The best scenario for an exponential function is Option B, as it describes a consistent percentage decrease annually, which is characteristic of exponential decay.
The situation that is best modeled by an exponential function is Option B, which describes the amount of a substance remaining after x years if it is decreasing at a rate of 25% annually. This exemplifies an exponential decay scenario where the rate of change of a quantity is directly proportional to its current value. Over time, the substance decreases by a consistent percentage, which is characteristic of exponential decay functions.
A key feature of exponential relationships is that they describe processes where the change at any given point is proportional to the current amount, which fits the description of a substance decreasing by a consistent percentage each year.
A pair of shoes is priced $35.99, but is on sale for 20% off.What is the sale price of the shoes
Answer: $7.20
Step-by-step explanation:
20% equals 1/5 and 35.99 divided by 1/5 is 7.198 now round to the nearest tenth and you got 7.20.
Ashley has a sprinkler that has several varieties of coverage. The quarter circle sprinkler head sprays water a distance of up to 20 feet from the lead. What area will be covered by the spray of the quarter-circle sprinkler head to the nearest square foot?
Answer:
314 square feet
Step-by-step explanation:
we know that
The area that will be covered by the spray of the quarter-circle sprinkler head, is equal to the area of a quarter circle with radius of 20 feet
so
The area of a quarter circle is
[tex]A=\frac{1}{4}\pi r^{2}[/tex]
we have
[tex]r=20\ ft[/tex]
[tex]\pi =3.14[/tex]
substitute
[tex]A=\frac{1}{4}(3.14)(20)^{2}=314\ ft^2[/tex]
The area covered by the quarter-circle sprinkler head to the nearest square foot is 314 square feet.
To find the area covered by the quarter-circle sprinkler head, we need to calculate the area of a quarter circle with a radius of 20 feet. The formula for the area of a circle is [tex]\( A = \pi r^2 \), where \( r \)[/tex] is the radius. Since we are dealing with a quarter circle, we will take [tex]\( \frac{1}{4} \)[/tex] of the full circle's area.
Given that the radius [tex]\( r \)[/tex] is 20 feet, the area of the full circle would be:
[tex]\[ A_{\text{full circle}} = \pi \times (20 \text{ feet})^2 \] \[ A_{\text{full circle}} = \pi \times 400 \text{ square feet} \] \[ A_{\text{full circle}} = 400\pi \text{ square feet} \][/tex]
Now, to find the area of the quarter circle, we divide the full circle's area by 4:
[tex]\[ A_{\text{quarter circle}} = \frac{1}{4} \times 400\pi \text{ square feet} \] \[ A_{\text{quarter circle}} = 100\pi \text{ square feet} \][/tex]
Using the value of [tex]\( \pi \)[/tex] as approximately 3.14159, we get:
[tex]\[ A_{\text{quarter circle}} \approx 100 \times 3.14159 \text{ square feet} \] \[ A_{\text{quarter circle}} \approx 314.159 \text{ square feet} \][/tex]
Rounding to the nearest square foot, the area covered by the quarter-circle sprinkler head is 314 square feet.
Manuela works as a security guard. She makes $15 per hour. Her employers deduct $125 from her weekly check to cover insurance and takes. If Manuela receives at least $205 in her weekly paycheck, what is the feast number of hours she works in a week show steps.
Manuela works at least 22 hours in a week.
Step-by-step explanation:
Given,
Per hour salary of Manuela = $15
Amount deducted = $125
Amount received = $205
Let,
x be the number of hours per week.
Per hour salary * Number of weeks - Amount deducted ≥ Amount received
[tex]15x-125\geq 205\\15x\geq 205+125\\15x\geq 330[/tex]
Dividing both sides by 15
[tex]\frac{15x}{15}\geq \frac{330}{15}\\x\geq 22[/tex]
Manuela works at least 22 hours in a week.
Keywords: inequality, division
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At a gas station a car wash costs $6.50 and gas is $2.75 a gallon. Enter the greatest number or gallons of gas you can purchase in addition to a car wash and not spend more than $23.00
Answer:
6 gallons
Step-by-step explanation:
23.00-6.50=16.50
16.50/2.75=6
The length of a rectangle is six more than triple the width. If the perimeter is 156 inches, find the dimensions.
The width is
inches.
The length is
inches.
Answer:
lenght= 60 inches
width = 18 inches
Step-by-step explanation:
parameter = 2(L+B)
let lenght be x
width be y
so
x = 3y+6
let's put this in formula
156 = 2( x+y )
156 = 2( 3y+6 + y )
156 = 2 ( 4y + 6 )
156/2 = 4y + 6
78 = 4y + 6
4y = 78-6
4y = 72
y = 72/4
y = 18
so width is 18 inches
and lenght is 3*18+6 = 60 inches
The width of the rectangle is 18 inches, and the length is 54 inches.
