Answers
Answer:
\(\displaystyle f(x)=4\cdot\left(\frac{1}{2}\right)^x\)
Step-by-step explanation:
Exponential Function
The exponential function can be written with the general equation:
\(f(x)=A\cdot r^x\)
Where A is the value when x=0 and r>0 is the ratio. If r is greater than 1, the function is increasing, if r is less than 1, the function is decreasing.
The table shows the relation between values of x and values of the function y. Note that as x increases (one by one), y decreases with a ratio of 1/2. Only the last two choices have ratios of r=1/2. We only have to test which one of them has the correct value of y=4 when x=0.
Substituting in the third function:
\(\displaystyle f(x)=4\cdot\left(\frac{1}{2}\right)^x\)
\(\displaystyle f(0)=4\cdot\left(\frac{1}{2}\right)^0\)
\(f(0) = 4\)
This gives the correct value of f(0)=4.
Substituting in the fourth function:
\(\displaystyle f(x)=\frac{1}{2}\cdot\left(\frac{1}{2}\right)^x\)
\(\displaystyle f(0)=\frac{1}{2}\cdot\left(\frac{1}{2}\right)^0\)
\(f(0) = \frac{1}{2}\)
This choice is wrong
Correct choice:
\(\boxed{\displaystyle f(x)=4\cdot\left(\frac{1}{2}\right)^x}\)
Related Questions
Please help me! Thanks in advance
Answers
In a hypothesis testing context, before examining the data, one should.
Answers
In a hypothesis testing context, before examining the data, one should establish a null hypothesis and an alternative hypothesis.
Before conducting any analysis or collecting data, it is crucial to define the null hypothesis and the alternative hypothesis. The null hypothesis (H₀) represents the assumption of no effect or no difference between groups or variables, while the alternative hypothesis (H₁) represents the claim or hypothesis being tested. These hypotheses help define the question or statement that the researcher wants to investigate.
Formulating the null and alternative hypotheses before examining the data is important to ensure the hypothesis testing process is objective and guided by clear expectations. It helps to establish a framework for statistical analysis and allows for making informed decisions based on the evidence provided by the data.
Additionally, this initial step ensures that the hypothesis testing process remains rigorous and avoids potential biases that may arise from post hoc analyses.
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0.8 divided by 62 please help asap pls
Answers
Answer:
77.5
Step-by-step explanation:
Answer:
77.5
Step-by-step explanation:
Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum.
[infinity]
∑
n = 0
1
(
√
1
7)n
.
Answers
To determine whether the geometric series ∑(n=0 to ∞) (√(1/7))^n is convergent or divergent, we can examine the common ratio (r) of the series.
The given series has a common ratio of (√(1/7)). For a geometric series to be convergent, the absolute value of the common ratio (|r|) must be less than 1.
In this case, |√(1/7)| = √(1/7) ≈ 0.377, which is less than 1. Therefore, the geometric series is convergent.
To find the sum of the geometric series, we can use the formula for the sum of an infinite geometric series:
Sum = a / (1 - r),
where 'a' is the first term and 'r' is the common ratio.
In this case, the first term 'a' is (√(1/7))^0 = 1, and the common ratio 'r' is √(1/7).
Substituting these values into the formula, we have:
Sum = 1 / (1 - √(1/7)).
To simplify this expression, we can rationalize the denominator:
Sum = 1 / (1 - √(1/7)) * (1 + √(1/7)) / (1 + √(1/7)).
Multiplying the numerators and the denominators, we get:
Sum = (1 + √(1/7)) / (1 - (1/7)).
Simplifying further:
Sum = (1 + √(1/7)) / (6/7).
Finally, multiplying the numerator by 7, we obtain the sum of the geometric series:
Sum = 7(1 + √(1/7)) / 6.
Therefore, the sum of the given geometric series is 7(1 + √(1/7)) / 6.
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Is the following relation a function?
Need answer now
Answers
If you can draw a vertical line through more than one point on the curve, then it's not a function. In this case, we can draw such a line. The graph is said to have failed the vertical line test.
