The function f(x) = (1/2)^x accepts any real number as an input, so its natural domain is the set of all real numbers. However, the question specifies that the domain is all real numbers greater than 1/2, which might be due to the context in which this function is used.
Explanation:The function f(x) = (1/2) x is a function that will accept any real number as an input. Therefore, the natural domain of this function would be the set of all real numbers. However, in your question, the function is given a specific domain, that is, all the real numbers greater than 1/2. This domain restriction might be due to the context in which this function is used.
Remember, the domain of a function is the set of all possible input values (x-values) that will give a valid output value (f(x)). For example, in the function f(x) = 1/x, the domain is all real numbers except zero because we cannot divide by zero.
In your function f(x) = (1/2)x, there is no value of x that will result in a not defined output, so unless stated otherwise, the domain is all real numbers. However, here we are given that the domain is all real numbers greater than 1/2.
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going down the river a boat went 13 km/h. going up the river it only 1 km/h. Find the speed of the boat in still water and the speed of the current.
The speed of boat is 7 km/h and speed of stream is 6 km/h.
What is speed ?
In unit time the distance covered by any object is called speed.
In mathematical term, Speed is express as S=D/T,
where S=speed, D=distance, T= time .
Let the speed of boat in N, and the speed of current is D,
Given that,
The speed in downward stream of a boat N+D= 13 km/h, (1)
And the speed in upward stream of a boat N-D= 1 km/h. (2)
To Find speed of boat in still water, add equation (1) and (2),
2N=14 ⇒ N=7 km/h
To Find speed of current, substract equation (1) and (2),
2D=12 ⇒ D=6 km/h.
The speed of boat is 7 km/h and speed of stream is 6 km/h.
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What is 763 thousandths in scientific notation?
what is the momentum of a 20-kg dog running at a speed of 8 m/s
The momentum of a 20-kg dog running at a speed of 8 m/s is 160 kg.m/s. This is calculated using the formula for momentum, which is the product of mass and velocity.
Explanation:To calculate the momentum of an object, you need to multiply its mass by its velocity. This is due to the fact that momentum is directly proportional to the object's mass and its velocity. Hence, a 20-kg dog running at a speed of 8 m/s would have a momentum of 160 kg.m/s.
Momentum (p) is represented as the product of mass (m) and velocity (v), hence expressed as p = m*v. Momentum is a vector quantity, which means it has both magnitude (amount) and direction. In this case, we're only concerned with its magnitude.
So, for the 20-kg dog running at 8 m/s, we substitute these values into the momentum formula to find its momentum:
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Danielle has a CD at crossland bank. she invest $22,350 for four years at 4.55% interest. compounded monthly. What is her ending balance? How much interest did she make?
Answer: Her ending balance is $26,703.837 and her interest is $4,353.837
Step-by-step explanation:
First year,
p =22350 R = 4.55 T = 1
Interest = PRT/100
= 22350 × 4.55 × 1 / 100
=$1016.925
P = $22350 + $1016.925 = $23366.925
For the 2nd year,
I = $23366.925 × 4.55 × 1 / 100
=$1063.195
p= $23366.925 + $1063.195 = $24,430.12
For the 3rd year,
I = $24,430.12 × 4.55 × 1 / 100
= $1111.57
p = $24,430.12 + $1111.57 = $25,541.68
For the 4th year;
I = $25541.68 × 4.55 × 1 / 100
= $1,162.147
P = $ 25541.69 + $1,162.147 = $26,703.837
Therefore th ending balance is $26,703.837
Her compound interest is , $26,703.837 - $22350 =$4,353.837
Solve for S.
3s + 2 = 12 - 2s
3s+2=12-2s
(3s-3s)+2=12(-2s-3s)
2=12-5s
2-12=(12-12)-5s
-10=-5s
-10/-5=-5s/-5
2=s
Check
(3*2)+2=12-(2*20
6+2=12-4
8=8
S=2
Which statement is true?
A)
0.4 is less than 0.07 because 4 is less than 7.
Eliminate
B)
0.4 is less than 0.07 because 40 is less than 70.
C)
0.4 is greater than 0.07 because 70 is greater than 40.
D)
0.4 is greater than 0.07 because 40 is greater than 7.
If a player always gets three cards, describe two different ways to recieve a score of 7.
Answer:
1 + 3 + 3 = 7
5 + 1 + 1 = 7
Step-by-step explanation:
If a player have the three cards. Each card will have a number and we have to find the numbers on each card that total 7.
Let card 1 gets 1
Then other two cards may have 3 and 3
So, 1 + 3 + 3 = 7
Now we take another combination which totals 7
5 + 1 + 1 = 7
Therefore, there may be two different ways are
1 + 3 + 3 = 7
5 + 1 + 1 = 7
Which expression is equivalent to −2.6+(−2.9)+(−7.1) ?
