The difference between book value and the amount received is $2000
What was the difference between the book value and the amount received ?
van cost = $16000
Estimated life= 4 years
Residual value= $4000
using straight line method of depreciation
Depreciation per year= 16000-4000/4= 3000
Therefore book value after two years = $16000- 2*3000= $10000
Selling price of book after 2 years= $8000
hence the difference between book value and the amount received
10000-8000= $2000
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help meeeeeeeeeee pleaseee
The pressure of 28 inches of mercury occurs about 6 miles from the eye of hurricane.
What is barometric air pressure?In essence, atmospheric pressure is the force that the weight of the air above a particular point on the Earth's surface exerts at that location.
In other words, the weight of the air molecules as a whole determines the atmospheric pressure, which is produced by the air that surrounds the Earth.
Lower pressure is felt by air molecules at higher altitudes because there are fewer molecules pressing down on them from above, while higher pressure is felt by air molecules at lower altitudes because they are closer together and are under more pressure from molecules piled on top of them.
F(x) is the pressure in inches of mercury
It is given pressure 28 inches of mercury
Put F(x) equal to 28
F(x) = 0.48㏑(x+2) +27
28 = 0.48㏑(x+2) + 27
28-27= 0.48㏑(x+2)
1= 0.48㏑(x+2)
1/0.48= ㏑(x+2)
25/12= ㏑(x+2)
x+2= [tex]e^{\frac{25}{12} }[/tex]
x+2=8.03119
x=8.03119-2
x= 6.03119
x = 6(round off)
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The admission fee at an amusement park is $1.50 for children and $4 for adults. On a certain day, 274 people entered the park, and the admission fees collected totaled 836.00 dollars. How many adults were admitted?
a. 209
b.170
c.104
Therefore in this question the solution of particular equation is 108 children and 175 adults in the amusement park on that particular day.
What is Equation ?When two expressions' values are set to be equal by a mathematical statement, that statement is known as an equation. To put it another way, it is a mathematical expression that means "this is equivalent to that." An equal sign, a mathematical expression, and a mathematical expression can all be seen on the left side of the symbol. The right ride of the equation frequently contains zero.
Let's first configure our system by giving x and y meaningful definitions. Let x be the total number of kids and y be the total number of adults.
Children cost $1.50, while adults cost $4.00. The number of kids, x, is multiplied by 1.5 to determine how much money a group of kids will cost. The 1.5x symbol stands for this. We will use 4y for adults, who must pay $4 to enter. On the specified day, $862 in total revenue was earned. We must add 1.5x and 4y to get at this sum.
1.5x + 4y = 862 equation required
Second equation: The total number of individuals present on the day is 283. X and Y, or the number of children and adults, must be added together to arrive at this figure.
x + y = 283
System of equations:
1.5x + 4y = 862
x + y = 283
Thus,
x + y = 283
y = 283 - x
Substitute y = 283 - x
862=1.5x + 4 (283 - x)
1.5x + 1132 - 4x = 862
1132 - 2.5x = 862
-2.5x = -270
x = 108
Substitute x =108 back into y = 283 - x
y = 283 - 108 = 175
Therefore there were 108 children and 175 adults in the amusement park on that particular day.
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Force An 8.0-pound weight is lying on a sit up bench at the gym. If the bench is
inclined at an angle of 15°, there are three forces acting on the weight, as shown
in Figure 12. Find the magnitude of N and the magnitude of F.
Answer: 7
Step-by-step explanation: 7+2
10. You are ordering shirts for the math club at your school. Short-sleeved shirts cost $ 8 each. Long-sleeved shirts cost $ 20 each. You have a budget of $ 200 for the shirts. The equation 8 x+20 y=200 models the total cost, where x is the number of short-sleeved shirts and y is the number of long-sleeved shirts. Graph the equation. Interpret the intercepts.
x-intercept:_____
y-intercept:_____
The x - intercept is (25, 0) and the y - intercept is (0, 10).
What is intercepts?
The x-intercept and y-intercept are the points at which a line crosses the x- and y-axes, respectively.
Put y = 0 and work out x to find the x-intercept.
Set x = 0 and work out y to find the y-intercept.
Given: You are ordering shirts for the math club at your school.
Short-sleeved shirts cost $ 8 each.
Long-sleeved shirts cost $ 20 each. You have a budget of $ 200 for the shirts.
