The fraction 1/4b + 1/4 = -1/2 is simplified to b = -12/4
What is a fraction?
A fraction can be defined as the part of a whole variable, or number.
The types of fractions are;
Mixed fractionsProper fractionsImproper fractionsComplex fractionsSimple fractionsFrom the information given, we have that;
1/4b + 1/4 = -1/2
Now, collect iike terms
1/4b = -1/2 - 1/4
find the lowest common denominator
1/4b = -2 -1 /4
Add the numerators
1/4b = -3/4
Now, divide both sides by the coefficient of b
b = -3/4 × 4/1
Multiply the values
b =-12/4
Hence, the value is - 12/4
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You are traveling west on the highway. At 1:00 you pass kilometer marker 485. At 4:30 you pass kilometer marker 154. What has your average velocity been.
technically a physical science question but i didn't know what to label it.
The average velocity is 94.6km / hour
What is average velocity?Average velocity is defined as the change in position or displacement (∆x) divided by the time intervals (∆t) in which the displacement occurs. The average velocity can be positive or negative depending upon the sign of the displacement. The SI unit of average velocity is meters per second (m/s or ms-1).
therefore average velocity = change in displacement / change in time
change in displacement = 485 - 154 = 331 km
change in time = 4:30-1:00 = 3 hours 30minutes = 3½ hrs
average velocity = 331/3.5
= 94.6km/hour
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In a club with 99 male and 1616 female members, how many 77-member committees can be chosen that have (a) all men? (b) all women? (c) 44 men and 33 women?
The probability for the question as per the information that has been provided, can be solved in the following manner:
a) Probability for picking an all men committee
P = picking a Male probability
= 99/1715
Now, P = picking a female probability
= 1616/1715
The number of 77-member committee is Binomial [1715,77]
The number of 77-member committee being male is Binomial [99,77]
The probability of 77 men committee is Binomial [1715,77] / Binomial [99,77] or 99C77/1715C77
b) Probability for picking an all women committee
P = picking a Male probability
= 99/1715
Now, P = picking a female probability
= 1616/1715
The number of 77-member committee is Binomial [1715,77]
The number of 77-member committee being women is Binomial [1616,77]
The probability of 77 men committee is Binomial [1715,77] / Binomial [1616,77] or 1616C77/1715C77
c) Probability for picking 44 men and 33 women
Desired set is 44 men and 33 women, which can be done in 99C44 and 1616C33 ways.
So, P(44 men and 33 women) = 99C44 × 1616C33 / 1715C77
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What do I put in the boxes
Step-by-step explanation:
6
7 47
42
-------
R 5
47 ÷ 7 = 6.71428571429
a square has side length of 7.37.3 inin. if the area is multiplied by 1919, what happens to the perimeter?
The perimeter should be multiplied by 1/3
The side length of the square, which is 7.3 inches,
The square's surface area
Side x Side is Area = 7.3 x 7.3 = 53.29
The square's new area is multiplied by 1/9,
so area is equal to
1/9 x 53.29 and s is equal to 2.4333.
Using the length of the new square as the new perimeter, the square's new perimeter is equal to 9.733 times its side times.
Now that we have calculated the perimeter ratios, we can see that the square's side length is 7.3.
the perimeter is equal to 7.3 times 4 and equals 29.12; nevertheless,
the ratio of the perimeters of the first and second lengths is equal to
29.12/9.733 and is
therefore 3:1.
so, perimeter multiplied by 1/3
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Can you give me great examples of buildup, unit ratio, and cross multiplication for proportional relationships? I am trying to get an A on this test and dont want to mess up.
Cross multiplying will help us identify the variable if it is the same variable that is present on both sides of the equation. Let's explain with the use of examples. Solve X/5 = 5/X, for instance.
