Answer:
a. 480 Then 384
b. 845 Then 591.5
c. 1,189 Then 653.95
d. 153.75 Then 149.90625
e. 315 Then 299.25
f. 430.5 Then 419.7375
find the greatest sum, difference, product, and quotient using two of the numbers below for each operation. Show your work. 23 3··52.75 218.3 6 24 9 1··
The greatest sum is 271.05, the greatest difference is 215.3, the greatest product is 11535.175, and the greatest quotient is approximately 4.142.
What is a number system?A numeral system is a way of writing numbers; it's a way of mathematically notating a set of numbers by using a consistent set of digits or other symbols.
To find the greatest sum, difference, product, and quotient using two of the given numbers, we can compare the results of each operation by pairing the numbers in different ways.
Note: For the quotient, we will only consider pairs of numbers where the denominator is not zero.
Sum:
The greatest sum will be obtained by adding the two largest numbers, which are 218.3 and 52.75.
218.3 + 52.75 = 271.05
Difference:
The greatest difference will be obtained by subtracting the smallest number from the largest number, which is 218.3 and 3.
218.3 - 3 = 215.3
Product:
The greatest product will be obtained by multiplying the two largest numbers, which are 218.3 and 52.75.
218.3 × 52.75 = 11535.175
Quotient:
The greatest quotient will be obtained by dividing the two largest numbers, which are 218.3 and 52.75.
218.3 ÷ 52.75 ≈ 4.142
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2 You collected $12 each from 15 family members, neighbors and friends as part of this year's school fundraiser. How much money did you collect in total, in dollars?
The total amount of money collected is $180.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given that, person collected $12 each from 15 family members.
Total money = Amount of money collected from each × Number of people
= 12×15
= $180
Therefore, the total amount of money collected is $180.
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Ricardo is half as likely to spin a 2 or 4 than an odd number
Based on the information provided, the statement "Ricardo is half as likely to spin a 2 or 4 than an odd number" is false.
How to test if this statement is true or false?To better understand if this is a valid statement, let's calculate the probability in each case.
Probability to get a 2 or 4:
1/ 8= 0.125 or 12.5% ( 0.125 x 100 = 12.5%)
Probability to get an odd number:
4/8 = 0.5 or 50% (0.5 x 100 = 50%)
This shows that the probability of getting a 2 or a 4 is 12.5%, while the probability of getting an odd number is 50%, which makes the statement false.
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2/5 x + 7 - 2/3x -15
Answer:
See below.
Step-by-step explanation:
We are asked to simplify the equation.
First, we should Combine Like Terms.
What is Combining Like Terms?
Combining Like Terms is adding terms that are alike.
For example, 4x and 11x are like terms since there's no differences than the coefficient, which can be different.
Let's combine like terms for this problem now.
Combine Like Terms:
[tex]\frac{2}{5} x+ 7 - \frac{2}{3} x -15\\\\\frac{2}{5} x - \frac{2}{3} x = \frac{6}{15} x - \frac{10}{15} x=-\frac{4}{15} x\\\\7 - 15 = -8[/tex]
We should have;
[tex]- \frac{4}{15} x - 8[/tex]
This will be our final answer.
ILL GIVE BRAINLY What is the surface area of the cube?
Drag and drop the correct surface area to match the cube.
Answer:
Below
Step-by-step explanation:
A cube has SIX sides of equal area
each side has area = L x W and L and W are the same = 4.5 m
so: Area = six X ( 4.5 X 4.5) = 6 * 4.5 * 4.5 = 121.5 m^2
Answer:
Hope the picture will help you...
Devon's annual income grows at a rate of 2.9% per year, and inflation is 3.1% per year. After one year, how much can Devon
buy with his annual income?
O less than today because 3.1% is greater than 2.9%
less than today because the inflation rate is greater than 0
O more than today because 3.1% is greater than 2.9%
O more than today because interest is earned on the account
Answer:
Step-by-step explanation:
After one year, Devon's income will have grown by 2.9%. However, because inflation is 3.1%, the purchasing power of his income will decrease. This means that Devon will be able to buy less than he could today.
