Answer:
1a) Increment in price = 5500 - 4500 = 1000 Naira
1b) Percentage increase in price = (increment in price / old price) x 100%
= (1000 / 4500) x 100%
= 22.22%
2) Marked price = selling price / (1 - discount percentage)
= 3000 / (1 - 0.1)
= 3333.33 Naira
3) Total cost of 30 crates of eggs = 30 x 30 = 900 Naira
Commission = (4/100) x 900
= 36 Naira
4) Commission = (7/100) x 49000
= 3430 Naira
5) Discount = marked price - selling price
= 44.48 - 39.28
= 5.20 Naira
6) Discount = (245 - 225) / 245 x 100%
= 8.16%
7) Commission = (3/100) x 33
= 0.99 Naira
8) New salary = old salary + 5% of old salary
= 250 + (5/100) x 250
= 262.50 Naira
9) Marketed price = selling price / (1 - discount percentage)
= 55 / (1 - 0.05)
= 57.89 Naira
10) Marketed price = selling price + discount
= 845 + 55
= 900 Naira
Percentage discount = (discount / marked price) x 100%
= (55 / 900) x 100%
= 6.11%
Step-by-step explanation:
i need help pleaseee
The dataset is evenly distributed, so the appropriate measure of variability is the range
The dataset is evenly has no outliers, so the appropriate measure of center is the mean
How to determine the appropriate measuresMeasure of variability
When the data set is evenly distributed, a measure of variability appropriate for stem and leaf plot would be the range
The range is simply the difference between the largest and smallest value in the data set.
It is a simple measure of spread that can be easily calculated from a stem and leaf plot.
Measure of center
When there are no outliers in a dataset, the appropriate measure of center to use in a stem and leaf plot is the mean
The mean, also known as the average, is calculated by summing all the values in the dataset and then dividing by the total number of values.
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17. A consumer survey in Econoland shows people consume pizza, soda, and cookies. The consumer spending is
listed below for the years 2019 and 2020. The base year is 2019.
Item
Pizza
Soda
Cookies
2019 Quantities
100
50
200
2019 Prices
$10.00
$3.00
$2.00
2020 Quantities
150
100
250
2020 Prices
$15.00
$3.25
$2.50
A. What and how much is in the market basket?
B. What did the market basket cost in 2019?
C. What did the market basket cost in 2020?
D. What was the inflation rate between 2019 and 2020?
Respond to each of the following using the data provided. Show all caculations where appropriate.
a. The market basket fοr 2020 is: $3200
b. The market basket cοst $1,550.00 in 2019.
c. The market basket cοst $3,200.50 in 2020.
d.The inflatiοn rate between 2019 and 2020 is 106.45%.
Hοw can we calculate inflatiοn?Inflatiοn aims tο evaluate the tοtal impact οf price changes οn a wide range οf gοοds and services. It allοws fοr the pοrtrayal οf the οverall increase in an ecοnοmy's prices fοr prοducts and services as a single value.
A. Tο calculate the market basket, we need tο multiply the quantity οf each item by its price and add up the results. Using the quantities and prices given, the market basket fοr 2019 is:
(100 pizzas × $10.00/pizza) + (50 sοdas × $3.00/sοda) + (200 cοοkies × $2.00/cοοkie)
= $1000 + $150 + $400
= $1550
Similarly, the market basket fοr 2020 is:
(150 pizzas × $15.00/pizza) + (100 sοdas × $3.25/sοda) + (250 cοοkies × $2.50/cοοkie)
= $2250 + $325 + $625
= $3200
B. Tο calculate the cοst οf the market basket in 2019, we need tο multiply the quantities by their respective prices and sum them up. The cοst in 2019 is:
(100 x $10.00) + (50 x $3.00) + (200 x $2.00) = $1,550.00
Therefοre, the market basket cοst $1,550.00 in 2019.
C. Tο calculate the cοst οf the market basket in 2020, we use the same methοd. The cοst in 2020 is:
(150 x $15.00) + (100 x $3.25) + (250 x $2.50) = $3,200.50
Therefοre, the market basket cοst $3,200.50 in 2020.
D. Tο calculate the inflatiοn rate between 2019 and 2020, we use the fοllοwing fοrmula:
Inflatiοn rate = ((Cοst in year 2 - Cοst in year 1) / Cοst in year 1) x 100%
Plugging in the values, we get:
Inflatiοn rate = (($3,200 - $1,550) / $1,550) x 100%
= 106.45%
Therefοre, the inflatiοn rate between 2019 and 2020 is 106.45%.
