The expression can be written as [tex]90,000(3.71)^{\frac{t}{5} }[/tex]
What is an exponential function?A function whose value is a constant raised to the power of the argument, especially the function where the constant is e.
Given that, we have to express the function [tex]f(t) = 90,000(1.3)^t[/tex] in the form of [tex]f(t) = ab^{\frac{t}{5} }[/tex]
Comparing both the functions,
[tex]b^\frac{t}{5} = (1.3)^t[/tex]
We can write, [tex](1.3)^t[/tex] as
[tex](1.3)^t = (1.3^5)^\frac{t}{5}[/tex]
[tex]= 3.71^\frac{t}{5}[/tex]
Therefore, the equation ca be written as, [tex]90,000(3.71)^{\frac{t}{5} }[/tex]
Hence, the expression can be written as [tex]90,000(3.71)^{\frac{t}{5} }[/tex]
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The volume of this sphere is 4500m³.
Find the length of the radius, r.
Answer:
[tex]r=\frac{15\sqrt[3]{\pi ^2} }{\pi }[/tex] meters
[tex]r=10.24[/tex] meters
Step-by-step explanation:
Here is the equation for the volume of a sphere
[tex]V=\frac{4}{3} \pi r^{3}[/tex]
Lets solve for [tex]r[/tex].
Multiply both sides of the equation by [tex]\frac{1}{\frac{4}{3}\pi}[/tex].
[tex]\frac{1}{\frac{4}{3}\pi}(\frac{4}{3}*(\pi r^3))=\frac{1}{\frac{4}{3}\pi}V[/tex]
Simplify the left side.
Combine [tex]\frac{4}{3}[/tex] and [tex]\pi[/tex].
[tex]\frac{1}{\frac{4\pi }{3}}(\frac{4}{3}*(\pi r^3))=\frac{1}{\frac{4}{3}\pi}V[/tex]
Multiply the numerator by the reciprocal of the denominator.
[tex]\frac{3}{4\pi } (\frac{4}{3}*(\pi r^3))=\frac{1}{\frac{4}{3}\pi}V[/tex]
Cancel the common factor of [tex]\pi[/tex] by factoring it out of the first term.
[tex]\frac{3}{4} (\frac{4}{3}*r^3)=\frac{1}{\frac{4}{3}\pi}V[/tex]
Combine [tex]\frac{4}{3}[/tex] and [tex]r^3[/tex].
[tex]\frac{3}{4}*\frac{4r^3}{3}=\frac{1}{\frac{4}{3}\pi}V[/tex]
Multiply the numerators on the left side of the equation. Then multiply the denominators.
[tex]\frac{12r^3}{4*3}=\frac{1}{\frac{4}{3}\pi}V[/tex]
[tex]\frac{12r^3}{12}=\frac{1}{\frac{4}{3}\pi}V[/tex]
Cancel the common factor of 12.
[tex]r^3=\frac{1}{\frac{4}{3}\pi}V[/tex]
Simplify the right side.
Combine [tex]\frac{4}{3}[/tex] and [tex]\pi[/tex].
[tex]r^3=\frac{1}{\frac{4\pi }{3}}V[/tex]
Multiply the numerator by the reciprocal of the denominator.
[tex]r^3=\frac{3V}{4\pi }[/tex]
Take the cube root of both sides of the equation to eliminate the exponent on the left side.
[tex]r=\sqrt[3]{\frac{3V}{4\pi } }[/tex]
Now we have an equation to find the radius.
Substituting our number for volume gives us
[tex]r=\sqrt[3]{\frac{3*4500}{4\pi } }[/tex]
Enter this into a calculator
[tex]\sqrt[3]{\frac{3*4500}{4\pi } }[/tex]
You can leave the answer in simplest radical form or as a decimal.
[tex]r=\frac{15\sqrt[3]{\pi ^2} }{\pi }[/tex]
[tex]r=10.24[/tex]
A rating/review would be much appreciated. Hope this helps!
A store sells the basic model of a phone for $60 and the upgraded model for $200. It costs the store $10 to buy each basic model and $50 to buy each upgraded model from the phone company. On Tuesday, the store has $1,800 in sales for these two models, and it paid the phone company $400 to buy these phones. How many upgraded models did the store sell on Tuesday?