The equation 8 x+20 y=200 models the total cost,
where x is the number of short-sleeved shirts and y is the number of long-sleeved shirts.
To find the x - intercept plug y = 0 in the above equation.
⇒ 8x + 20(0) = 200
8x = 200
x = 25
So, the point becomes, (25, 0).
To find y - intercept plug x = 0 in the above equation.
⇒ 8(0) + 20y = 200
20y = 200
y = 10
So the point becomes, (0, 10).
Hence, the x - intercept is (25, 0) and the y - intercept is (0, 10).
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g(x) = -2(3x + 4)(x - 1)(x – 3)^2 be a polynomial function.
State the leading term, degree, and if the leading coefficient is positive or negative.
I mostly understand this, but don't know how the square affects things.
The polynomial is of degree 4, and the leading coefficient is -6.
How to find the degree of the polynomial?A polynomial of degree N with a leading coefficient A and the zeros {x₁, x₂, x₃, ..., xₙ} (notice that we have as many zeros as the degree of the polynomial) is written as:
p(x) = A*(x - x₁)*...*(x - xₙ)
Here we have the polynomial:
g(x) -2*(3x + 4)*(x - 1)*(x - 3)²
We can expand this as:
g(x) = -2*(3x + 4)*(x - 1)*(x - 3)*(x - 3)
Think that as we have "two zeros" at x = 3.
So we have 4 factors, then the degree of the polynomial is 4.
To find the leading coefficient we just need to look at the term that comes by multiplying all the terms with "x", we will get:
-2*(3x)*x*x*X
-6*x⁴
The leading coefficient is negative.
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Teri invested $1500 in an account with an interest rate of 2.25% compounded continuously. How long will it take for Teri's account to earn $5000?
It will take 54 days for Teri's account to earn an amount of $5000.
What is compound interest?Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.
It occurs when interest is reinvested, or added to the loaned capital rather than paid out, or when the borrower is required to pay it, so that interest is generated the next period on the principal amount plus any accumulated interest. In finance and economics, compound interest is common.
It is given by formula
A = [tex]p*e^{r*t}[/tex]
where:
A is final amount
p is principal amount
r is rate of interest and
t, is time period
Given: A= $5000, p=$1500, r=2.25% = 0.0225
To find: time period to get compounded amount
5000=1500×[tex]e^{0.0225*t}[/tex]
[tex]e^{0.0225t}[/tex] = [tex]\frac{10}{3}[/tex]
0.0225t = ㏑ ([tex]\frac{10}{3}[/tex])
t = 53.5099 ≈ 54 days
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Sue and her brother wanted to buy 25 pieces of candy for their family's stockings. They chose to buy Kit Kats and Skittles. After shopping they spent $ 20.70. Skittles
cost 80 cents each and kit kats cost 90 cents each. How many of each candy did they get at the store? Let s-skittles and k=kit kats.
Which systems of equations represents this situation?
Answer:
18 Skittles and 7 Kit Kats
Linear system of equations in two variables
Step-by-step explanation:
We a linear system of two equations which can be solved simultaneously
Total pieces of candy equation
s + k = 25 [1]
Total cost equation
0.8s + 0.9k = 20.70 [2]
Multiply [1] by 0.80
0.80s + 0.80k = 20 [3]
Subtract [3] from [2]
0.80s + 0.90k = 20.70
[tex]-[/tex]
0.80s + 0.80k = 20
[tex]\cdots\cdots\cdots\cdots\cdots\cdots\cdots\cdots\cdots\cdots\cdots[/tex]
0.1k = 0.70
k = 0.70/0.10 = 7
In [1]
[tex]s + 7 = 25\\\\s = 25-7\\\\s = 18\\\\[/tex]
Answer: 18 Skittles and 7 Kit Kats
Simplify and state the restrictions on the domain:
The required simplification of given function is [tex]\frac{(x-1)^{2}}{x-2}[/tex] and restriction on domain are x ≠ 1, 2.
Explain domain of the function?The domain of a function is the set of all possible inputs for the function. For example, the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0. We can also define special functions whose domains are more limited.
According to question:We have,
[tex]\frac{(x+3)(x-1)}{x-2}[/tex] ÷ [tex]\frac{x+3}{x-1}[/tex]
[tex]\frac{(x+3)(x-1)}{x-2}[/tex] × [tex]\frac{x-1}{x+3}[/tex]
[tex]\frac{(x-1)^{2}}{x-2}[/tex]
For domain, Function should have solution should not be not defined.