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Ball Bearings, Inc., faces costs of production as follows:
Quantity
Total Fixed Costs
Total Variable Costs
(Dollars)
(Dollars)
0 120 0
1 120 60
2 120 80
3 120 100
4 120 140
5 120 200
6 120 320
Complete the following table by calculating the company's total cost, marginal cost, average fixed cost, average variable cost, and average total cost at each level of production.
Quantity
Total Cost
Marginal Cost
Average Fixed Cost
Average Variable Cost
Average Total Cost
(Dollars)
(Dollars)
(Dollars)
(Dollars)
(Dollars)
0
1
2
3
4
5
6
The price of a case of ball bearings is $60. Seeing that the company can't make a profit, the company's chief executive officer (CEO) decides to shut down operations.
The firm's profit in this case is
$
. (Note: If the firm suffers a loss, enter a negative number in this cell.)
True or False: This was a wise decision.
True
False
Vaguely remembering an introductory economics course, the chief financial officer tells the CEO it is better to produce 1 case of ball bearings, because marginal revenue equals marginal cost at that quantity.
At this level of production, the firm's profit is
$
. (Note: If the firm suffers a loss, enter a negative number in this cell.).
True or False: This is the best decision the firm can make.
True
False
The firm's profit in this case is = $360.
What is the total cost?
The total economic cost of production is made up of two types of costs: the variable cost, which changes depending on how much of a good is produced and includes inputs like labour and raw materials, and the fixed cost, which is unaffected by how much of a good is produced and includes inputs like buildings and machinery that cannot be changed in the short term, possibly including sunk costs.
In economics, the whole cost of each unit of production, whether fixed or variable, includes the total opportunity cost (benefits from the next-best alternative).
Example:
Q Fixed Variable Total Marginal Aver. Aver. Aver.
Costs Costs Cost Cost FC VC TC
0 100 0 100 - - - -
1 100 50 150 150 100 50 150
2 100 70 170 20 50 35 85
3 100 90 190 20 33.33 30 63.33
4 100 140 240 50 25 35 60
5 100 200 300 60 20 40 60
6 100 360 460 160 16.67 60 76.67
The firm's profit in this case is = $360.
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Which of the following represent a linear inequality in open-sentence form? (Select all that apply.) 2x + 8 = 10y 2x - 7y > 10 8 + x > 5 3 < 5
The linear inequality in open-sentence form are
2x - 7y > 10 8 + x > 5 What are open sentences?An open sentence is a mathematical statement that contains at least one blank or unknown and that becomes true or false when the blank is filled or a quantity is substituted for the unknown.
Now, since we have the expressions,
2x + 8 = 10y 2x - 7y > 10 8 + x > 5 and3 < 5First, we note that there are 3 open sentences and only two of them are inequalities.
The 3 open sentences are
2x + 8 = 10y 2x - 7y > 10 8 + x > 5The two inequalities are
2x - 7y > 10 8 + x > 5So, the linear inequality in open-sentence form are
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The number 72 lies between the perfect squares. So the square root of 72 lies between the numbers
Answer:
To find the numbers between which the square root of 72 lies, we need to determine the perfect squares that are closest to 72.
The perfect squares closest to 72 are 64 (8^2) and 81 (9^2). Since 72 is closer to 81 than to 64, we know that the square root of 72 is closer to 9 than to 8.
Therefore, the square root of 72 lies between the numbers 8 and 9. We can write this as:
8 < √72 < 9y-step explanation:
PLEASE HELP ASAP!! i really really need it
Answer:
The number of hamburgers is 136.
Step-by-step explanation:
What we know:
We got cheeseburgers and hamburgers
The total: 408
The number of cheese burgers was 2 times the number of hamburgers
This is pretty much all the info we need to know.
Lets define our variables:
x = hamburgers
y = cheeseburgers
Now, we need our two equations to make a system.
[tex]x+y=408[/tex]
[tex]y=2x[/tex]
To find hamburgers, x, we plug the value of y into our first equation.
[tex]x+2x=408[/tex]
Add like terms
[tex]3x=408[/tex]
Divide by 3
[tex]x=136[/tex]
The number of hamburgers is 136.
Just to check our work, lets find the cheeseburgers.
[tex]y=2(136)[/tex]
[tex]y=272[/tex]
[tex]272+136=408[/tex]
Bridgette and her friends, Jill and Barb, are talking about how much money they earn. Bridgette makes $615 biweekly, Jill makes $670 semimonthly, and Barb makes $300 a week. Who earns the most?
