Answer:
To find out how much interest you will earn, you need to multiply the bond principal amount ($1,000) by the interest rate (5%) and the number of years the bond matures (5).
The interest rate is expressed as a percentage, so you need to convert it to a decimal by dividing it by 100.
Interest = Principal x Interest Rate x Time
Interest = $1,000 x 0.05 x 5
Interest = $1,000 x 0.05 x 5 = $250
So, you will earn $250 in interest over the 5-year period.
Is x = 6 a solution to the equation 5(x – 3) = x + 13? Follow the steps to find out.
1. Rewrite the equation 5(x – 3) = x + 13 with 6 substituted for x. Write a question mark over the equal sign to show that you're testing to see if the equation is true.
2. Simplify both sides. Show your work.
3. Is x = 6 a solution to the equation? Why or why not?
4. Find a value of x that is a solution to 5(x – 3) = x + 13. Describe how you found the solution. (3 points)
Answer:
see below
Step-by-step explanation:
Step 1
5(x – 3) = x + 13
Step 2
See if x is a solution
5 (6-3) ?= 6+13
5 (3) ?= 19
15 ?= 19
Step 3
This is not true so it is not a solution
Step 4
5(x – 3) = x + 13
Distribute
5x-15 = x+3
Subtract x from each side
5x-x -15 = x+13-x
4x-15 = 13
Add 15 to each side
4x-13+13 = 15+13
4x =28
Divide each side by 4
4x/4 = 28/4
x = 7
7 is a solution
Answer:
First you substitute 6 for x!
5(6 - 3) = 6 + 13
6 - 3 = 3
The equation is now:
5 * 3 = 6 + 13
5 * 3 = 15
6 + 13 = 19
The result is:
15 = 19 which is not a true statement.
x is not equal to 6.
Now lets try 7.
5(7 - 3) = 7 + 13
7 - 3 = 4
7 + 13 = 20
5 * 4 = 20
Thus: x = 7
Step-by-step explanation:
Hope it helps! =D
Need help with 9,10,13,14 also explain
The rule for divisibility by 9 is similar to divisibility rule for 3. That is, if the sum of digits of the number is divisible by 9, then the number itself is divisible by 9.
What is divisibility?the capacity of being divided. Math. the capacity of being evenly divided, without remainder.
Divisibility rules or Divisibility tests have been mentioned to make the division procedure easier and quicker. If students learn the division rules in Math's or the divisibility tests for 1 to 20, they can solve the problems in a better way. For example, divisibility rules for 13 help us to know which numbers are completely divided by 13. Some numbers like 2, 3, 4, 5 have rules which can be understood easily. But rules for 7, 11, 13, are a little complex and need to be understood in-depth.
Divisibility rule for 10 states that any number whose last digit is 0, is divisible by 10.
Example: 10, 20, 30, 1000, 5000, 60000, etc.
For any given number, to check if it is divisible by 13, we have to add four times of the last digit of the number to the remaining number and repeat the process until you get a two-digit number. Now check if that two-digit number is divisible by 13 or not. If it is divisible, then the given number is divisible by 13.
For example: 2795 → 279 + (5 x 4)
→ 279 + (20)
→ 299
→ 29 + (9 x 4)
→ 29 + 36
→65
Number 65 is divisible by 13, 13 x 5 = 65.
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Find the Area of the figure below, composed of a rectangle with a semicircle removed from it. Round to the nearest tenths place.
Answer:
39.9
Step-by-step explanation:
Rectangle: area = length × width
Semicircle: area = 0.5πr²
total area = 9 × 6 - 0.5 × 3.14159 × 3²
total area = 39.9
you and friends go to the state fair . it costs $6 to get into the fair and $2 each time you go on a ride consider the relationship between number of rides (x) and total cost (y)
It costs $6 to enter the fair, and each ride costs $2, thus the equation is x = 6+ 2y.
what is equation ?Its core idea is understood to be the number's minimal equivalent fraction. How to determine the simplest form. A fractional figure can be checked to discover if it is a prime number. A phrase having two equal sides and now an equal sign in the middle is referred to as a mathematical equation. Every variable's degrees are listed in ranking in the general form of any equation. Its general form of a two-variable linear equation is an x + b y + c = 0. (or something similar). Perhaps conditional equations of identities are categories for equations.
given
Suppose the total cost is x and there are y rides.
Each ride costs two dollars. Thus, the price of the rides will be:
= Number of rides * Price per ride
=> y * 2
=> 2 y
Thus, the final price will be:
Total price = Admission price + ride prices
Total cost: $6 plus $2. (Number of rides)
x = 6 + 2y
It costs $6 to enter the fair, and each ride costs $2, thus the equation is x = 6+ 2y.
