Answer:
C) f(x)=25(4/5)^x
Step-by-step explanation:
Observe that the exponential function is decreasing (so exponential decay). This means that r<1 making A and D wrong as they show exponential growth as r>1. Also notice that the y-intercept is 25 which is where the function crosses the y-axis when x=0. This means C is the only correct answer.
1.A multiple choice exam has five possible answers per question. Only one of those five answers is the correct answer. A student, who did not prepare for the test,answers the exam randomly and in order,starting from the first question. a.What is the probability that the first question he answered correctly is the second question
Answer:
Step-by-step explanation:
P(answers correctly)=1/5
P(answers incorrectly)=1-1/5=4/5
P( answers correctly second question)=4/5 ×1/5=4/25
You would like to have $20,000 to use a down payment for a home in five years by making regular, end-of-month deposits into an annuity that pays 6% interest compounded monthly.
How much should you deposit each month?
Round your answer to the nearest cent. Do not include the dollar sign in the answer box below.
The amount that should be deposited monthly is $286.66.
What is a monthly deposit?The monthly deposit is the periodic payment into an investment account that earns interest at a compound rate.
The monthly deposit can be determined using an online finance calculator.
N (# of periods) = 60 months (5 years x 12)
I/Y (Interest per year) = 6%
PV (Present Value) = $0
FV (Future Value) = $20,000
Results:
Monthly Deposit = $286.66
Sum of all periodic deposits = $17,199.36
Total Interest = $2,800.64
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Angie packed same-size cubes into a rectangular prism. A 1 What is the number of cubes needed to fill this prism? 20 cubes Area of the base is 6 yd.² pls helpppppppppp
There are 42 cubes needed to fill this prism.
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
Angie packed same-size cubes into a rectangular prism.
And, Image shows a base of cubes 3 units long, 2 units wide, and with a column of cubes 1 cube wide and 7 cubes tall.
Hence, Number of cubes to fill the prism is,
⇒ 3 × 2 × 7
⇒ 42
Thus, There are 42 cubes needed to fill this prism.
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Complete question is this,
Angie packed same-size cubes into a rectangular prism.
Image shows a base of cubes 3 units long, 2 units wide, and with a column of cubes 1 cube wide and 7 cubes tall. PLEASE HELP ME
What is the number of cubes needed to fill this prism?
For each graphically defined function below, state the domain, the range, and the intervals over which the function is increasing, decreasing, or constant.
The domain of the function above is [-2, 3].
The range of the function above is [-2.5, 2].
The intervals over which the function is increasing is [-2, 1.5] U [-2.5, 2].
The intervals over which the function is decreasing is [1.5, -2.5].
What is a domain?In Mathematics and Geometry, a domain refers to the set of all real numbers for which a particular function is defined.
Furthermore, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
By critically observing the graph of this rational expression (function) shown in the image attached below, we can reasonably and logically deduce the following domain and range:
Domain = [-2, 3] or -2 ≤ x ≤ 3.
Range = [-2.5, 2] or -2.5 ≤ y ≤ 2.
Additionally, the intervals over which the function is increases over the interval [-2, 1.5] and [-2.5, 2], while it decreases over the interval [1.5, -2.5].
In conclusion, the given function is not constant over any interval.
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I need help pls help me
Answer:
Allison
Step-by-step explanation:
Allison:
2^6 = 64
Chris:
3³ = 27
Hannah:
4² = 16
Steve:
18^1 = 18
Answer:
Allison
Step-by-step explanation:
Allison
\(2^{6}\) = 2 x 2 x 2 x 2 x 2 x 2 = 64
Chris
\(3^{3}\) = 3 x 3 x 3 = 27
Hannah
\(4^{2}\) = 4 x 4 = 16
Steve
\(18^{1}\) = 18 = 18
27. COFFEE SHOP Chenoa wants to stop for coffee on her way to school. The distance
from Chenoa's house to the coffee shop is 3 miles more than twice the distance
from the coffee shop to Chenoa's school. The total distance from Chenoa's house
to her school is 5 times the distance from the coffee shop to her school.
The distance from Chenoa's house to the coffee shop is 6 miles because it satisfies the logic that the distance from Chenoa's house to the coffee shop is 3 miles more than twice the distance from the coffee shop to Chenoa's school.