Answer: Jill earns the most money.
Step-by-step explanation:
Bridgette:1230
Jill: 1340
Barb:300
A certain airline requires that rectangular packages carried on an airplane by passengers be such that the sum of the three dimensions is at most 270 centimeters. Find the dimensions of the square-ended rectangular package of greatest volume that meets this requirement.
The dimensions of the square-ended rectangular package of greatest volume that meets the airline's requirement are x = y = 90 cm and z = 90 cm.
What is dimensions?Dimensions refer to measurements or quantities that describe the size, shape, or extent of an object or space, often expressed in length, width, and height.
Let x, y, and z represent the dimensions of the rectangular package. Since the package has square ends, we know that x = y.
We want to maximize the volume of the package, which is given by V = x² × z.
The airline requires that the sum of the three dimensions is at most 270 centimeters, so we have the constraint x + y + z ≤ 270.
Substituting x = y, we get 2x + z ≤ 270.
We can solve for z in terms of x: z ≤ 270 - 2x.
Substituting this inequality into the expression for V, we get V = x^2 * (270 - 2x) = 270x² - 2x³.
To maximize V, we take the derivative of V with respect to x, set it equal to zero, and solve for x:
dV/dx = 540x - 6x² = 0
6x(90 - x) = 0
x = 0 or x = 90
Since x represents a length, it must be positive, so x = 90.
Since x = y, y = 90 as well.
Substituting x = y = 90 into the inequality z ≤ 270 - 2x, we get z ≤ 270 - 2(90) = 90.
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I will mark you brainiest!
Which of the following choices is matched with ∠MLA to make alternate interior angles? A) ∠GAL
B) ∠FAH
C) ∠LMB
D) ∠CLH
Answer:BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB TRUST ME
Step-by-step explanation:
Differentiate in respect to yS(siny + y cosy)dy
Suppose that the local government of Tulsa decides to institute a tax on soda producers. Before the tax, 35,000 liters of soda were sold every week at a price of $11 per liter. After the tax, 30,000 liters of soda are sold every week; consumers pay $14 per liter, and producers receive $6 per liter (after paying the tax).
The amount of the tax on a liter of soda is
$
per liter. Of this amount, the burden that falls on consumers is
$
per liter, and the burden that falls on producers is
$
per liter.
12. The large triangular figure below is composed of triangles that each have a base and height of 4 cm.
What is the area of the large figure?
A. 64 cm2
B. 72 cm 2
C. 128 cm 2
D. 144 cm2
By answering the above question, we may state that The solution is triangle closest to option d: 58% x, 42% y.
What precisely is a triangle?A triangle is a polygon because it contains four or more parts. It features a simple rectangular shape. A triangle ABC is a rectangle with the edges A, B, and C. When the sides are not collinear, Euclidean geometry produces a single plane and cube. If a triangle contains three components and three angles, it is a polygon. The corners are the points where the three edges of a triangle meet. The sides of a triangle sum up to 180 degrees.
The total sales of product x may be computed as follows: 5,000 units * $110/unit selling price = $550,000
The total sales of product y may be computed as follows: 35,000 units * $70/unit selling price = $2,450,000
The total sales of both goods are as follows: $550,000 + $2,450,000 = $3,000,000
Hence the proportion of revenue provided by product x is: $550,000 / $3,000,000 = 0.1833 or 18.33%
And the proportion of sales produced by product y is: $2,450,000 / $3,000,000 = 0.8167 or 81.67%
As a result, Rusty Co.'s sales mix was 18.33% x and 81.67% y last year.
The solution is closest to option d: 58% x, 42% y.
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You currently have $9,300 (Present Value) in an account that has an interest rate of 5% per year compounded annually (1 times per year). You want to withdraw all your money when it reaches $15,810 (Future Value). In how many years will you be able to withdraw all your money?
Answer:
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Ben went to buy some brushes and oaints to finish a project.he bought 25 brushes and paints in total.if each brush cost IDR 1.500 , each paint IDR 800 and the total pruchase cost was IDR 27.000. how many brushes and paints did he buy
The number of brushes and number of paint bought by Ben are 7 and 18 respectively.
What is an equation system, and how can one be utilised to address issues?A group of equations that are concurrently solved to determine the values of the variables involved is referred to as a system of equations. A system of equations can have any number of variables and equations and can be either linear or nonlinear.
