Answer:
Decay, 60%
Step-by-step explanation:
Remember that the exponential function is written in the form [tex]y=ab^x[/tex]. In this problem, a=57 and b=0.4. A function is considered a growth function when [tex]b>1[/tex]. Since 0.4 not greater than 1, this is an exponential decay function.
Now, to find the rate of decrease we can use part of the form [tex]y=a(1-r)^x[/tex].
[tex]1-r[/tex] represents the percentage decrease, in this case, 0.4. If that entire term is 0.4, we need to solve for [tex]r[/tex].
[tex]1-r=0.4\\r=0.6[/tex]
So, the rate of percentage decrease is 60%.
I hope this helps!
13,406,109 pennis into dollars
Answer:
$134,061.09
Step-by-step explanation:
hope this helps
Answer:
134,061.09
Step-by-step explanation:
Divide 13,409,109 by 100
$134,061.09This can also be expressed as 134, 061 dollars, and 9 pennies.
Find the measure of CD.
mCD= [?] degrees
Given:
A circle with radius 7 units and chord CD = 7 units.
To find:
The measure of arc CD.
Solution:
Let O be the center of the circle.
In triangle OCD,
[tex]OC=7[/tex] (Given)
[tex]OC=OD=7[/tex] (Radii of same circle)
[tex]CD=7[/tex] (Given)
Since [tex]OC=CD=OD[/tex] all sides are equal, therefore, the triangle OCD is an equilateral triangle.
Measure of each angle of an equilateral triangle is 60 degrees. So,
[tex]m\angle COD=60^\circ[/tex]
The measure of central angle is equal to the measure of corresponding arc.
[tex]m(arcCD)=m\angle COD[/tex]
[tex]m(arcCD)=60^\circ[/tex]
Therefore, the measure of arc CD is 60 degrees.
Given f(x)=x^3-2, find the equation of the secant line passing through (-4,f(-4)) and (2,f(2))
Given:
The function is
[tex]f(x)=x^3-2[/tex]
The secant line passing through (-4,f(-4)) and (2,f(2)).
To find:
The equation of the secant line.
Solution:
We have,
[tex]f(x)=x^3-2[/tex]
At x=-4,
[tex]f(-4)=(-4)^3-2[/tex]
[tex]f(-4)=-64-2[/tex]
[tex]f(-4)=-66[/tex]
At x=2,
[tex]f(2)=(2)^3-2[/tex]
[tex]f(2)=8-2[/tex]
[tex]f(2)=6[/tex]
The secant line passes through the points (-4,-66) and (2,6). So, the equation of the secant line is
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
[tex]y-(-66)=\dfrac{6-(-66)}{2-(-4)}(x-(-4))[/tex]
[tex]y+66=\dfrac{6+66}{2+4}(x+4)[/tex]
[tex]y+66=\dfrac{72}{6}(x+4)[/tex]
On further simplification, we get
[tex]y+66=12(x+4)[/tex]
[tex]y+66=12x+48[/tex]
[tex]y=12x+48-66[/tex]
[tex]y=12x-18[/tex]
Therefor, the equation of the secant line is [tex]y=12x-18[/tex].
I need help with this
What is the product?
213 × 314
Answer:
66882
Step-by-step explanation:
Answer:
product
Step-by-step explanation:
213×314=66,882
The histogram on the left shows the number of hours students in a British Literature class read last week, rounded to the nearest hour. Which of the following statements offers the best description of the median number of hours students in the class read last week?
Answer:The median number of hours is between 5 and 9
Step-by-step explanation:
The median number of hours students in the class read last week is between 5 and 9
Histogram A histogram is an approximate representation of the distribution of numerical dataHistogram is a diagram consisting of rectangles whose area is proportional to the frequency of a variable and whose width is equal to the class interval.How to solve this problem?The steps are as follow:
Give class interval; Hours of reading0-4;20
5-9;24 32th median
10-14;10
15-19;4
20-24;2
25-29;3 ∑ = 63 i.e. odd
M = 1/2 (63+1) = 32th observation
So the median number of hours students in the class read last week is between 5 and 9
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Can someone help me find the distance between the points (-5,3) and (-4,2)
Answer: 1.4142
Step-by-step explanation:
Input Data :Point 1 (xA,yA) = (-5, 3) Point 2(xb,yB) = (-4, 2)
Objective : Find the distance between two given points on a line?
