Answer:
8+8+12+5= 33
Step-by-step explanation:
8+8+12+5=33
Which of the following is not true about two integers p and q, where p is even and g is odd? A p+q is odd. B. pq is even C q +1 even. D. q + 5 is odd.
Answer:
The statement "q + 5 is odd" is FALSE.
Step-by-step explanation:
Let p = 2 and q = 3.
A. p + q is odd ... 2 + 3 = 5 TRUE
B. pq is even ... 2*3 = 6 TRUE
C. q + 1 is even ... 3 + 1 = 4 TRUE
D. q + 5 is odd ... 3 + 5 = 8 FALSE
Ivan bought two magazines for $4.95 each. If the sales tax was 6.75% what was the total amount that he paid for the magazines?
Step-by-step explanation:
the total sale price for the magazines were
2×4.95 = $9.90
so,
100% = 9.9
1% = 100%/100 = 9.9/100 = 0.099
6.75% = 6.75×1% = 6.75×0.099 = 0.66825 ≈ $0.67
so, he paid in total
$9.90 + $0.67 = $10.57
1. In a class of 60 students, a survey was conducted, 30 students had applied for Addis Ababa University, 25 students applied for Bahir Dar University and 24 students applied for Wachemo University. 11 students applied for both Addis Ababa and Bahir Dar Universities, 6 applied for both Addis Ababa and Wachemo Universities, 9 applied for both Wachemo and Bahir Dar Universities while 4 applied neither of the aforementioned universities. Find number of students that applied at most two universities.
The number of students who applied at most two universities is 26 students.
How is the calculation for the number done?The population of students in a class = 60 students
Number of students who applied for Addis Ababa University = 30 students
Number of students who applied for Bahir Dar University = 25 students
Number of students who applied for Wachemo University = 24 students
Number of students who applied for Addis and Bahir = 11 students
Number of students who applied for Addis and Wachemo = 6 students
Number of students who applied for Wachemo and Bahir = 9 students
The number of students who applied at most two universities is 26 (11+ 6 + 9).
Thus, the number of students who applied at most two universities is 26.
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Mike drove 40 miles from his home to his office, and he then drove back home using the same route. The average speed on his return trip was 10 miles/hour more than the average speed on his trip to the office. The total time for the trip is represented by this expression, where x is the average speed on the trip from his home to his office.
The average speed on Mike’s drive home is represented by
x + 10
.
When Mike drives at an average speed of 55 mile/hour on his way home, it takes him approximately
1.6 hours
to drive to work and back.
Mike's speed driving to his office is 45 miles/hour, which is 10 miles less than his average speed driving back.
How is speed calculated?Speed is an average value of a scalar measurement of the distance covered over the time taken.
Speed is the equation, r = d/Δt, where r = speed or rate, d = distance, and Δt is the change in time.
Thus, when the distance covered by a traveler is divided by the time consumed, one can determine the average speed for the travel.
Data and Calculations:Distance from Mike's home to his office = 40 miles
Distance to and from = 80 miles (40 miles x 2)
Hours covered from office = 1.6 hours
Average speed for the trip = 50 miles/hour (80/1.6)
Average speed to return home = 55 miles/hour
Average speed to office = 45 miles/hour (55 - 10)
Thus, Mike's speed of driving to his office is 45 miles/hour.
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Question Completion:What is Mike's speed driving to his office?
Adult tickets to the fall play cost $8 and student tickets cost $4. The drama class sold 20 more adult tickets han student tickets to the fall play. to If the
class collected $880 from ticket sales, how many adult tickets were sold?
The drama class sold
adult tickets.
The solution
Answer:
80
Step-by-step explanation:
Let the number of adult tickets sold be a and the number of student tickets sold be s.
"The drama class sold 20 more adult tickets han student tickets to the fall play." means that a-20=s."the class collected $880 from ticket sales" means that 8a+4s=880, which is the same as 2a+s=220.Substituting the first equation into the second,
[tex]2a+a-20=220 \\ \\ 3a-20=220 \\ \\ 3a=240 \\ \\ a=80[/tex]
A survey was conducted among the students at Elmwood High School. What are the individuals in this study?
the types of sports
the music groups
the clubs
the students
Based on the information provided, the individuals in this study are: D. the students.