They could depict connections between various values, restrictions on resources or attributes, or optimization goals.
Let us suppose the number of brushes = b.
Let us suppose the number of paints = p.
Thus,
b + p = 25
1500b + 800p = 27000
Multiplying the first equation by 1500 and subtracting it from the second equation, we get:
800p - 1500b = -7500
p = (1500b + 7500) / 800
Substituting the value of p in first equation:
b + (1500b + 7500) / 800 = 25
Multiplying both sides by 800 and simplifying, we get:
2000b + 7500 = 20000
b = 6.25 = 7
Substitute the value of b in first equation:
7 + p = 25
p = 18
Hence, the number of brushes and number of paint bought by Ben are 7 and 18 respectively.
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Revise the suggested questionnaire so that it is more suitable. Include 5 reasons for taking a GAP YEAR. Submit a copy of a new revised questionnaire
The revised questionnaire that is more suitable that includes reasons for taking a GAP year is given below:
The QuestionnaireThe new questionnaire includes four questions aimed at gaining insight into the participant's motivations, goals, and timeframe for taking a gap year:
Have you considered taking a gap year before starting your next academic or professional endeavor?
What are your top 5 reasons for considering a gap year? (Please list in order of importance)
What are your goals for your gap year? (e.g., travel, volunteer work, internships, personal development, etc.)
How long do you plan to take for your gap year?
Reasons for taking a gap year may vary from person to person, but here are five common motivations for doing so:
To gain life experience and personal growth
To travel and explore new cultures
To gain work experience or internships in a desired field
To take a break from academic or professional responsibilities
To pursue passions or hobbies that may not be feasible during a regular academic or work schedule.
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Revise the suggested questionnaire so that it is more suitable. Include 5 reasons for taking a GAP YEAR. Submit a copy of a new revised questionnaire
Have you considered taking a gap year before starting your next academic or professional endeavor?
What are your reasons for considering a gap year?
What are your goals for your gap year?
How long do you plan to take for your gap year?
Need help with question
penny would love to open a coffee shop at her local shopping centre, so she decides to hand out a questionnaire at the shopping center's entrance in order to do market research. draw up a questionnaire that penny could use to gather the information she requires
Penny plans to distribute a questionnaire at the entrance to the coffee shopping center in order to do market research because she would love to build a coffee shop there which are explained.
Explain about the term questionnaire?Market research is crucial for helping you understand the present status of the coffee shop business as well as for figuring out how to shape various areas of your company to draw in the suitable clients.
Penny plans to distribute a questionnaire at the entrance to the shopping center in order to do market research because she would love to build a coffee shop there.
Penny may utilize a questionnaire to collect the data she needs, which would include the following:
What are the current consumption patterns of customers at coffee shops? Do they stop by for a quick take-out latte on their way to work or come in for a sit-in coffee plus snack at lunchtime?What qualities define a normal coffee shop patron? Are families as well as teenage groups of friends much more prevalent than offices?What is the typical client budget?What are the best-selling products? What about flapjacks and scones for a snack or a flat white or an americano?know more about the questionnaire
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What is the total payment
required to pay off a promissory
note issued for $600.00 at 10%
ordinary interest and a 180-day
term?
Answer:
$630.00
Step-by-step explanation:
IF THIS IS WRONG I AM SORRY BUT I KNOW THIS IS RIGHT AND IF YOU NEED MORE ANSWERS I AM ALWAYS OPEN!
Find all critical points for the function
4x + 6
x² + x + 1
on (-∞, ∞) and then list them (separated by commas) in the box below.
List of critical points:
f(x) =
Answer: [tex]\frac{-3+\sqrt{7}}{2}, \ \frac{-3-\sqrt{7}}{2}[/tex]
========================================================
Explanation:
Let
g(x) = 4x+6h(x) = x^2+x+1Each derivative is,
g ' (x) = 4h ' (x) = 2x+1which will be useful in the next section.
--------------
[tex]f(\text{x}) = \frac{4\text{x}+6}{\text{x}^2+\text{x}+1} = \frac{g(\text{x})}{h(\text{x})}\\\\f(\text{x}) = \frac{g(\text{x})}{h(\text{x})}\\\\[/tex]
Apply the derivative with respect to x. We'll use the quotient rule.
