let's firstly convert the mixed fractions to improper fractions and them sum them up.
[tex]\stackrel{mixed}{7\frac{5}{12}}\implies \cfrac{7\cdot 12+5}{12}\implies \stackrel{improper}{\cfrac{89}{12}}~\hfill \stackrel{mixed}{11\frac{2}{3}} \implies \cfrac{11\cdot 3+2}{3} \implies \stackrel{improper}{\cfrac{35}{3}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{89}{12}+\cfrac{35}{3}\implies \cfrac{(1)89~~ + ~~(4)35}{\underset{\textit{using this LCD}}{12}}\implies \cfrac{89+140}{12}\implies \cfrac{229}{12}\implies {\Large \begin{array}{llll} 19\frac{1}{12} \end{array}}[/tex]
Eight: Adding & Subtracting K Subtract and simplify your answer. (5x)/(x^(2)-49)-(6)/(x+7)
The simplified answer is (5x)/(x^(2)-49)-(6)/(x+7) = -(x - 42)/((x + 7)(x - 7)).
To subtract and simplify the given expression, we need to find a common denominator and combine the numerators. The common denominator in this case will be (x^2 - 49), which can be factored into (x + 7)(x - 7).
So, the expression becomes:
(5x)/((x + 7)(x - 7)) - (6)/(x + 7)
To get a common denominator, we need to multiply the second term by (x - 7)/(x - 7):
(5x)/((x + 7)(x - 7)) - (6(x - 7))/((x + 7)(x - 7))
Now we can combine the numerators:
(5x - 6(x - 7))/((x + 7)(x - 7))
Simplifying the numerator gives us:
(-x + 42)/((x + 7)(x - 7))
And finally, we can simplify the expression by factoring out a -1 from the numerator:
-1(x - 42)/((x + 7)(x - 7))
So the final answer is:
-(x - 42)/((x + 7)(x - 7))
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Suppose you applied for positions at four different companies and let X be the number of offers you received.
a- Find the mean
b- standard deviation
of the number of offers you received. Round your answer to two decimal places
The answer of the number of offers you received are as follow,
1. Mean is equal to 1.96.
2. Standard deviation is equal to 1.17 (rounded to two decimal places) .
1.Mean (or expected value) is represented by E(X)
Formula of the expected value is,
E(X) = ∑xP(x)
Substitute the value from the table we get,
⇒E(X) = (0)(0.19) + (1)(0.12) + (2)(0.38) + (3)(0.16) + (4)(0.15)
⇒E(X) = 0 + 0.12 + 0.76 + 0.48 + 0.6
⇒E(X) = 1.96
2. Standard deviation of the number of offers received ,
⇒ Standard deviation 'σ' = √[ Σ(x - E(X))² P(x) ]
Substitute the values from the table we get,
⇒ Standard deviation 'σ'
= √[ (0 - 1.96)² (0.19) + (1 - 1.96)² (0.12) + (2 - 1.96)² (0.38) + (3 - 1.96)²(0.16) + (4 - 1.96)²(0.15) ]
= √[ 1.3728 ]
≈ 1.171665
≈1.17(rounded to two decimal places)
Therefore, the mean and the standard deviation of the number of offers received is approximately 1.96 and 1.17 (rounded to two decimal places) respectively.
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The above question is incomplete, the complete question is:
Suppose you applied for positions at four different companies and let X be the number of offers you received
X : 0 1 2 3 4
P(x) : 0.19 0.12 0.38 0.16 0.15
1. Find the mean
2. standard deviation
of the number of offers you received. Round your answer to two decimal places
Talia deposits $350 in her savings account. The account earns 2.5% simple interest per year. What is the balance in the account after 4 years?
Answer:385
Formulate and substitute:F=350+350rt
Calculate the product or quotient:350x1+0.1
Calculate the sum or difference:350x1.1
Calculate the product or quotient:385
What the pOH of a solution containing [OH-] = 4.91 x
10-11 mol L-1 ?
Report your answer to at least 1 decimal place
The pOH of a solution containing [OH-] = 4.91 x 10-11 mol L-1 is 10.3. We can round the pOH to 10.3.