What is a study?A study can be defined as a strategic process or technique through which a scientist (researcher) observes and measures the effect of a risk factors, diagnostic test, or treatments on a particular population of interest.
What is a variable?In Mathematics, a variable can be defined as the measurable conditions, events, characteristics, individuals, or behaviors that a scientist (researcher) can control or observe when performing a study.
Based on the information provided, the individuals in this study are the students and these include the following subclasses:
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The students are the individuals in this study and is therefore denoted as option D.
What is a Sample?This refers to a group of people which are chosen or taken from a large population for measurement or surveys.
In this scenario, the study was conducted in a school with different types of students according to their grades such as freshman, sophomore etc. This therefore makes the individuals in the study to be students and is the most appropriate choice.
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The Mogul Runners ski club planned a trip to Park City. Of the total number of club members, 11 signed up to go. If this is 25% of the club, how many members does the ski club have?
The ski club has 44 members in all
What is population?
Population refers to the total number of items or individuals that form a group.
In this case, the population means the total number of all members in the Mogul Runners ski club.
What is sample?
Sample means a fraction of the total population, in other words, the 25% of the members, whose number is 11, that signed up to go for the planned trip.
We can convert 25% to 100% by equation 25% to 11 members that signed up to go for the planned trip.
25% of club members=11 members
divide both sides by 25%
25%/25% of club members=11/25% members
club members=44 members
The ski club has 44 members altogether as computed above.
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Find the value of b.
Step-by-step explanation:
The value of b will be 43° as it is vertically opposite angle.. !!
Mr. Gosain?(1 Aana = 31.8 m²) b) A real estate agent bought two triangular Kittas' having a common side as shown in the figure from two people for Rs 20,00,000 altogether. If he immediately sold the land in the shape of a quadrilateral at Rs 15,00,000 per Kattha, find his profit or loss.(1 Kattha= 338.63 sq. m) danta Excel in Mathematics - Book 9 86 36 m Approved by Curriculum Development Cen 20 m 29 m 25 m 21 m aktapur
The information given regarding the computation of the profit or loss shows that there's a loss of RS 500,000.
How to calculate the profit?From the information given, it was stated that the real estate agent bought two triangular Kittas' having a common side as shown in the figure from two people for Rs 2000,000 altogether.
It was further depicted that he sold the land in the shape of a quadrilateral at Rs 1,500,000. In their case, the sale is less than the cost and therefore, there's a loss.
The loss will be:
= 2,000,000 - 1,500,000
= 500,000
Therefore, the information given regarding the computation of the profit or loss shows that there's a loss of RS 500,000.
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Pls help w this question
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
According to given figure,
Angle 11, Angle 20 and Angle 16 forms angles of a triangle,
so, by angle sum property of a triangle :
[tex]\qquad❖ \: \sf \: \angle11 + \angle20 + \angle16 = 180 \degree[/tex]
[tex]\qquad❖ \: \sf \: \angle11 +66 + 43 = 180 \degree[/tex]
[tex]\qquad❖ \: \sf \: \angle11 +109 = 180 \degree[/tex]
[tex]\qquad❖ \: \sf \: \angle11 = 180 \degree - 109[/tex]
[tex]\qquad❖ \: \sf \: \angle11 =71 \degree [/tex]
[tex] \qquad \large \sf {Conclusion} : [/tex]
Option B is correctyou are considering an investment into Company XYZ and need to determine the company's value and the appropriate investment amount. You have been provided with historical financial statements for the past three years in order to build a forecast model. Key assumptions to use include:
Future sales revenue is assumed to increase at 2.5% annually.