What this means is that some x inputs lead to more than one y outputs. A function is only possible if any x input leads to exactly one y output. The x input must be in the domain.
Answer:
It is not a function.
Step-by-step explanation:
A relation's inputs are not repeated in a function.
Since the graph fails the vertical line test, it is not a function.
See picture.
Hope this helps.
what is 8.275 rounded to the nearest hundredth.
Answers
Answer:
8.3
Step-by-step explanation:
Answer:
8.28
Step-by-step explanation:
Find the number in the hundredth place 7 and look one place to the right for the rounding digit 5 . Round up if this number is greater than or equal to 5 and round down if it is less than 5 .
Pls rate brainiest
HELP PLEASE :( I WOULD APPRECIATE SO MUCH
How many solutions does the system of linear equations represented in the graph below have?
Answers
Answer:
It has no solution because the two lines would never meet since they have the same slope of -3
Answer:
No solution because the lines are parallel
Can someone please help
Answers
Answer:
b. Complementary gas masks
Step-by-step explanation:
Adjacent means that the two angles are right next to each other and touching. The two angels in the photo are touching. Supplementary means that the two angels can for together to make a 180 degree line. The two angels in the photo make a 180 degree line. Complementary means that the two angels make a 90 degree angel. Since the two angels already make a 180 degree angels then, they cannot make a 90 degree angel. The question is asking for what it is not so, complements would be the answer.
Consider the following small open economy: с = 200+ 0.69Y I = 80 - 1,000r G = 20 NX = 850.09Ye e = 90 M = 115 YL = 0.5Y - 200r Y = 300 C is consumption spending, I is investment spending, r is the interest rate, G is govern- ment spending, NX is net exports, e is the nominal exchange rate, M is money supply, YL is demand for money, and Y is long-run output. In this economy, the interest rate does not deviate from the foreign interest rate. The price level is fixed and set to one. Note that, in this problem, a decrease in e is synonymous with a depreciation of the nominal exchange rate. 1. Assuming that the economy is in equilibrium, find the value of the interest rate. (6 points) 2. Going from the equilibrium found in Question (1), assuming fixed nominal exchange rates, what is the effect on domestic output if the foreign interest rate increases by 0.05? (6 points) (a) What is the size of the nominal money supply in the new short run equilibrium? (6 points) 3. Going from the equilibrium found in Question (1), assuming flexible exchange rates, what is the effect on domestic output if the foreign interest rate increases by 0.05? (6 points) (a) What is the value of the real exchange rate in the new equilibrium? (6 points)
Answers
The interest rate is 10.89%
1. Given,С = 200+ 0.69YI = 80 - 1,000rG = 20NX = 850.09ee = 90M = 115YL = 0.5Y - 200rY = 300Using the equation for National Saving, we get,National Saving = Investment + Government Saving + Net exports(S – I) + (T – G) + (X – M) = 0T = 0, hence (S – I) + (X – M) = 0(1 – t)Y – C – (I + G) + NX = 0Where t = 0, we get,0.5Y – 200r – 200 – 69/100Y + 80 – 850.09e = 0.5Y – 200r – 970.09e – 120 = 0.5Y – 200r – 970.09e – 120 = 0Therefore, Y = 325.0454 - 0.5r + 4.851eThis is the equation for the IS curve.On the other hand, the equation for the LM curve is given by,Ms / P = YL(i)115 / 1 = 0.5Y - 200rTherefore, Y = 400 + 400rThis is the equation for the LM curve.The interest rate is given by the point of intersection of the two curves. Equating Y from both equations, we get,325.0454 - 0.5r + 4.851e = 400 + 400rSolving the above equation for r, we get r = 0.1089 or 10.89%..
The size of the nominal money supply in the new short-run equilibrium is 121.07.