Explanation:Let's denote the width of the rectangle as 'w'. According to the problem, the length of the rectangle can be expressed as 3w + 6. The problem also states that the perimeter of the rectangle is 156 inches. Remember that the formula for the perimeter of a rectangle is 2(length + width). Given that the length is expressed as 3w + 6 and the width as w, we can plug these values into the perimeter formula: 2(3w + 6 + w) = 156. Simplifying, we get 8w + 12 = 156. Isolating w, we have w = 18 inches. We also need to find the length, which is 3w + 6 = 54 inches. This gives us a width of 18 inches and a length of 54 inches.
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2. If the whole bar is 3 units long, what is the length of the shaded part of the bar? Write a multiplication
equation for the diagram, and then solve.
Answer:
The length of the shaded part is [tex]\frac{9}{4}[/tex]
Step-by-step explanation:
The original figure, which you may have unintentionally missed to add, is attached below.
From the figure, it is easy to figure out that:
The whole bar is 3 units long.The bar has 4 total parts.The shaded region has 3 parts.So, the ratio of shaded parts to total parts will be: [tex]\frac{3}{4}[/tex]
In order to determine length of the shaded part, just multiply the ratio of the shaded parts to total parts by the total length of the bar.
So,
[tex]\frac{3}{4} \times3=\frac{9}{4}[/tex]
Therefore, the length of the shaded part is [tex]\frac{9}{4}[/tex]
Keywords: ratio, length
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Answer:
see the explanation
Step-by-step explanation:
The picture of the question in the attached figure
we know that
The fraction of the shaded part is equal to divide the number of shaded parts divided by the total number of parts
so
Let
x ----> the number of shaded parts
y ----> the total number of parts
we have
x=3, y=4
so
[tex]\frac{3}{4}[/tex]
To find out the length of the shaded part, multiply the fraction of the shaded parts by the total length of the bar
so
[tex]\frac{3}{4}(3)=\frac{9}{4}=2.25\ units[/tex]
a needle palm tree at the park is growing an average of 4.35 cm per day. A cabbage palm tree next to it is growing an avrege of 1.26 in per day. which? one is growing faster?
Answer:
The needle palm tree is growing faster.
Step-by-step explanation:
The rate of growth of needle palm tree = 4.35 cm / day
The rate of growth of cabbage palm tree = 1.26 cm /day
From the given data we can clearly see ,
4.35 > 1.26
So the needle palm tree is growing faster.
if f(x)=2x-5 and g(x)=x^2+1, what is g(f(x))
Answer:
4x² - 20x + 26
Step-by-step explanation:
To evaluate g(f(x)), substitute x = f(x) into g(x), that is
g(2x - 5 )
= (2x - 5)² + 1 ← expand factor using FOIL
= 4x² - 20x + 25 + 1
= 4x² - 20x + 26
A pack of cinnamon-scented pencils sells for $5.00. What is the sales tax rate if the total cost of the pencils is $5.40?
Answer:
The sales tax rate is 5%
Given:
Sales price = 5.00
Total amount paid = 5.25
Sales tax value = Total amount paid - sales price
= $5.25 - $5.00
Sales tax value = $0.25
Sales tax rate = Sales tax / Sales price
= 0.25/5
Sales tax rate = 0.05 or 5%
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Thanks to taskmasters.
Step-by-step explanation:
Which of the following will lower your interest rate?
Answer:points
Step-by-step explanation:
25. CHARITY In the first hour of a charity auction, $4800 was raised. This was at most
$1200 more than was raised in the second hour of the auction. Write an inequality that
represents the amount raised in the second hour.
Answer:
6000
Step-by-step explanation:
if you do 200+800=1000 and the if you do 4000+1000=5000+1000=6000
The inequality that represents the amount raised in the second hour of the charity auction is x ≤ 6000.
Explanation:To represent the amount raised in the second hour of the charity auction, let's use the variable x. According to the information given, the amount raised in the first hour is $4800, which is at most $1200 more than the amount raised in the second hour. This can be represented as the inequality:
x ≤ 4800 + 1200
Simplifying the inequality, we have:
x ≤ 6000
Therefore, the inequality that represents the amount raised in the second hour is x ≤ 6000.