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(v) (5-6i)+(3+4i) - (5-7)
Answer:
Step-by-step explanation
A biologist is studying the plant diversity in 15 million acres of the Sierra Nevada Mountains. He will count the number of species in 150 acres. Match the strategies to their corresponding sampling techniques.
The biologist goes to his 150 favorite hiking places and looks at an acres along each trail.
The biologist orders the 15 million acres by latitude and then surveys every 100000th acre on the list.
The biologist classifies the Sierras into 10 different ecological types and then makes sure that the proportion of each ecological type from the sample is the same as the proportion of that of the population.
The biologist goes to 15 diverse locations that have 10 acres each and surveys all 10 acres for each of these 15 locations.
The biologist enters the 15 million acres into a data base and had a computer randomly select 150 of these acres.
Cluster Sampling
Systematic Sampling
Convenience Sampling
Stratified Sampling
Simple Random Sampling
Answer:
The biologist goes to his 150 favorite hiking places and looks at an acre along each trail: Random Sampling.
The biologist orders the 15 million acres by latitude and then surveys every 100000th acre on the list: Stratified Sampling.
The biologist classifies the Sierras into 10 different ecological types and then makes sure that the proportion of each ecological type from the sample is the same as the proportion of that of the population: Stratified Sampling.
The biologist goes to 15 diverse locations that have 10 acres each and surveys all 10 acres for each of these 15 locations: Cluster Sampling.
The biologist enters the 15 million acres into a data base and had a computer randomly select 150 of these acres: Random Sampling.
give me brainiestMultiply mentally 70 • 100 • 400 = (Type a whole number)
f(x) = 3x and g(x)=x-2, find f(g(4))
If f(x) = 3x and g(x)=x-2, then the value of f(g(4)) is 6.
What is a function?
A function is a mathematical object that assigns exactly one output to each input of a specified type. In other words, a function is a rule that takes in certain inputs (or "arguments") and produces a unique output. The inputs to a function are called the domain, while the set of possible outputs is called the range.
The given functions are f(x) = 3x and g(x)=x-2.
To find f(g(4)), we first need to evaluate g(4). The function g is defined as g(x) = x - 2, so g(4) = 4 - 2 = 2.
Next, we need to evaluate f(2), where f is defined as f(x) = 3x. So, f(2) = 3 * 2 = 6.
Therefore, f(g(4)) = f(2) = 6.
Hence, if f(x) = 3x and g(x)=x-2, then the value of f(g(4)) is 6.
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Ian travels 225 km in 2.5 hours. At what speed does he travel?
Answer:
90 km/h
Step-by-step explanation:
speed = distance/time
speed = 225 km / 2.5 h
speed = 90 km/h
Answer:
90km/hr
Step-by-step explanation:
To find the speed, take the distance and divide it by the time.
225 km/ 2.5 hours
90km/hr
Graph the inequality below on the number line.
y>-10
The graph of the inequality y > -10 is given by the image presented at the end of the answer.
What are the inequality symbols?The four inequality symbols, along with their meaning, are presented as follows:
> x: greater than x.< x: less than x.≥ x: at least x.≤ at most x.The inequality for this problem is given as follows:
y > -10.
Which means that the solution is the numbers that are greater = to the right of -10, with an open interval.
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suppose you have a street light at a height . you drop a rock vertically so that it hits the ground at a distance from the street light. denote the height of the rock by . the shadow of the rock moves along the ground. let denote the distance of the shadow from the point where the rock impacts the ground. of course, and are both functions of time. to enter your answer into webwork use the notation to denote : then the speed of the shadow at any time while the rock is in the air is given by
The speed of the shadow at any time while the rock is in the air is given by v(1-s) / (H-h).
By the AAA congruency theorem, the two triangles are formed and are similar. Here, the ratio of their sides must be equal, and thus -
= H/d+s = h/s
= Hs = h(d+s)
= Hs = hd + hs
= Hs - hs = hd
= s(H-h) = hd
Differentiating both sides with respect to t -
= {s' (H- h)} + {sh'} = h'
Since we know that h' = v -
= {s' (H- h)} + {sv} = v
= s'(H-h) = v - sv
= s'(H-h) = v(1-s)
= s' = v(1-s) / (H-h)
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big lake bob spends his time carving fishing lures and duck decoys. if big lake bob spends all of his time carving fishing lures he can carve 125 lures in a week. if he spends all of his time carving duck decoys he can carve 20 decoys in a week. for every 4 duck decoys big lake bob carves he must give up 25 fishing lures. Fill in the values in the table below to complete Big Lake Bob's production possibilities schedule. Fising Lures Duck Decoys 100 0 0 30
50 fishing lures are carved in a week.
