The worth of the book after 10 years is $1061.1
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
First edition book worth = $262
Rate of increase per year = 15%
The worth of the book after t years can be given by the expression.
= 262 x [tex]1.15^{t}[/tex]
Now,
The worth of the book when t = 10.
= 262 x [tex]1.15^{10}[/tex]
= 262 x 4.05
= $1061.1
Thus,
The book is worth $1061.1 after 10 years.
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A particular car is 16 ft long. A model of it was built with a scale of 1 in: 2 ft. How long is the model car?
The car that is 16 feet long has a length of 8 inches on the scale.
How to find the length of the modelled car?Scale is used to represent the relationship between a measurement on a model and the corresponding measurement on the actual object.
Therefore, the particular car is 16 feet long. A model of it was built with a scale of 1 in: 2 ft. The length of the car can be found as follows:
2 feet = 1 inches
16 feet = ?
cross multiply
length of the model car = 16 / 2
Therefore,
length of the model car = 8 inches
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1/4(12k-4) ''simplify''
Using the distributive property, the simplified form of the expression 1/4(12k-4) is 3k-1.
In the given question we have to simplify the given expression.
The given expression is 1/4(12k-4).
To simplify the given expression we use the distributive property.
According to property; a(b+c) = ab+bc
Now simplifying the expression;
1/4(12k-4) = 1/4*12k-1/4*4
1/4(12k-4) = 3k-1
Hence, the simplified form of the expression 1/4(12k-4) is 3k-1.
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Factorise the following:
a) x + 3x - 4
b) x-2x-3
c) x +2x-8
Please Answer!
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each graph with its description.
the function increases on the interval (-∞, 1)
and decreases on the interval (1, ∞)
the function has a maximum at (3,1)
the function has a minimum at (1,3)
the function has a minimum at (3,1)
The matching of the quadratic functions with their features is given by the image at the end of the answer.
What are the features of a quadratic function?The first feature of the function on the problem is when it is increasing, and the definition is that it is increasing when the graph of the function is moving to the right and up on the graph, that is, when x increases, y also increases.
It is decreasing when it is moving right and down. Hence, a quadratic function increases until it's vertex, so for item 1, we want a function that is concave down, as it is increasing and then decreasing, and does the turn at x = 1, which is the third function on the second row.
The maximum and minimum points are given at the turning points, as follows:
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Answer: Its correct
Step-by-step explanation:
Right on Edmentum. Absolute legend
A school had 1 200 students last year and only 1 080 students this year.
What was the percent decrease in the number of students?
Answer:The percentage decrease in the number of students is -10%.
Given that,
The school has 1,200 students last year.
And, this year it is 1,080.
Based on the above information, the calculation is as follows:
Therefore we can conclude that the percentage decrease in the number of students is -10%.
Step-by-step explanation: noice
A new gaming chair costs $239.87. You have already saved $118.37 and earn $40.50 each week babysitting. Write and solve an equation to determine how many weeks, w, you must babysit to earn enough money to buy the new gaming chair.
40.5w + 118.37 = 239.87; w = 3
40.5w − 118.37 = 239.87; w = 9
40.5w − 239.87 = 118.37; w = 9
40.5 + 118.37w = 239.87; w = 3
Answer:
40.5w + 118.37= 239.87; w=3
Step-by-step explanation:
You already saved 118.37.
239.87
118.37
111.50
40x3=120. So you'll need 3 more weeks to buy a gaming chair. And you also get 8.50 dollars extra in profit.
Answer:
40.5w + 118.37= 239.87; w=3
Step-by-step explanation:
Determine which set of side measurements could be used to form a triangle.
A. 13, 19, 7
B. 25, 12, 13
C. 18, 2, 24
D. 3, 1, 5
Option A. The set of side measurement that can be used to form a triangle is given as A. 13, 19, 7
What is a triangle?A triangle in geometry is a three-sided polygon with three edges and three vertices. The fact that a triangle's internal angles add up to 180 degrees is its most crucial characteristic. This characteristic is known as the triangle's angle sum property.
If ABC is a triangle, it is written as ABC, where A, B, and C represent the triangle's vertices. In Euclidean geometry, a triangle is a two-dimensional shape that is represented by three non-collinear points in a single plane.