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Multiply simplest form
Answer:
4 [tex]\frac{8}{9}[/tex]
Step-by-step explanation:
2 [tex]\frac{1}{5}[/tex] × 2 [tex]\frac{2}{9}[/tex]
[tex]\frac{11}{5}[/tex] × [tex]\frac{20}{9}[/tex] = [tex]\frac{220}{45}[/tex] = 4 [tex]\frac{8}{9}[/tex]
What number is 7 hundreds 1 tens 12 ones
Answer:
.712
Step-by-step explanation:
Answer:
i think the answer is 722
Find the tenth term in the sequence: 12, 10, 8, ...
Answer:
-6
Step-by-step explanation:
12, 10, 8, 6, 4, 2, 0, -2, -4, -6
Subtracting two each time
Answer:
-6
Step-by-step explanation:
It subtracts 2 each time in the sequence.
The first term is 12.
You subtract 2 ten times to get to the tenth number in this sequence. 10*2 = 20. 12-20 = -6
If a number is divisible by 3 and 5 then it is divisible by 15
Answer:
Yes!
Step-by-step explanation:
Besides 15 and one, 3 and 5 are the greatest common factors of 15. Those numbers are therefore divisible by any product of 15.
Example:
45
45/3 = 15
45/5 = 9
45/15 = 3
Answer:
Yes it is
Step-by-step explanation:
Since the multiplication of 3 and 5 will give 15
I.e 3 × 5 = 15
Then any number that can be divided by 3 and 5, can also be divided by 15.
5. Name the property the equation illustrates.
WILL GIVE BRAINLIEST!!!! Which of the values for x and y make the equation 2x + 3y + 4 = 15 true? (4 points) x = 6, y = 3 x = 3, y = 5 x = 6, y = 4 x = 1, y = 3
2x + 3y + 4 = 15
2(1) + 3(3) + 4 = 15
2 + 9 + 4 = 15
11 + 4 = 15
15 = 15
x = 1 and y = 3
Hope this helps! ;)
Answer: The correct answer choice is D.
Step-by-step explanation: I will show all the work done for each answer choice so it is more clear.
First Answer Choice's Work:
2(6) + 3(3) + 4
12 + 9 + 4
12 + 9
21
21 + 4
25.
Second Answer Choice's Work:
2(3) + 3(5) + 4
6 + 15 + 4
21 + 4
25.
Third Answer Choice's Work:
2(6) + 3(4) + 4
12 + 12 + 4
24
24 + 4
28.
Fourth Answer Choice's Work:
2(1) + 3(3) + 4
2 + 9 + 4
11
11 + 4
15.
Therefore, the correct answer choice is D.
The total price of a bag of peaches varies directly with the cost per pound. If 3 pounds of peaches cost $3.60, how much would 5.5 pounds cost?
A: $1.20
B: $6.60
C: $6.00
D: $1.96
Step-by-step explanation:
Given , the total price of a bag of peaches varies directly with the cost per pound. If 3 pound of peaches cost $3.60.
Therefore,
[tex]{\textrm{beg of peaches}}\propto{\textrm{cost}}[/tex]
[tex]\Leftrightarrow {\textrm{beg of peaches}}= {\textrm{k cost}}[/tex].......(1) [ k is a constant]
cost = $3.60 when beg of peaches = 3 pounds
[tex]3 = 3.60 k[/tex]
[tex]\Leftrightarrow k = \frac{3}{3.60}[/tex]
[tex]\Leftrightarrow k = \frac{1}{1.20}[/tex]
Therefore the equation (1) becomes
[tex]{\textrm{beg of peaches}}=\frac {cost}{1.20}[/tex]
[tex]\Leftrightarrow {\textrm{beg of peaches}}\times 1.20={cost}[/tex]
When beg of peaches = 5.5 pound
[tex]cost = 5.5 \times 1.20[/tex]
[tex]\Leftrightarrow cost = 6.60[/tex]
Therefore the cost of 5.5 pound of peaches is $ 6.60.
Apply the distributive property to factor out the greatest common factor 70-40p
Answer:
10(7-4p)
Step-by-step explanation:
decimal and integers are both classified as ______ numbers
Answer:whole numbers
Step-by-step explanation:
Donato is 6 feet 2 inches tall. His sister is 68 inches tall. Donato is how many inches taller.
6 inches taller
Step-by-step explanation:
There’s 12 inches in a foot. So 12•6 is 72 then plus another 2 then you get 74. Then subtract 74 by 68 and you get 6
Answer:
Step-by-step explanation: since 1 foot =12 inches then we multiply 12*6=72 inches +2 inches =74 inches therefore Donato is 74 inches which is obviously bigger than 64 inches so we subtract 74-64=10
As a result ,Donato is 10 inches taller than his sister
You can buy 5 cans for green beans at the Village Market for $3.70. You can buy 10 of the same cans of beans at Sam’s club for $6.30. Which place is the the better buy?