Gross margin for 2021E is assumed to be equal to the average gross margin % for 2019 and 2020, but will decrease by 2.5% (i.e. 250 bps) each year thereafter
SG&A expense is assumed to be a percentage of revenue for the forecast period. That percentage is equal to the 2018-2020 average
Depreciation expense is assumed to be a percentage of revenue for the forecast period. That percentage is equal to the 2018-2020 average
The tax rate for the forecast period is assumed to be equal to the effective tax rate for 2018
Capital expenditures for any given year in the forecast period is assumed to be 3x the prior year's depreciation expense. For example, 2021 capital expenditures is equal to 3x 2020 depreciation expense.
No new debt or equity is assumed to be issued
Download CFI_-_FMVA_Practice_Exam_Case_Study_A.xlsx and answer the following 12 questions.
1
What is Gross Profit in 2028E using the assumptions listed above and on the Control Panel?
$17,545
$30,704
$27,780
$40,938
Option A is correct. The gross profit that has been calculated for this year is given as 17545
How to solve for the gross profit22050 × 97.5%(100-2.5%) = 21498.75
= 21498.75 × 0.975 = 20961.28
= 20961.28 x 0.975 = 20437.24
= 20437.24 x 0.975 = 19926.31
= 19926.31 × 0.975 = 19428.15
= 19428.15 x 0.975 = 18942.45
= 18942.45 x 0.975 = 18468.80
= 18468.89 × 0.975 = 18017
= 18007 × 0.975 = $17545
Hence we can see at the end of the solution that the value of the gross profit in 2028 = $17545
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A large bakery buys flour in 20-pound bags. The bakery uses an average of 1050 bags a year. Preparing an order and receiving a shipment of flour involves a cost of $15 per order. Annual Carrying costs are $ 55 per bag. a) Determine the economic order quantity? b) What is the average number of bags on-hand? c) How many orders per year will there be? d) Compute the total cost of ordering and carrying flour? e) If holding costs were to increase by $5 per year, how much would the minimum total annual cost?
Given the following:
Demand = 1050Ordering cost = 15Holding cost = 55The economic order quantity is 24.
What is the economic order Quantity?Eoq = √2 * demand * ordering cost / holding cost)
= √(2 * 1050 * 15 / 55)
EOQ = 24
What is the average number of bags on-hand?The Average inventory = EOQ / 2
= 24 / 2
= 12
How many orders per year will there be?Expected number of orders = demand / EOQ
= 1050 / 24
= 44
What is the total cost of ordering and carrying flour?Annual holding cost (AHC) = (EOQ / 2) * Holding cost
= (24 / 2) * 55
= 660
Annual ordering cost (AOC) = (demand / EOQ) * ordering cost
= (1050 / 24) * 15
= 656
Thus,
Total cost of managing = AHC + AOC
= 660 + 656
TCM = 1,316
If holding costs were to increase by $5 per year, how much would the minimum total annual cost?5. For holding cost of 60
EOQ= √(2 * demand * ordering cost / holding cost)
= √(2 * 1050 * 15 / 60)
= 23
Annual holding cost = (EOQ / 2) * holding cost
this gives us
= (23 / 2) * 60
= 690
Annual ordering cost = (demand / EOQ) * ordering cost
= (1050 / 23) * 15
= 685
Total cost of managing = AHC+ AOC
= 690 + 685
= 1375
Change in total annual cost = new - old
= 1375 - 1316
= 59
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A triangle with a base of 16 cm and a height of 9 cm.
Answer: 288
Step-by-step explanation:
(16x9)x2
Solve this system. Write your answer as an ordered pair.
-5x + y = -3
3x - 8y = 24
[tex]\begin{cases} -5x+y=-3\\ 3x-8y=24 \end{cases} \\\\\\ \stackrel{\textit{using the 1st equation}}{-5x+y=-3}\implies \underline{y=-3+5x} \\\\\\ \stackrel{\textit{substituting on the 2nd equation}}{3x-8(\underset{y}{-3+5x})=24}\implies 3x+24-40x=24\implies 3x-40x=0 \\\\\\ -37x=0\implies \boxed{x=0}~\hfill \underline{y=-3+5(\stackrel{x}{0})}\implies \boxed{y=-3} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill (0~~,~~-3)~\hfill[/tex]
Answer:
( 0, -3 )
Step-by-step explanation:
-5x + y = -3 ⇒ ( 1 )
3x - 8y = 24 ⇒ ( 2 )
We can make y the subject of equation 1.
y = 5x - 3 ⇒ ( 3 )
Now let us take equation 2.