The pOH of a solution is the negative logarithm of the concentration of hydroxide ions (OH-) in the solution. It can be calculated using the formula:
pOH = -log[OH-]
In this case, the concentration of hydroxide ions is [OH-] = 4.91 x 10-11 mol L-1. Plugging this value into the formula, we get:
pOH = -log(4.91 x 10-11)
Using a calculator, we can find the pOH to be 10.309.
To report the answer to at least 1 decimal place, we can round the pOH to 10.3.
Therefore, the pOH of a solution containing [OH-] = 4.91 x 10-11 mol L-1 is 10.3.
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Lube used to 9 cups of milk for a pancake recipe to drink another 394 cups of milk how about about how much milk did Luke is using on
To find the total amount of milk used, we simply add the amount of milk used for the pancake recipe and the amount used for drinking. So we add 9 cups and 394 cups together, giving us a total of 403 cups of milk.
We can calculate the total amount of milk that Luke used for the pancake recipe and the additional amount he used for drinking.
For the pancake recipe, Luke used 9 cups of milk.
For drinking, Luke used an additional 394 cups of milk.
Total amount of milk used = Milk used for pancake recipe + Milk used for drinking
= 9 cups + 394 cups
= 403 cups of milk.
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The complete question is:
Lube used to 9 cups of milk for a pancake recipe to drink another 394 cups of milk how about about how much milk did Luke is using on the recipe?
Lennox Madrid Polynomial Long Division (Level 1) Feb 18, 1:52:23 PM Use the long division method to find the result when 2x^(3)+4x^(2)+7x+5 is divided by x+1.
The result of the given polynomial division (2x^(3)+4x^(2)+7x+5 divided by x+1) using long division method is 2x^(2) + 2x + 5.
To find the result of the given polynomial division using long division method, we need to follow the steps below:
Step 1: Write the dividend and the divisor in long division form.
______________________
x + 1 | 2x^(3) + 4x^(2) + 7x + 5
Step 2: Divide the first term of the dividend by the first term of the divisor. In this case, 2x^(3)/x = 2x^(2). Write the result above the dividend.
2x^(2) _______________
x + 1 | 2x^(3) + 4x^(2) + 7x + 5
Step 3: Multiply the result by the divisor and write the product under the dividend.
2x^(2) _______________
x + 1 | 2x^(3) + 4x^(2) + 7x + 5
- (2x^(3) + 2x^(2))
---------------------
Step 4: Subtract the product from the dividend and bring down the next term.
2x^(2) _______________
x + 1 | 2x^(3) + 4x^(2) + 7x + 5
- (2x^(3) + 2x^(2))
---------------------
2x^(2) + 7x + 5
Step 5: Repeat the process until the degree of the remainder is less than the degree of the divisor.
2x^(2) + 2x + 5 _______________
x + 1 | 2x^(3) + 4x^(2) + 7x + 5
- (2x^(3) + 2x^(2))
---------------------
2x^(2) + 7x + 5
- (2x^(2) + 2x)
---------------------
5x + 5
- (5x + 5)
---------------------
0
Step 6: Write the final result as the quotient plus the remainder over the divisor.
[tex](2x^{3} + 4x^{2} + 7x + 5)/(x + 1) = 2x^{2} + 2x + 5[/tex]
Therefore, the answer is 2x^(2) + 2x + 5
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solve question please
Answer:
kindly update the question
Youve made it to Lookout Point and want to to just a little tarther for the day. Determise the distances ta dedide which is dorer. (Round to one decimal places) Question 3 Woire at Clear Sorhes and you get a call Erom friendi who are at fiogeri valey you decide fo mert ha fwary Using the map for coordinater (where the car. is at io,00 where mould you mect rour friends? Round coced inates to one ded mal olare) Mertat: Question 4 Now wa tore to hin
The midpoint is [(Yx + Fx)/2, (Yy + Fy)/2]
The distance between 2 points in the map is √[(FVx - CSx)^2 + (FVy - CSy)^2]
To determine the distance between two points on a map, we can use the distance formula:
d = √[(x2 - x1)^2 + (y2 - y1)^2]
In this case, we are trying to find the distance between Clear Springs (x1, y1) and Finger Valley (x2, y2). Plug in the coordinates for each point into the formula and solve for d.
d = √[(x2 - x1)^2 + (y2 - y1)^2]
= √[(Finger Valley x - Clear Springs x)^2 + (Finger Valley y - Clear Springs y)^2]
= √[(FVx - CSx)^2 + (FVy - CSy)^2]
Round the answer to one decimal place to get the distance between the two points.
