The exponential equation of the given statement will be equal to, 1262 ×[tex](2)^x[/tex].
What is an equation?Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.
This relationship is illustrated by the left and right expressions being equal. The left-hand side equals the right-hand side is a basic, straightforward equation.
As per the given information in the question,
Total number of downloads initially = 1,262
Let the number of months be x.
Then, the equation will be,
y = 1262[tex](2)^x[/tex]
Here, y is the total number of songs.
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Find −1/4(−8.6) . Write your answer as a decimal to the nearest hundredth.
Answer:
2.15
Step-by-step explanation:
I will assume that "−1/4(−8.6)" is telling us to multiply (-8.6) times -(1/4):
(-1/4)*(-8.6)
= (8.6/4)
= 2.15
Find the distance between the points (0,9) and (6,1).
Write your answer as a whole number or a fully simplified radical expression. Do not round.
______units
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{0}~,~\stackrel{y_1}{9})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{1})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(~~6 - 0~~)^2 + (~~1 - 9~~)^2} \implies d=\sqrt{(6 +0)^2 + (1 -9)^2} \\\\\\ d=\sqrt{( 6 )^2 + ( -8 )^2} \implies d=\sqrt{ 36 + 64 } \implies d=\sqrt{ 100 }\implies d=10[/tex]
to properly examine the effect of a categorical independent variable in a multiple linear regression model we use an interaction term. group of answer choices true false
to properly examine the effect of a categorical independent variable in a multiple linear regression model we use an interaction term then it is a true statement
we have given that the by which method we use the different levels of a qualitative independent variable and we have to explain about it.
So, For his purpose, we know that the
A dummy variable is a variable that takes values of 0 and 1, where the values indicate the presence or absence of something.
And in the multiple regression method there are a lot of different variables which are used for a qualitative and for this a variable is used which is called the dummy variables.
By this variables we show the analysis between the given data. it gives the output in the 0 and 1 numbers.
So, For the levels of qualitative, the variable called dummy variables is used in the multiple regression method.
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What is the height and area of the triangle below?
Answer:
height: 27 area: 176
Step-by-step explanation:
If the toss of a coin comes down heads, you win two dollars. If it comes down tails, you lose fifty cents. How much would you expect to gain after 16 tosses (in $ dollars)? $______.
The expected gain after 16 tosses of the coin is $400.
State the term equally likely events?Equally likely denotes the probability that each experiment's result will occur. For instance, if you throw a fair, six-sided die, any of the faces (1, 2, 3, 4, 5, or 6) has the same chance of coming up. A fair coin has an equal chance of landing on its head (H) or tail (T).Let x stand in for your entire savings.
There is a 0.5 likelihood of heads and a 0.5 possibility of tails. (equally likely events).
The value of accepting this offer is 1.5. The formula is as follows:
2 heads.
0.5 = P(Heads)
Value anticipated if the coin came out heads: 2x*0.5 = x
Plus
(1 - 0.5)x = 0.5x for tails.
0.5 = P(Tails)
Value anticipated if the coin came up tails: 0.5x*0.5 = 0.25x
Total projected value is equal to 1.25x.
For x = $20
Thus,
Amount = 1.25(20) = $25.
Thus, for the 16 tosses = $25 x 16 = $400.
Therefore, the expected gain after 16 tosses of the coin is $400.
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The amount of a sample remaining after t days is given by the equation P(t)- A
(9) *
the sample and h is the half-life, in days, of the substance. A sample contains 18% of its original amount of Radon-
222. The half-life of Radon-222 is about 3.8 days. Which is the best estimate for the age of the sample?
O 1.5 days
O 2.5 days
O 9.4 days
O 21.1 days
Mark this and return
Save and Exit
where A is the initial amount of
4
Next
Submit
The best estimate for the age of the sample is; 9.4 days
How to solve Exponential decay functions?We are told that;
The amount of a sample remaining after t days is given by the equation; P(t) = A(¹/₂)^(t/h)
Where;
A is the initial amount of the sample.