A) Big Lake Bob
Production Possibilities Schedule:
Fishing Lures Duck Decoys
100 0
90 5
80 10
70 15
60 20
50 25
40 30
30 35
20 40
10 45
0 50
50 fishing lures are carved in a week.
25 duck decoys are crafted in a week.
This implies that Big Lake Bob forgoes 10 fishing lures for every 5 duck decoys he carves.
Large Lake Schedule of Bob's productivity potentials
B) Bob's potential for production The schedule is a table of numbers that shows the various combinations of two items that can be created using the restricted resources (labor hours, capital, materials, etc.) and technology in Bob's economy.
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Find the value of x PLEASE HELP FOR BRAINLIEST
Answer:
31.81
Step-by-step explanation:
the dotted line ² = (22²-16²)
x = sq root of [dotted line² +(44-16)² ]
= sq root of [22²-16²+28²]
31.81
Exercise 2:
Identify the missing terms:
4a (-2a³+4__+3)+ 2a(__a³- 2a+_)= -2a*+12a²+26a
JE
The complete expression of the algebra is;
4a(-2a³ + 4a + 3) + 2a(3a³ - 2a + 7) = -2a⁴ + 12a² + 26a
How to expand algebraic expressions?We are given the expression as;
4a(-2a³ + 4__ + 3) + 2a(__a³ - 2a + _) = -2a* + 12a² + 26a
Expanding the left hand side gives;
-8a⁴ + __(16a) + 12a + __(2a⁴) - 4a² + __(2a)
Grouping like terms gives;
-8a⁴ + __(2a⁴) + 12a + __(2a) + __(16a) - 4a²
Factorizing out exponents gives;
a⁴(-8 + __(2)) + a(12 + __(2)) + a²((16/a) - 4)
Comparing this with the right hand side gives;
a⁴(-8 + __(2)) = -2a* -----(1)
((16/a) - 4)a² = 12a² -----(2)
(12 + __(2))a = 26a ----(3)
From eq 1, we can see that;
* = 4
From eq 2;
((16/a) - 4) = 12
16/a = 12 + 4
a = 16/16
a = 1
From eq 3;
(12 + __(2)) = 26
___ * 2 = 26 - 12
___ = 14/2
___ = 7
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The average pencil has 5,425 pencil shavings. How many pencils are found in 76,450 pencil shavings?
Answer:
14
Step-by-step explanation:
We can divide 76,450 shavings by the average shavings per pencil, 5,425 to get an answer of 14.09... This can be rounded to 14.
using a table or diagram write an equation that represents the linear function shown in the table or mapping diagram
An equation that represents the linear function shown in the table or mapping diagram is y = -x/4 - 3.
How to write an equation that represents the linear function?In order to write an equation that represents the linear function, we would use the point-slope form. Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represents the slope.x and y are the points.Next, we would determine the linear function representing the line which passes through the data points (-4, 6) and (8, 3) by using the point-slope form as follows:
y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
y - 6 = (3 - 6)/(8 - (-4))(x - (-4))
y - 6 = (3 - 6)/(8 + 4)(x + 4)
y - 6 = -3/12(x + 4)
y - 6 = -x/4 - 9
y = -x/4 - 9 + 6
y = -x/4 - 3
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Any one help me please the question is in the screenshot.
The answers include the following below:
The sale price is 85% of the regular price.The equation which can be used to find the sale price, s, of an oil change is s = 0.85(30).What is Sale price?This is referred to as the discounted price at which goods or services are being sold.
Since we were told that the discount is 15%, then the sale price will be (100-85)% of $30 which is 85% of $30.
This therefore means that the equation to find the sale price will be 85/100 × 30 = 0.85(30).
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The sum of two numbers is 62. 3 times the smaller number exceeds twice the larger number by one. What are the numbers.
The smaller number is 25 and larger number is 37
What are linear equations?Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.
Given here; The sum of two numbers is 62 and 3 times the smaller number exceeds twice the larger number by one.
let the smaller number be x and the larger number be y then we have
x+y=62
3x-2y=1
Thus solving this system of linear equations by method of elimination we get
5y=185
y=37
∴ x=25
Hence, The smaller number is 25 and larger number is 37
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Round 11,900 to the nearest thousand.
Answer:
12,000
Step-by-step explanation:
How can we do this?
We can do this by taking the number 11,900,
11,900
looking at the hundredths place,
11,900
and figuring out if it is closer to 10, or 0. 9 is closer to 10, so we round up.
12,000
Therefore, 11,900 rounded to the nearest thousand is 12,000.