To find the coordinates of the meeting point between you and your friends, we can use the midpoint formula:
Midpoint = [(x1 + x2)/2, (y1 + y2)/2]
In this case, we are trying to find the midpoint between your location (x1, y1) and your friends' location (x2, y2). Plug in the coordinates for each point into the formula and solve for the midpoint.
Midpoint = [(x1 + x2)/2, (y1 + y2)/2]
= [(Your x + Friends' x)/2, (Your y + Friends' y)/2]
= [(Yx + Fx)/2, (Yy + Fy)/2]
Round the coordinates to one decimal place to get the midpoint, which is the meeting point between you and your friends.'
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What is the answer? Please help!
Answer:
the answer is 88 square inches
Step-by-step explanation:
[tex]2(6 \times 4) + 2(4 \times 2) + 2(6 \times 2) = 88[/tex]
Hi. _______________________________________________________________________________
Answer:
.
Step-by-step explanation:
solve asap
4- Determine whether the variable is discrete or continuous, and determine its level of measurement.
The number of residents in a city
Discrete, interval level
Continuous, interval level
Discrete, ratio level
Continuous, ratio level
11)A pair of dice are rolled. Identify the pair of mutually exclusive events. Getting an even number on the first die; getting a double 5 Getting an odd number on the first die; getting a 4 on the second die Getting a 2 on the first die; getting a sum of 4 Getting a 3 on the first die; getting a sum more than 8
11)A pair of dice are rolled. Identify the pair of mutually exclusive events.
Getting an even number on the first die; getting a double 5
Getting an odd number on the first die; getting a 4 on the second die
Getting a 2 on the first die; getting a sum of 4
Getting a 3 on the first die; getting a sum more than 8
The number of residents in a city is a discrete variable with ratio level of measurement. Therefore, the correct option is option 3. When a pair of dice are rolled, the pair of mutually exclusive events are getting an odd number on the first die; getting a 4 on the second die. Therefore, the correct option is option 2.
The number of residents in a city is a discrete variable because it can only take on whole number values. The level of measurement for this variable is ratio level because there is a true zero point (a city with zero residents) and the differences between values are meaningful. Therefore, the correct answer is discrete, ratio level which is the third option.
Mutually exclusive events are events that cannot occur at the same time. In the case of rolling a pair of dice, the pair of mutually exclusive events is "Getting an odd number on the first die; getting a 4 on the second die." This is because if the first die is an odd number, the second die cannot be a 4 at the same time.
The other options are not mutually exclusive because they can occur at the same time. For example, it is possible to get an even number on the first die and a double 5 at the same time. Therefore, the correct answer is "Getting an odd number on the first die; getting a 4 on the second die" which is the second option.
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Combine like terms and write the resulting polynomial in descending 2x^(7)+5x^(6)+9x^(7) Select one:
The resulting polynomial in descending order is 11x7 + 5x6
To combine like terms and write the resulting polynomial in descending order, we need to first identify the like terms and then add or subtract their coefficients. Like terms are terms that have the same variable and the same exponent.
In this case, the like terms are 2x^(7) and 9x^(7).
We can combine these like terms by adding their coefficients:
2x^(7) + 9x^(7) = 11x^(7)
Now we have:
11x^(7) + 5x^(6)
Since the exponents are different, we cannot combine these terms.
Therefore, the resulting polynomial in descending order is 11x7 + 5x6
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A line L is said to be tangent to a circle C at a point P if and only if L meets C at P and at no other point besides P. Given a circle centered at a point O, a point P on the circle, and a line L passing through P, show that L is tangent to the circle at P if and only if L is perpendicular to the line OP.
We have shown that a line L is tangent to a circle C at a point P if and only if L is perpendicular to the line OP.
A line L is said to be tangent to a circle C at a point P if and only if L meets C at P and at no other point besides P. Given a circle centered at a point O, a point P on the circle, and a line L passing through P, we can show that L is tangent to the circle at P if and only if L is perpendicular to the line OP.