How to get the measurement that can produce a triangle.
a + b > c = 13 + 19 > 7
a + c > b = 13 + 7 > 19
b + c > a = 7 + 9 > 13
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in a field hockey championship, 120 matches were played. every pair of team played one match with each other. the number of teams in the tournament is therefore:
The number of teams in the field hockey championship tournament is 16.
The total number of matches played in the field hockey championship are 120 matches.
Each pair of team played one match with each other.
So, let us say that there are N teams in the tournament.
So, we can chose any two teams for a match,
So, applying the permutation formula,
ⁿC₂ = 120
Solving further,
N!/2!(N-2)! = 120
N(N-1)/2 = 120
N(N-1) = 240
On observing closely and applying hit and trial method,
16(15) = 240
So, the values of N is 16.
Hence, 16 teams participated in the tournament.
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The sum of the ages of pam,dion, and their three children, in years, is 5x - 99. where x is dion's age. pam is five years younger than dion. what is the usm of the ages of their children?
The sum of the ages of the children would be 3x - 94 years.
We have the total sum of the ages of pam ,dion and their children
as 5x - 99
here , x is the age of Dion .
we see , pam is five years younger than Dion , so
age of Pam = x - 5
Now as the sum of all the ages = 5x - 99
therefore ,
Age of Dion + Age of Pan + Age of children = 5x - 99
x + x - 5 + Age of children = 5x - 99
2x - 5 + Age of children = 5x - 99
therefore ,
Age of children = 3x - 94
So the age of their children would be 3x - 94 years
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how to find the vertex
Answer: To find the vertex: use formula x= -b/2a.
plug x into the given equation to find y value.
now you have (h,k)
find a point on the graph and plug in to the vertex form equation to find "a"
Step-by-step explanation:
Suppose each data value in a data set is multiplied by 8. What will
happen to the mean?
Select one:
- It will be 4 times as much.
- It will increase by 4.
- It will be 8 times as much.
It will increase by 8, as well.
The fraction is equivalent to which of the following decimal numbers?
0.2
0.1616
0.166
0.1 6
The fraction of 1/6 is equivalent to this following decimal number:
0.166.
How to convert a fraction to a decimal number?A fraction is represented by the division of a term x by a term y, as follows:
Fraction = x/y.
The terms that represent x and y are given as follows:
x, which is the top term of the fraction, is called the numerator.y, which is the bottom term of the fraction, is called the denominator.In this problem, the fraction is given as follows:
1/6.
1 is less than 6, hence the equivalent decimal can be obtained as follows:
0.10/6.
10 divided by 6 is one with a remainder by 4, hence 1.4/6 = 1.6667.
Thus the equivalent decimal representing the fraction 1/6 is given as follows:
1/6 = 0.1666.
Missing informationThe problem asks for which decimal number the fraction 1/6 is equivalent.
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help with this math problem
The solution of the linear equation:
(2x + 6)/5 = 4x - 3
is x = 7/6
How to solve the equation?
Here we have the following equation:
(2x + 6)/5 = 4x - 3
To solve this, we need to isolate x in one of the sides of the equation, we can start by multiplying both sides by 5.
2x + 6 = 5*(4x - 3)
Expanding the right side we get:
2x + 6 = 20x - 15
Now you can see that this is a simple linear equation, now we need to group like terms:
6 + 15 = 20x - 2x
21 = 18x
Now we can divide both sides by 18 to get:
21/18 = x
Finally, if we divide both numerator and denominator of the fraction by 3, we get:
21/3 = 7
18/3 = 6
Then 21/18 = 7/6
Finally, we conclude that the solution is:
x = 7/6
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Please help will mark brainiest!!!
1.) Rowan graphs the function f (x) = 7x + 1 and then transforms the function by horizontally translating it 5 units to the right. What is the newly transformed function, g (x)?
g(x) = 7(x+5) + 1 is the newly transformed function
How to find the newly transformed function, g (x)?