h is the half-life, in days, of the substance
The equation is:
P(t) = A(¹/₂)^(t/h)
If a sample contains 18% of the original amount of Radon - 222 and h = 3.8, then we have;
0.18 * A = A * (0.5)^(t/3.8)
divide both sides of the equation by A to get;
0.18 = ( 0.5 )^(t/3.8)
(t/3.8)log 0.5 = log 0.18
(t/3.8) = log 0.18/log 0.5
t/3.8 = 2.47
t = 3.8 * 2.47 ≈ 9.4 days
This is the best estimate for the age of the sample
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The complete question is;
The amount of a sample remaining after t days is given by the equation P(t)=A(1/2)^(t/h), where A is the initial amount of the sample and h is the half-life, in days, of the substance. A sample contains 18% of its original amount of Radon-222. The half-life of Radon-222 is about 3.8 days. Which is the best estimate for the age of the sample?
Answer:
It's C
Step-by-step explanation:
1/2(3x-2/3)+6 less or equal to x+5
The inequality which represents the given phrase is 1/2(3x - 2/3) + 6 ≤ x+5 and the solution are x ≤ -4/3.
What is inequality?A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.
In other words, inequality is just the opposite of equality for example 2 =2 then it is equal but if I say 3 =6 then it is wrong the correct expression is 3 < 6.
As per the given,
1/2(3x - 2/3) + 6 ≤ x+5
3/2 x - 1/3 + 6 ≤ x+5
3/2 x + 17/3 - x ≤ 5
x/2 ≤ -2/3
x ≤ -4/3
Hence "The inequality 1/2(3x - 2/3) + 6 ≤ x+5 represents the provided sentence, and the answer is x ≤ -4/3.".
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Translate
What are the x-intercepts of the quadratic function shown?
A
B
C
(3.-4) and (-5-4)
(1.0) and (-3,0)
(0, 1) and (0-3)
D (-1, -2)
Search
A
Answer:
(1,0) and (-3,0)
Step-by-step explanation:
Solve the following quadratic by
completing the square.
y = x² - 6x + 7
x = [?] + √[]
Steps to Remember
1. Set the y-value equal to O.
2. Remove the constant term from both sides using the
opposite operation.
3. Add (2)² to both sides (to complete the square).
4. Factor (write as a perfect square).
5. Solve for x like normal.
The solution to the given quadratic equation by completing the square is; x = 3 ± √2
How to solve quadratic equation by completing the square?We are given the quadratic equation;
y = x² - 6x + 7
1) Set the value of y to zero to get;
x² - 6x + 7 = 0
2) Remove the constant term from both sides using the opposite operation to get;
x² - 6x = -7
3) Take half of the x term and square it and add to both sides of the equation to get;
x² - 6x + 9 = -7 + 9
4) Rewrite the perfect square on the left to get;
(x - 3)² = 2
5) Take the square root of both sides to get;
x - 3 = ±√2
6) The solution will be;
x = 3 ± √2
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What
property is illustrated in: If ∠A ≅ ∠B, ∠B ≅ ∠C, then ∠A ≅ ∠C.a.
Reflexive Propertyb. Symmetric Propertyc. Transitive Propertyd. Addition
Property
The property illustrated in the statement "If ∠A ≅ ∠B, ∠B ≅ ∠C, then ∠A ≅ ∠C" is the Transitive Property.
This property states that if two elements are related by a certain relationship, and another element is related to the second element by the same relationship, then the first and third elements are related by the same relationship.
In this statement, the relationship is that of congruency, meaning that each angle has the same measure. Therefore, the Transitive Property states that if angle A is congruent to angle B, and angle B is congruent to angle C, then angle A is congruent to angle C.
The other three properties listed do not apply to this statement. The Reflexive Property states that a given element is related to itself by a certain relationship, which does not apply to this statement.
The Symmetric Property states that if two elements are related by a certain relationship, then the two elements are related to each other in the same way, which is not applicable in this statement.
Lastly, the Addition Property states that the sum of two elements related by a certain relationship is related to the two elements by the same relationship, which is not applicable in this statement.
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Q. 10. Prove that the sum of the (interior) angles of a pentagon is 540°.
using geometry**
- Like line segments, ray XY, angles etc
please don't answer with (n-2)180 formula.
answer related to proving by lines and angles
like - <ABC + <BCA + <CAB = 180° etc...