For this, denominator must not equal to zero
Then, x -2 ≠ 0, x - 1 ≠ 0
x ≠ 2, x ≠ 1
Thus, option(3) [tex]\frac{(x-1)^{2}}{x-2}[/tex] x ≠ 1,2 is correct.
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Answer:
(b) (x -1)²/(x -2), x ≠ -3, 1, 2
Step-by-step explanation:
You want to know the domain restrictions and the simplified form of ...
[tex]\dfrac{(x+3)(x-1)}{(x-2)}\div\dfrac{x+3}{x-1}[/tex]
SimplifyWe can "invert and multiply", then cancel the common factor from numerator and denominator.
[tex]\dfrac{(x+3)(x-1)}{x-2}\div\dfrac{x+3}{x-1}=\dfrac{(x+3)(x-1)}{x-2}\times\dfrac{x-1}{x+3}=\dfrac{(x+3)(x-1)^2}{(x+3)(x-2)}\\\\=\dfrac{(x-1)^2}{x-2}\qquad x\ne -3[/tex]
DomainThe values of x that must be excluded from the domain are those values for which any part of this expression is undefined. The expression is undefined when any denominator is zero: at x = 2 (left "factor"), at x = 1 (right "factor"), and at x = -3.
The factor (x +3) doesn't show up in the simplified form, but it is a "hole" in the graph of the original expression—a value of x where the function is not defined.
Here is a summary of what you get at the restricted values:
-3: (0)(-4)/-5 ÷ 0/-4 . . . . division by 01: (4)(0)/-1 ÷ 4/0 . . . . . . . divisor undefined2: (5)(1)/0 ÷ 5/1 . . . . . . . division by 0The simplified form with restrictions is ...
[tex]\boxed{\dfrac{(x-1)^2}{x-2},\ x \ne -3,1,2}[/tex]
Find the slope Y intercept in the equation for the data in the table and in the graph
Answer:
slope 6
y intercept 4
y = 6x + 4
Step-by-step explanation:
The slope is the change in y over the change in x.
Look at he two points (0,4) and (1,10)
The y started at 4 and went up to 10. That is a distance of 6.
AT the same time, the x changes from 0 tp 1 (0,4) (1,10). That is a distance of 1.
6/1 = 6
The y intercept is where the line crosses the y axis. It crosses at (0,4). 4 is the y intercept
y = mx + b Put the slope is for m and the y intercept for b
y = 6x + 4
The Christmas lights on the tree and the lights on the porch blink at a consistent rate. The tree lights blink every 4 seconds which the porch lights blink every 6 seconds after how many second will they blink together
Answer:
The tree lights and the porch lights will blink together every 12 seconds.
Step-by-step explanation:
In order to determine when the two sets of lights will blink together, you must find the least common multiple (LCM) of the time periods for each set of lights. The LCM of 4 and 6 is 12, which means that the tree lights and the porch lights will both blink again after 12 seconds have passed. Therefore, they will blink together every 12 seconds.
Janessa loves to travel. She earns $2,500 per month, and saves 3% of each paycheck for travel. After a full year of saving, she plans her annual trip. For her most recent trip, two-thirds of her savings went to plane fare and lodging. After plane fare and lodging, how much of her trip savings does Janessa have left?
The amount the she had in her savings before the trip was $825.
How much of Janessa's travel funds remains?Calculating amount
From the question, we are to calculate how much Janessa has in her savings before the trip
Let the amount she has in her savings before the trip be x
From the given information,
Janessa spent a third of her savings on airfare for a vacation"
That is,
She spent (1/3)x
The amount remaining after this time will be x - (1/3)x = (2/3)x
"She then spent another $300 on hotels"
The amount remaining after this time will be (2/3)x - $300
"If she has $250 left for meals and souvenirs"
That is,
(2/3)x - $300 = $250
Now, solve for x
(2/3)x - $300 = $250
(2/3)x = $250 + $300
(2/3)x = $550
x = $550 × 3/2
x = $825
Hence, the amount the she had in her savings before the trip was $825
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During a football game, a team lost 10 yards on its first play and 20 yards on its third play.
Write an integer to represent the loss on each play.
The required integer to represent the loss on each play is -5m-5.