To calculate how much Devon can buy with his annual income after one year, we can use the following formula:
Purchasing power = Income / (1 + inflation rate)
Substituting the values given in the problem:
Purchasing power after one year = Income / (1 + 0.031)
Purchasing power after one year = Income / 1.031
Therefore, Devon will be able to buy approximately 0.97 times (or 97% of) what he could buy with his income today. In other words, his purchasing power will have decreased by approximately 3%.
Answer:
Devon's annual income increases at a rate of 2.9% per year, which means that after one year, his income will be 1.029 times his current income. However, due to inflation of 3.1% per year, the purchasing power of money decreases, which means that after one year, the amount of goods and services that can be purchased with the same amount of money will be 1/1.031 times what it is today.
Therefore, after one year, Devon can buy (1.029/1.031) times what he can buy today with his annual income. Simplifying this expression gives:
1.029/1.031 = 0.9971
So, Devon can buy about 99.71% of what he can buy today with his annual income after one year. In other words, he can buy slightly less than he can buy today, because inflation is greater than the rate at which his income is increasing.
How would you graph f(x)=x+3 ? And could you leave an explanation?
Answer:
Step-by-step explanation:
To graph the function f(x) = x + 3, we need to plot a series of points that satisfy the equation. We can do this by picking some values of x and then finding the corresponding values of f(x).
For example, when x = 0, f(x) = 0 + 3 = 3. So we have the point (0, 3) on our graph.
Similarly, when x = 1, f(x) = 1 + 3 = 4. So we have the point (1, 4) on our graph.
We can continue this process for other values of x, and we'll get more points on the graph. For example, when x = -1, f(x) = -1 + 3 = 2. So we have the point (-1, 2) on our graph.
Once we have enough points, we can connect them with a straight line to get the graph of the function. In this case, we'll notice that the graph is a line with a slope of 1 and y-intercept of 3. The slope of the line tells us how much y changes when x increases by 1, and in this case, it changes by 1 unit.
So, to graph f(x) = x + 3, we can start by plotting the point (0, 3) and then draw a line that passes through this point and has a slope of 1. We can use a straightedge or ruler to draw the line as accurately as possible. The resulting graph will be a straight line that intersects the y-axis at the point (0, 3) and has a slope of 1.
40. Critical Thinking The GCF of two numbers p and q is 5. What is the GCF of p² and q2? Explain your answer.
The GCF of p² and q² is 25. And the explanation is mentioned below.
What is GCF ?The acronym GCF means "Greatest Common Factor." It is often referred to as the "Highest Common Factor" or the "Greatest Common Divisor" (GCD) (HCF). The biggest number that divides two or more other numbers without producing a residue is known as the GCF.
If the GCF of two numbers p and q is 5, then we can express the numbers as:
p = 5a
q = 5b
where a and b are integers, and 5 is the greatest common factor.
Now, let's consider p² and q²:
p² = (5a)² = 25a²
q² = (5b)² = 25b²
We can factor out 25 from both expressions:
p² = 25(a²)
q² = 25(b²)
Notice that the expression for p² has a factor of 25 and a factor of a², while the expression for q² has a factor of 25 and a factor of b².
Since the GCF of p and q is 5, we know that a and b do not have any common factors besides 1 and 5.
Therefore, a² and b² also do not have any common factors besides 1 and 5.
This means that the GCF of p² and q² is simply the factor of 25 that they have in common, which is 25.
So, the GCF of p² and q² is 25.
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Find the solution to 1/9 divided by 3, using either the flip and multiply method or common denominator method.