What is cross multiplication in ratio and proportion?When you multiply the denominator of one ratio by the numerator of another, you get a cross product. In the event when the cross products are equal, the ratios are proportionate. In the case of ratios and, and are proportional and can be expressed as a b = c d.So 4×32=128. Moreover, we obtain the result 726=182 when we cross-multiply these two. The fact that 182 is greater than 128 enables us to conclude that 732 is greater than 426. The number we multiplied by our numerator symbolises the matching fraction, and we must always keep this in mind.For comparison of fractions, cross multiply. The most typical application of cross multiplication is the comparison of fractions. multiplying the numerator while paying closer attention to the procedure.To learn more about Cross multiplying refer to:
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a survey was conducted on 218 undergraduates from duke university who took an introductory statistics course in spring 2012. among many other questions, this survey asked them about their gpa and the number of hours they spent and studying per week. based on this study, can we conclude that studying longer hours leads to higher gpas?
No, we cannot conclude that studying longer hours leads to higher GPAs based on this survey.
This survey only provides us with the average GPAs and average hours per week spent studying for a sample of 218 undergraduates from Duke University who took an introductory statistics course in spring 2012. This is not enough information to draw a conclusion about the correlation between hours of study and GPA. To do this, we would need to look at the correlation between the two variables. To calculate the correlation, we would need the individual data points of the GPAs and hours of study for each respondent. We could then calculate the Pearson correlation coefficient and the significance of the correlation. This would provide us with a more definitive answer to our question.
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John is making apple pies and apple cobblers to sell at his stand at the Farmer's Market.
A pie uses 4 cups of apples and 3 cups of flour.
A cobbler uses 2 cups of apples and 3 cups of flour.
John has 16 cups of apples and 15 cups of flour.
When John sells the pies and cobblers at the Farmer's Market, he will make $3.00 profit per pie and $2.00 profit per cobbler.
Let x = the number of pies John makes.
Let y = the number of cobblers John makes.
Since John cannot make a negative number of pies or cobblers, what additional constraints exist on the variables?
Since John cannot make a negative number of pies or cobblers, the additional constraints that exist on the variables include the following:
B. x ≥ 0.
y ≥ 0.
How to write an equation to model this situation?In order to write an equation that model this situation, we would assign a variable to the number of pies John makes and the total number of cobblers John makes respectively, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the number of pies John makes.Let the variable y represent the total number of cobblers John makes.However, it should be noted that John cannot make a negative number of pies or cobblers and as such, the number of pies he makes must be greater than or equal to zero (0) such as 0 pies, 1 pies, 2 pies, 3 pies, 4 pies, etc. Similarly, the aforementioned constrain applies to the number of cobblers John makes.
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Determine whether each set of side lengths could be the sides of a right triangle.
The side length that could be a right triangle are
6 8 105 12 13How to find out side lengths of right triangleApplying Pythagoras theorem, for each side length we solve for the longest side in each case assuming the longest side is x
Using Pythagoras theorem given by the the formula
hypotenuse² = opposite² + adjacent²
checking for 4 7 8
let x be the required distance
x² = 4² + 7²
x² = 16 + 49
x² = 65
x = √65
this is not a right triangle
checking for 6 8 10
let x be the required distance
x² = 6² + 8²
x² = 36 + 64
x² = 100
x = √100
x = 10
this is a right triangle
checking for 5 12 13
let x be the required distance
x² = 5² + 12²
x² = 25 + 144
x² = 169
x = √169
x = 13
this is a right triangle
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A number increased by 15 is greater than 124. Find the smallest integer that satisfies the inequality.
The smallest integer that satisfies the inequality is 110
How to find the smallest integer to satisfy the inequalityThe least number is calculated by first generation g the inequality equation
The statement "A number increased by 15 is greater than 124" is written in an equation form, assuming the number is x
x + 15 > 124
Solving for x with the generated expression
x + 15 > 124
isolating x
x + 15 - 15 > 124 - 15
x > 124 - 15
x > 109
since x is greater than 109 the least integer greater than 109 is 110
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Help w math homework pls
Part A - The area of the deck is approximately equal to 691.150 square feet.