Please helppp with this question
On solving the system of linear equations 3x + 3y = 45 and x + 2y = 24, the cost for each shirt is obtained as $6, and cost for each pair of pants is obtained as $9.
What is a linear equation?
A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.
Let the cost of shirts be x and the cost of pair of pants be y.
The number of shirts bought by person A = 3
The number of pair of pants bought by person B = 3
The total cost for person A = $45
The equation for person A is -
3x + 3y = 45....(1)
The number of shirts bought by person B = 1
The number of pair of pants bought by person B = 2
The total cost for person B = $24
The equation for person B is -
x + 2y = 24....(2)
Multiply equation (2) by 3 -
3(x + 2y) = 24 × 3
3x + 6y = 72....(3)
Subtraction equation (1) from equation (3) -
3x + 6y - (3x + 3y) = 72 - 45
3x + 6y - 3x - 3y = 27
3y = 27
y = 9
Substitute the value of y in equation (2) -
x + 2(9) = 24
x + 18 = 24
x = 24 - 18
x = 6
Therefore, the cost of shirts and pants is x = 6 and y = 9 respectively.
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Solve the inequality and the graph the solution
An inequality with two variables has a graph, which is a collection of points that shows all possible solution is x≤ 5 3/10.
How to find the calculation?The boundary line between the coordinate plane's two halves, one of which represents the inequality's solutions, is created by a linear inequality.
x + 1 1/2 ≤ 6 8/10 :
Solution : x ≤ 5 3/10
Decimal : x ≤ 5.3
Interval notation : (-∝ , 53/10)
Steps:
x + 1 1/2 ≤ 6 8/10 :
Convert mixed Number to improper Fraction : 1 1/2 = 3/2
1 1/2
Convert mixed numbers to improper fraction ; a (b/c ) = a. c +b /c
1 1/2 = 1.2 + 1 /2
=3/2.
x + 1 1/2 ≤ 6 8/10 :
Convert mixed Number to improper Fraction : 6 8/10 = 68/10
6 8/10
Convert mixed numbers to improper fraction ; a (b/c ) = a. c +b /c
6 8/10 = 6.10 + 8 /10
=68/10
x+ 3/2 ≤ 68/10
Cancel the Common factor :2
x + 3/2 ≤ 34/5
Move 3/2 to the right side
x ≤ 53/10
Convert improper Fraction to mixed Numbers: 53/10 = 5 3/10
53/10 = 5 Reminder 3
Convert to mixed Number : Quotient (Remainder / Divisor)
53/10 = 5 3/10
x≤ 5 3/10
x≤ 5 3/10.
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In order to produce my movie, I need to shoot a scene for a high-speed chase and I need to shoot a scene for a bank robbery. The film production crew will be putting the movie together. I have the stunt crew for the chase scene from 10 am to 11 am and I have the stunt crew for the robbery from 6pm to 7 pm. Will the order I shoot the scenes in matter? What mathematical property did you use to answer this question?
The order in which you shoot the scenes will not matter in terms of the final outcome of the movie.
The mathematical property that one can use to answer this question is scheduling.
How to illustrate the information?From the information, in order to produce the movie, one needs to shoot a scene for a high-speed chase and need to shoot a scene for a bank robbery.
Here, the film production crew will be putting the movie together. However, it may impact the logistics of the production process and the scheduling of the crews. It is not a mathematical property that I used to answer this question. It is simply a matter of logistics and scheduling.
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The perimeter of a certain rectangle is 26 m. Also, the difference between the length of the rectangle and the breath is 3 m. Find the length and the breadth of the rectangle.
A rectangle having perimeter 26 m has a length of 8m and breadth of 5m.
What is perimeter?
The complete length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges. Its dimensions are expressed in linear units like centimetres, metres, inches, and feet.
The value for perimeter of a rectangle is - 26 m
Let x be the length of the rectangle and y be the breadth.
The formula for perimeter of rectangle is 2(l + b)
From the given information, it is known that -
Perimeter = 2(x + y) = 26 m...(1)
Difference between the length and breadth = x - y = 3 m....(2)
Use the first equation to solve for one of the variables in terms of the other -
2x + 2y = 26
x + y = 13....(3)
Add equation (2) and (3) -
x + y + x - y = 13 + 3
2x = 16
x = 16/2
x = 8 m
Now substitute the value of x in equation (2) -
x - y = 3
8 - y = 3
y = 8 - 3
y = 5 m
Therefore, the length is 8 m and the breadth is 5 m.
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(-1.2) (-3.5) (-2.7) (-0.4) a positive product?