Answer:
Step-by-step explanation:
Just multiply the denominator just that 1/9 divided by 3 is 1 /27 your welcome have a good day :)
Answer:
[tex]\frac{1/9}{3/1}=[/tex] [tex]\frac{1}{27}[/tex]
Step-by-step explanation:
[tex]skip:[/tex] [tex]\frac{1}{9}[/tex]
[tex]flip:[/tex] [tex]\frac{3}{1} = \frac{1}{3}[/tex]
[tex]Equation Now: \frac{1/9}{1/3}[/tex]
[tex]Multiply: \frac{1}{9}*\frac{1}{3}=\frac{1}{27}[/tex]
[tex]Answer=[/tex][tex]\frac{1}{27}[/tex]
Use the graph to answer the question. Graph of polygon ABCD with vertices at 1 comma 3, 3 comma negative 1, 7 comma negative 1, 5 comma 3. A second polygon A prime B prime C prime D prime with vertices at negative 5 comma 3, negative 3 comma negative 1, 1 comma negative 1, negative 1 comma 3. Determine the translation used to create the image. 6 units to the right 6 units to the left 2 units to the right 2 units to the left
The translation of the polygon is 6 units to the left
What is Translation?A translation moves a shape up, down, or from side to side, but it has no effect on its appearance. A transformation is an example of translation. A transformation is a method of changing a shape's size or position. Every point in the shape is translated in the same direction by the same amount.
A translation in the coordinate plane moves every point on a figure a given distance in a given direction. The position of any point (x, y) on the figure changes to (x + a, y + b), where a and b are real numbers.
Given data ,
Let the polygon be represented as ABCD
Now , the coordinates of the polygon is given as
The coordinate of A = A ( 1 , 3 )
The coordinate of B = B ( 3 , -1 )
The coordinate of C = C ( 7 , -1 )
The coordinate of D = D ( 5 , 3 )
Now , the translated polygon is having the coordinates as
The coordinate of A' = A' ( -5 , 3 )
The coordinate of B' = B' ( -3 , -1 )
The coordinate of C' = C' ( 1 , -1 )
The coordinate of D' = D' ( -1 , 3 )
So , the translation rule is ( x , y ) → ( x - 6 , y )
And , the figure is translated 6 units to the left
Hence , the translation is 6 units to the left
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900 p (into rupees)
400 cm (into metre)
Rs. 27.70, Rs. 32.40 and Rs. 44.80 (Add)
9m 80 cm (into centimetre)
6480 m (into kilometres and metre)
Rs. 820.00 - Rs. 512.10 (Subtract)
The conversion addition and subtraction of the numbers are done.
Explain about the unit conversions?The system you use to express how big or tiny something is is called a unit of measurement. Suppose it depends on the subject you're measuring, the unit will change. For instance, you can determine how many pounds or kilograms you are when you step upon that weight machine to weigh yourself.We now need convert between units in order to ensure accuracy and prevent measurement misinterpretation. For example, we would not measure a pencil's length in kilometers. In this situation, one must convert from kilometers (km) to centimeters (cm).So, Solution are:
A. 900 p (into rupees)
1 rupee = 100 p
900 p = 9 rupees
B. 400 cm (into metre)
1 m = 100 cm
400 cm = 4.00 m
C. Rs. 27.70, Rs. 32.40 and Rs. 44.80 (Add)
= Rs. 27.70 + Rs. 32.40 + Rs. 44.80
= 104.9
D. 9m 80 cm (into centimetre)
1 m = 100 cm
= 9m 80 cm
= 9m + 0.80m
= 9.8 m
E. 6480 m (into kilometres and metre)
1 m = 100 cm
6480 m
1 km = 1000m
6480 m = 6.480 km
F. Rs. 820.00 - Rs. 512.10 (Subtract)
Rs. 307.9
Thus, the unit conversion, addition and subtraction of the numbers are done.
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Tebogo pays a R4350 a month for house that she is renting.calculate the amount she will pay after a year.
Answer:
R52200
Step-by-step explanation:
I'm making the assumption that R is a currency symbol.
There are 12 months in a year. Simply multiply the cost for one month by 12 to find the total cost for a year:
4350 * 12 = 52200
Use the drawing tools to form the correct answer on the graph.
Plot function h on the graph.
J-4,
lz + 5,
h (x)
=
x < -3
X -3
Answer:
I do not have access to drawing tools to create a graph. However, I can explain how to plot the function h on the graph based on the given information.
The function h(x) has two parts:
For x < -3, the value of h(x) is J-4.
For x >= -3, the value of h(x) is x-3.
To plot this on a graph, you would need to draw a vertical line at x = -3 to separate the two parts of the function. Then, for x < -3, you would plot a horizontal line at a height of J-4 to represent the constant value of h(x) in that region. For x >= -3, you would plot the line y = x-3.