[tex]f(\text{x}) = \frac{g(\text{x})}{h(\text{x})}\\\\\\f'(\text{x}) = \frac{g'(\text{x})h(\text{x})-g(\text{x})h'(\text{x})}{\big[h(\text{x})\big]^2}\\\\\\f'(\text{x}) = \frac{4(\text{x}^2+\text{x}+1)-(4\text{x}+6)(2\text{x}+1)}{(\text{x}^2+\text{x}+1)^2}\\\\[/tex]
The critical value(s) occur when either...
f ' (x) = 0f ' (x) doesn't exist, when x is in the domain of f(x)The first criteria will be handled in the next section.
The second criteria is handled in the section after that.
-------------------------
f ' (x) is in the format A/B. It means f ' (x) = 0 leads to A/B = 0 and A = 0.
We set the numerator equal to zero and solve for x.
[tex]4(\text{x}^2+\text{x}+1)-(4\text{x}+6)(2\text{x}+1) = 0\\\\4(\text{x}^2+\text{x}+1)-(8\text{x}^2+16\text{x}+6) = 0\\\\4\text{x}^2+4\text{x}+4-8\text{x}^2-16\text{x}-6 = 0\\\\-4\text{x}^2-12\text{x}-2 = 0\\\\-2(2\text{x}^2+6\text{x}+1) = 0\\\\2\text{x}^2+6\text{x}+1 = 0\\\\[/tex]
From here we use the quadratic formula.
Plug in a = 2, b = 6, c = 1.
[tex]\text{x} = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\\text{x} = \frac{-6\pm\sqrt{(6)^2-4(2)(1)}}{2(2)}\\\\\text{x} = \frac{-6\pm\sqrt{28}}{4}\\\\\text{x} = \frac{-6\pm2\sqrt{7}}{4}\\\\\text{x} = \frac{2(-3\pm\sqrt{7})}{4}\\\\\text{x} = \frac{-3\pm\sqrt{7}}{2}\\\\\text{x} = \frac{-3+\sqrt{7}}{2} \text{ or } \text{x} = \frac{-3-\sqrt{7}}{2}\\\\[/tex]
If x is equal to either of those values, then f ' (x) = 0 would be the case. Therefore, these are the critical points of f(x).
There may be other critical values. We'll still need to check the second criteria.
-------------------------
f ' (x) doesn't exist when we divide by zero.
Set the denominator equal to 0 and solve for x.
[tex](\text{x}^2+\text{x}+1)^2 = 0\\\\\text{x}^2+\text{x}+1 = 0\\\\[/tex]
Plug a = 1, b = 1, c = 1 into the quadratic formula.
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-1\pm\sqrt{(1)^2-4(1)(1)}}{2(1)}\\\\x = \frac{-1\pm\sqrt{-3}}{2}\\\\[/tex]
We have a negative number as the discriminant, which leads to complex number solutions in the form a+bi where [tex]i = \sqrt{-1}[/tex]
Therefore, there aren't any real number values for x that lead [tex](\text{x}^2+\text{x}+1)^2[/tex] to be zero.
No matter what we pick for x, the expression [tex](\text{x}^2+\text{x}+1)^2[/tex] will never be zero.
In short, the second criteria yields no real value critical points (assuming your teacher is only focused on real-valued functions and not complex-valued functions).
-------------------------
Summary:
The first criteria f ' (x) = 0 led to [tex]\text{x} = \frac{-3+\sqrt{7}}{2} \text{ or } \text{x} = \frac{-3-\sqrt{7}}{2}[/tex] as the critical valuesThe second criteria, f ' (x) doesn't exist where x is in the domain of f(x), leads to no critical values (assuming your teacher is not focusing on complex-valued functions).Therefore, the only critical values are [tex]\text{x} = \frac{-3+\sqrt{7}}{2} \text{ or } \text{x} = \frac{-3-\sqrt{7}}{2}[/tex]
-------------------------
Extra info:
A critical value is where a local/absolute min, a local/absolute max, or a saddle point would be at this x value. The 1st derivative test or 2nd derivative test would be used to determine the nature of each critical value.
A real world application of a critical value would be to determine the max revenue. Another example is to minimize the surface area while holding the volume constant. Linear regression relies on a similar concept.
To check the answer, you can type in "critical points of (4x+6)/(x^2+x+1)" without quotes into WolframAlpha.
Using Formulas
Ava's minimum payment is 2.5% of her new balance. What is her minimum
payment if her new balance is $760.00?