What are integers?Any positive or negative number without fractions or decimal places is known as an integer, often known as a "round number" or "whole number."
Given:
During a football game, a team lost 10 yards on its first play and 20 yards on its third play.
To write an integer to represent the loss on each play:
Use -10 to represent losing 10 yards.
Use -20 to represent losing 20 yards.
Add both of the expression,
(-10) + (-20)
= -10 -20.
Whenever we add two negative values, the sum is negative.
(-10) + (-20) = -10 -20 = - 30
Let m be the required integer.
So, -5m-5 is the loss on each play.
Where m is the number of play.
Therefore, the required integer is -5m-5.
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PLEASE HELPED I"M TIMED I WILL GIVE BRAINLIST
Answer:
Below
Step-by-step explanation:
Angle 2 or angle HFE
Vertex is F
GF and FE are the sides of angle 1
[tex]\frac{1}{10} +\frac{7}{10}[/tex]
Answer given in the screenshot below. ↓
The ratio of hybrid cars to gasoline-powered cars in the parking lot of a
local office building is 3:11. If a car in the lot is selected at random to get
the reserved parking space nearest the building, find the probability the car
selected is a hybrid. Express your answer as a simplified fraction.
The probability of getting a Hybrid car = 3/14
Probability:The probability formula states that the ratio of favorable outcomes to all outcomes determines the likelihood that an event will occur.
The formula for the probability of an event is given by
P(E) = No of favorable outcomes/ total number of outcomes
Here we have
The ratio of hybrid cars to gasoline-powered cars is 3:11
Let 3x and 11x be the number of hybrid cars and gasoline-powered cars
[ Since they are in 3: 11 ratio]
Then total number of cars = 3x + 11x = 14x
From the given data,
Total number of cars = 280
=> 14x = 280
=> x = 20
Number of Hybrid cars, 3x = 3(20) = 60
Here we select a car from a random experiment
Number of outcome = 280
Number of outcomes that we get Hybrid car = 60
Thus the probability of getting a Hybrid car = [tex]\frac{60}{280}[/tex]
= [tex]\frac{6}{28}[/tex] = [tex]\frac{3}{14}[/tex]
Therefore,
The probability of getting a Hybrid car = 3/14
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Complete question:
The ratio of hybrid cars to gasoline-powered cars in the parking lot of a local office building is 3:11. if there are 280 cars in the lot and one is to be selected at random to get the reserved parking space nearest the building, find the probability the car selected is a hybrid. express your answer as a fraction.
A quadrilateral has 4 sides. One angle of a regular quadrilateral measures (6w+13) Determine the value of w. Round to the nearest whole number.
Ow=13
Ow=23
Ow=59
Ow=90
The value of w for the expression of angle 6w + 13 will be 13. The correct option is A.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that a quadrilateral has 4 sides. One angle of regular quadrilateral measures (6w+13).
The value of 'w' will be calculated as,
6w + 13 = 90
6w = 90 - 13
6w = 77
w = 12.83 or 13
Therefore, the value of w for the expression of angle 6w + 13 will be 13. The correct option is A.
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Which equation represents the volume of the box
The equation represents the volume of the box as V = - 4s³ + 250s².
The correct option is option A
What is volume?The volume of any object is the capacity. How much it can hold.
What is the formula of volume?The formula of volume is a product of length, breadth and height.
Volume = L × B × H
Given:
The perimeter of the square base of side s plus height h = 250cm
as per the given question,
The perimeter of the square base of side s plus height h = 250cm
2( s + s ) + h = 250
2 (2s) + h = 250
4s + h = 250
We can express h in the terms of s as,
h= 250 - 4s
Volume = length X breadth X height
Volume = s × s × h
V = s² × h
V = s² × (250 - 4s)
V = 250s² - 4s³
The equation represents the volume of the box as V = - 4s³ + 250s².
The correct option is option A
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Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
By using the concept of circle, it can be concluded that-
Center = (1, 0) lies on x axis
The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
What is a circle?
Circle is a two dimensional round figure in which every point on the circle maintains a fixed distance from a point known as the center of the circle and the fixed distance is called radius of the circle
The equation of circle is
[tex]x^2 + y^2 - 2x - 8 = 0.[/tex]
[tex]x^2 - 2x + 1 - 1-8+y^2 =0\\(x -1)^2 + y^2 = 9\\(x - 1)^2 + y^2 = 3^2[/tex]
Center = (1, 0) lies on x axis
Radius of the given circle is 3 units
Radius of x² + y² = 9 is 3
So, the radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
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How much simple interest is made on an investment of $800 for 7 years at 6%
Answer:
$1,136
Step-by-step explanation:
The simple interest equation is A = P(1 + rt)create three equations for quadratics in vertex form that have roots at 3 and 5 but have different maximum and/or minimum values.