I hope this explanation helps you to plot the function h on the graph!
Step-by-step explanation:
What is 31 divided 4,208
Answer:
if you mean 4,208 divided by 31 its 135.7 (in case you formatted it wrong)
but if your asking 31 divided by 4,208 its 0.007
which triangle has three angles with the same measure?
Answer:
equilateral triangle
Step-by-step explanation:
40 points!
You are framing a picture with a frame of equal width on each side.
a. Write a polynomial that represents the area of the picture including the frame
b. Find the area of the picture including the frame when the width of the frame is 2 inches
a. a polynomial that represents the area οf the picture including the frame [tex]\mathrm{A = (x + 2w) \times (x + 2w) = (x + 2w)^2}[/tex]
b. The area οf the picture including the frame when the width οf the frame is 2 inches is [tex](x + 4)\²[/tex]
Why is it referred to as a polynomial?The English wοrd "polynomial" is derived from the Greek words "poly" and "nominal," which together denote "many sentences". The number of terms a polynomial can have is unbοunded.
a. Let x be the width οf the picture. Then the length of the picture is alsο x. Let w be the width οf the frame. The total width of the picture including the frame is (x + 2w), and the tοtal length of the picture including the frame is (x + 2w). Therefοre, the area of the picture including the frame is:
[tex]\mathrm{A = (x + 2w) \times (x + 2w) = (x + 2w)^2}[/tex]
b. If the width οf the frame is 2 inches, then w = 2. Substituting w = 2 into the polynomial above gives:
[tex]\mathrm{A = (x + 2w) \times (x + 2(2)) = (x + 4)^2}[/tex]
Therefore, the area οf the picture including the frame when the width οf the frame is 2 inches is (x + 4)² square units.
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a. What are the distances in feet covered in 4 steps, 6 steps, 12 steps, and 30 steps? Type your answers in the table.
Answer: 4 steps: 12 feet
6 steps: 18 feet
12 steps: 36 feet
30 steps: 90 feet
Step-by-step explanation:
Select all the equations where � = 3 x=3x, equals, 3 is a solution. Choose 2 answers: Choose 2 answers: (Choice A) � + 4 = 7 x+4=7x, plus, 4, equals, 7 A � + 4 = 7 x+4=7x, plus, 4, equals, 7 (Choice B) � 9 = 3 9 x =3start fraction, x, divided by, 9, end fraction, equals, 3 B � 9 = 3 9 x =3start fraction, x, divided by, 9, end fraction, equals, 3 (Choice C) 5 − � = 2 5−x=25, minus, x, equals, 2 C 5 − � = 2 5−x=25, minus, x, equals, 2 (Choice D) 8 � = 32 8x=328, x, equals, 32 D 8 � = 32 8x=328, x, equals, 32 (Choice E) � − 10 = 7 x−10=7x, minus, 10, equals, 7 E � − 10 = 7 x−10=7
All of the equations where x = 3 is a solution include the following:
A. x + 4 = 7.
C. 5 - x = 2.
How to determine the equation with a solution of x = 3?Based on the information provided, we have the following equation:
x + 4 = 7
3 + 4 = 7
7 = 7 (True).
When x = 3, we have the following equation:
x/9 = 3
3/9 = 3
1/3 = 3 (False).
When x = 3, we have the following equation:
5 - x = 2
5 - 3 = 2
2 = 2 (True).
When x = 3, we have the following equation:
8x = 32
8(3) = 32
24 = 32 (False).
When x = 3, we have the following equation:
x - 10 = 7
3 - 10 = 7
-7 = 7 (False).
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given that -3/2 is one of the root of the equation 2y^2+6y+p=0, find the value of p
Answer:
p = [tex]\frac{9}{2}[/tex]
Step-by-step explanation:
given y = - [tex]\frac{3}{2}[/tex] is a root of the equation , then this value makes the equation true.
substitute y = - [tex]\frac{3}{2}[/tex] into the equation and solve for p
2( - [tex]\frac{3}{2}[/tex] )² + 6(- [tex]\frac{3}{2}[/tex] ) + p = 0
2( [tex]\frac{9}{4}[/tex]) - 9 + p = 0
[tex]\frac{9}{2}[/tex] - [tex]\frac{18}{2}[/tex] + p = 0
- [tex]\frac{9}{2}[/tex] + p = 0 ( add [tex]\frac{9}{2}[/tex] to both sides )
p = [tex]\frac{9}{2}[/tex]
Triangle ABC is congruent to triangle DEF. If DE = 41, EF = 23, DF = 36, and BC = 4x − 7, what is x? Round to the nearest tenth.