6 upgraded phones
10 upgraded phones
15 upgraded phones
42 upgraded phones
Answer:
Step-by-step explanation:
C.) 15 upgraded phones
How many milliliters of chocolate milk are in the container shown? Enter your answer in the box.
Answer:
3000ml
Step-by-step explanation:
3 liters= 3000ml
formula: multiply the volume by 1000 to find the milliliters
The temperature at a mountain cabin on
Saturday morning measured -12 degrees
Fahrenheit. The temperature decreased
another 8 degrees Saturday night. In
degrees Fahrenheit, what was the
temperature at the cabin Saturday night?
G-12 H 12
F -20
J -4
On Saturday night, the temperature at the mountain cabin decreased another 8 degrees from -12 degrees Fahrenheit, so the temperature at the cabin on Saturday night was -12 degrees - 8 degrees = -20 degrees Fahrenheit.
What is the area of the shape below?
square inches
What’s the answer pls?
Therefore ,option 3 is hence the appropriate choices. By the Side-Angle-Side Triangle Congruence Theorem, these triangles are congruent.
Triangle definitionAny three points in a plane can be connected to create triangles, which have three sides and three angles. They were one of the very first geometric shapes to be studied. They are particularly important because any polygon, whether it has four, five, six, or n sides, may be split into a triangle.
Here,
From the provided figure, it is clear that there are two triangles.
ABC and EFG are the triangles.
AB = EF
AC = FG
BC = EG
As a result, the triangles ABC and EFG are congruent according to the triangle's SSS theorem, and angle A is equal to angle D.
Therefore ,D and E are hence the appropriate choices. By the Side-Angle-Side Triangle Congruence Theorem, these triangles are congruent.
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HELP ME!! PLEASE 10 POINTSSS
Answer:
The answer is 47°
Step-by-step explanation:
90°- 43°
Answer:
x = 47
Step-by-step explanation:
subtract 43 from 90
Determine how many tablets, capsules, or ml to give to the patient. Answers should be either expressed as 1/2 tablets or rounded to the nearest whole tablet.
Ordered: Voltaren 450 mg
Label reads: Voltaren 150 mg tablets
How many tablet(s) should you give?
Answer: We know that the order from the doctor is 450mg
The stock available has a value of 150mg
Order/Available stock=450mg/150mg=3 tablets
Step-by-step explanation:
what is the closest estimate of x where f(x) = g(x)?
If given the following scenario: The half-life of Sodium-24 is 15
hours. If you start with 352 grams of Sodium-24 how much would
be left after 8 days?
0.049 grams
Approximately 0 grams
1.375 grams
95.965 grams
Sodium has two radioactive cosmogenic isotopes (22Na, half-life = 2.605 years; 24Na, half-life = ~ 15 hours) that have been used as tracers in hydrologic studies.
Sodium-24 how much would be left after 8 days?Sodium-24, a radioactive isotope having a half life of 15 hours is used medically in blood studies and it decays by beta decay.
Na has received considerable attention in hydrologic research because it is a mobile element that participates in precipitation and dissolution reactions in ground water (clay formation, albitization of plagioclase). Their short half-lives (i.e. high decay rate) make their measurement relatively easy by common radioanalytical techniques.
Substantial concentrations of 22Na and 24Na have been measured in precipitation (Roedel, 1970; Perkins et al., 1970). However, no studies have as yet been published documenting the cosmogenic sodium systematics in ground or surface waters.
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Answer the problem in the photo below! Please answer simply:)
Answer:
32
Step-by-step explanation:
Let's start with x to the third power. x=4 So that would be 4 to the third power. that would be 4x4=16. 16x4=64. So that would be 1/2*64. That equals 32
order these numbers from least to the greatest, 47/10,4.606,4+13/20,4.64
Answer:
From lowest to highest, the numbers would follow the following order:
1) 4.606, 2) 4.64, 3) 4 + 13/20, 4) 47/10.
Step-by-step explanation:
Given that the numbers 47/10, 4.606, 4 + 13/20 and 4.64 are presented, to order these from lowest to highest, the following calculations must be performed:
47/10 = 4.70
4,606
4 + 13/20 = 4 + 0.65 = 4.65
4.64
Therefore, from lowest to highest, the numbers would follow the following order:
1) 4.606, 2) 4.64, 3) 4 + 13/20, 4) 47/10.