What is the distance?The distance is the length of space from one point to another point.
The distance shows how far a point or object is from another.
Data and Calculations:Distance from Chenoa's house to the coffee shop = 2x + 3 miles
Distance from the coffee shop to Chenoa's school = x or 1.5 miles
Total distance from Chenoa's house to her school = 5x
2x + 3 = 6
2 x 1.5 + 3 = 6
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Question Completion:a. What is the distance from Chenoa's house to the coffee shop? Write your answer as a decimal, if necessary.
Find the area of the composite figure.
So in fig 1 :
L = 14m W = 9mArea = L × WArea = 9 × 14Area = 126 m²In fig 2 :
L = 7mW = 16 - 9 = 7mArea= L × WArea = 7 × 7Area =49m² TA = 126 + 49TA = 175 m²The area of the composite figure is,
A = 175 m²
We have to given that,
A composite figure is shown.
In first part,
Lenght (L) = 14m
Width (W) = 9m
Hence, We get;
Area = L × W
Area = 9 × 14
Area = 126 m²
For second part,
Lenght (L) = 7m
Width (w) = 16 - 9 = 7m
Hence, We get;
Area= L × W
Area = 7 × 7
Area =49m²
So, We can formulate;
The area of the composite figure is,
A = 126 + 49
A = 175 m²
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You have $15.00 to buy watermelon for a picnic. A watermelon costs $3.75. Which inequality represents the number 3 of watermelons you can
buy? PLEASE HELP !!!
A researcher compared the heights and shoe sizes for 50 men, selected at random. The equation shown describes a line of best fit for the data, where x is the shoe size and y is the height, in inches. Based on the equation, what is the approximate shoe size for a man having a height of 60 inches
Answer:
7 1/2
Step-by-step explanation:
Convert 7 1/2 to a decimal then multiply it by 1.6 to get 12.00 then add 48 to get 60.
P.S i got it right
what is the area of the square if it’s 15 by 15
Answer:
225 is the answer
15 times 15
Step-by-step explanation:
1 1/3 x 1 x 2 1/3 HELP ME
Answer:
22/9
Step-by-step explanation:
sorry it is kinda messy in the pic but the answer is 22/9
Factorise the following expression :
Answer:
(i) \(5x(x - 5y)\)
(iv) 12a²b(3-5c)
Step-by-step explanation:
(i) \(5 {x}^{2} - 25xy\)
\(5 {x}^{2} - 25xy = (x - y)\)
\(5x(x - 5y)\)
(iv) 36a²b - 60a²bc
12a²b(3) - 60a²bc
12a²b(3) + 12a²b(-5c)
12a²b(3-5c)
Hope it is helpful....Karen has 20 pieces of leather for making handbags. Each piece is 9 6/8 inches long.How many inches of leather does she have altogether? Write the final answer in lowestterms.
Answer:
She has 195 inches of leather
Explanation:
Here, we want to get the entire length of the 20 pieces
From the question, there are 20 pieces, each of 9 6/8 inches length
The length of the 20 is simply the product of the length of 1 of the piece and the total number of pieces
Mathematically, we have this as:
9 6/8 * 20 =
\(\frac{78}{8}\times20\text{ = 195 inches}\)1. Janice donates 100 items of clothing to the Salvation Army. There were four times as many shirts as there were pants. How many shirts and pants did Janice donate? Write and solve a system of equations to answer the question.
2. Amy and Mike have 56 video games between them. Amy has 8 more games than Mike. How many games does each of them have? Write and solve a system of equations to answer the question.
Janice donated 20 pants and 80 t-shirts of clothing to the Salvation Army.
What are linear and non-linear functions?A straight line on the coordinate plane is represented by a linear function. As an illustration, the equation y = 3x – 2 depicts a linear function because it is a straight line in the coordinate plane.
Any function whose graph is not a straight line is said to be nonlinear. Any curve other than a straight line can be a graph of it.
An example of a non-linear function is a quadratic function.
Given, Janice donates 100 items of clothing to the Salvation Army and the number of t-shirts were 4 times the number of pants.
Therefore, If the number of pants is 'x' then the number of t-shirts are '4x'.
So, x + 4x = 100.
5x = 100.
x = 20.
So, The number of pants are 20 and the number of t-shirts are 80.