Part B - The deck requires 3.379 gallons of weather treatment.
Part C - The weather treatment have a cost of $ 121.48.
How to determine the deck area around the poolIn this problem we must find the area of the deck around the pool, how many gallons of weather treatment are required and how much is needed to.
Part A - The area of the deck is a circular corona, whose formula is:
A = π · (R² - r²)
Where:
A - Area of the circular corona, in square feet.r - Inner radius, in feet.R - Outer radius, in feet.If we know that r = 6 ft and R = 16 ft, then the area of the deck is:
A = π · [(16 ft)² - (6 ft)²]
A = 220π ft²
A ≈ 691.150 ft²
Part B - If we know that a gallon is effective for an area of 204.5 square feet, the number of gallons can be determined by cross multiplication:
x = (691.150 ft² / 204.5 ft²) × 1
x = 3.379
A number of 3.379 gallons are required for weather treatment.
Part C - The cost of the number of gallons (C), in monetary units, is equal to the product of the number of gallons (n), in gallons, and unit cost (c), in monetary units per gallon:
C = n · c
If we know that n = 3.379 gal and c = $ 35.95 / gal, then the cost of the number of gallons is:
C = (3.379 gal) · ($ 35.95 / gal)
C = $ 121.48
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Nick is splitting 3 quarts of ice cream with 15 members of thw team. If the ice cream is split evenly how many cups will each person get 1 quart equals=
whixh equals = _cups
so 3 quarts equaks _cups divibg thw ice cream among _ people means each gets _ cups
1 quart equals 2 pints, which equals 4 cups, so 3 quarts equals 12 cups. Dividing the ice cream among 15 people means each gets 1 3/12 cup(s).
Nick has 3 quarts of ice and he wants to split it with 15 members of the team.
To solve this, we have to convert quarts to cups. We have that:
1 quart = 2 pints
and 1 pint = 2 cups
This means that:
1 quart = 2 × 2 cups
1 quart = 4 cups
So, 3 quarts will be:
3 quarts=3 × 4
3 quarts =12
Therefore, dividing the ice cream among 15 people would mean that we have to divide 12 cups by 15 people.
That is:
= 15/12
= [tex]1\frac{3}{12}[/tex]
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The complete question is:
Nick is splitting 3 quarts of ice cream with 15 members of the team. If the ice cream is split evenly, how many cups will each person get?
Explain 1 quart equals _ pints, which equals _ cups, so 3 quarts equals _ cups. Dividing the ice cream among _ people means each gets _ cup(s).
Please help the question is a photo! We need to find the area and we use 3.14 or 22/7
The area of the circular figure which is the top of a can drink with a diameter of 3 inches is about 7.065 square inches
What is a circular figure?A circular figure is one that has no edges or sharp corners, and which is essentially round (in the form of a disc or the path described by rotary motion) in shape.
A circular object occupies the largest area per diagonal compared to other regular shapes, as the circular inscribes other regular shapes within its circumference.
The shape in the figure is a circle
The diameter of the circle, D = 3 in.
The formula for finding the area of a circle, A, for which the diameter is presented as follows;
Area of the circle, A = π·D²/4
The approximation of the value of π to be used are 3.14 or 22/7
The area is obtained by plugging in the values of D and π in the formula for the area of a circle as follows;
The area of the figure is; A = 3.14 × 3²/4 = 7.065
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Solve 35 / 2 using an area model. Use long division and the distributive property to record your work
Answer by solving the expression 35 /2 using different methods are:
a. Area model : 35 /2 can be expressed as 17. 5 + 17.5 .(attached figure)
b. Long division method : 35 /2 = 17 + 1/2
c. Distributive property expressed as 35/2 = ( 34 + 1 ) × 1/ 2.
a. Area model.
Expression 35 /2 solved by area model is attached in the figure.
One part of 35 is divided into two parts each of 17.5 .
17.5 + 17.5 = 35
b. Long division.
How many 2's are there in 3
Answer is 1.