Answer:
Step-by-step explanation:
The answer is that yes it is because a pentagon has three triangles inside it and a triangle is equal to 180 degrees so you times 180 times three and you get 540 degrees so yes that is correct!
A student has some pennies and dimes. All total, he has 21 coins. If he adds them up, he has $1.56. How many dimes does he have?
[Show and explain how you solved this word problem, please.]
Answer:
15 dimes and 6 pennies
what is the probability that washing dishes tonight will take me between 15 and 16 minutes? give your answer accurate to two decimal places.
The probability of washing dishes by me tonight will take between 15 and 16 minutes is 14.29%.
The term "uniform distribution" refers to a type of probability distribution in which the likelihood of each potential result is equal.
Let's consider, the lower limit for this distribution as a and the upper limit for this distribution as b.
The following formula gives the likelihood that we will discover a value for X between c and d,
[tex]P(c\leq X\leq d)=\frac{d-c}{b-a}[/tex]
Given the time it takes me to wash the dishes is 11 minutes and 18 minutes. From this, a = 11 and b = 18.
Then,
[tex]P(15\leq X\leq 16)=\frac{16-15}{18-11}=0.1429=14.29\%[/tex]
The answer is 14.29%.
The complete question is -
The time it takes me to wash the dishes is uniformly distributed between 11 minutes and 18 minutes. What is the probability that washing dishes tonight will take me between 15 and 16 minutes?
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what will it cost to carpet of a rectangular floor measuring 27 feet by 24 feet if the carpet costs $15.8 per square yard
To carpet the rectangular floor, it will cost $1,137.6. The result if obtained by multiplying the area of the carpet by the cost per square yard.
How to calculate the cost of a product?To calculate the cost of a product, multiply the product price for one item by the quantity.
We have a rectangular floor with a dimension of 27 feet by 24 feet. The carpet cost is $15.8 per square yard. Find the total cost to carpet it!
Let's change the unit of length.
27 feet = 27/3 yard = 9 yard24 feet = 24/3 yard = 8 yardThe area of the carpet is
A = 9 yard × 8 yard
A = 72 square yard
The total cost is
C = A × price/square yard
C = 72 × $15.8
C = $1,137.6
Hence, the total cost to carpet the floor is $1,137.6.
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Hannah, Ben, Stephanie, and Brayden bought a gift for their Mom. The total cost of the gift, including tax, was $64.80. Hannah paid $21, Ben paid 1/3 of the cost, Stephanie paid 15% of the cost, and Brayden paid the remaining cost. Who paid the greatest part of the cost?
Answer: Ben paid the most
Step-by-step explanation: Okay, to find the prices of the 4, we need to follow what the problem says. So, we know Hannah paid 21, so we know that is how much she paid. Now, we need to find 1/3 of the total cost ($64.80) So, we do 1/3 divided by $64.80 and get $21.60. For Stephanie, we need to find 15% of $64.80, so we can write it as a proportional relationship, so 15 x $64.80 / 100 is 9.27. (as a decimal) Now, we subtract all of those numbers from the total cost ($64.80) to find Brayden's pay. After I subtracted all of the amounts, I got $12.93. I'll list all the amounts.
Hannah - 21
Ben - 21.60
Stephanie - 9.27
Brayden- 12.93
So, as we see Ben paid the most. I hoped this LONG explanation helped you!
it should be ben.
Hannah paid $21;
ben paid 1/3 of 64.80 and that's $21.6 (64.84÷3);
Stephanie paid 15% of $64.80 and that's $9.72 (15÷100×64.80);
Brayden paid $12.48 [64.80-(21+21.6+9.72)].
hope I helped (btw sorry for any mistake english isnt my forst language)
What is 100-2938? I'm in 5th grade but I want to know if people can explain thoroughly how they got that answer. Please and thank you.
Answer:
-2,838
Step-by-step explanation:
A good way to do this is 2,938-100 which equals 2,838. Then since you know it will be a negative number add the negative sign.
What is the best unit to measure the capacity of a swimming pool.
A) milliliter
B) liter
Answer:
1 liter
Step-by-step explanation:
A milliliter is 1/1000 of a meter; measuring a pool by millimeters wouldn't make sense.