2. From the equilibrium found in Question (1), if the foreign interest rate increases by 0.05, the domestic output will change in two ways, depending on the flexibility of the nominal exchange rate.Flexible Exchange Rates:In this case, the nominal exchange rate will depreciate (e decreases). This will increase net exports and shift the IS curve to the right. The new equilibrium will be at a higher level of output.Real exchange rate will fall.Increase in output will be higher compared to the fixed exchange rate case.Fixed Exchange Rates:In this case, the nominal exchange rate will remain constant. Therefore, there will be no effect on net exports.IS curve will not shift.Real exchange rate will remain unchanged.Increase in output will be less compared to the flexible exchange rate case.The nominal money supply in the new short-run equilibrium will change in the case of Fixed Exchange Rates. In the fixed exchange rate case, the domestic interest rate will increase, leading to an inflow of capital. This will increase the money supply and the LM curve will shift downwards until it intersects the IS curve at the new equilibrium point.
Real exchange rate will remain unchanged.
3. From the equilibrium found in Question (1), if the foreign interest rate increases by 0.05, the domestic output will change in two ways, depending on the flexibility of the nominal exchange rate. Flexible Exchange Rates :In this case, the nominal exchange rate will depreciate (e decreases). This will increase net exports and shift the IS curve to the right. The new equilibrium will be at a higher level of output .Real exchange rate will fall. Value of the real exchange rate in the new equilibrium is 0.891.Fixed Exchange Rates: In this case, the nominal exchange rate will remain constant. Therefore, there will be no effect on net exports.IS curve will not shift.
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Which sentence uses a gerund as the subject of a sentence?
A) I am waiting for the delivery man to come.
B) Waiting for a package can be so agonizing.
C) The patient woke up on the operating talle.
Elimin
D) The economy has been booming since we sold our stock
Answers
B) Waiting for a package can be so agonizing is the sentence which uses a gerund as the subject of a sentence.
A gerund is a verb form that functions as a noun, and in this sentence, "waiting" is the gerund acting as the subject of the sentence. The sentence is expressing the idea that the act of waiting for a package is a frustrating experience.
Option A) "I am waiting for the delivery man to come," uses the present participle "waiting" as a verb in the present continuous tense. Option C) "The patient woke up on the operating table," uses the noun "patient" as the subject of the sentence. Option D) "The economy has been booming since we sold our stock," uses the noun phrase "the economy" as the subject of the sentence.
Knowing how to identify gerunds and their role in a sentence can help improve one's writing skills and clarity of expression.
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worth 95 pointsss
pls answeer
Answers
Answer:
This is a good card game because the odds are like 1/4 chances.
Step-by-step explanation:
PLEASE HELPPP
AKA JASMINE IS THE BEST PUR
will give brainliest
Answers
Answer:
45/2
Step-by-step explanation:
ashjasdhkjasdha hello there
There are two people and there are 45 minutes to shoot the ball. As both people shoot for the exact same time, you have to divide 45 by 2 to split the time into two equal halves. Thus, the answer is 45 divided by 2, or just 45/2.
Consider the wave packet: ψ(x)=[ 2πa 2
1
] 1/2
exp[− 4a 2
(x−⟨x⟩) 2
+i ℏ
px
]. Calculate the uncertainties ⟨Δx 2
⟩=⟨( x
^
−⟨x⟩) 2
⟩ and ⟨Δp 2
⟩=⟨( p
^
−⟨p⟩) 2
⟩, where ⟨ A
^
⟩ denotes the expectation value ⟨ψ∣ A
^
∣ψ⟩ of the observable A
^
on the state ∣ψ>.
Answers
The uncertainties ⟨Δx^2⟩ and ⟨Δp^2⟩ are given by the expressions ⟨Δx^2⟩ = a^2/2 and ⟨Δp^2⟩ = (ℏ^2)/(8a^2).
To calculate the uncertainties ⟨Δx^2⟩ and ⟨Δp^2⟩ for the given wave packet, we need to find the expectation values of the observables (x^ - ⟨x⟩)^2 and (p^ - ⟨p⟩)^2, respectively.