Which term below refers to events that all have the same probability of occurring?
(1) same chance occurrences
(2) equal probability events
(3) evenly divided happenings
(4) equally likely outcomes
The term below that refers to events that all have the same probability of occurring is; (2) equal probability events
What is the probability of occurrence?By definition, we can say that the probability of occurrence of an event is defined as the number of trials in which a particular event happened divided by the total number of trials.
Probability = number of trials in which event happened/total number of trials.
Now, when we say that all items have the same probability of occurring, what we simply mean is they all have equal chance of occurrence or they all have equal outcomes. For example when we flip a coin, we have equal chance of getting a head or tail.
Thus, the term that best defines the above would be Option 2.
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Which mixed number is equivalent to the improper fraction?
41/4
A. 10 1/4
B. 3 11/10
C. 9 5/4
D. 4 1/10
please hellllp!Thank you so much.
(see the picture)
Answer:
147.33
Step-by-step explanation:
mupitply 26*17 and then dived my 3
Coupon A: $16 rebate on a $55 jacket
Coupon B: 35% off a $55 jacket
Coupon A gives the lower price ?
The price of coupon A is ? less than the price with Coupon B
Coupon B gives the lower price?
The price of coupon B is ? less than the price with Coupon A
Yes. Coupon B gives the lower price.
The price of coupon B is less than the price with Coupon A
How to determine which price is lower?Discount is defined as a deduction from the usual cost of something
Since there is a $16 rebate on a $55 jacket using Coupon A. The price when Coupon A is used will be:
price using Coupon A = $55 - $16 = $39
Since Coupon B gives a 35% discount on the price of the jacket. The price when Coupon B is used will be:
price using Coupon B = $55 - (0.35×55) = $35.75
Thus, the price of coupon B is less than the price with Coupon A
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The triangles shown are similar. Which similarity statement expresses the relationship between the two triangles?
Answer:
C
Step-by-step explanation:
if you got this answer ED 2022
help asap ill mark brainliest
Answer:
Step-by-step explanation:
put all of the sets in a mean median and mode calcultor then add the three numbers toghter
WHAT IS THE ANGLE MEASUREMENTS?? AND TELL ME HOW YOU GOT IT.
PLEASE ANSWER !! ILL GIVE BRAINLIEST !!
50 POINTS !!
FAKE ANSWERS WILL GET REPORTED .
Answer:
18,72,90
Step-by-step explanation:
Let the measure of /_M be 'x'. As reported,
/_N is 5 times of x = 5x
/_O is 4 times of x = 4x
In any ∆, sum of interior angles is 180°.
=> /_M + /_O + /_N = 180
=> x + 4x + 5x = 180
=> 10x = 180
=> x = 180/10 = 18
Angles are x = 18°
4x = 4(18°) = 72°
5x = 5(18°) = 90°
Trevor covered a cylindrical can with paper for a project. The
can is 18 centimeters tall and has a 5 centimeter radius.
Which is closest to the minimum amount of paper Trevor
needed to cover the entire can?
Answer:
722 cm ^2
Step-by-step explanation:
Complete the graph
Red Paint 4, 8, 12, 16
Blue Paint 6, _, _, _
Please help
Answer:
Step-by-step explanation:
10,14,18
Help me with this math equation.
Answer:
7y+21
Step-by-step explanation:
7(y+4)-7
=7y+28-7
=7y+21
[tex]{\boxed{\mathcal{\red{7\:y\:+\:21}}}}[/tex] ✔
Also,
The value of [tex]\sf\purple{"y"\:is\:-3.}[/tex] ✅
Step-by-step explanation:-[tex]7(y + 4) - 7 = 0 \\ ➪ \: 7 \: y + 28 - 7 = 0 \\ ➪ \: 7 \: y + 21 = 0 \\ ➪ \: 7 \: y = - 21 \\ ➪ \: y = \frac{ - 21}{7} \\ ➪ \: y = - 3[/tex]
To verify:-[tex]7 \: ( \: y + 4 \: ) - 7 = 0 \\ ⇢ \: 7 \: ( - 3 + 4) - 7 = 0 \\ ⇢ \: 7 \: (1) - 7 = 0 \\ ⇢ \: 7 - 7 = 0 \\ ⇢ \: \: 0 = 0[/tex]
[tex]\longrightarrow{\purple{L.H.S\:=R.H.S}}[/tex]
Hence Verified.