The three quadratic equation with different maximum and/or minimum values are y = (x-4)² – 1, y = -(x-4)² + 1, and y = -3(x-4)² + 3.
Quadratic equation:
In math, quadratic equation is the algebraic equation of the second degree in x.
The general form of quadratic equation is
ax² + bx + c = 0,
where a and b are the coefficients, x is the variable, and c is the constant term. The first condition for an equation to be a quadratic equation is the coefficient of x² is a non-zero term(a ≠ 0).
Given,
Here we need to find the three equations for quadratics in vertex form that have roots at 3 and 5 but have different maximum and/or minimum values.
As per the definition of quadratic equation, here we have to write the quadratic equation, that have the roots of 3 and 5,
Here the problem was going to call for two equations but then we have realized that it could be as simply as multiplying the a and c values by -1. Therefore, the equation are,
=> y = (x-4)² – 1,
=> y = -(x-4)² + 1,
=> y = -3(x-4)² + 3.
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Which is a strict inequality?
A. y>4
B. y≤4x+2
C. y≥x
D. y=−8x+3
The option that is a strict inequality is A. y>4
How can you tell if an inequality is strict?It should be noted that inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal.
Inequalities involving < or ">" are considered "strict inequalities," whereas those involving "" or "" are not. If you "switch" the two sides of an inequality, you must then reverse the inequality symbol's direction. For example, because 4 5 is true, it follows that 5 > 4.
In conclusion, the correct option is A.
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Use the following function rule to find f(11).
f(x)=12|x+8|
f(11)=____
Answer:
f(11) = 228
Step-by-step explanation:
opinions: y= -3x + 5, y = - 1/5x + 3, y= 1/3x + 1/5, y=1/3x + 5, y= 3x + 1/5
The required matches for the given equation of line are explain below.
Explain general equation of line.The general equation of a straight line is y = mx + c, where m is the inclination, and y = c is the worth where the line cuts the y-hub. This number c is known as the block on the y-pivot. The condition of a straight line with slope m and block c on the y-hub is y = mx + c.
According to question:We will find the graph, by using general form of equation
y = -3x + 5
Its y-intercept is 5,and angle is negative,So graph(3) is matches
similarly,
y = - 1/5x + 3
Its y-intercept is 3,So graph(1) is matches
y=1/3x + 5
Its y-intercept is 5,and angle is Positive,So graph(4) is matches
y= 3x + 1/5
Its y-intercept is 1/5,and angle is more than one,So graph(2) is matches
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Solve for a
2x-2=-3x+13
X =
To solve for x, we need to isolate x on one side of the equation. To do this, we can first move all the terms that do not contain x to the right side of the equation by adding 3x and 2 to both sides:
2x - 2 + 3x + 2 = -3x + 13 + 3x + 2
5x = -3x + 15
8x = 15
Dividing both sides by 8, we get:
x = 15/8
= 1.875
Therefore, the value of x is approximately 1.875.
The value of x in equation 2x-2= -3x+13 is 3
To solve this equation we need to find the value of x so that all x terms should be one side and all constants should be at ones side:
2x+3x=13+2
5x=15
Now divide both side with 5 then, we get:
5x/5=15/5
x=3
Therefore, the value of x is 3
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Old Faithful in Yellowstone National Park has a mean time between eruptions of 85 minutes. If the interval of time between eruptions is normally distributed with a standard deviation of 21.25 minutes. What is the probability that a randomly selected sample of 35 time intervals between eruptions has a mean longer than 95 minutes?
The probability that the randomly selected time interval is longer than 95 minutes while solving for the mean time of the eruptions is 0.3192.
How to solve for the probability of a ramdom sample?mean of x = 85 minutes
σ = 21.25 minutes
x ~ N(σ², μ)
p(x < 95)
1-p(x≤95)
1 - p(z≤0.47)
Using the z table here
1-0.6808 = 0.3192
Probability of x > 95 = 0.3192
b. n = 20
from central limit theorem
1 - p (z < 2.1045)
1-0.99826 = 0.0174
1 - p (z < 2.58)
1-0.9951
= 0.0049
. What we can observe from these results is that as the sample increase is increasing from 1, 20 to 30, the probability keeps decreasing.e. The probability is very small so one has to be doubtful if they are a really the population mean or if it has to be more than that.