Let us assume that L is perpendicular to OP. Then, since L is perpendicular to the radius at P, it is also perpendicular to the circumference of the circle at P. This means that the line L only meets the circumference of the circle at the one point P, and so L is tangent to the circle at P.
Conversely, let us assume that L is tangent to the circle at P. This implies that the line L only meets the circumference of the circle at the one point P. Thus, since the line L must pass through the point P, it must be perpendicular to the line OP.
Therefore, we have shown that a line L is tangent to a circle C at a point P if and only if L is perpendicular to the line OP.
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C=15.50-0.20x How much credit is left on the card after Deshaun uses it for 30 minutes of calls?
The correct answer is $9.50 of credit is left on the card. To find out how much credit is left on the card after Deshaun uses it for 30 minutes of calls, we need to plug in the value of x into the equation C=15.50-0.20x.
Deshaun has a card with $15.50 of credit on it. He is using it to make calls and the cost of each minute of calling is $0.20. To calculate how much credit Deshaun has left on his card after 30 minutes of calls, we need to use the equation C=15.50-0.20x, where x is the number of minutes of calls.
Since x represents the number of minutes of calls, we will plug in 30 for x:
C = 15.50 - 0.20(30)
C = 15.50 - 6
C = 9.50
Therefore, there is $9.50 of credit left on the card after Deshaun uses it for 30 minutes of calls.
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Can somebody PLEASE help me ASAP? It’s due today!!
Answer: 3rd one
Step-by-step explanation:
formula : 2πrh+2πr^2
You are planning to sell children's fairy wings at a craft fair. It costs you $5 in supplies to make each set of fairy wings and you will sell them for double your cost.
You have 100 sets of fairy wings and sell 60 of them by 2pm. The craft fair ends at 4pm and you want to sell the rest of your wings faster so you mark the price down by 30%.
With c = supply cost to make a set of wings, and P(c) = price, the equation for the price you first sell the wings is A) P(c)=2c B) P(c)=.7c C) P(c)=.5c D) P(c)=1.5c
The new equation to sell the wings faster with N(p)=new price is A) N(p)=.3p B) N(p)=p-.3 C) N(p)=.7p D) N(p)=.5p
The composed equation N(P(c) is A) .9c B) 1.4c C) .7c D) 2.7c
and represents A) the markup of the discounted price over your supply cost B) your markup profit on all the wings C) how much money you will lose by selling the wings at a lower price
The domain of all the functions is A) [0, infinity) B) (-infinity, 0] C) (-infinity, infinity)
because A) the prices will always be positive numbers B) the wings make it possible to fly C) you can hace any possible answer in these questions D) anything is possible
Answer: Dragonfly wings for the boys cost $1 while fairy wings for the girls cost $2. Phoebe's mom spent $18 on the gifts. How many dragonfly wings and fairy wings
Step-by-step explanation:
Answer:
The answer to the first question is A) P(c) = 2c, because the wings will be sold for double the cost of supplies.
The answer to the second question is B) N(p) = p - 0.3, because the price will be marked down by 30%.
The answer to the third question is A) 0.9c, which represents the markup of the discounted price over the supply cost.
The domain of all the functions is A) [0, infinity), because prices and costs must be positive numbers. Therefore, options B, C, and D are incorrect.
simply the expression (6^2)4
Answer:
144
Step-by-step explanation:
6*6=36
36*4=144
Find an equation of the circle that has center(-1,2) and passes through(-6,6).
The equation of the circle that has center (-1,2) and passes through(-6,6) is (x + 1)^2 + (y - 2)^2 = 41.
The equation of a circle with center (h,k) and radius r is given by (x-h)^2 + (y-k)^2 = r^2. In this case, the center of the circle is (-1,2) so h = -1 and k = 2. We can use the given point (-6,6) to find the radius of the circle.
The distance between the center and the given point is the radius of the circle, and we can use the distance formula to find it:
r = √((-6 - (-1))^2 + (6 - 2)^2)
r = √((-5)^2 + (4)^2)
r = √(25 + 16)
r = √41
So the equation of the circle is:
(x - (-1))^2 + (y - 2)^2 = (√41)^2
(x + 1)^2 + (y - 2)^2 = 41
Therefore, the equation of the circle that has center(-1,2) and passes through(-6,6) is (x + 1)^2 + (y - 2)^2 = 41.
