yr is
n=1
[tex]f(t)= 15000(1-\frac{12}{100} )^1\\\f(t)= 15000(1-0.12 )\\\f(t)= 15000(0.88)[/tex]
Which linear inequality is represented by the graph?
Answer:
A. y ≤ 1/2x + 2
Step-by-step explanation:
Well look at the graph,
It is a solid line with it shaded down,
meaning it is y ≤,
So we can cross out B. and D.
So the y intercept is 2, we know this because the y intercept is the point on the line that touches the y axis.
now the slope can be found by seeing how far away each points are from each other,
Hence, the answer is A. y ≤ 1/2x + 2
Evaluate the given algebraic expressions replacing x with −2 and y with 1. 3x2
Answer:
No solutions
Step-by-step explanation:
3x^2=y
3(-2)^2=1
Follow P.E.M.D.A.S.
3(4)=1
12=1