Answer:
-12.6
Step-by-step explanation:
To evaluate the given expression
-2.6+(−2.9)+(−7.1, first we will open out the brackets and multiply the signs. Before that, we must take note of the following sign operations
-×- = +
-×+ = -
+×- = -
+×+ = +
The equation above becomes;
-2.6-2.9-7.1 (all the signs are now minus since the product of plus and minus sign gives a minus sign)
(-2.6-2.9)-7.1
= -5.5-7.1
= -12.6
Since all the values in the equation are negative values, our resulting answer will be a negative value.
tyler can shovel the driveway in 2 hours. dakota can complete the job in 90 minutes. if they work together, how long will it take
You have $ 2 0 $20dollar sign, 20 to spend on taxi fare. The ride costs $ 5 $5dollar sign, 5 plus $ 2 . 5 0 $2.50dollar sign, 2, point, 50 per mile. Let m mm represent the number of miles ridden. Write an inequality to determine how many miles you can ride for $ 2 0 $20dollar sign, 20.
Answer:
6 x $2.5 = $15
$15 + $5 = $20
PLEASE YOU CAN ANSWER NUMBER 1 OR 2 OR BOTH PLEASE I JUST NEED HELP WITH BOTH AND NO ONE WILL ANSWER MY QUESTIONS!!!!!!!! :(
1.)In two or more complete sentences, explain how to find the time it takes for a rocket following the path, h(x) = -4x 2 + 16x, to hit the ground.
2.)A ball is thrown straight up from the top of a building that is 280ft high with an initial velocity of 48ft/s. The height of the object can be modeled by the equation s(t) = -16t 2 + 48t + 280.
In two or more complete sentences explain how to determine the time(s) the ball is higher than the building in interval notation.
1.) You plug a number into the variable x. Then you will solve the equation for h(x) to find the time it takes for the rocket to travel the path given.
Answer:
Step-by-step explanation:
Given that a rocket path is given by
[tex]h(x) = -4x^2 + 16x[/tex]
When it hits the ground h(x) =0
Hence we get
[tex]-4x^2 + 16x=0\\x=0, 4[/tex]
i.e. after 4 minutes the rocket hits the ground
2) Given that
[tex]s(t) = -16t^2 + 48t + 280.[/tex]
We have to find time t when height >280
[tex]s(t) = -16t^2 + 48t + 280>280\\\\t=0, 3[/tex]
Between 0 and 3 seconds the object would be above the building.
A spinner is separated into 3 equal pieces, as shown below: A spinner is shown with three colors, red, yellow, and purple, marked on it. The arrow points towards the red color. Mary spins the spinner 6 times. What is the theoretical probability that it stops on the red sector on the last spin?
The theoretical probability that it stops on the red sector on the last spin is 1 by 3.
Calculation of the theoretical probability:Since A spinner is separated into 3 equal pieces. A spinner is shown with three colors, red, yellow, and purple, marked on it. Mary spins the spinner 6 times.
So, the theoretical probability is
Probability= Successful outcome ÷ Possible outcome
= 1÷3
Therefore, The theoretical probability that it stops on the red sector on the last spin is 1 by 3.
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a table is 6 feet long and 3 feet wide. You extend the table by inserting two identical table leaves. The longest side length of each rectangular leaf is 3 feet. The extended table is rectangular with an area of (18+6x) square feet. a) write an algebraic expression that represents the length of the extended table b) what does your variable represent?
a. The algebraic expression that represents the length of the extended table is 6 + 2x
b. The variable 'x' represents the length added by inserting each identical table leaf.
How to write an algebraic expression
a) To write an algebraic expression representing the length of the extended table, consider the original length of the table (6 feet) and the length added by inserting two identical table leaves (each with a longest side length of 3 feet).
Let's denote the length added by inserting the table leaves as 'x'.
Since we're inserting two identical leaves, the total length added would be 2x.
The length of the extended table can be expressed as the sum of the original length (6 feet) and the length added by the table leaves (2x):
Length of the extended table = 6 + 2x
b) The variable 'x' represents the length added by inserting each identical table leaf. It quantifies the extra length that extends the original table when the leaves are inserted.
A hiker is walking down a mountain. She walked 5,978 feet in 17 minutes. In that time, she descended 1,024 feet from the top of the mountain. She then walked 3,972 feet in 7 minutes. In that time, she descended 500 more feet. Express the average rate of change in altitude of the hiker from her starting point to her ending point as a unit rate.
The average rate of change in altitude of the hiker from her starting point to her ending point is -63.5 feet per minute.
The following can be deduced based on the information provided in the question:
During the first walk, she descended 1024 feet and during the second walk, she descended 500 feet. Therefore, the total will be:
= 1024 feet + 500 feet = 1524 feet
During the first walk, the time taken was 17 minutes while for the second walk, the time taken was 7 minutes. Therefore, the total time taken will be:
= 17 minutes + 7 minutes
= 24 minutes.