S
Mrs. Juarez graded ten English papers and recorded the scores. 92, 95, 100, 62, 88, 90, 100, 96, 89, 98 Which statements are true? Check all that apply. The range of scores is 38. Without the outlier, the range of scores would be 12. The outlier impacts the range more than it impacts the interquartile range. The interquartile range is 9. The interquartile range is 4. Without the outlier, the interquartile range would be 9.5. Mark this and return Save and Exit Next 4655
The interquartile range, according to the provided assertion, is 9.5.
The interquartile range is what?
The spread of your data's centre quarter is measured by the interquartile range (IQR). It is the limit for your sample's centre 50%. Assess the diversity where the majority of your numbers are by using the IQR. Larger numbers denote a wider distribution of your data's centre region.
The following statements are true:
The range of scores is 38.
The spread of results without the outlier would be 12.
The interquartile range is less affected by the anomaly than the range.
9 is the interquartile number.
The interquartile range would indeed be 9.5 if there were no anomaly.
To calculate the range, we subtract the smallest score from the largest score
Range = 100 - 62 = 38
If we remove the outlier, 62, then the range becomes:
without an anomaly= 100 - 88 = 12
The outlier has a greater impact on the range than on the interquartile range because the interquartile range only considers the middle 50% of the data, whereas the range considers all of the data.
To calculate the interquartile range, we need to find the values of the first and third quartiles. The median of a lower half of the data is represented by the first quartile (Q1), and the median of the higher half is represented by the third quartile (Q3).
Arranging the scores in ascending order:
62, 88, 89, 90, 92, 95, 96, 98, 100, 100
The median is the middle value, which is 93.
Q1 is the median of the lower half of the data, which is 62, 88, 89, 90, 92. The median of this set is (88 + 89) / 2 = 88.5.
Q3 is the median of the upper half of the data, which is 95, 96, 98, 100, 100. The median of this set is (98 + 100) / 2 = 99.
The disparity between Q3 and Q1 is the interquartile range (IQR):
IQR = Q3 - Q1 = 99 - 88.5 = 10.5 ≈ 9
If we remove the outlier, the scores become:
88, 89, 90, 92, 95, 96, 98, 100, 100
Q1 is the median of the lower half of the data, which is 88, 89, 90, 92. The median of this set is (89 + 90) / 2 = 89.5.
Q3 is the median of the upper half of the data, which is 95, 96, 98, 100, 100. The median of this set is (96 + 98) / 2 = 97.
The IQR is:
IQR = Q3 - Q1 = 97 - 89.5 = 7.5 ≈ 9.5
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Consider the following function.
h(x)=(x−4)2−1
Step 3 of 4 : Find two points on the graph of the parabola other than the vertex and x-intercepts.
Two points on the graph of the parabola h(x) = (x-4)^2 - 1 other than the vertex and x-intercepts are (1, 8) and (6, 3).
How to determine the points on the functionTo find two points on the graph of the parabola other than the vertex and x-intercepts
We can simply choose two values of x and find their corresponding y values using the function h(x).
Let's choose x = 1:
h(1) = (1-4)^2 - 1 = 9 - 1 = 8
So one point on the graph is (1, 8).
Now let's choose x = 6:
h(6) = (6-4)^2 - 1 = 4 - 1 = 3
So another point on the graph is (6, 3).
Hence, the two points are (1, 8) and (6, 3)
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Martin recorded data on the temperature one day in two of his favorite places.
Temperature
-12 degrees F
82 degrees F
He was surprised when he calculated the difference as 94 degrees F. Do you think he was correct?
The actual difference between the twο temperatures is: 94 degrees F
What is Temperature?Temperature is measure οf degree οf hοtness οr cοldness οf οbject οr substance. It is physical quantity that describes average kinetic energy οf particles that make up οbject οr substance.
Temperature is a usually measured using thermοmeter, which cοnsists οf narrοw, unifοrm tube filled with liquid, like mercury οr alcοhοl
Nο, Martin's calculatiοn is nοt cοrrect. The difference between twο temperatures cannοt be greater than the sum οf the twο temperatures. In this case, the difference Martin calculated is 94 degrees F, which is greater than the sum οf the twο temperatures (-12 degrees F + 82 degrees F = 70 degrees F). Therefοre, Martin must have made an errοr in his calculatiοn οr recοrded the temperatures incοrrectly.
The actual difference between the twο temperatures is:
82 degrees F - (-12 degrees F) = 94 degrees F
This cοnfirms that Martin must have recοrded οne οf the temperatures incοrrectly οr made a mistake in his calculatiοn.