3−1⋅2=3−2=1
Write down the next digit of the dividend.
How many 2's are there in 15
Answer is 7
15−7⋅2=15−14=1.
( 35 /2 ) = 17 + ( 1/2)
c. Distributive property
35 /2
= ( 34 + 1 ) × 1/ 2
= 34 /2 + 1 /2
= 17 + 1 /2
= 17 + 0.5
= 17.5
Therefore, the solution of 35/2 using different methods are:
a. Using area model : 17.5 + 17.5 represent 35/2.
b. long division : 35 /2 = 17 + 1/2
c. Distributive property: 35/2 = ( 34 + 1 ) / 2
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answer choices:
x=22
x=68
x=90
x=112
Answer: I think x=22.
Step-by-step explanation:
If you look at half of the circle you can see a line in it right? This line measures to 180 degrees. This is a right triangle. Usually triangles have a little box in the corner to tell you that is it indeed a right triangle. I don't know why this one doesn't. anyways, if you add 90+68, you get 158. Now you need to get to 180 by simply adding 22. Thats why i think the answer is 22. Sorry if im wrong.
A water sample shows 0. 097 grams of some trace element for every cubic centimeter of water. Owen uses a container in the shape of a right cylinder with a radius of 6. 7 cm and a height of 13. 3 cm to collect a second sample, filling the container all the way. Assuming the sample contains the same proportion of the trace element, approximately how much trace element has Owen collected? Round your answer to the nearest tenth
The amount of trace element collected by Owen is 59.3 g.
To calculate the amount of trace element collected by Owen, we first need to find the volume of the container. Given the radius of 6.7 cm and the height of 13.3 cm, the volume of the cylinder is given by:
V = π * r^2 * h = π * (6.7)^2 * 13.3 = 615.96 cm^3
Since there are 0.097 grams of the trace element per cubic centimeter of water, the amount of trace element in the container can be calculated as:
m = V * 0.097 g/cm^3 = 615.96 cm^3 * 0.097 g/cm^3 = 59.32 g
Rounding to the nearest tenth, the answer is 59.3 g.
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Target is having a sale, Every item in the store is 20% off the orignal price . if a tvs oringal price is 250$ , what was the sale price
The final sales price is equal to $200.
What is a percentage?In Mathematics, a percentage simply refers to any number that is expressed as a fraction of hundred (100). This ultimately implies that, a percentage indicates the hundredth parts of any given number.
In order to decrease 250 dollars by 20 percent (20%), we would have to multiply the given amount of money by 80 percent (80%) because it denotes a percentage decrease:
Percentage decrease = 250 × 80/100
Percentage decrease = 250 × 0.8
Percentage decrease = $200.
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Question #14:
Brandon is filling a flower bed with soil. The flower bed is shaped like a rectangular prism and
measures 15 feet long and 3 feet tall. If it holds 405 cubic feet of soil, how many feet wide is
Brandon's flower bed?
The width of rectangular prism shaped Brandon's flower bed is 9 meters.
As per the known information, the formula to calculate volume of rectangular prism is -
Volume of rectangular prism = length × width × height
Keep the values in formula to find the volume of rectangular prism
405 = 15 × 3 × width of rectangular prism
Performing multiplication on Right Hand Side of the equation
405 = 45 × width of rectangular prism
Rewriting the equation
Width of rectangular prism = 405/45
Performing division
Width of rectangular prism = 9 meters
Thus, the width is 9 meters.
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Give your answer in point notation with the x and y coordinates. If there are
multiple solutions, separate the answers with commas and no spaces. For example,
if your answers are (0,2) and (-3,1), you would type it as: (0,2),(-3,1). Order does not
matter.
V
N
AV
The points (2,2) and (-2,2) are both solutions to the equation y=2.