Here we can replace y with ( 5x - 3 ) to find the value of x.
Value of x.
3x - 8y = 24
3x - 8 (5x - 3) = 24
3x - 40x + 24 = 24
-37x = 0
x = 0
Now let us take equation 3 to find the value of y.
Here we can replace x with 0.
Let us find it now.
y = 5x - 3
y = 5 × 0 - 3
y = 0 - 3
y = -3
Now, let us write the answer as an ordered pair.
( x, y )
( 0, -3 )
find the zeros x^4-2x^3-44x^2-88x-32
The zeros which are the roots of the polynomial expressions are:
x = -4; x = - 2; x = 4 - 2√5; x = 2(2 + √5)
What are the zeros of a polynomial expression?The zeros of a polynomial f(x) are really the values of x that answer the equation f(x) = 0. Thus, f(x) is a function of x, and the polynomial zeros refer to the values of x, which makes the f(x) value equal to zero. The digit of zeros in a polynomial is decided by the degree of equation f(x) = 0.
For a polynomial, there may be specific values of the variable for which the polynomial is zero. These are known as polynomial zeros. They are also known as polynomial roots. In essence, we look for the zeros of quadratic equations to discover the solutions to the given equation.
From the given equation, the zeros of x^4-2x^3-44x^2-88x-32 can be computed as follows:
Using the rational root theorem:
[tex]\mathbf{= (x+2)\dfrac{x^4-2x^3-44x^2-88x-32}{x+2} }[/tex]
[tex]\mathbf{=(x+2) (x^3-4x^2-36x-32) }[/tex]
By factorization, we have:
= (x + 2) (x + 4) (x² - 8x - 4)
The zeros which are the roots of the polynomial expressions are:
x = -4; x = - 2; x = 4 - 2√5; x = 2(2 + √5)
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If the formula r=1/n-1 .....following data, what would be the value of x?
The solution or the value of x = 14 (Option C). See the explanation below.
Where x (bar) is the mean.
What is the calculation for the above?x = (12 + 13 + 14 + 15 + 16)/5
= 14
Hence option C is correct.
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A 22-ft ladder leans against a building so that the angle between the ground and the ladder is 64°. How high does the ladder reach on the building?
The height of the ladder on the building is 19.77 feet
How high does the ladder reach on the building?Represent the height of the ladder on the building with h
So, the given parameters are:
Angle, x = 64 degrees
Length of ladder, l = 22 feet
The height of the ladder on the building is calculated using
sin(x) = h/l
Substitute the known values in the above equation
sin(64) = h/22
Multiply both sides by 22
h = 22 * sin(64)
Evaluate the product
h = 19.77
Hence, the height of the ladder on the building is 19.77 feet
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Find the critical value. Assume that the test is two -tailed and that n denotes the number of pairs of data. n =
20, α = 0.01
A) -0.570
B) 0.570
C) +0.447
D) +0.570
Using a calculator, the critical value for the t-distribution, with a confidence level of 99%, a sample size n = 20 and a two-tailed test is of Tc = 2.8609.
How to find the critical value of the t-distribution?It is found using a calculator, with three inputs, which are given by:
The confidence level.The number of degrees of freedom, which is one less than the sample size.The tail.In this problem, the inputs are given as follows:
Confidence level of 99%, as 1 - 0.01 = 0.99 = 99%.19 df, as 20 - 1 = 19.Two-tailed test, as stated in this problem.Hence, using a calculator, the critical value is of is of Tc = 2.8609.
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what is the length of the hypotenuse of a right triangle whose legs have lengths 12 cm and 16 cm?