Formula :Distance between two points = √(xB-xA)^2+(yB−yA)^2
Solution :
Distance between two points = √(−4−−5)2+(2−3)2= √12+(−1)2= √1+1= √2 = 1.4142
Distance between points (-5, 3) and (-4, 2) is 1.4142
May I please have brainlest I'm trying to achieve a new rank
J.B. earns $16.60 an hour with time-and-a-half for hours worked over 8 a day. His
hours for a week are 8.25, 8.25, 9.5, 11.5, and 7.25. Determine his gross earnings
for that week.
Answer:
The gross pay for the week is $701.32
Step-by-step explanation:
J.B. earns $16.60 per hour, and half of it ($16.60/2) for each hour worked over the 8th-hour range.
On the first day, he works 8.25 hours.
We have 8 hours, plus 0.25 hours past the limit, then for the first day he wins:
8*$16.60 + 0.25*($16.60/2) = $134.86
On the second day, he works again 8.25 hours, so he wins the same amount $134.86
On the third day, he works 9.5 hours, then:
We have 8 hours plus 1.5 hours past the limit, then for this day he wins:
8*$16.60 + 1.5*$16.60/2 = $145.25
On the fourth day, he works 11.5 hours, then:
We have 8 hours plus 3.5 hours pást the limit, then for this day he wins:
8*$16.60 + 3.5*$16.60/2 = $161.85
For the last day, he works 7.25 hours, (in this case, we do not have hours worked over the 8-hour limit) then this day he wins:
7.25*$16.60 = $124.50
The gross pay for this week will be equal to:
G = $134.86 + $134.86 + $145.25 + $161.85 + $124.50 = $701.32
PLEASE HELP GEOMETRY
Answer:
Step-by-step explanation:
Triangle R Q S is cut by line segment T V. Line segment T V goes from side Q R to side R S. The length of R V is x + 10, the length of V S is x, the length of R T is x + 4, and the length of T Q is x minus 3. Which value of x would make Line segment T V is parallel to Line segment Q S?
PLEASE HURRY
9514 1404 393
Answer:
x = 10
Step-by-step explanation:
In order for TV to be parallel to QS, it must divide the sides of the triangle proportionally.
RT/TQ = RV/VS
(x+4)/(x-3) = (x+10)/(x)
1 +7/(x-3) = 1 +10/x . . . . expand each fraction
7/(x -3) = 10/x . . . . . . . . subtract 1
7x = 10(x -3) . . . . . . . . . cross multiply
30 = 3x . . . . . . . . . . . . add 30-7x, simplify
10 = x . . . . . . . . . . . . . . divide by 3
The value of x that makes the segments parallel is 10.
_____
Alternate solution
You can cross multiply the first fraction we wrote to get ...
x(x +4) = (x -3)(x +10)
x^2 +4x = x^2 +7x -30 . . . eliminate parentheses
30 = 3x . . . . . . subtract x^2+4x-30 from both sides
Answer: C. 10
Step-by-step explanation:
i got it right on the test
In one building, an elevator takes 15 seconds to go up 5 floors.
In another building, an elevator goes up for 60 seconds at the
same rate. How many floors did the elevator in the second
building travel?
Answer:
20 floors
Step-by-step explanation:
15 sec to go up 5 floors is climbing one floor every 3 seconds
3 sec x 20 = 60 seconds
1 fl x 20 = 20 floors
Leon’s older brother is 4 3/4 feet tall Leon is a 1/3 foot shorter than his brother how. tall is Leon?
Answer:
Leon is 4 5/12
Step-by-step explanation:
4 3/4 - 1/3 change 4 4/12 - 4/12 = 4 5/12
The area of a circle is 100π ft². What is the circumference, in feet? Express your answer in terms of π.