We have the product of 4 negative numbers, by the rule of signs, we can see that the product is positive.
Is the product positive?Here we need to reember the rule of signs for the product, it is:
(-)*(-) = +
(+)*(+) = +
(+)*(-) = -
(-)*(+) = -
So the product between two negative numbers is positive, now let's look to our product.
(-1.2)*(-3.5)*(-2.7)*(-0.4)
We can rewrite this as:
(-1.2*-3.5)*(-2.7*-0.4)
The negative sings cancell, then we get:
(-1.2*-3.5)*(-2.7*-0.4)
(4.2)*(1.08)
Now we have the product of two positive numbers, this will be positive.
(4.2)*(1.08) = 4.536
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Kylli began a trip with 18 1/2 gallons of gas in the gas tank of her car. If she used 17 3/4 gallons on the trip, how many gallons did she have left when she finished the trip?
Answer:
3/4 of a tank of gas
Step-by-step explanation:
18 1/2-17 3/4= 3/4
or the easiest way for me is to change the faction to decimals
18.5-17.75= 0.75 which is 3/4
item 18 time remaining 4 hours 13 minutes 48 seconds 04:13:48 ebook item 18 time remaining 4 hours 13 minutes 48 seconds04:13:48 if bob can produce more donuts in one day, if
If Bob is able to produce more donuts than Sue in one day, that means that Bob has an absolute advantage in the production pf donuts.
Absolute advantage is when a particular person is able to produce more amount of product than the other with the same amount of input of resources, for example, time. Comparative advantage on the other hand is based on the opportunity cost.
Comparative advantage is basically the ability to produce a good or a service for an opportunity cost which is lower than that of a competitor. Since, Bob is able to produce more donuts than Sue, Bob has an absolute advantage over Sue.
--The given question is incomplete, the complete question is
If Bob can produce more donuts in one day than Sue can produce in one day, then:
a. Bob has a comparative advantage in the production of donuts.
b. Sue has a comparative advantage in the production of donuts.
c. Bob has an absolute advantage in the production of donuts.
d. Sue has an absolute advantage in the production of donuts."--
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Evaluate the given function as required.
Calculate R(0) and R(30) if R(t) is as shown below. (Round your answer to two decimal places.)
R(t)=328-296e⁻o.oo4t
The numeric values of the function R(t) = 328 - 296e^(-0.004t) at t = 0 and t = 30 are given as follows:
R(0) = 32. R(30) = 65.47.How to find the numeric value of a function or of an expression?To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.
The function for this problem is defined as follows:
R(t) = 328 - 296e^(-0.004t)
At t = 0, the numeric value is found replacing the lone instance of t by zero, hence:
R(0) = 328 - 296e^(-0.004(0))
R(0) = 32.
At t = 30, the numeric value is found replacing the lone instance of t by 30, hence:
R(30) = 328 - 296e^(-0.004(30))
R(30) = 65.47.
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please help will mark BRAINLIEST
We can see here that Side AC is the longest side. A. Side AC.
What is an angle?An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. Dihedral angles are these.
We see here that triangles that have an angle of 90° are usually known to be right angle. The angles in a triangle are equal to 180°.
We see here that the above answer. This is because the side opposite to the largest angle is the longest angle.
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Need help with question attached below in an image.
We can apply the order of four transformations to the graph of f(x) in order to sketch the graph of g(x): A 3-unit horizontal shift to the left : The graph becomes f(x-3 ) as a result, with a vertical asymptote at x = 0 rather than x = 3.
A ( -2 ) stretch in the vertical direction: The graph is now -2f(x-3), with a slope of -2 for x greater than 3 and 2 for x less than 3.An observation regarding the x-axis: The graph is now -2|f(x-3)|, which is the x-axis-reflecting graph of f(x-3) as a result of this change.A shift up one unit in the vertical: The result of this transformation is the final graph of g(x) = -2|x-3|+1, which is -2|f(x-3)|+1.2. To move from f(x) to g(x), four transformations are used:
A three-unit horizontal shift to the left: The graph thus shifts by a factor of -2 three units in the direction of the left A vertical stretch.
How does one plot a graph?You must first define the function and its domain before you can plot its graph. We can begin by sketching the piecewise linear graph of f(x) = |x|, which has a slope of 1 for x greater than 0 and -1 for x less than 0 in order to sketch the graph of g(x) = -2|x-3|+1. The vertical asymptote is shown by the x axis. For all real numbers, the definition of the f(x) graph exists.
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please help will mark BRAINLIEST
Answer:
100
Step-by-step explanation:
total angles of any triangle is 180
it tells you one of the base angles is 40, so 2 of them are 80
so the top one is 180-80 =100