[tex]\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘[/tex]
Which of the following is the graph of the function shown above? A.W, B. X C.Y D.Z
The given function will be represented by a straight line graph, as shown below in the attachment.
What is a function in graph?On a coordinate plane, functions can be graphed. To graph a function, first select several input values and compute the outputs. The x value is the independent variable, and the y value is the dependent variable. Plot the points and connect them with a line or a curve, depending on whether the function is linear or curvilinear.
Linear functions are written as y = mx + b, where m is the slope of the line and b is the y-intercept. A linear function's graph is a straight line that represents a constant rate of change between two variables. All other functions are curvilinear or non-linear.
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what is 3 3/4 - 1 1/4?
Answer:
2 2/4 or 2 1/2
Step-by-step explanation:
3-1=2
3/4-1/4=2/4
2/4=1/2
A circular pool has a footpath around the circumference. The equation x2 + y2 = 2,500, with units in feet, models the
outside edge of the pool. The equation x2 + y2 = 3,422.25, with units in feet, models the outside edge of the footpath.
What is the width of the footpath?
8.5 ft
17 ft
O 30 ft
O 58.5 ft
Answer:A. 8.5 ft
Step-by-step explanation:
edge2021
The width of the footpath is 8.5 feet.
What is radius in a circle?Radius of a circle is the distance from the center of the circle to any point on it's circumference.
given equation is :x² + y² = (r)²
We have for the pool:
x² + y² = 2500 or x² + y² = (50)²
So, for the outside edge of the footpath
x² + y² = 3422.25 or x² + y² = (58.5)²
So, we find the radius of each circumference
For the outside edge of the poolr₁ = 50 feet
For the outside edge of the footpathr₂ = 58,5 feet
Then the width of the footpath is58,5 - 50 = 8,5 feet
Thus, width of the footpath is 8.5 feet.
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The cost c in pounds of hiring a van for d days is given by the formula c=10+45d work out the cost for 5 day
The cost c in pounds of hiring a van is 235
The cost c in pounds for 1 day =45
Then cost c in pounds for five days is c=10+45d
Which is multiple 5 days to the 45
5 x 45 = 225
Add the 10 to the answer
225 + 10 = 235
The cost of a van hiring for number of days is 5
Then the final answer for cost c in pounds of hiring a van for five days are 235
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17
i already did the test
Answer:
17
Step-by-step explanation:
I believe the answer is 17.
Simplify
17
=17
Now,
Consider point O at zero on the number line.
Mark a point A such at number 4 such that OA= 4
Draw a perpendicular AB at point A of unit length.
Join AB
Taking radius of length AB draw an arc to intersect the number line at C.
Finally, OC=\sqrt{17}
Thus proving the answer is 17 or [tex]\sqrt{289} = 17[/tex]
A 1,000-gallon holding tank initially contains 200 gallons of water that is contaminated by 100 pounds of gunk. A pipe is dumping more contaminated water into the tank at a rate of 16 gallons per minute. The concentration of gunk in this incoming water is 0.6 pounds per gallon. A second pipe is taking the well mixed solution out of the tank at a rate of 14 gallons per minute. How much gunk will be in the tank when the tank is full
Answer:
600 pounds of gunk
Step-by-step explanation:
Given data:
Initial volume of water = 200 gallons
Initial mass of gunk = 100 pounds
dumping rate of pipe( contaminated water into tank ) = 16 gallons per minute
concentration of Gunk = 0.6 pounds / gallon
removal rate of second pipe = 14 gallons per minute
Determine how much gunk will be in the tank when the tank is full
Amount of gunk when tank is full = 599.99 pounds ≈ 600 pounds ≈
Attached below is a detailed solution
i love yall thx for helping
Answer:
A is the answer check once before you submit
Step-by-step explanation:
No need to say thank
One bucket of gravel has a mass of 7.05 KG. What is the mass of 20 buckets of gravel in kilograms?
Is it either
A 14.1 KG
B 150 KG
C 27.05 KG
Or
D 141 KG
Answer:
D: 141 KG
Step-by-step explanation:
7.05 x 20 = 141
Just multiply the mass of the object by however many objects there are if they all weigh the same.