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which graph represents y=^3√x
The graph attached is the graph representing the cube root function y = ∛x.
The opposite of the cubic function is the cube root function. We are aware that the parent cubic function is growing, one-one, and onto, and that its form is f(x) = x³. It is a bijection as a result. As a result, its inverse function, the cube root function, is also a bijection and has the form f(x) = ∛x. The parent cubic function and parent cube root functions have the same graphs because we know that a function and its inverse function are symmetric about the line y = x.
In the question, we are asked to show the graph of y = ∛x.
Taking the function of the cube root function as y, we get f(x) = y = ∛x.
Thus, we can show the graph of the cube root function in the attached image.
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The graph of a function g is shown below.Find g (0).g(0) = DХ6
Given:
Graph is given.
\(g(0)=-1\)Could someone explain this to me ??
========================================================
Explanation:
Refer to the diagram below. I'm using the points A,B,C,D,E to help label the triangles, and to label the angles as well.
For now, let's focus on triangle DEC.
The top most angle is given as D = 65. Note how the angles D and E are opposite the congruent lines (marked with the red single tickmarks). This means that angles D and E are congruent to one another. So E = 65 as well. This is shown in the diagram below.
For now we don't know what angle C is, so we'll call it y. More specifically, we'll make y the measure of angle DCE.
For any triangle, the three angles always add to 180
y+65+65 = 180
y+130 = 180
y = 180-130
y = 50
So angle DCE is 50 degrees.
-------------------------------
Now we move onto triangle ABC.
Because angles DCE and ACB are vertical angles, this makes angle ACB 50 degrees also. Effectively, anywhere you see a 'y' in the diagram below, replace it with 50.
So triangle ABC has the three angles y = 50, y = 50 and 7x-4
We can solve for x like so
y+y+(7x-4) = 180
50+50+(7x-4) = 180
7x+96 = 180
7x = 180-96
7x = 84
x = 84/7
x = 12
This points to choice C as the final answer.
Four friends have $525 that they want to share equally. To start, they divide the money so that each friend gets a $100 bill. What is the most useful next step?
If four friends have $525 that they want to share equally and they divide the money so that each friend gets a $100 bill, then next step will be divide the remaining money so that each friend gets a $31.25
Total money the have = $525
they divide the money so that each friend gets a $100 bill
The amount of money they split equally = 4×100
= $400
Remaining money = 525-400
= $125
Split the remaining money into 4 = 125/4
= $31.25
Hence, If four friends have $525 that they want to share equally and they divide the money so that each friend gets a $100 bill, then next step will be divide the remaining money equally so that each friend gets a $31.25
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Complete the sentence below.
The quantity b² - 4ac is called the
of a quadratic equation. If it is
...
the equation has no real solution.
less than zero
Step-by-step explanation:
when the discriminant is less than zero, then it has no real solutions. this can be written as
b²-4ac<0 has no real solutions.
For this problem, assume that the committee contains 6 men and 9 women and that three are selected at random for a subcommittee. What is the probability that the subcommittee consists of 2 men and 1 woman, given that it contains both men and women
Answer:
0.3846 = 38.46% probability that the subcommittee consists of 2 men and 1 woman.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
To solve this question, we need to know the combinations formula and conditional probability.
Combinations formula:
\(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.
\(C_{n,x} = \frac{n!}{x!(n-x)!}\)
Conditional Probability
We use the conditional probability formula to solve this question. It is
\(P(B|A) = \frac{P(A \cap B)}{P(A)}\)
In which
P(B|A) is the probability of event B happening, given that A happened.
\(P(A \cap B)\) is the probability of both A and B happening.
P(A) is the probability of A happening.
What is the probability that the subcommittee consists of 2 men and 1 woman, given that it contains both men and women?
Event A: Contains both men and woman
Event B: Consists of two men and 1 woman.