A home gardener estimates that 18 apple trees will produce an average yield of 80 apples per tree. But because of the size of the garden, for each additional tree planted, the yield will decrease by four apples per tree. How many trees should be planted to maximize the total
19 trees should be planted to maximize the total
How many trees should be planted to maximize the totalFrom the question, we have the following parameters:
Number of apples, x = 18
Yield, f(x) = 80 per tree
When the number of apple trees is increased (say by x).
We have:
Trees = 18 + x
The yield decreases by four apples per tree.
So, we have
Yield = 80 - 4x
So, the profit function is
P(x) = Apples * Yield
This gives
P(x) = (18 + x) *(80 - 4x)
Expand the bracket
P(x) = 1440 - 72x + 80x - 4x^2
Differentiate the function
P'(x) = 0 - 72 + 80 - 8x
Evaluate the like terms
P'(x) = 8 - 8x
Set P'(x) to 0
8 - 8x = 0
Divide through by 8
1 - x = 0
Solve for x
x = 1
Recall that:
Trees = 18 + x
So, we have
Trees = 18 + 1
Evaluate
Trees = 19
Hence, 19 trees should be planted to maximize the total
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The perimeter is 54 m. The apothem is \root(3)(3) . To the nearest tenth, what is the area of this regular polygon?
The area of this regular polygon is 46.8 square units
How to determine the area of this regular polygon?The given parameters are:
Perimeter, p = 54 m
Apothem, a = √3
The area of this regular polygon is then calculated as:
Area = 0.5 * Apothem * Perimeter
Substitute the known values in the above equation
Area = 0.5 * √3 * 54
Evaluate the product
Area = 46.8
Hence, the area of this regular polygon is 46.8 square units
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The large rectangle was reduced to create the small rectangle.
A large rectangle has a length of 18 inches and width of 12 inches. A smaller rectangle has a length of 6 inches and width of x inches.
Not drawn to scale
What is the missing measure on the small rectangle?
2 inches
3 inches
4 inches
5 inches
Answer:
4 inches
Step-by-step explanation:
large rectangle - 18:12 ratio = 3:2
small rectangle - 6:4 = 3:2
A certain brand of coffee comes in two sizes. A 12.3-ounce package costs $2.99 . A 33.9-ounce package costs $8.74 . Find the unit price for each size. Then state which size is the better buy based on the unit price. Round your answers to the nearest cent.
Answer:
[tex]12.3 - 33.9 = 21.6 \div 10 = 2.16[/tex]
Can someone explain the steps I’m confused
Answer:
x = 8 ± [tex]\sqrt{10}[/tex]
Step-by-step explanation:
x² - 16x + 54 = 0 ( subtract 54 from both sides )
x² - 16x = - 54
to complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(- 8)x + 64 = - 54 + 64
(x - 8)² = 10 ( take the square root of both sides )
x - 8 = ± [tex]\sqrt{10}[/tex] ( add 8 to both sides )
x = 8 ± [tex]\sqrt{10}[/tex]
then
x = 8 - [tex]\sqrt{10}[/tex] , x = 8 + [tex]\sqrt{10}[/tex]
3(q+ 4/3 )=2 solve for Q
Answer: q = -2/3
Step-by-step explanation:
First, we need to apply the Distributive Law in order to proceed with the problem.
3(q + 4/3) = 2
3q + 3(4/3) = 2
We already know that 3(4/3) = 4, since the 3's cancel out. Or, 3(4/3) = 12/3 = 4.
Our new equation is,
3q + 4 = 2
Through transposition and isolation of variables, we get,
3q = -2
Dividing by 3 on both sides...
q = -2/3
y = x^3 - 52x^2 + 15x^4 + 16 + 20x
The factors of the equation of power 4, [tex]y=x^{3}-52x^{2} +15x^{4} +16+20x[/tex] are x=1, -2, 4/3, -2/5.