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Weights of female cats of a certain breed are normally distributed with mean 4.1 kg and standard deviation 0.6 kg.
Six female cats are chosen at random. What is the probability that exactly one of them weights more than 4.5 kg.
(I did the first part to this question already, the probability that one chosen at random will weigh more than 4.5 kg is 0.2514.)
The prοbabiIity that exactIy οne οf the six chοsen femaIe cats weighs mοre than 4.5 kg is apprοximateIy 0.2834 οr 28.34%.
The binοmiaI distributiοn fοrmuIa:
The binοmiaI distributiοn fοrmuIa gives the prοbabiIity οf οbtaining exactIy k successes in n independent BernοuIIi triaIs, where each triaI has a prοbabiIity οf success p.
The formuIa is:
[tex]P(X = k) = ^{n}C_{k} P^{k} \times(1-P)^{n-k}[/tex]
Here we have
Weights οf female cats οf a certain breed are nοrmally distributed with a mean οf 4.1 kg and a standard deviatiοn οf 0.6 kg.
The prοbability that οne chοsen at randοm will weigh mοre than 4.5 kg is 0.2514.
Tο find the prοbability that exactly οne οf the six chοsen female cats weighs mοre than 4.5 kg, we can use the binοmial distributiοn with parameters
Using the binοmial distributiοn fοrmula
[tex]P(X = k) = ^{n}C_{k} P^{k} \times(1-P)^{n-k}[/tex]
where:
n = 6 and p = 0.2514,
The probabiity of exacty one success in six trias can be cacuated as
P(X = 1) = (6 choose 1) × 0.2514¹ × (1 - 0.2514)⁵
P(X = 1) = 6 × 0.2514 × 0.7486⁵
P(X = 1) = 0.2834
Therefore, The probabIIty that exacty one of the sIx chosen femae cats weIghs more than 4.5 kg Is approxImatey 0.2834 or 28.34%.
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The equation, A=P(1+0.045/12)^12t
represents the amount of money earned on a compound interest savings account with an annual interest rate of 4.5% compounded monthly. if after 20
years the amount in the account is $18,539.38, what is the value of the principal investment? Round the answer to the nearest hundredths place.
$6,872.98
$7,550.25
$10,989.13
$17,202.73
Therefοre , the sοlutiοn οf the given prοblem οf amοunt cοmes οut tο be Optiοn B ($7,550.25) is the cοrrect chοice.
What is an amοunt?Aggregate attempting tο calculate the duratiοn, tοtal cοst, οr quantity. The quantity that is in frοnt οf οurself οr οn yοur mind is extremely busy. the result, its impοrtance, οr its relevance. Principal, interest, and third bοοkkeeping make up the tοtal. Amοunted, amοunts, and amοunting are sοme οf the wοrd variants. flexible term Its quantity refers tο hοw much that anything is.
Here,
The cοmpοund interest expressiοn is as fοllοws:
=> [tex]A = P(1 + r/n)^{(nt)[/tex]
Here are the facts:
=> A = $18,539.38 (the sum after 20 years) (the amοunt after 20 years)
The yearly interest rate, which is 4.5 percent, is r = 0.045.
n = 12 (the interest is cοmpοunded mοnthly, sο there are 12 cοmpοunding times per year) (the interest is cοmpοunded mοnthly, sο there are 12 cοmpοunding periοds per year)
t = 20 (the periοd in years) (the time in years)
By rearranging the sοlutiοn, we can find P:
=>[tex]A = P(1 + r/n)^{(nt)[/tex]
Adding the numbers we are familiar with
=>[tex]P = \$18,539.38 / (1 + 0.045/12)^{(12*20)[/tex]
=> P ≈ $7,550.25
Cοnsequently, the initial investment is wοrth rοughly $7,550.25. The number is $7,550.25, rοunded tο the nearest hundredth.
Optiοn B ($7,550.25) is the cοrrect chοice.
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what us the order of 5 x 10^4, 7 x 10^-5, 3 x 10^-9, 8 x 10^4 from the least to greatest
Answer: 5x10^4, 8x10^4, 10^-5, 10^4
Step-by-step explanation: calculator
How do I solve for the answer please?
The value of the 5 measurements according to the given function is 66.
What is summation of values?When a group of numbers, known as addends or summands, are added together in mathematics, the outcome is their sum or total. Functions, vectors, matrices, polynomials, and, generally, any sort of mathematical object on which an operation labelled "+" is specified can all be added together, in addition to integers. The position of the items in a sequence is frequently used to characterise them through a regular pattern. Long sequences can be summarised for basic patterns by replacing most summands with ellipses.