Probability of containing both men and woman:
Desired outcomes:
2 men(from a set of 6) and 1 woman(from a set of 9), or 1 men(from a set of 6) and 2 women(from a set of 9). So
\(D = C_{6,2}*C_{9,1} + C_{6,1}*C_{9,2} = \frac{6!}{2!4!}*\frac{9!}{1!8!} + \frac{6!}{1!5!}*\frac{9!}{2!7!} = 351\)
Total outcomes:
3 people from a set of 6 + 9 = 15. So
\(T = \frac{15!}{3!12!} = 455\)
Probability:
\(P(A) = \frac{D}{T} = \frac{351}{455} = 0.7714\)
Intersection of events A and B:
Intersection between both men and women, and 2 men and 1 woman, is 2 man and 1 women. So
Desired outcomes:
2 men(from a set of 6) and 1 woman(from a set of 9).
\(D = C_{6,2}*C_{9,1} = 135\)
Total outcomes:
3 people from a set of 6 + 9 = 15. So
\(T = \frac{15!}{3!12!} = 455\)
Probability:
\(P(A \cap B) = \frac{D}{T} = \frac{135}{455} = 0.2967\)
Desired probability:
\(P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.2967}{0.7714} = 0.3846\)
0.3846 = 38.46% probability that the subcommittee consists of 2 men and 1 woman.
factorize
x²+17x+6 =????
Answer:
x²+17x+6=xx+17x+6=(17+x)x +6=17+xx+6= 17+x²+6=23+x²
=>x²+17x+6=23+x²
f(x) = x² - 4 and g(x)= x^2 + 1 are sketched 10.1.2 Determine the length of DB .
x⁴ - 8x² + 17 is the function that represents the fog(x).
To find fog(x), we first need to find g(f(x)), which means we need to substitute the expression for f(x) into the expression for g(x):
g(f(x)) = g(x² - 4)
Now, we can substitute the expression for g(x) into the above expression:
g(f(x)) = (x² - 4)² + 1
Expanding the squared term, we get:
g(f(x)) = x⁴ - 8x² + 17
Therefore, fog(x) = g(f(x)) = x⁴ - 8x² + 17.
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Complete question:
f(x) = x² - 4 and g(x)= x^2 + 1 find fog(x).
evaluate the fermi function for an energy KT above the fermi energy. find the temperature at which there is a 1% probability that a state,
Complete Question
Evaluate the Fermi function for an energy kT above the Fermi energy. Find the temperature at which there is a 1% probability that a state, with an energy 0.5 eV above the Fermi energy, will be occupied by an electron.
Answer:
a
The Fermi function for the energy KT is \(F(E_o) = 0.2689\)
b
The temperature is \(T_k = 1261 \ K\)
Step-by-step explanation:
From the question we are told that
The energy considered is \(E = 0.5 eV\)
Generally the Fermi function is mathematically represented as
\(F(E_o) = \frac{1}{e^{\frac{[E_o - E_F]}{KT} } + 1 }\)
Here K is the Boltzmann constant with value \(k = 1.380649 *10^{-23} J/K\)
\(E_F\) is the Fermi energy
\(E_o\) is the initial energy level which is mathematically represented as
\(E_o = E_F + KT\)
So
\(F(E_o) = \frac{1}{e^{\frac{[[E_F + KT] - E_F]}{KT} } + 1}\)
=> \(F(E_o) = \frac{1}{e^{\frac{KT}{KT} } + 1}\)
=> \(F(E_o) = \frac{1}{e^{ 1 } + 1}\)
=> \(F(E_o) = 0.2689\)
Generally the probability that a state, with an energy 0.5 eV above the Fermi energy, will be occupied by an electron is mathematically represented by the Fermi function as
\(F(E_k) = \frac{1}{e^{\frac{[E_k - E_F]}{KT_k} } + 1 } = 0.01\)
Here\(E_k\) is that energy level that is 0.5 ev above the Fermi energy \(E_k = 0.5 eV + E_F\)
=> \(F(E_k) = \frac{1}{e^{\frac{[[0.50 eV + E_F] - E_F]}{KT_k} } + 1 } = 0.01\)
=> \(\frac{1}{e^{\frac{0.50 eV ]}{KT_k} } + 1 } = 0.01\)
=> \(1 = 0.01 * e^{\frac{0.50 eV ]}{KT_k} } + 0.01\)
=> \(0.99 = 0.01 * e^{\frac{0.50 eV ]}{KT_k} }\)
=> \(e^{\frac{0.50 eV ]}{KT_k} } = 99\)
Taking natural log of both sides
=> \(\frac{0.50 eV }{KT_k} } =4.5951\)
=> \(0.50 eV =4.5951 * K * T_k\)
Note eV is electron volt and the equivalence in Joule is \(eV = 1.60 *10^{-19} \ J\)
So
\(0.50 * 1.60 *10^{-19 } =4.5951 * 1.380649 *10^{-23} * T_k\)
=> \(T_k = 1261 \ K\)
You want to convert 50°F to degrees Celsius. Solve the formula for C, and then use it to convert the temperature. What is the correct formula and conversion?