A coordinate pair(2,2),(3,1)When solving a system of equations, one way to find the solution is by graphing.To graph the given system of equations, start by plotting the two equations on the coordinate plane.The first equation, x + y = 4, can be written in the form y = -x + 4.Plot this line on the coordinate plane, with any two points that satisfy the equation. In this case, the two points could be (0,4) and (4,0).Plot the second equation, x - y = 2, in the same way.This line can be written in the form y = x - 2.Plot two points that satisfy this equation, such as (0,-2) and (2,0).After plotting the two lines, look for the point of intersection, which is the solution to the system.In this case, the point of intersection is (2,2) and (3,1).Therefore, the solution to the system is (2,2),(3,1).This equation is a line that has a y-intercept of 2, meaning that the line crosses the y-axis at the point (0,2). The slope of the line is 0, meaning that the line is vertical and does not cross the x-axis.Therefore, any point along this line will have the same y-coordinate, which in this case is 2. In other words, for any given x-coordinate, the y-coordinate will always be 2. This means that both (2,2) and (-2,2) are valid solutions for the equation y=2.To learn more about a coordinate pair refer to:
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true or false: a parallel gateway with three sequence flows would have three tokens leaving the gateway.
A parallel gateway with three sequence flows would have three tokens leaving the gateway - True.
Reason: Each path has a token.
A parallel gateway can synchronize or merge the parallel flows once more, or split the sequence flow into two or more parallel flows. Awaiting the arrival of all incoming sequence flows is synchronization. After that, the flow resumes.
Instead, two concurrent jobs in a business flow are represented by a parallel gateway. In a UML activity diagram, it is equivalent to a fork. The business process in the example below uses a parallel gateway because the company is trying to have its cake and eat it too. With Lucid chart, diagramming is quick and simple.
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The bug has friends in nearby trees.
For each description, write equations similar to Problem 2.
Assume each bug starts at the same position as the bug in Problem 2.
1. The equation when Buggo crawls did 28 minutes at a rate of -2 centimeters per minute will be x = -2 × 28
2. The equation when Buggy slides for 3.2 seconds at -8.1 millimeters per second will be: y = -8.1 × 3.2
3. The equation when Buggum creeps for 3.5 seconds and finishes at -28.5 centimeters will be 3.5x = -28.5
How to solve the equation?An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.
The equation when Buggo crawls did 28 minutes at a rate of -2 centimeters per minute will be:
Let x = total centimeters
x = -2 × 28
The equation when Buggy slides for 3.2 seconds at -8.1 millimeters per second will be:
Let y = ital millimeters
y = -8.1 × 3.2
The equation when Buggum creeps for 3.5 seconds and finishes at -28.5 centimeters will be 3.5x = -28.5
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define partial products. what partial products can you use to find how many 6 bags of cat food will cost?
Partial products can be used to multiply two or more numbers.
In Mathematics, partial products mean multiplying each digit of a number with each digit of another number where each digit maintains its place value6 bags × cat food cost
simplify the following monomials (-a²b)ª
Answer:
[tex]\displaystyle{(-1)^aa^{2a} b^a}[/tex]
Step-by-step explanation:
The following expression can be rewritten as:
[tex]\displaystyle{\left((-1)\cdot a^2 \cdot b\right)^a}[/tex]
In this case, we have to separate -1 out of a² since if a becomes even, the value of (-a)ª will become positive while (-a)ª becomes negative when a is odd.
We can apply the law of exponent when:
[tex]\displaystyle{\left(a \cdot b \cdot c \right)^m = a^m \cdot b^m \cdot c^m}[/tex]
Therefore:
[tex]\displaystyle{\left((-1)\cdot a^2 \cdot b\right)^a = (-1)^a\cdot a^{2a}\cdot b^a}\\\\\displaystyle{\left((-1)\cdot a^2 \cdot b\right)^a = (-1)^aa^{2a} b^a}[/tex]
This will make when a = even numbers, the expression is positive while negative when a is odd.
And no, the answer is not [tex]-a^{2a} b^a[/tex] since this will make the expression negative only but the problem can be positive when a = even number which is why we have to separate -1 out of -a² so that it meets the condition.