Answer:
Answer: 20pi is the circumference
Step-by-step explanation:
The circumference of the circle is 20π ft when the area of the circle is 100π ft².
What is circle?A circle is a locus of the points drawn at an equidistant from a fixed point. The fixed point is called Centre of the circle and the distance from the fixed point to the circle is called radius.
Given, area of a circle is 100π.
Therefore, πr² =100π, where r is the radius of the circle.
So, r²=100
Thus, r= 10 ft.
now, circumference = 2πr
=2π×10
=20π ft.
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Find the midpoint of A and B where A has coordinates (8,5)
and B has coordinates (3, 7).
Answer:
Step-by-step explanation:
Average of x-coordinates = (8+3)/2 = 5.5
Average of y-coordinates = (5+7)/2 = 6
Midpoint at (5.5,6)
Find the length of side x in simplest radical form with a rational denominator
Answer:
[tex] x = \sqrt{2} [/tex]
Step-by-step explanation:
[tex] \tan 30 \degree = \frac{x}{ \sqrt{6} } \\ \\ \frac{1}{ \sqrt{3} } = \frac{x}{ \sqrt{6} } \\ \\ x = \frac{ \sqrt{6} }{ \sqrt{3} } \\ \\ x = \frac{ \: \sqrt{3} \times \sqrt{2} }{ \sqrt{3} } \\ \\ x = \sqrt{2} [/tex]
PLZ HELP ME YOU GUYS ARE MY ONLY HOPE!!! I WILL GIVE BRAINLIEST PLZ ANSWER<3
2a+3c=5a+2c=1
There is an ordered pair that is the solution of the system of equations shown. The value of one of the variables in the solution of the system can be obtained by using which of the following substitutions?
Answer:
a = 9, c = -4?
Step-by-step explanation:
i think these are the two equations, let me know if i'm wrong
2a + 3c = 5; a + 2c = 1
rearrange second equation : a = -2c +1
plug in:
2(-2c +1) +3c = 5
-4c +1 +3c = 5
-c +1 = 5
-c = 4
c = -4
a + 2(-4) = 1
a - 8 = 1
a = 9
Find the volume of the cylinder and cone, then add them together.
★ Volume of cylinder :-
V = πr²hHere,
r is radius h is heightWe have :
r = 2cm h = 7cmSubstituting the values :
> V = π (2 × 2) × 7
> V = 4π × 7
> V = 28π
★ Volume of cone :-
V = ⅓ π²hWe have :
r = 2cm h = 6 cmSubstituting the values :
> V = ⅓ × π × (2 × 2) × 6
> V = ⅓ × π × 4 × 6
> V = ⅓ × π × 24
> V = 8π
★ According to the question :-
Adding them together,
> Total Volume = 8π + 28π
> Total Volume = 36π
[tex]Total \: \: \: Volume = (88+176) {cm}^{2} \\ \\ = 264 {cm}^{2} .[/tex]
Which line has a slope of -1/2?
A large rectangular movie screen in an IMAX theater has an area of 7,875 square feet. Find the dimensions of the screen if it is 30 feet longer than it is wide.
Answer:
Width=75
length=105
Step-by-step explanation:
Width=x
length=30+x
= 7875=x*30+x
x^2+30x-7875=0
x^2+105x-75x-7875=0
x(x+105)-75(x+105)=0
Amber has determined that the experimental probability of making a free throw in basketball is 12/15. What it the probability of missing a basket?
Answer:
3/15, 1/5, or 0.2 probability. Highly unlikely
Explanation:
12/15 is the shown probability. The leftover is 3/15, so 3/15 is the chance of missing the basket.
~Hope this helps~
What is the perimeter of a rectangle with two lentghs of 5
Answer:
20
Step-by-step explanation:
in perimeter you have to add all the sides but rectabgless all have the same size so 5 x 4 since rectangle has 4 sides equls 20 so 20 is the answer
Formula for parallelogram law of addition
Answer:
answers?
Step-by-step explanation:
If a watch costs $40 and you must pay 6.5 % sales tax, how much will the tax be?