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A pre-paid phone company charges $17.75 as a monthly access fee and $0.13 per minute of calling time.
What will the monthly cost be if you make 176 minutes of calls this month?
Answer:
$40.63
Step-by-step explanation:
If the phone company charges $17.75 already, and each minute costs $0.13, then we can do an equation that looks something like this:
17.75 + (0.13 × 176) = total price
We need to figure out how much 0.13 multiplied by 176 is.
0.13 × 176 = 22.88
Now that we figured out that 0.13 multiplied by 176 is equal to 22.88, we need to add the monthly access fee.
22.88 + 17.75 = 40.63
The monthly cost will be $40.63.
an 8 oz soda can costs $0.96, a 12 oz soda can costs $0.72 and a 32 oz cup of soda costs $2.24. which is the lowest cost per ounce?
The lowest cost per ounce is 12 ounces of soda which cost $0.72.
How to find the lowest cost per ounce?An 8-ounce of soda can costs $0.96, a 12-ounce soda can costs $0.72 and 32 ounces of a cup of soda costs $2.24.
The lowest cost per ounce can be calculated as follows:
For 8 ounces of soda can costs $0.96.
cost per ounces = 0.96 / 8
cost per ounce = 0.12 dollars per ounce
For 12 ounces soda can costs $0.72.
cost per ounces = 0.72 / 12
cost per ounce = 0.06 dollars per ounce
For 32 ounces soda can cost $2.24.
cost per ounces = 2.24 / 32
cost per ounce = 0.07 dollars per ounce
Therefore, the lowest is 12 ounces of a soda can.
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In the diagram below of triangle PQR, S is the midpoint of PR and the midpoint of QR. If
ST= -22+9x and PQ+ 9x-8 what is the measure of PQ?
Answer PQ=_____
The measure of PQ in the triangle is 28 units.
How to find mid point of a triangle?The line segment connecting the midpoints of two sides of a triangle is parallel to the third side and is congruent to one half of the third side.
Therefore, using the mid point theorem, Let find the measure of PQ.
ST = -22 + 9x
PQ = 9x - 8
The measure of PQ can be found as follows:
ST = 1 / 2 (PQ)
-22 + 9x = 1 / 2 × (9x - 8)
-22 + 9x = 9x - 8 / 2
cross multiply
2(-22 + 9x) = 9x - 8
-44 + 18x = 9x - 8
-44 + 8 = 9x - 18x
- 36 = - 9x
x = - 36 / - 9
x = 4
Therefore,
PQ = 9(4) - 8 = 36 - 8 = 28 units
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The pattern below has been created by placing toothpicks together a) Find an expression for the total number of toothpicks in any set up b) How many toothpicks should there be in the 45th set up? Show your work.
For 45th set up 140 toothpicks are required.
What is Arithmetic Progression?A progression of numbers in which the difference between any two succeeding numbers is always a fixed amount is known as arithmetic progression (AP). It also goes by the name Arithmetic Sequence.
given:
For First Figure, 8 toothpicks are used
For Second Figure, 11 toothpicks are used
For Third Figure, 14 toothpicks are used
So, we get the series 8, 11, 14, ...
Now, for n= 45
Using Arithmetic Progression
[tex]a_{45} = a+ (45- 1) d[/tex]
= 8 + 44(3)
= 140
Hence, for 45th set up 140 toothpicks are required.
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An interior designer is designing a room. Her options include 6 paint colors, 4 types of flooring, 6 different curtains, 3 furniture sets, and 3 light fixtures. How many
different room designs can be created from these options?
Answer
The total number of different room designs is 1296.
What is the fundamental principle of counting?According to the fundamental counting principle, if there are n ways to do one thing and m ways to do another, then there are n×m methods to accomplish both things.
Given that, there are 6 paint colors, 4 types of flooring, 6 different curtains, 3 furniture sets, and 3 light fixtures.
As per the basic principle of counting, the total number of different room designs is:
6 × 4 × 6 × 3 × 3
= 1296
Hence, the total number of different room designs is 1296.
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