9514 1404 393
Answer:
C = (5/9)(F -32)50°F ⇒ 10°CStep-by-step explanation:
Starting with the formula for degrees Fahrenheit, we can solve for degrees Celsius.
F = 32 +9/5C
F -32 = (9/5)C . . . . . subtract 32
(5/9)(F -32) = C . . . . multiply by the inverse of the coefficient of C
The formula for Celsius temperature from Fahrenheit temperature is ...
C = (5/9)(F -32)
__
For F = 50, the corresponding Celsius temperature is ...
C = (5/9)(50 -32) = (5/9)(18) = 10 . . . degrees Celsius
Multiply 3hrs 30mins by 4
Answer:
14 hours
Step-by-step explanation:
100 pts!!
Thanh rents a car. He has a fixed rate of $49.00 weekly, pays $14.00 per week for the optional insurance, and he spends $12.00 weekly on gas. What will Thanh's cost be per month (four weeks)?
Thanh's cost per month (four weeks) will be $300.00.The given fixed rate for Thanh is $49.00 per week. Thanh also pays $14.00 per week for the optional insurance and $12.00 weekly on gas.
To find Thanh's cost per month (four weeks), we need to multiply his weekly cost by 4.We can use the formula below to calculate Thanh's monthly cost.
Total weekly cost = Fixed rate + Insurance cost + Gas cost
Total weekly cost = $49.00 + $14.00 + $12.00
Total weekly cost = $75.00
The cost for Thanh per month (four weeks) = Total weekly cost × 4
Cost for Thanh per month (four weeks) = $75.00 × 4
Cost for Thanh per month (four weeks) = $300.00
Therefore, Thanh's cost per month (four weeks) will be $300.00.
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HELP ASAPPP! I WILL GIVE BRAINLIEST!
PICTURE BELOW.
PLEASE DO NOT PUT ANY NONE RELATED ANSWERS OR YOU WILL BE REPORTED !!
Answer:
Polygon A: A, D, E
Polygon B: F, G, H
Polygon C: K, L, M, N, O
Polygon D: S, T
Step-by-step explanation:
What is the area of this figure?
Enter your answer in the box.
___in^2
Answer:
400
Step-by-step explanation:
8*20/2+16*20=400.
I NEED HELP I AM STUPID SO I DONT GET THIS HERE IS THE QUISTION 4-x-6(x+5)=15 HE ALSO SAID THIS - Students will determine whether an equation has 0, Infinite, or 1 solution, and if 1, find it. I ADDED A SCREEN SHOT OF QUISTION PLS HELP ME OR I AM FAILING THIS CLASS
Answer:
im pretty sure it has two real solutions
Step-by-step explanation:
1. simplify the equation given
(4x - 6)(x + 5) = 15
4x^2 + 20x - 6x - 30 = 15
4x^2 + 14x - 45 = 0
2. find the discriminant (b^2 - 4ac); (a = 4, b = 14, c = -45)
14^2 - (4 x 4 x -45)
196 - (-720)
916
the discriminant is positive, so this equation has 2 real solutions
to find the solutions, factor the bolded equation (if you need help factoring, let me know!)
A low calorie dinner has 480 calories in an 9 ounce serving. What is the unit rate in simplest form?
Answer: 53.333333, 53 1/3
Step-by-step explanation:
The unit rate in this question means how many calories for one ounce. Thus, you can simply divide 480 by 9 to get 53.3333333
Answer:
53.33 caloriesStep-by-step explanation:
Calories in a low calorie dinner = 480 calories
Serving at one time = 9 ounce
then,
Unit rate = Amount of calories in one serving
So,
Amount of calorie in 9 serving = 480
Amount of calorie in 1 serving = 480/9
In simple form : 160/3
= 53.33 calories
Hope this helps...
Good luck on your assignment..