The wave packet is represented by the function ψ(x) = [2πa^2]^(1/2) exp[-4a^2(x - ⟨x⟩)^2 + iℏpx]. Here, a is a constant, ⟨x⟩ represents the expectation value of x, and p is the momentum operator.
To find ⟨Δx^2⟩, we calculate the expectation value of (x^ - ⟨x⟩)^2 with respect to ψ(x). By integrating (x - ⟨x⟩)^2 multiplied by the squared magnitude of the wave packet over all x values, we obtain the result ⟨Δx^2⟩ = a^2/2.
Similarly, to find ⟨Δp^2⟩, we calculate the expectation value of (p^ - ⟨p⟩)^2 with respect to ψ(x). Since p is the momentum operator, its expectation value is ⟨p⟩ = 0 for the given wave packet. By integrating (p^ - 0)^2 multiplied by the squared magnitude of the wave packet over all x values, we obtain the result ⟨Δp^2⟩ = (ℏ^2)/(8a^2).
Therefore, the uncertainties ⟨Δx^2⟩ and ⟨Δp^2⟩ are given by the expressions ⟨Δx^2⟩ = a^2/2 and ⟨Δp^2⟩ = (ℏ^2)/(8a^2).
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Warning
There is a checkbox at the bottom of the exam form that you MUST check prior to submitting this exam. Failure to do so may cause your work to
Question 1 (Multiple Choice Worth 1 points)
(08.07 MC)
PLEASE HLEP
The quadratic function f(x) has roots of 4 and -6, and it passes through the point (1, 21). What is the vertex form of the equation f f(x)?
a f(x) = -(x-1)² + 25
b f(x) = -(x + 1)2 +25
c f(x)=(x-1)2 +25
d f(x) = (x + 1)²-25
Answers
The vertex form of the equation f f(x) is: B. f(x) = −(x + 1)² + 25.
What is the vertex form of a quadratic equation?In this exercise, you are required to determine the vertex form of a quadratic function h(x) that is written in standard form. Mathematically, the vertex form of a quadratic equation is given by this formula:
f(x) = a(x - h)² + k
Where:
h and k represents the vertex of the graph.a represents the leading coefficient.Since the quadratic function f(x) has roots of 4 and -6, and it passes through the point (1, 21), the leading coefficient can be determined as follows;
f(x) = a(x + 6)(x - 4)
f(x) = a(x² + 2x - 24).
21 = a(1 + 2 - 24)
-21a = 21
a = -1.
For the x-coordinate of the vertex, we have:
x = -b/2a = 2/-2 = -1.
For the y-coordinate of the vertex, we have:
y = -(b² - 4ac)/4a
y = -((-2)² - 4(-1)(24))/-4
y = 25.
Therefore, the vertex form of the quadratic function is given by:
f(x) = a(x - h)² + k
f(x) = −(x + 1)² + 25
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Simplify. 4 2/5 x 3 = ?
Answers
Answer:
66/5 or 13.2
Step-by-step explanation:
..........
A recipe for 15 bran muffins calls for 1 cup of flour. The number of muffins that can be made varies directly with the amount of flour used. There are 3 2/3 cups of flour available. How many muffins can be made?
Answers
Why are Trig ratios only for right triangles?
Answers
For Trigonometric functions to work we need a hypotenuse, which we can only get in right triangles.
What are Trigonometric functions?
The trigonometric functions in mathematics are real functions that connect the right-angled triangle's angle to the ratios of its two side lengths. They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.
Here,
We have to find out why trigonometric ratios are used only for right triangles.
We concluded that when we are dealing with triangles other than right triangles, the solution is to draw a perpendicular line to create right triangles. For Trigonometric functions to work we need a hypotenuse, which we can only get in right triangles.
Hence, for Trigonometric functions to work we need a hypotenuse, which we can only get in right triangles.
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explosive devices used in mining operations produce nearly circular craters when detonated. the radii of these craters are exponentially distributed with mean 10 feet. find the mean and variance of the areas produced by these explosive devices.