Given equation is [tex]y=x^{3}-52x^{2} +15x^{4} +16+20x[/tex],
By performing L-division method, we get
[tex]y = (x-1)(15x^{3} +16x^{2} -36x-16)[/tex]
Then again doing the same L-division method to the cubic equation [tex]15x^{3} +16x^{2} -36x-16[/tex], we get
[tex]15x^{3} +16x^{2} -36x-16 = (x+2)(15x^{2} -14x-8)[/tex]
Therefore, [tex]y = (x-1)(x+2)(15x^{2}-14x-8)[/tex]
Then finally the roots of the quadratic equation [tex]15x^{2}-14x-8[/tex] are (x-(4/3)) and (x+(2/5))
Hence, [tex]y=x^{3}-52x^{2} +15x^{4} +16+20x = (x-1)(x+2)(x-\frac{4}{3} )(x+\frac{2}{5} )[/tex]
Therefore, the roots of the equation of power 4, [tex]y=x^{3}-52x^{2} +15x^{4} +16+20x[/tex] are x=1, -2, 4/3, -2/5.
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Fatima purchased a new mattress when it was on sale. The sale price was 20% less than the regular price. If the sale price was $358, what was the original price? (Round your answer to the nearest dollar).
well, the regular price is really "x", which oddly enough is 100%, but we also know that $358 is really the discounted price by 20%, namely 100% - 20% = 80%, so we know that 358 is really just 80% of "x", so
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 358& 80 \end{array} \implies \cfrac{x}{358}~~=~~\cfrac{100}{80} \\\\\\ \cfrac{x}{358}=\cfrac{5}{4}\implies 4x=1790\implies x=\cfrac{1790}{4}\implies x\approx 448[/tex]
a swimming pool charges £3.60 for entry. you can save 1/3 of entry fee with a membership card. on his first visit, ken spends £5 on a membership card plus the reduced entry fee. how many times does ken visit before he gets back his £5
The number of times Ken visits, given the £3.6 pool charge, and 1/3 savings per visit is 5 times.
Which method can be used to find the number of times Ken visits the pool to get back his £5?The entry fee = £3.60
Amount saved on entry fee by having a membership card = 1/3 of the entry fee
Amount Ken spends on the membership card and the reduced entry fee = £5
Therefore;
Reduced entry fee = £3.60×(1 - 1/3) = £2.4
Amount saved per visit = £3.6 - £2.4 = £1.2
The number of visits, n, before he gets back his £5 is therefore;
n = £5/(£1.2/visit) ≈ 4.17 visitsKen has to visit the swimming pool more than 4 times to get his £5 back.
Rounding to the next larger whole, therefore;
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Which expression correctly represents "six more than the quotient of three and a number, decreased by eight"?
6+3/n-8
6+n/3-8
6+3/n+8
6+n/3+8
The option A is correct because the value of the statement is 6+3/n-8.
According to the statement
we have given that the statement and we have to write the statement in the numerical form.
So, For this purpose
we know that the given statement is
"Six more than the quotient of three and a number, decreased by eight".
In this statement "Six more than" indicates the sum between the quotient and 6.
And "The quotient of three and a number" indicates a fraction where the numerator is 3 and the denominator is , a number.
"Decreased by eight" indicates a subtraction between the quotient an 8 units".
If we unit all parts of the statements, we would have
6+3/n-8
So, From the given statement, The option A is correct because the value of the statement is 6+3/n-8.
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Which of the following number 1001,1002,1004 will be the sum of 994 and a 2 digit number
The number that will be the sum of 994 and a 2 digit number is 1004 (option 3). Details about digits of numbers can be found below.
What is a 2-digit number?A digit is the whole numbers from 0 to 9 and the arabic numerals representing them, which are combined to represent base-ten numbers.
A 2-digit number is any number between 10 and 99.
According to this question, 994 is said to be added to a 2 digit number to result into either 1001, 1002 or 1004.
1001 - 994 = 7 (1 digit)1002 - 994 = 8 (1 digit)1004 - 994 = 10 (2 digit)Therefore, the number that will be the sum of 994 and a 2 digit number is 1004.
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