Hence, the answer is [tex]\displaystyle{(-1)^aa^{2a} b^a}[/tex]
PLEASE HELP!! 100 POINTS
Answer:
see explanation
Step-by-step explanation:
the total cost is dependent on the number of rides she takes, then
the number of rides is the independent variable and the total cost is the dependent variable.
----------------------------------------------------------------------------
(2)
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given m = - 2 , then
y = - 2x + c ← is the partial equation
to find c substitute (- 4, 2 ) into the partial equation
2 = - 2(- 4) + c = 8 + c ( subtract 8 from both sides )
- 6 = c
y = - 2x - 6 ← equation of line
--------------------------------------------------------------------------
(3)
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 3, 6 ) and (x₂, y₂ ) = (9, - 2 )
m = [tex]\frac{-2-6}{9-(-3)}[/tex] = [tex]\frac{-8}{9+3}[/tex] = [tex]\frac{-8}{12}[/tex] = - [tex]\frac{2}{3}[/tex] , then
y = - [tex]\frac{2}{3}[/tex] x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (9, - 2 )
- 2 = - [tex]\frac{2}{3}[/tex] (9) + c = - 6 + c ( add 6 to both sides )
4 = c
y = - [tex]\frac{2}{3}[/tex] x + 4 ← in slope- intercept form
multiply through by 3 to clear the fraction
3y = - 2x + 12 ( add 2x to both sides )
2x + 3y = 12 ← equation in standard form
----------------------------------------------------------------------------
(4)
linear function has the form
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 200) and (x₂, y₂ ) = (2, 500) ← 2 ordered pairs from the table
m = [tex]\frac{500-200}{2-0}[/tex] = [tex]\frac{300}{2}[/tex] = 150
the ordered pair (0, 200 ) indicates that c = 200
y = 150x + 200 ← linear equation
--------------------------------------------------------------------------
(5)
money left over f(x) is
f(x) = initial amount - expenses
= 125 - (15 + 40 + 5x)
= 125 - (55 + 5x)
= 125 - 55 - 5x
= 70 - 5x
that is
f(x) = - 5x + 70
How do you do this problem
Answer: C)39
Step-by-step explanation:
6x+507+317+3x=122
9x+824=122
9x=122-824
9x=-702
x=-78
6x+507
6(-78)+507
-468+507
=39
I need help with the x and y intercepts I’m to exhausted to comprehend anything please help me
The solutions to the x and y intercepts are;
1) The slope will be positive.
2) The student is incorrect because (0, 5) is not the x-intercept.
3) The point at which the graph crosses the x axis is; x = 2
4) The point at which the graph crosses the y axis is; y = 6
5) x-intercept is x = 4 and the y-intercept is; y = 2
6) The x-intercept is x = 6 and the y-intercept is; y = 2
7) The x-intercept is x = 2 and the y-intercept is; y = 10
How to find the x and y-intercepts?1) The formula for the slope of a graph is;
Slope = Change in y value/change in x value
Thus, if both x and y intercepts are negative, then the slope will be positive.
2) The equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
The equation can be rewritten as;
y = -¹/₂x + 5
At y =0,
0 = -¹/₂(x) + 5
x = 8
Thus, (0, 5) is not the x-intercept.
3) The point at which the graph crosses the x axis is the x-intercept which is when y = 0. Thus;
2x + 0 = 4
2x = 4
x = 2
4) The point at which the graph crosses the y axis is the y-intercept which is when x = 0. Thus;
3(0) + y = 6
y = 6
5) 2x + 4y = 8
x-intercept; 2x + 4(0) = 8
x = 4
y-intercept; 2(0) + 4y = 8
y = 2
6) x + 3y = 6
x-intercept; x + 3(0) = 6
x = 6
y-intercept; 0 + 3y = 6
y = 2
7) 5x + y = 10
x-intercept; 5x + 0 = 10
x = 2
y-intercept; 5(0) + y = 10
y = 10
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During a single day at radio station WMZH, the probability that a particular song is
played is 23%. What is the probability that this song will be played on at least 2 days
out of 4 days? Round your answer to the nearest thousandth.