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In the figure, each small cube has edges that are 1/3 yd long. Which expression can you use to find the volume of the rectangular prism is cubic yards?
The expressiοn (B) 2 × 4 × 5 × 1/3 × 1/3 × 1/3 can be used tο find the vοlume οf the rectangular prism is cubic yards.
What is equatiοn?A mathematical equatiοn links twο statements and utilises the equals sign (=) tο indicate equality. In algebra, an equatiοn is a mathematical assertiοn that prοves the equality οf twο mathematical expressiοns. Fοr instance, in the equatiοn 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical fοrmula may be used tο determine hοw the twο sentences οn either side οf a letter relate tο οne anοther. The lοgο and the particular piece οf sοftware are usually identical. like, fοr instance, 2x - 4 = 2.
Vοlume is calculated using the fοrmula LWH
Here each cube has side 1/3 yd
Sο vοlume = (2 × 1/3) × (4 × 1/3) × (5 × 1/3)
It can be written as 2 × 4 × 5 × 1/3 × 1/3 × 1/3
Thus, οptiοn B is cοrrect.
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Complete question:
Can someone answer this, please? I need the help
Answer:
Proofs attached to answer
Step-by-step explanation:
Proofs attached to answer
Find the monthly payment on a 30-year, $100,000 mortgage if the
interest rate is 6 percent. hundred.
The monthly payment on a 30-year, $100,000 mortgage with an interest rate of 6 percent is $599.55.
To find the monthly payment on a 30-year, $100,000 mortgage with an interest rate of 6 percent, we need to use the following formula:
Monthly Payment = (Loan Amount * Interest Rate) / (1 - (1 + Interest Rate)^(-Number of Payments))
First, we need to convert the interest rate from a percentage to a decimal by dividing it by 100:
Interest Rate = 6 / 100 = 0.06
Next, we need to calculate the number of payments over the life of the loan. Since there are 12 months in a year, and the loan is for 30 years, the number of payments is:
Number of Payments = 12 * 30 = 360
Now we can plug these values into the formula:
Monthly Payment = ($100,000 * 0.06) / (1 - (1 + 0.06)^(-360)) = $599.55
Therefore, A $100,000 mortgage with a 30 year term and a 6% interest rate has a $599.55 monthly payment.
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Use the ruler provided to measure the dimensions of the parallelogram shown to the nearest 0.5 centimeter.
Which measurement is closest to the area of the parallelogram in square centimeters?
F.14 cm2
G.16.5 cm2
H. 4114
cm2
J.8.5 cm2
F. 14 [tex]cm^2[/tex] is the measurement that most closely resembles the
the parallelogram's area in square centimeters.
what are parallelograms?A parallelogram is a geometric object with sides that are parallel to one another in two dimensions. It is a form of a polygon with four sides (sometimes known as a quadrilateral) in which each parallel pair of sides have the same length. A parallelogram has adjacent angles that add up to 180 degrees. You must have studied a variety of 2D shapes and sizes in geometry, including circles, squares, rectangles, rhombuses, etc. Each of these forms has a unique set of characteristics.
from the question:
We must multiply the parallelogram's base and height in order to determine its area. We can observe from the photograph that the parallelogram's height is around 3 cm, and its base is about 5 cm. Hence, the parallelogram's area is:
Area = Base x Height
= 5 cm x 3 cm
= 15 [tex]cm^2[/tex]
15 square centimeters is the result of rounding this response to the nearest whole number. F. 14 cm2 is the measurement that most closely approximates the parallelogram's area in square centimeters.
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Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the high temperature of 98 degrees occurs at 6 PM and the average temperature for the day is 85 degrees. Find the temperature, to the nearest degree, at 7 AM. degrees
The temperature at 7 AM is approximately 87 degrees.
The outside temperature over a day can be modeled as a sinusoidal function. In this case, we know that the high temperature of 98 degrees occurs at 6 PM and the average temperature for the day is 85 degrees. To find the temperature at 7 AM, we can use the equation:
T(t) = A sin(B(t - C)) + D
where T(t) is the temperature at time t, A is the amplitude, B is the frequency, C is the horizontal shift, and D is the vertical shift.
We know that the average temperature is 85 degrees, so D = 85. We also know that the high temperature of 98 degrees occurs at 6 PM, so A = (98 - 85)/2 = 6.5 and C = 6.