Work out the urface area of thi olid quarter-cylinder. Give your anwer in term of π
The total surface area of a solid quarter-cylinder is 10(13π + 32) cm².
Given:-
The radius of a solid quarter-cylinder = 10 cm.
Height of solid quarter-cylinder = 16 cm.
To calculate the surface area we have a formula:-
Total surface area of solid quarter-cylinder = (TSA of cylinder / 4) + 2(Area of rectangle)= 2πr(h + r)/4 + 2(r * h) = πr(h + r)/2 + 2rh .
Solution:-
r = 10 cm.
h = 16 cm.
So,
→ Area of rectangle so formed = r * h = 10 * 16 = 160 cm².
then,
→ Area of two rectangles so formed = 2 * 160 = 320 cm².
Therefore,
→ Total surface area of solid quarter-cylinder = πr(h + r)/2 + Area of two rectangles.
→ Total surface area of solid quarter-cylinder = π * 10 * (10 + 16) / 2 + 320
→ Total surface area of solid quarter-cylinder = 5π * 26 + 320
→ Total surface area of solid quarter-cylinder = 5(26π + 64)
→ Total surface area of solid quarter-cylinder = 5*2(13π + 32)
→ Total surface area of solid quarter-cylinder = 10(13π + 32) cm².
Hence, the Total surface area of a solid quarter-cylinder is 10(13π + 32) cm².
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How much is 23.98 in cents
Answer:
2398 cents
Step-by-step explanation:
Every dollar equals 100 cents
So 23 times 100 equals 2300, then we add the 98 cents left over from the dollar
Which would be 2398 cents
Which of the following sets of ordered pairs represents a function?
Answer: D
Step-by-step explanation:
A function in a set of ordered pairs cannot have repeating x values
A have a repeated x values of -12
B have a repeated x values of 8
C have a repeated x values of 13
D does not have a repeated x value.
D is the correct answer.
Write the fraction below in its simplest form
5(x+6)5 (x-7) 5 (x+8)
15(x+6)⁹ (x−7)(x−8)
Watch video
Answer:
Step-by-step explanation:
172. Alex the geologist is in the desert, 10 km from the nearest point N on a long, straight
road. Alex's jeep can do 50 kph on the road, and 30 kph in the desert. Find the shortest
time for Alex to reach an oasis that is on the road (a) 20 km from N; (b) 30 km from N.
Shortest time taken for a is 0.666hours and for b is 0.866hours.
How to calculate Shortest time?Take a variable x on the possible road. Evaluate an equation of time in terms of x and find the extrema of the function. To find extrema differentiate the function and equal it to zero. Then find the roots of equation to get the extreme value, which should be the minimum time path.
Calculation:A is initial point
P is oasis
S is intermediate point
Let us assume he directly reaches x km from N at S.
then AS=[tex]\sqrt{100+X^2}[/tex] and SP=20-X
Time taken:
[tex]\frac{\sqrt{100+X^2}}{30}[/tex]+[tex]\frac{20-X}{50}[/tex]
Differentiating it and putting this to zero gives extrema value
[tex]\frac{2x}{60(\sqrt{100+X^2})}[/tex]=[tex]\frac{1}{50}[/tex]
⇒[tex]\frac{50x}{30}[/tex]=[tex]\sqrt{100+X^2}[/tex]
⇒By squaring on both sides
⇒100+X^2=[tex]\frac{25x^2}{9}[/tex]
⇒x=7.5km
x is independent of PN as while differentiating PN term became 0
Now time:
a) t= [tex]\frac{\sqrt{100+7.5^2}}{30}[/tex]+[tex]\frac{20-7.5}{50}[/tex]=0.666hours
b) t=[tex]\frac{\sqrt{100+7.5^2}}{30}[/tex]+[tex]\frac{30-7.5}{50}[/tex]=0.866hours
Shortest time taken for a is 0.666hours and for b is 0.866hours.
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Slope-intercept form
Answer: 5
Step-by-step explanation:
slope is m in the formula y=mx+b
plug in the numbers for m and that's the slope
What is the domain of the red curve in the graph below?
graph
x > 0
x < 0
x > 5
x > 4
The domain of the red curve in the given graph is
x > 4
How to find the domain of the graphThe domain is controlled by the input values. considering the graph the input values are in the x axis
The least number and the maximum number is what makes the domain as it shows the extents the input values can go
The maximum number is not showing so we assume infinity since the curve continued.