Please give me the correct answer this is for a test and im on a time limit :(
Answer:
$2.60
Step-by-step explanation:
40 x 0.065 = $2.60
Answer:
the tax would be 2.60$
Step-by-step explanation:
6.5% of 40 is 2.6
(6.5 x .40=2.6)
Find the area of the figure
Answer:
Step-by-step explanation:
Just add it
f (x) = 5x -3 what is f (5) =
Answer:
22is answer
f (x) = 5x -3
f (5) =5×5-3=25-3=22
Answer:
5
Step-by-step explanation:
f(x)=5x−3
The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^n is nax^n−1 .
5x^1−1
Subtract 1 from 1.
5x^0
For any term t except 0, t^0 =1.
5×1
For any term t, t×1=t and 1t=t.
5
E=mc squared m=3 c=6
Answer:
E = 108
Step-by-step explanation:
E = 3 * [tex]6^{2}[/tex]
= 108
Answer:
e=mc^2 if m=3 and c=6
e=3([tex]6^2[/tex])
e=3[tex](36)[/tex]
e=108
Step-by-step explanation:
hope this helps have a good rest of your day/afternoon :) ❤
Exercise 2.4.2: Proving statements about rational numbers with direct proofs. About Prove each of the following statements using a direct proof. (a) The product of two rational numbers is a rational number. Solution (b) The quotient of a rational number and a non-zero rational number is a rational number. Solution (c) If x and y are rational numbers then is also a rational number.
Answer:
See Explanation
Step-by-step explanation:
(a) Proof: Product of two rational numbers
Using direct proofs.
Let the two rational numbers be A and B.
Such that:
[tex]A = \frac{1}{2}[/tex]
[tex]B = \frac{2}{3}[/tex]
The product:
[tex]A * B = \frac{1}{2} * \frac{2}{3}[/tex]
[tex]A * B = \frac{1}{1} * \frac{1}{3}[/tex]
[tex]A * B = 1 * \frac{1}{3}[/tex]
[tex]A * B = \frac{1}{3}[/tex]
Proved, because 1/3 is rational
(b) Proof: Quotient of a rational number and a non-zero rational number
Using direct proofs.
Let the two rational numbers be A and B.
Such that:
[tex]A = \frac{1}{2}[/tex]
[tex]B = \frac{2}{3}[/tex]
The quotient:
[tex]A / B = \frac{1}{2} / \frac{2}{3}[/tex]
Express as product
[tex]A / B = \frac{1}{2} / \frac{3}{2}[/tex]
[tex]A / B = \frac{1*3}{2*2}[/tex]
[tex]A / B = \frac{3}{4}[/tex]
Proved, because 3/4 is rational
(c) x + y is rational (missing from the question)
Using direct proofs.
Let x and y be
Such that:
[tex]x = \frac{1}{2}[/tex]
[tex]y = \frac{2}{3}[/tex]
The sum:
[tex]x + y = \frac{1}{2} + \frac{2}{3}[/tex]
Take LCM
[tex]x + y = \frac{3+4}{6}[/tex]
[tex]x + y = \frac{7}{6}[/tex]
Proved, because 7/6 is rational
The above proof works for all values of A, B, x and y; as long as they are rational values
Find the slope of the line passing through the points (-2,-3) and (2,5) 
Answer:
Undefined
Step-by-step explanation:
Zack has an old car. He wants to sell it for 60% off the current price. The market price is $500. How much money would he receive in exchange for the car if he were able to sell it at that rate? What if he wanted to sell it for 25% more than the market price?
60% of 500 is 300
So if Zack wanted to sell the car 60% of the markets price, it would be 300.
125% of 500 is 625
If Zack wanted to sell the car for 25 more than the price at market, it would be 125%, and 125% of 500 is 625.
How many 1/3 are in 2 3/4?
Answer: For example, in order to explain why 1/3 + 1/4 = 7/12, we considered the task of dividing 7 apples between 12 boys under the restriction that an apple ... How many halves are in the whole? ... 1 = 3 × 1/3, 2 = 6 × 1/3, 3 = 9 × 1/3, 4 = 12 × 1/3.
Step-by-step explanation:
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