Now we can plug in the values and solve for the temperature at 7 AM:
T(7) = 6.5 sin(B(7 - 6)) + 85
Since we want to find the temperature to the nearest degree, we can round the answer to the nearest whole number:
T(7) = 6.5 sin(B) + 85 ≈ 87 degrees
Therefore, the temperature at 7 AM is approximately 87 degrees.
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You want to have $5000 in two years so that you can go on a vacation. How much should do you need put into your
account to have enough money if it pays 5.89% interest compounded weekly? Hint: You have A, you need to find P!**
You need to deposit $13 into a account to have amount $5000 in 2 years.
What is the compound interest?Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.
The formula used to find the compound interest = [tex]A=P(1+\frac{r}{100})^{nt}[/tex].
Given that, Amount =$5000, rate of interest =5.89% and time period = 2 year = 104 weeks.
Now, 5000=P(1+5.89/100)¹⁰⁴
5000=P(1+0.0589)¹⁰⁴
5000=P(1.0589)¹⁰⁴
5000=384.5P
P=5000/384.5
P=$13
Therefore, you need to deposit $13 into a account to have amount $5000 in 2 years.
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Which change, if any, is needed to the underlined text?
“Taking up to six months, hikers who plan to complete the entire
journey”
-A journey of up to six months, hikers planning to complete it entirely
-Taking up to six months to complete, hikers who plan the entire journey
-The entire journey takes up to six months to complete, so hikers who plan to
finish it
-No change
No change is needed. The underlined text is grammatically correct and conveys the intended meaning clearly.
What is the meaning of the underlined test?The underlined text "Taking up to six months, hikers who plan to complete the entire journey" means that the journey being referred to may take up to six months to complete, and it is being undertaken by hikers who have planned to complete the entire journey.
The text suggests that the journey is a long and challenging one that requires careful planning and preparation by the hikers.
Therefore, the correct answer is as given above. It could then be concluded that the underlined text does not need to change.
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without evaluating the expression, why is 3^4 -1 even
Without evaluating the expression, the sum of given expression is 80 is this why its even number.
What are expressions?Using letters or alphabets to represent numbers without giving their exact values is the idea behind algebraic expressions. The fundamentals of algebra taught us how to express an unknown value using letters like x, y, and z. These letters are referred to here as variables.
In an algebraic expression, both constants and variables can be used. Any amount that is added before a variable and then multiplied by it is referred to as a coefficient.
An algebraic expression in mathematics is one that contains variables, constants, and algebraic operations (addition, subtraction, etc.). Expressions are built upon terms.
Calculate the power: 81
Calculate the sum or difference: 81 - 1
Answer is 80
Thus, here we know that 80 is an even number.
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20% of $509 and how to work it out
Answer:
101.80
Step-by-step explanation:
Well this is fairly simple, if you can use a calculator. There not much to it so first you convert 20% to a decimal which is 0.2 or 0.20 either works. Then you multiply 0.2 by 509 to get 101.80. I used a calculator to multiply those two but Im not sure how else to do it without a calculator. Hope this helps.
A new movie is coming out that you and your family really want to see. You are going to buy tickets for
opening day as soon as they go on sale and want to get extra tickets so friends could come too. You
have $224.50 and wants to get as many tickets as possible. You want to get at least 5 adult tickets and
4 kids tickets.
Use the ticket prices from your local movie theater or look up the average prices of child and adult
tickets for the movie theater.
In your discussion post, share the equations that you used to model this situation and answer the
following questions:
1. Can you get at least 5 adult tickets and 4 kids tickets?
2. What is the most tickets you could have bought and met the given conditions? What number of
each type of ticket is that?
3. After doing more research, you find out that you can rent out a whole theater for $190. If you rent
the theater out, you can have up to 24 people, regardless of whether they are children or adults. In
what situations would it be a better deal to rent out the theater?