The function is given as:
[tex]\sum_{i = 1}^5 (x_i^2)\\\\\sum_{i = 1}^5 = x_1 + x_2 + x_3 +x_4 + x_5\\\\\sum_{i = 1}^5 (x_i^2) = 12 + 14 + 16 + 7 + 17 = 66[/tex]
Hence, the value of the 5 measurements according to the given function is 66.
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Simplify to a single trig function with no fractions.
The simplified cos(t)/sec(t) to the trig function 1 - sin²(t), which is equivalent to cos²(t).
Recall that the secant function is defined as the reciprocal of the cosine function. In other words, sec(t) = 1/cos(t). Therefore, we can rewrite cos(t)/sec(t) as cos(t)/(1/cos(t)).
To simplify this expression, we can multiply both the numerator and the denominator by cos(t), which gives:
cos(t)/(1/cos(t)) = cos(t) * (cos(t)/1) = cos²(t)
Now, we have simplified cos(t)/sec(t) to cos²(t). Alternatively, we could have used the identity cos²(t) = 1 - sin²(t) to simplify the expression. This identity follows directly from the Pythagorean identity cos²(t) + sin²(t) = 1.
Starting with cos(t)/sec(t), we can substitute sec(t) = 1/cos(t) to get:
cos(t)/sec(t) = cos(t)/(1/cos(t)) = cos²(t)/1
Then, we can use the identity cos²(t) = 1 - sin²(t) to substitute cos²(t) in terms of sin(t):
cos(t)/sec(t) = cos²(t)/1 = (1 - sin²(t))/1 = 1 - sin²(t)
So, we have simplified cos(t)/sec(t) to the trig function 1 - sin²(t), which is equivalent to cos²(t).
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Please help and show a method, I have no idea how to do this :/
Answer:
30.4 meters
Step-by-step explanation:
Just plug in the given values of
V = 24.4 and
g = 9.8
in the given equation and you can solve for H
[tex]H = \dfrac{V^2}{2g}\\\\= \dfrac{(24.4)^2}{2\times 9.8}\\\\= 30.37551 \dots\\\\= 30.4\\\\[/tex]correct to 3 significant figures
Find a 5th degree polynomial with real coefficients that has zeros 0, -7i, and 2-i. show work
Answer:
f(x) = x^5 - 4x^4 + 54x^3 - 196x^2 + 245x.
Step-by-step explanation:
If a polynomial has a complex root, then its conjugate is also a root. Therefore, if 0 and -7i are zeros of the polynomial, then so are 7i and the conjugate of 2-i, which is 2+i.
The factors of the polynomial are then:
(x-0)(x-7i)(x+7i)(x-(2-i))(x-(2+i))
Simplifying the factors, we get:
x(x^2+49)(x^2-4x+5)
Expanding the last factor, we get:
x^5 - 4x^4 + 5x^3 + 49x^3 - 196x^2 + 245x
Finally, we have the 5th degree polynomial:
f(x) = x^5 - 4x^4 + 54x^3 - 196x^2 + 245x
Therefore, the polynomial with zeros 0, -7i, and 2-i and 5th degree with real coefficients is f(x) = x^5 - 4x^4 + 54x^3 - 196x^2 + 245x.
The solution is, f(x) = x^5 - 4x^4 + 54x^3 - 196x^2 + 245x, is a 5th degree polynomial with real coefficients that has zeros 0, -7i, and 2-i.
What are Polynomials?Polynomials are sums of k-xⁿ terms, where k can be any number and n can be any positive integer.
here, we have,
If a polynomial has a complex root, then its conjugate is also a root. Therefore, if 0 and -7i are zeros of the polynomial, then so are 7i and the conjugate of 2-i, which is 2+i.
The factors of the polynomial are then:
(x-0)(x-7i)(x+7i)(x-(2-i))(x-(2+i))
Simplifying the factors, we get:
x(x^2+49)(x^2-4x+5)
Expanding the last factor, we get:
x^5 - 4x^4 + 5x^3 + 49x^3 - 196x^2 + 245x
Finally, we have the 5th degree polynomial:
f(x) = x^5 - 4x^4 + 54x^3 - 196x^2 + 245x
Therefore, the polynomial with zeros 0, -7i, and 2-i and 5th degree with real coefficients is f(x) = x^5 - 4x^4 + 54x^3 - 196x^2 + 245x.
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