For the minimum this is the point before 5 which is 4
The domain starts from 4, with 4 not inclusive to infinity and the correct option is x > 4
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What is the third quartile of this set?
{-26, -15, -7, 0, 1. 6. 9, 15, 22, 22, 26, 28)
Answer:
22 is the third quartile for this set
Can someone help me with Questions 1 and 2 on this assignment? I am not really understanding them. I would deeply appreciate it!
Add 5 to 2 = 2 will make 7 = 7 a true statement and adding 5 to 2 ≠ 3 to make 7 ≠ 8 will make a true statement.
What is a number system?A way to express or represent numbers is through the number system.
We often employ decimal numbers because they are so widely used.
The Number System includes any of the several sets of symbols and the rules for using them to represent numbers.
(1)
As per the given,
2 = 2
Add 5 on both sides of the above equation,
2 + 5 = 2 + 5
7 = 7 (True)
(2)
As per the given
2 ≠ 3
Add 5 on both sides of the above equation,
2 + 5 ≠ 3 + 5
7 ≠ 8 (True)
Hence "It is correct that if you add 5 to 2 = 2, you will get 7 = 7, and if you add 5 to 2 ≠ 3, you will get 7 ≠ 8".
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-2x+3 Helpppppppppppppppppppppp
Answer: 1
Step-by-step explanation: -2 times x the x would just be 1 so -2 times 1 equals -2 then -2 plus 3 is 1
please someone help me with this problem
Answer question with steps get brainliest!ASAP Answer with steps. Use photo above
The value of f(g(5)) is obtained as -2.
What are the properties of a composite function?For two functions f(x) and g(x), a composite function is defined as f(g(x)) or g(f(x)). The properties of this function are as follows,
The inverse of a composite function is the same as the composition of the inverse of both functions.
The composition of two one to one functions is always one to one.
The value of f(g(5)) is equal to the value of the composite function f(g(x)) at x = 5.
The value of g(5) from the graph is 2.
Now, f(g(5)) = f(2)
The value of f(2) from the graph is -2.
Thus, f(g(5)) = -2
Hence, the value of the given composite function is f(g(5)) = -2.
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Suppose f(x) = x + 2 and g(x) = square root of x
Step 1: Find the value of f(g(16))
Step 2: Use your output from step 1 as the input for f(x). Find f(g(16))
Step 3: Find f(g(x)). Show your work (use g(x) as the input for f(x)
Thank you!!!
Answer:
[tex]f(g(16)) = 6[/tex] and [tex]f(g(x)) = \sqrt{x} + 2[/tex]
Step-by-step explanation:
Step 1 and Step 2 appear to be asking the same thing, so I will assume you meant for g(16) to be found in Step 1 and for f(g(16)) to be found in Step 2.
Step 1: Find g(16)
[tex]g(x) = \sqrt{x}[/tex], so we must plug in 16 for x to find g(16)
[tex]g(16) = \sqrt{16} = 4[/tex]
Step 2: Find f(g(16))
In order to do this, we must plug the value we found for g(16) into the equation for f(x). Thus, we must plug in 4 (the value we found in Step 1) for x in f(x).
[tex]f(x) = x + 2[/tex], so we must plug in 4 to find f(4)
[tex]f(4) = 4 + 2 = 6[/tex]
Thus, [tex]f(g(16)) = 6[/tex]
Step 3: Find f(g(x))
We must plug in the value of g(x) into f(x) to find f(g(x)).
These are the expressions for f(x) and g(x): [tex]g(x) = \sqrt{x}[/tex], [tex]f(x) = x + 2[/tex]
We find that [tex]f(g(x)) = \sqrt{x} + 2[/tex]
The required value of the function f(g(16)) is given as f(g(16)) = 6.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
f(x) = x + 2
g(x) = √x
In order to determine f(g(16)),
g(16) = √16
g(16) = 4
Now,
f(g(16)) = 4 + 2 = 6
f(g(16)) = 6
Thus, the required value of the function f(g(16)) is given as f(g(16)) = 6.
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