A function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input
Given that: He graphs the function f (x) = 7x + 1 and then transforms the function by horizontally translating it 5 units to the right
To solve this problem, we need to understand the direction of movement. In the cartesian plane or graph, the x-axis is either a movement to the left(negative) or right(positive)
Since the function f (x) = 7x + 1 translates by 5 units to the right. You need to add 5 to x i.e. 7(x+5) + 1
Therefore, the newly transformed function, g (x) = 7(x+5) + 1
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The function f(t)=9300(0.994)t represents the change in a quantity over t minutes. What does the constant 0.994 reveal about the rate of change of the quantity?
The function is ________exponentially at a rate of _______% every _______.
Please!!!! Help
Answer:
Step-by-step explanation:
NOSEEEEEE
9) For a job, Phillippa is paid three times as much as Peter. Pavin is paid £10 more than Phillippa, Write an algebraic expression for the total of everyone's wages
Answer:
Step-by-step explanation:
Peter=x
Phillippa= 3x then x
Palvin= 10 then Phillippa
Step 2: Answer: Phillipa 3x+x+10
Which graph represents an odd function?
Answer:
Step-by-step explanation:
taking π=22/7, find the circumference of a circle 70cm
The circumference of circle of radius 70 cm is 440 [tex]cm^{2}[/tex].
According to the question,
We have the following information:
Radius of the circle = 70 cm
(Diameter is twice that of its radius..)
We know that the following formula is used to find the circumference of circle:
Circumference of circle = 2πr
(More to know: the formula to find the area of circle is π[tex]r^{2}[/tex].)
(More to know: there are two values of π. One is 3.14 and one is 22/7.)
Circumference of circle = 2*(22/7)*70
Circumference of circle = 440 [tex]cm^{2}[/tex]
Hence, the circumference of the circle of radius 70 cm is 440 [tex]cm^{2}[/tex].
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Triangles geometry . I neeed help pls
The value of PQ is 43.
What is an isosceles triangle?
A triangle with at least two equal-length sides is known as an isosceles triangle in geometry.
From the figure,
PQ=3x+10, QR=5x-12
Given that, PQ=QR
So, 3x+10=5x-12
Find x:
3x+10=5x-12
Separate variable terms and constants
5x-3x=10+12
2x=22
x=22/2=11
we have PQ=3x+10=3(11)+10=33+10=43
So, PQ=43
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Help me on this please.
The steps and reason to prove the angle theorems is; Table 3
What is the proof of the angles in the triangle?The internal angles of the given triangle are given as;
a, b, c and d.
Now, we know that the sum of interior angles in a triangle is equal to 180°;
∠a + ∠b + ∠c = 180°
Now, ∠c and ∠d are angles that form a straight line and as such they sum up to 180° as they are supplementary angles.
∠c + ∠d = 180°
Thus, by transitive properties, we can say that;
∠a + ∠b + ∠c = ∠c + ∠d
Therefore by subtraction property of equality we have;
∠a + ∠b = ∠d
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each law firm in one state registers its phone number with the state court system. an employee of the state court system uses a computer to select 500500500 random registered phone numbers, and the law firms associated with those numbers will be selected for an audit. what type of sample is this?
In this "Simple Random Sample" scenario, 500500500 selected randomly registered phone numbers were chosen.
Define the term Simple random sample?A subset of either a population is chosen at random in a basic random sampling. Each individual in the population has had an exact equal probability of getting selected using this sampling technique.Among all of the probability sampling techniques, this one is the easiest to understand because it only includes one random selection and little prior population knowledge. Any research conducted on this sample must have excellent validity both internally and externally because it uses randomization.For the given data in the question.
Every law firm in a state registers it phone number only with state court system as a result.Thus, 500500500 random registering phone numbers are randomly chosen by a state court employee using a computer, and the law firms connected to all those numbers are randomly chosen for an audit.
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Lyle and Ming are painting an art room. They started with 44 gallons of paint. On the first day, Lyle used \frac{1}{2} 2 1 gallon of paint and Ming used 1\frac{1}{4}1 4 1 gallons of paint. How many gallons of paint were left when they completed their first day of painting?
The initial 4 gallons and the fractions of [tex]\frac{1}{2}[/tex] and [tex]1\frac{1}{4}[/tex] gallons of paint used on the first day indicates;
The number of gallons of paint left when they completed the first day of painting is [tex]2\frac{1}{4}[/tex] gallonsWhat is a fraction in mathematics?A fraction is the representation of a number in quotient form such that the value of the number is obtained by dividing the numerator by the denominator.