1. The equation for the cost of adult tickets is:
$8.97 x number of adult tickets
The equation for the cost of child tickets is:
$6.79 x number of child tickets
The equation for the cost of renting out the theater is:
$190
2. Yes, you can get at least 5 adult tickets and 4 kids tickets.
3. The most tickets you could have bought and met the given conditions is 9 adult tickets and 8 kids tickets.
4. It would be a better deal to rent out the theater if you had more than 24 people.
You must be aware of the costs of adult and child tickets in order to determine if you can purchase at least 5 adult tickets and 4 child tickets. A cinema ticket for an adult costs $8.97 on average, while a ticket for a child costs $6.79 on average. 4 children's tickets would cost $27.16 and 5 adult tickets would cost $44.85 as a result. You would then have $202.49 remaining, which would be enough to pay for 7 additional child tickets. Thus, you can purchase at least 5 adult and 4 child tickets.
The most tickets you could have purchased while still fulfilling the requirements is nine adult and eight child tickets. The total price would be $135.05. The adult tickets would cost $80.73 and the child tickets would cost $54.32. You would now have $89.45, which is insufficient to purchase any additional tickets.
Renting out the theater might be a great option if you have more than 24 individuals. This is due to the fact that hiring out the theater costs $190 and allows for a maximum of 24 guests, both adults and children. Consequently, renting the theater would be less expensive than purchasing individual tickets if you had more than 24 individuals.
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Johnston & Deegan-Packel index (Math & Politics)
Consider a voting system for the six New England states where there are a total if seventeen votes and twelve or more are required for passage. Votes are distributed as follows:
MA:4 ME:3 NH:2
CT:4 RI:3 VT:1
a) Calculate the Johnston index of each voter
b) Calculate the Deegan-Packel index of each voter
The Johnston index of each voter is 3.317 and the Deegan-Packel index of each voter is 0.154
The Johnston index and the Deegan-Packel index are two measures of voting power that take into account the number of votes each voter has and the number of votes required for passage.
a) The Johnston index is calculated by taking the square root of the product of the number of votes a voter has and the number of votes they need for passage. In this case, the Johnston index for each voter is:
MA: √(4*(12-4)) = √32 = 5.657
ME: √(3*(12-3)) = √27 = 5.196
NH: √(2*(12-2)) = √20 = 4.472
CT: √(4*(12-4)) = √32 = 5.657
RI: √(3*(12-3)) = √27 = 5.196
VT: √(1*(12-1)) = √11 = 3.317
b) The Deegan-Packel index is calculated by taking the number of winning coalitions that a voter is a part of and dividing it by the total number of winning coalitions. In this case, the Deegan-Packel index for each voter is:
MA: 20/26 = 0.769
ME: 14/26 = 0.538
NH: 8/26 = 0.308
CT: 20/26 = 0.769
RI: 14/26 = 0.538
VT: 4/26 = 0.154
Overall, the Johnston index and the Deegan-Packel index provide different perspectives on the voting power of each voter. The Johnston index takes into account the number of votes each voter has and the number of votes required for passage, while the Deegan-Packel index takes into account the number of winning coalitions each voter is a part of.
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The perimeter of the rectangle below is 80 units. Find the length of side CD.
Write your answer without variables.
D
4z + 2
C
3z + 3
B
CD
The required length of side CD is 22 units.
How to use perimeter to solve for variable?Since the perimeter of the rectangle is 80 units, we can use the formula for the perimeter of a rectangle, which is:
perimeter = 2(length + width)
In this case, we know that the perimeter is 80 units, so we can write:
80 = 2(length + width)
We also know that CD is a side of the rectangle, so it must be either the length or the width. Let's assume that CD is the length, so we can write:
CD = 4z + 2
Substituting this expression for the length into the formula for the perimeter, we get:
80 = 2(4z + 2 + width)
Simplifying the right-hand side, we get:
80 = 8z + 4 + 2width
Subtracting 4 from both sides, we get:
76 = 8z + 2width
Dividing both sides by 2, we get:
38 = 4z + width
Now we can use the fact that CD is a side of the rectangle to substitute for width. Since the opposite side of the rectangle must also have length 4z + 2, we can write:
width = 3z + 3
Substituting this into the previous equation, we get:
38 = 4z + 3z + 3
Simplifying the right-hand side, we get:
38 = 7z + 3
Subtracting 3 from both sides, we get:
35 = 7z
Dividing both sides by 7, we get:
5 = z
Now we can substitute this value of z into the expression for CD:
CD = 4z + 2 = 4(5) + 2 = 22
Therefore, the length of side CD is 22 units.
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