Answer:
Sams club
Step-by-step explanation:
3.70/5= $.74 per can
6.30/10=$.63 per can
Which is greater 2.6 or 4.07
Answer:
4.07 is greater
Answer:
4.07
Step-by-step explanation:
Bryan has a summer job of unloading fruit crates. Last week he unloaded 243 crates. This week he unloaded 361. How many more did Bryan unload this week than last week?
Answer:
The answer is 118
Step-by-step explanation:
In order to solve this you need to subtract this weeks, to last weeks.
361 - 243 = 118.
Hope this helps :)
Bryan unloaded 118 more crates this week than last week.
Explanation:To find out how many more crates Bryan unloaded this week than last week, we can subtract the number of crates unloaded last week from the number of crates unloaded this week.
So, to find the difference, we subtract 243 from 361:
= 361 - 243
= 118
Therefore, Bryan unloaded 118 more crates this week than last week.
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6x-y=8
7x-y=9
Solve linear systems by Multiplying first
What is 1/9 (2m - 16) = 1/3 (2m +4)
Answer:
-7
Step-by-step explanation:
Hope it helped!
Helpppp pleaseeeeeeeeeeeeeee
Answer:
Find below the calculations of the two areas, each with two methods. The results are:
Upper triangle:[tex]Area=5000\sqrt{3}units^2[/tex]
Lower triangle:[tex]Area=14,530m^2[/tex]
Explanation:
A) Method 1
When you are not given the height, but you are given two sides and the included angle between the two sides, you can use this formula:
[tex]Area=side_1\times side_2\times sin(\alpha)[/tex]
Where, [tex]\alpha[/tex] is the measure of the included angle.
1. Upper triangle:
[tex]side_1=200units\\ \\ side_2=100units\\ \\ \alpha =60\º\\ \\ Area=200units\times 100units\times sin(60\º)/2\\ \\ Area=5000\sqrt{3}units^2[/tex]
2. Lower triangle:
[tex]side_1=231m\\ \\ side_2=150m\\ \\ \alpha =123\º\\ \\ Area=231m\times 150m\times sin(123\º)/2\\ \\ Area=14,529.96m^2\approx14,530m^2[/tex]
B) Method 2
You can find the height of the triangle using trigonometric properties, and then use the very well known formula:
[tex]Area=(1/2)\times base\times height[/tex]
Use it for both triangles.
3. Upper triangle:
The trigonometric ratio that you can use is:
[tex]sine(\alpha)=opposite\text{ }leg/hypotenuse[/tex]
Notice the height is the opposite leg to the angle of 60º, and the side that measures 100 units is the hypotenuse of that right triangle. Then:
[tex]sin(60\º)=height/100units\\ \\ height=sin(60\º)\times100units\\ \\ height=50\sqrt{3}units[/tex]
[tex]Area=(1/2)\times base\times height=(1/2)\times 200units\times 50\sqrt{3}units=5,000\sqrt{3}units^2[/tex]
3. Lower triangle:
[tex]sin(180\º-123\º)=height/231m\\ \\ height=sin(57\º)\times 231m\\ \\ height=193.7329m^2[/tex]
[tex]Area=(1/2)\times base\times height=(1/2)\times 150m\times 193.7329m^2\\\\ Area=14,529.96m^2\approx 14,530m^2[/tex]
Decide whether 3(x-2)+5 and 3x+1 are equivalent expressions. explain how you know.
Answer:
Not equivalent
Step-by-step explanation:
Let,
3(x-2) + 5 = 3x + 1
By Multiplying
3x - 6 + 5 = 3x + 1
3x - 1 = 3x + 1
So, the expressions are not equal
a teacher uses 36 centimeters of tape to hang up 9student projects. At this rate, how much tape would the teacher need to hang up 10 student projects?
PLSSSSS HELP What is the period of the function f(x)=sin1/6x ? π/6 12/π 6π 1/6
the answer is 12pi
just took the quiz :)
The period of the function is 12π, the correct option is B.
What is the period of a function?The period of a function is the distance in which the graph repeats itself.
For a trigonometric function, the length of one complete cycle is called the periodic function.
For the function
y = a sin (bx + c)
Here,
a is the amplitude,
b is the period of the sine curve, and
c is the phase shift of the sine curve
The amplitude is the height of the curve.
The coefficient of b = 1, for a period of 2π
To find the period of the sine curve for any coefficient b,
Divide 2π by the coefficient of b to get the new period of the curve.
The coefficient b and the period of the sine curve have an inverse relationship,
As b gets smaller, the length of one cycle of the curve gets bigger. Similarly, on increasing the value of b, the period will decrease.
The function is y = sin1/6x
The period of the function is,
= 2π / ( 1/6)
= 12π
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