Therefore, the average rate will be:
= 1524 / 24
= 63.5 feet per minute
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The bus driver made 6 stops on his way into town. No passengers exited the bus. By stop 3, there were 9 passengers on the bus. This graph shows this information.
How many stops did it take to have 13 passengers on the bus?
A:2
B:3
C:4
D:5
The number of bus stops is 4 if the bus driver made 6 stops on his way into town option (C) 4 is correct.
What is a dot plot?A dot plot also referred to as a dot chart or stripe graph, is a sort of simple histogram-like figure used in statistics for little data sets with values falling into a number of discrete bins.
It is given that:
The bus driver made 6 stops on his way into town. No passengers exited the bus. By stop 3, there were 9 passengers on the bus
The graph is shown in the picture.
The x-axis represents the bus stops
The y-axis represents the number of passengers
From the graph point to the 13 on the y-axis and locate the related value of x on the x-axis.
The number of bus stops corresponds to 13 = 4
Thus, the number of bus stops is 4 if the bus driver made 6 stops on his way into town option (C) 4 is correct.
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GIVEN: ab perpendicular to BC AND DC PERPENDICULAR TO BC
AC = BD
PROVE:AB =DC
Proofs
Answer with Step-by-step explanation:
We are given that AB is perpendicular to BC and DC perpendicular to BC.
AC=BD
We have to prove that AB=DC
In triangle ABC and triangle DCB
AC=BD (Given)
[tex]\angle B=\angle C=90^{\circ}[/tex]
[tex]BC=BC[/tex]
Reason:Reflexive property
[tex]\triangle ABC\cong \triangle DCB[/tex]
Reason:RHL postulate
[tex]AB\cong DC[/tex]
Reason:CPCT
Therefore, AB=DC when two sides are congruent then the sides are equal.
Hence, proved.
a group of 4 people go out to eat. they decide to split the bill so each person pays 1/4 of the total price. appetizers are $6 and main dishes are $9. write an expression to show how many each person pays.
Which graph represents the solution set of the system of inequalities?
{3y≤2x+62x+y>0
we have
[tex]3y\leq 2x+6[/tex] ---> inequality A
[tex]2x+y > 0[/tex] ---> inequality B
using a graphing tool
see the attached figure
The solution is the shaded area
the answer in the attached figure
Two events, X and Y, are independent of each other. P(Y) = 5/6 and P(X and Y) =1/3 . What is P(X) written as a decimal?
help me divide y over x??
In a recent year, the population of California was about 2.52 x 10^7 people. Its land area is about 4.05 x 10^5 km^2. What was the average number of people per square kilometer? Write your answer in scientific notation.
PLEASE I NEED HELP ASAP!!!!!!!!!!!!
The average number of people per square kilometer in California is [tex]6.22 \times 10^1.[/tex]
To find the average number of people per square kilometer in California, we divide the total population by the land area.
Given:
Population of California = [tex]2.52 \times 10^7[/tex] people
Land area of California = [tex]4.05 \times 10^5 km^2[/tex]
Calculate the population density.
Population density = Population / Land area
Population density = [tex](2.52 \times 10^7) / (4.05 \times 10^5) people/km^2[/tex]
Divide the numbers and simplify.
Population density = (2.52 / 4.05) x 10^(7-5) people/km^2
Population density = [tex]0.622 \times 10^2 people/km^2[/tex]
Rewrite in scientific notation.
Population density = [tex]6.22 \times 10^1 people/km^2[/tex]
So, the average number of people per square kilometer in California is [tex]6.22 \times 10^1[/tex].
expand and simpilify
(3x-2)^2-(x+6)(x-8)
What is the acceleration of a wagon of mass 20 kg if a horizontal force of 64 N is applied to it? (Ignore friction)
The acceleration of the wagon is 3.2 m/s².
Explanation:To find the acceleration of the wagon, we can use Newton's second law of motion, which states that the acceleration of an object is equal to the net force applied to it divided by its mass. In this case, the net force is 64 N (the horizontal force applied) and the mass of the wagon is 20 kg. So the acceleration can be calculated as follows:
A = F/M = 64 N / 20 kg = 3.2 m/s²
Therefore, the acceleration of the wagon is 3.2 m/s².
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The table shows the distances and times that four rowboats traveled. Which rowboat was the fastest?
Answer:
Rowboat C traveled the fastest.
Step-by-step explanation:
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Are the expressions below equivalent 3(4x+8) 12x+24
what is the solotion to the equation 1/3(3+2x) -1=10
An MP3 player can hold 350 hours of music. Each song on an MP3 player is about 2.5 minutes in lenght. Abut how many songs can the MP4 player store?
Write words to match the expression of 4x(10 -2)
Someone please help me find this
Mark put his dog on a diet. The dog's total weight change for the first 2 weeks was −3/4 pound. The dog lost the same amount of weight each week. What was the change in the dog's weight after the first week of the diet? Enter your answer in the box.