A) 7.5
B) 8.0
C) 8.7
D) 10.8
According to given information, x is 7.5 to the nearest tenth.
What is Triangle?
In geometry, a triangle is a two-dimensional closed shape with three straight sides and three angles. It is formed by connecting three non-collinear points with line segments. The three points of a triangle are called its vertices, and the line segments connecting them are called its sides.
If triangles ABC and DEF are congruent, then their corresponding sides are equal in length. Therefore, we have:
AB = DE = 41
BC = EF = 23
AC = DF = 36
We are given that BC = 4x - 7, so we can set up the following equation:
4x - 7 = BC = EF = 23
Solving for x, we get:
4x = 30
x = 7.5
Therefore, according to given information x is 7.5 to the nearest tenth.
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3(-4q² - 1)
needs help quickly!
Answer:
= 12q² - 3
Step-by-step explanation:
3(-4q² - 1)
= -12q² - 3
PLEASE HELP NEED ASAP
Write the quadratic function in the form f(x) = a (x-h)² + k.
Then, give the vertex of its graph.
f(x) = -x²+2x-5
The vertex of the function is,
⇒ Vertex = (1, - 4)
What is Quadratic equation?An algebraic equation with the second degree of the variable is called an Quadratic equation.
Given that;
The function is,
⇒ f (x) = -x² + 2x - 5
Now,
We can change the quadratic function in the form,
⇒ f (x) = a (x - h)² + k
Hence, We get;
⇒ f (x) = - x² + 2x - 5
⇒ f (x) = - (x² - 2x + 1 - 1) - 5
⇒ f (x) = - (x - 1)² + 1 - 5
⇒ f (x) = - (x - 1)² - 4
Thus, The vertex of the function is,
⇒ Vertex = (1, - 4)
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What is the area of this trapezoid?
140 in²
147 in²
196 in²
228 in²
Answer:
140in^2
Step-by-step explanation:
Split the area into 3 different shapes, and solve for the area of each (see picture below)
For the first area, the left triangle, we have a length of 4 and a height of 7. So we're going to multiply these two numbers together, then divide by 2 since we're only solving for the area of a triangle and not a rectangle. This gives us 14in^2.
Next, we can simply multiply 15 by 7 to get an area of 105in^2, since this is a rectangle.
For the last area, we can do the same thing as the first. Multiply 6 by 7, then divide by 2, giving us 21in^2.
Finally, we can add up all of these areas to get the total area, and our final answer:
14+105+21=140in^2
To pay for an 18,800 motorcycle, Salma made a down payment of 3500 and took out a loan for the rest. On the loan, she paid monthly payments of for 5 years.
Salma borrowed $15,300 and paid $295.24 per month for 5 years to pay off the loan.
What is loan?
In a loan, a certain quantity of money is given to another person in exchange for the value or main amount being repaid at a later date. In many circumstances, the lender increases the principal value by adding interest or finance charges, which the borrower must pay in addition to the principal sum.
To find out how much Salma borrowed, we can subtract her down payment from the cost of the motorcycle -
Loan amount = Cost of motorcycle - Down payment
Loan amount = 18,800 - 3,500
Loan amount = 15,300
Salma paid monthly payments for 5 years, which is equivalent to 60 months.
To calculate the monthly payments, we need to use the loan amount, the interest rate, and the loan term.
Let's assume the interest rate is 6%, which is a common rate for motorcycle loans.
We can use a loan calculator to find out the monthly payments -
Loan amount = 15,300
Interest rate = 6%
Loan term = 60 months
Using a loan calculator, we get a monthly payment of $295.24.
Therefore, Salma borrowed $15,300 and paid $295.24 per month.
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what are three consecutive even numbers that have a sum of 5760?