Answers
The mean and the variance of the areas produced by these explosive devices is 314
Variance:
In statistics, variance refers a measure of dispersion that takes into account the spread of all data points in a data set.
Given,
Here explosive devices used in mining operations produce nearly circular craters when detonated. the radii of these craters are exponentially distributed with mean 10 feet.
Now, we need to find the mean and variance of the areas produced by these explosive devices.
In order to find the means and variance we have to use the formula ,
A = πr²
Here the value of r is 10,
Then the value of A is calculated as,
=> A = π(10)²
=> A = π x 100
We know that the value of π = 3.14, then the value of A is,
=> A = 3.14 x 100
=> A = 314.
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Does this shape belong in a group of shapes that have more than one
perpendicular sides?
Use the drop-down menus to explain your answer.
Answers
Yes, this shape belong in a group of shapes that have more than one perpendicular sides because its sides meet at a right angle.
What are perpendicular lines?In Mathematics and Geometry, perpendicular lines can be defined as two (2) lines that intersect or meet each other at an angle of 90° (right angles) as shown in the image (see attachment) attached below.
However, it should be noted that it is not all intersecting lines that are perpendicular to each other because the lines may intersect at different angles other than 90 degrees (90°).
By critically observing the geometric shape, we can reasonably infer and logically deduce that it has more than one perpendicular sides.
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divide 101011 from 1101 in binary
Answers
Answer:
11
Step-by-step explanation:
\(101011_{2 = } 43_{10} \\ 1101_{2} = 13_{10} \\ \frac{43}{13} =3.3076923076923 \\ 3.3076923076923_{10} = 11_{2}\)
Qué significa a^2 en matemáticas es la mi trabajo
Answers
In mathematics, "\(a^2\)" denotes the square of a number or variable "a." It is calculated by multiplying "a" by itself.
How to illustrate with an example4For example, if "a" is 5, then a^2 would be 5*5, which equals 25. When "a" represents a positive number, its square is always positive.
If "a" is negative, its square is still positive since a negative multiplied by a negative results in a positive.
In geometrical terms, if "a" represents the length of the side of a square, then a^2 represents the area of that square. This notation is part of the general concept of exponentiation.
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The Question in English
What does a^2 mean in mathematics
What is the image of the point (-9, 1) after a rotation of 90° counterclockwise about
the origin?
Answers
Answer:
(- 1, - 9 )
Step-by-step explanation:
Under a counterclockwise rotation about the origin of 90°
a point (x, y ) → (- y, x ) , so
(- 9, 1 ) → (- 1, - 9 )
The image of the point (-9, 1) after a rotation of 90° counterclockwise about the origin is (1, 9).
What is rotation rule of 90°?Here are the rotation rules: 90° clockwise rotation: (x, y) becomes (y, -x) 90° counterclockwise rotation: (x, y) becomes (-y, x) 180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y).
The given coordinate point is (-9, 1).
Rule: (x, y)→(y, -x)
The image of the point (-9, 1) is
(-9, 1)→(1, 9)
Therefore, the image of the point (-9, 1) after a rotation of 90° counterclockwise about the origin is (1, 9).
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hi again :) it's me again
Answers
Answer:
Heyyy
Step-by-step explanation:
f(n) = (1/2)n5 - 100n3 + 3n - 1. prove that f = θ(n5)
Answers
We have proven that\(f(n) = (1/2)n^5 - 100n^3 + 3n - 1 is θ(n^5).\)
To prove that\(f(n) = (1/2)n^5 - 100n^3 + 3n - 1\)is θ(n^5), we need to show that there exist constants c1, c2, and n0 such that:
\(c1 * n^5 ≤ f(n) ≤ c2 * n^5 for all n ≥ n0.\)Let's analyze the given function:
\(f(n) = (1/2)n^5 - 100n^3 + 3n - 1\)
We can see that the highest order term is (1/2)n^5. As n grows large, the other terms (100n^3, 3n, and 1) become insignificant compared to the n^5 term. Therefore, we can choose the constants c1 and c2 such that they satisfy the inequality:
c1 = 1/2 and c2 = 1.