The probability that this song will be played on at least 2 days out of 4 days is 40.71%.
How to calculate the probability?To calculate the probability that a song will be played on at least two days, you would need to find the probability that it is not played on any of the days (the complement) and then subtract that from 1.
The probability that a song is not played on a given day is 1 - 0.23 = 0.77. To find the probability that it is not played on at least two days, you would raise that probability to the power of the number of days, in this case 2.
So, 0.77^2 = 0.5929. To find the probability that it is played on at least two days, you would subtract that from 1: = 1 - 0.5929
= 0.4071
=40.71%.
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I buy 4 gallons of milk at the grocery store. Each gallon sells for $3. 50. Is this relationship a function? Justify your claim
Yes, this relationship is a Funtion.
The relationship between the no of gallons of milk purchased and the total cost can be represented by this equation:
y = 3.5x
where y is the total cost and x represents the number of gallons of milk purchased. A function is a collection of ordered pairs (x, y) with exactly one value of y for each value of x. for each input (x), just one output (y) is created.
In this situation, there is only one equivalent value of y for each value of x .We may see this by putting different value of x into the equation and get ing a different result for y.
For example, when x = 1, y = 3.5 ×1 = 3.5
when x = 2, y = 3.5 × 2 = 7
when x = 3, y = 3.5 × 3 = 10.5
and so on.
So, the relationship between the number of gallons of milk purchased and the total cost is a Funtion.
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1/3y = 4 5/6
the options are
a. 1 11/8
b. 4 5/18
c. 12 5/6
d. 14 1/2
Xander is making soup for his youth group's annual dinner party for the elderly people in their community. His group
leader told him to mix the number of cans of soup concentrate and the number of cans of water in the ratio
1:5. Construct a ratio table for all possible combinations of cans of soup concentrate and cans of water that will giv
Xander up to 24 total cans of heated soup to serve. Let s represent the number of cans of soup concentrate and let
w represent the number of cans of water.
The ratio table is presented below and a total of 4 cases of possible.
Given that,
s: the number of cans of soup concentrate
w: the number of cans of water
Ratio: 1:5
so w = 5s
Therefore,
s w Total cans of heated soup to serve
1 5 6
2 10 12
3 15 18
4 20 24
Therefore, a total of four cases are possible to make up to 24 total cans of heated soup to serve at the party.
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243 (0) If 8; 2x; 2y forms an arithmetic sequence and 2x; 2y; 36 forms a geometric sequence determine the values of x and y.
Answer:
(x, y) = (0.5, -3) or (8, 12)
Step-by-step explanation:
You want x and y such that 8, 2x, 2y is an arithmetic sequence and 2x, 2y, 36 is a geometric sequence.
Arithmetic sequenceThe difference of successive terms is a constant for an arithmetic sequence.
2x -8 = 2y -2x
2x -4 = y . . . . . . . . divide by 2, add x
Geometric sequenceThe ratio of successive terms is a constant for a geometric sequence.
2y/2x = 36/2y
y² = 18x . . . . . . . . . simplify and cross multiply
SolutionWe can substitute the expression for y from the arithmetic sequence into the expression for y² in the geometric sequence:
(2x -4)² = 18x
4x² -16x +16 = 18x . . . . . expand
2x² -17x +8 = 0 . . . . . . . divide by 2, subtract 9x
(2x -1)(x -8) = 0 . . . . . . . factor
The values of x that make the factors zero are x = 1/2 and x = 8. The corresponding values of y are 2{1/2, 8} -4 = {1, 16} -4 = {-3, 12}.
The values of x and y are (1/2 and -3) or (8 and 12).
__
Additional comment
The two sequences are ...
8, 1, -6 and 1, -6, 36 — difference of -7, ratio of -6
or
8, 16, 24 and 16, 24, 36 — difference of 8, ratio of 3/2