Answer:
Hey i'll give you a step-by-step explanation but what do u mean by consecutive even number's do you mean like: 0, 2, 4, 6, 8, 10, 12, ect..?Step-by-step explanation:
The first equation from the previous system of
equations is graphed. Graph the second equation to
find the solution of the system of equations.
y =-2x + 4,
y =-;
[*-1
What is the solution to the system?
The solution to the system of equations is x = 1.8, y = 0.4.
What is the solution to the system?
To graph the second equation, we can start by plotting the y-intercept of -1 on the y-axis. Then, using the slope of -1/3, we can find another point on the line.
For example, we can move down one unit and to the right three units from the y-intercept, which gives us the point (3,-2).
Graph of the two equations:
y = −2x + 4,
y = − 1/3x − 1
From the graph (check the image attached), we can see that the two lines intersect at the point (1.8, 0.4).
Therefore, the solution to the system of equations is x = 1.8, y = 0.4.
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The complete question is below:
The first equation from the previous system of equations is graphed. Graph the second equation to find the solution of the system of equations.
y = −2x + 4,
y = − 1/3x − 1
What is the solution to the system?
A randomized study compared two drugs that are designed to increase a child's human growth hormone level. It was found that over a 1-year period, those receiving Drug A increased their hormone level by a mean of 28 IU. Those receiving Drug B increased their hormone level by a mean of 15 IU (IU = International unit).
To determine whether the results are significant, the data are rerandomized and the difference of the means is shown in the dot plot.
What is the best conclusion to make based on the data?
The greatest inference we can draw from the data presented and the dot plot, however, is that there is proof indicating that Drug A is much more likely than Drug B to increase levels of human growth hormone.
What does the term "growth" mean?the process of developing; progressive expansion; the act or activity of growing.
According to the provided dot plot, there appears to be a considerable variance in both medications' capacities to raise levels of human growth hormone. There is little crossover in the pieces of data for the two medicines, and the mean rise for Drug A is obviously greater than the average rise for Drug B.
We would need to do a formalized hypothesis test, which might involve a t-test, and generate a p-value to establish to see if this variance has statistical significance. We could conclude that the variation in averages is statistically significant if the p-value is less than a predetermined significance criterion (for example, 0.05).
The most important conclusion that can be made from the data and dot plot is the existence of evidence that suggests Drug A is much more probable that Drug B to enhance levels of growth hormone in humans. Further statistical analysis would be required to confirm the relevance of this divergence.
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Problem 5
Explain what you could do first to each side of the equation so that there would be no fractions.You do not have to solve the equations (unless you want more practice).
The first thing to do to each side of the equation so that there would be no fractions is to cross product.
The unknown number, a is -48
How to solve fractions?A fraction refers to a number which has a numerator (top value) and a denominator (bottom value).
2(a - 7) / 15 = (a + 4) / 6
cross product
6{2(a - 7)} = 15(a + 4)
open parenthesis
6(2a - 14) = 15a + 60
12a - 84 = 15a + 60
combine like terms
12a - 15a = 60 + 84
-3a = 144
divide both sides by -3
a = 144/-3
a = -48
In conclusion, the solution to the fraction is a = -48
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what are the terms missing in given number square 5,6,8___,15___
Answer:
11, 20.
Step-by-step explanation:
5,6,8, 11 ,15, 20.
6. What is the slope of the line through the points (-2, -1) and (4, 3)
5/2
2/5
2/3
3/2
Answer: 2/3
Step-by-step explanation: y1-y2 3-(-1) = 4 simplify 4/6=2/3
x1-x2 4-(-2)= 6
Slope is described as "the rise over the run," meaning that it's the fraction of "the change in the y-values compared to the change in the x-values."
In this situation
- the change in the y-values is 3 - (-1) = 4.
- the change in the x-values is 4 - (-2) = 6.
so the fraction is 4/6 or 2/3.
As a general formula, the formula for slope is [tex]m = \dfrac{y_2-y_1}{x_2-x_1}[/tex].
[tex]m = \dfrac{3-(-1)}{4-(-2)}=\dfrac{4}{6}=\dfrac{2}{3}[/tex]