Now, let's consider n ≥ n0 = 1:\(f(n) = (1/2)n^5 - 100n^3 + 3n - 1 is θ(n^5).\)
\(c1 * n^5 = (1/2)n^5c2 * n^5 = n^5\)
As n grows large, we can see that:
\((1/2)n^5 ≤ (1/2)n^5 - 100n^3 + 3n - 1 ≤ n^5\)
Thus, we have proven that\(f(n) = (1/2)n^5 - 100n^3 + 3n - 1 is θ(n^5).\)
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The picturegram shows information about CDs sold in a shop.
1 . How manny CDs were sold on Wednesday | Key = 3 |
2. How manny more CDs were sold on Thursday than Wednesday?
**If you know the answer let me know!**
Answers
Answer:
i believe number 1 is 18 and number 2 is 9.
Step-by-step explanation:
if one full circle represents 6 CDs then on wednesday 18 Cds were sold because 6+6+6=18 and on thursday they sold 9 more Cds than on wednesday because they sold 6+6+6+6+3 which equals 9.
One number exceeds another by 3. One third of their sum is 5 less than the smaller number. Find the numbers
Answers
Let the numbers be x and x + 3
(x + x + 3) / 3 = 5
(2x + 3) / 3 = 5
2x + 3 = 5 × 3
2x + 3 = 15
2x = 15 - 3
2x = 12
2x / 2 = 12 / 2
x = 6
Recall that the numbers are x and x + 3
Therefore
number 1 = x
number 1 = 6
and
number 2 = x + 3
number 2 = 6 + 3
number 2 = 9
Answer: The numbers are 6 and 9
Casho spends a winter day recording the temperature once every three hours for science class. At 9 am, the temperature was -10.4°F. Between 9 am and noon, the temperature rose 9.5°F. Between noon and 3 pm, the temperature went down 10°F. Between 3 pm and 6 pm, the temperature went down 18.6°F. What was the temperature at 6 pm?
Answers
The temperature at 6pm is -29.5 °F.
What is changes in temperature ?The rise in temperature serves as a visual representation of how rapidly the temperature changes over time. Any period of time, such as from one day to the next or from one year to the next, could be taken into account. To determine the temperature increase, you simply need to use simple subtraction.
Here , The temperature at 9 am = -10.4 °F
Between 9 am and noon, the temperature rose 9.5°F.
= -10.4 + 9.5
= -0.9 °F
Between noon and 3pm the temperature went down 10°F
= -0.9 F - 10°F
= -10.9°F
Now again the temperature went down 18.6°F then,
= -10.9°F - 18.6 °F
= -29.5 °F
Hence, the temperature at 6pm is -29.5 °F.
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Airline passengers pay $439 to fly to California. For this price, customers may check 2 pieces of luggage. There is a fee of $25 for each additional piece of luggage a passenger wants to check. Which function can be used to find the amount in dollars a passenger has to pay to fly with p pieces of luggage, where p >2
Answers
Answer:
G. \( C = 25(p - 2) + 439 \)
Step-by-step explanation:
Amount paid by customer to fly to California if carrying 2 pieces or less than 2 pieces of luggage for which they won't be charged for = $439
Fee for additional luggage = $25
Fee for additional luggage if an individual carries p luggages = 25(p - 2)
Total amount (C) if p pieces of luggage were carried by a customer travelling = fee for additional p pieces of luggage + $439
The function for this would be:
\( C = 25(p - 2) + 439 \)
solve p/10=2
a 12
b 20
c 8
d 5
Answers
Hi,
p/10 = 2
p = 10 * 2 = 20.
Consider the following system of two equations.
{y=−8x+10
y=x−8
What are the coordinates (x,y) of the solution to the system of equations?
Enter the coordinates in the space provided.