The amount of paint Lyle and Ming started painting the room with = 4 gallons
Amount of paint Lyle used on the first day = [tex]\dfrac{1}{2}[/tex] gallons of paint
The amount of paint Ming used on the first day = [tex]1\frac{1}{4}[/tex] gallons of paint
Required; The amount of paint remaining after the first day of painting
The paint left after the first day of painting, V, is the difference between the amount of paint with which the painting was started and the amount used by Lyle and Ming on the first day
Therefore; [tex]V = 4 - \left(\dfrac{1}{2} + 1\dfrac{1}{4} \right) = 4 - \left(\dfrac{1}{2} +\dfrac{5}{4} \right) = 4 - \dfrac{7}{4}[/tex]
[tex]V = 4 - \dfrac{7}{4} = \dfrac{16-7}{4} = \dfrac{9}{4} = 2\dfrac{1}{4}[/tex]
The amount of paint left after the first day is [tex]2\frac{1}{4}[/tex] gallonsLearn more about fractions here:
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Two planes are parallel and each plane contains a line. Are the two lines skew? Explain your reasoning.
If Two planes are parallel and each plane contains a line, the two lines are not skew because In the event that any two lines fall on a single plane, they will either intersect or be parallel to one another. Both instances violate the concept of a skew line because the skew lines are neither parallel nor intersect.
Do two parallel lines on a plane have a skew?Infinitely many lines cross through, yet only one of them is parallel to. Lines that never intersect and are in distinct planes are known as skew lines. Parallel lines and skew lines are distinguished by the fact that they both reside in the same plane, whereas skew lines do not.
The two lines would overlap at some point if the two planes on which they are located weren't parallel, which again defies the definition of skew lines.
Therefore, The skew lines are thus present if and only if both lines fall on a pair of parallel planes.
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Explain why (5 + 4) (5 + 4) could be used to determine the total number of computers.
Answer:
The numbers that we use are expressed in base 10. Every 10 1s equals 1 ten For example, if you are adding 5 + 4, you get: 0101 + 0100.
The perimeter of an equilateral triangle is 10 inches more than the perimeter of a square, and the side of the triangle is 6 inches longer than the side of the square. Find the side of the triangle. (Hint: An equilateral triangle has three sides the same length.)
Answer:
The side of the triangle is 14 in======================
Let the sides be t for triangle and s for square.
Difference of perimeters3t = 4s + 10Difference of sidest = s + 6Rearrange the second equations = t - 6Substitute this into first equation and solve for t3t = 4s + 103t = 4(t - 6) + 103t = 4t - 24 + 103t = 4t - 144t - 3t = 14t = 14Answer:
14 inches
Step-by-step explanation:
The side lengths of an equilateral triangle are the congruent.
The side lengths of a square are the congruent.
Let x be the length of one side of the equilateral triangle.
⇒ Perimeter of triangle = 3x
Let y be the length of one side of the square.
⇒ Perimeter square = 4y
Given:
The perimeter of the triangle is 10 inches more than the perimeter of the square.The side of the triangle is 6 inches longer than the side of the square.Create a system of equations with the given information and defined variables:
[tex]\begin{cases}3x = 4y + 10\\x = y + 6\end{cases}[/tex]
Substitute the second equation into the first equation and solve for y:
[tex]\implies 3(y+6)=4y+10[/tex]
[tex]\implies 3y+18=4y+10[/tex]
[tex]\implies 18=y+10[/tex]
[tex]\implies y=8[/tex]
Therefore, the side length of the square is 8 inches.
Substitute the found value of y into the second equation and solve for x:
[tex]\implies x=8+6[/tex]
[tex]\implies x=14[/tex]
Therefore, the side length of the triangle is 14 inches.
Suppose that the height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning. after 11 hours of burning, a candle has a height of 19.4 centimeters. after 23 hours of burning, its height is 12.2 centimeters. what is the height of the candle after 15 hours?
The height of the candle after 15 hours of burning is 17 cm.
According to the question,
We have the following information:
Height of the candle after 11 hours of burning = 19.4 cm
Height of the candle after 23 hours of burning = 12.2 cm
Now, we will find the rate at which the height of the candle is decreasing. It means that we will find the decrease in height per centimeter.
Difference between hours and height:
23-11 = 12 hours
19.4-12.2 = 7.2 cm
So, we have:
12 hours = 7.2 cm
1 hour = 7.2/12
1 hour = 0.6 cm
So, the height is decreasing at the rate of 0.6 cm per hour.
Now, we have to find the height after 15 hours.
Height at 11 hours = 19.4 cm
Difference between 15 hours and 11 hours is 4 hours.
Change in height = 0.6*4 cm
Decrease in height = 2.4 cm
So, the height after 15 hours:
19.4-2.4
17 cm
Hence, the height of the candle after 15 hours of burning is 17 cm.
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at a certain clothing store, the clothes are displayed on racks. the clothes on each rack have similar prices, but the prices among the racks are very different. to estimate the typical price of a single piece of clothing, a consumer will randomly select four pieces of clothing from each rack. what type of sample is the consumer selecting? responses a census a census a cluster sample a cluster sample a simple random sample a simple random sample
The clothing in the store is separated into strata, each of which is a rack of items with comparable prices. An illustration of the use of a stratified random sample is the mean price calculated using the randomly chosen articles of clothing from the strata.
Describe a random sample.In the random sampling method of sampling, each sample has an equal chance of being chosen. In order to fairly represent the entire population, a sample is chosen at random. From a pool of 250 employees, 25 names could be chosen at random to represent a simple random sample. The sample in this case is random, and the population in this case is the employees since each has an equal chance of being chosen.
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The length of segment AE is 5 centimeters. a. what is the length of segment CD? b. what is the length of segment AB? c. Name a segment that had the same length ...
a) The length of segment CD is; CD = 10 cm
b) The length of segment AB is; AB = 5 cm
c) Another segment with same length as segment AB is;
Segment AC
What is the length of the line segment?From the attached image, we see that Segment AE is a radius of the circle with center of A.
Now, any segment with origin from the center of the Circle that goes on to hit the circumference of the circle, is also a radius, and would be equal in length to segment AE.
a) Segment CD divides the circle into 2 equal parts and as such it will be the diameter of the circle.
Diameter = 2 × radius.
Diameter; CD = 2 × AE
CD = 2 × 5
CD = 10 cm
b) AB is a radius as defined earlier and as such; AB = AE
Thus; AB = 5 cm
c) The other segments that are also radius of the circle and have the same length as segment AB are;
Segment AC
Segment AD
Segment AG
Segment FA
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Y=1/2x+5
Y= -5/2x-1 ???
Answer:
It's correct
Step-by-step explanation:
Solve for the first variable in one of the equations, then substitute the result into the other equation. Point Form: (-2, 4) Equation Form : X= -2, Y = 4.
rite the equation for the logarithmic function that has the following
ansformations from the parent logarithmic function. The function will
ave a base of 10. You will not have to write the 10. It is assumed.
- Shifted 3 units left
Vertical compression by a factor of 2
Reflected across the y-axis
Shifted down 5 units
The given function shifted 3 units left is log(x+3), vertical compression by factor 2 is 2log(x+3), Reflection across the y-axis is 2log (-x+3) and shifted down by 5 units is 2log(-x+3)-5.
Given the parent function with base 10.
We want to find the given transformations.
The given parent function is y=log(x)
Firstly, we want to shift the given parent function 3 units left means we will add 3 in the parent function, we get
y=log(x+3)
Now, we want to do vertical compression by a factor of 2 means we will multiply the above function with 2, we get
y=2log(x+3)
Further, we want to reflected the above function across the y-axis means we will multiply the x with minus, we get
y=2log(-x+3)
Furthermore, we want to shift the above function down with 5 units means we will subtract 5 from the above function, we get
y=2log(-x+3)-5
Hence, the given parent function y=log(x) when shifted 3 units left is log(x+3), vertical compression by factor 2 is 2log(x+3), Reflection across the y-axis is 2log (-x+3) and shifted down by 5 units is 2log(-x+3)-5.
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