Answers
Therefore, the distance between the 90 degree angle and the hypotenuse is approximately 0.829 units.
What is triangle?A triangle is a two-dimensional geometric shape that is formed by three straight line segments that connect to form three angles. It is one of the most basic shapes in geometry and has a wide range of applications in mathematics, science, engineering, and everyday life. Triangles can be classified by the length of their sides (equilateral, isosceles, or scalene) and by the size of their angles (acute, right, or obtuse). The study of triangles is an important part of geometry, and their properties and relationships are used in many areas of mathematics and science.
Here,
1. To find HF, we can use the angle bisector theorem, which states that if a line bisects an angle of a triangle, then it divides the opposite side into two segments that are proportional to the adjacent sides. Let's denote the length of HF as x. Then, by the angle bisector theorem, we have:
JF/FH = JG/HG
Substituting the given values, we get:
15/x = 18/21
Simplifying and solving for x, we get:
x = 15 * 21 / 18
x = 17.5
Therefore, HF is 17.5 cm.
2. Let's denote the length of the hypotenuse as h and the length of the leg opposite the 18-unit perpendicular as a. We can then use the Pythagorean theorem to write:
h² = a² + 18²
We are told that the hypotenuse is divided into segments of length x and 6 units, so we can write:
h = x + 6
Substituting this expression into the first equation, we get:
(x + 6)² = a² + 18²
We are also told that the leg adjacent to the angle opposite the 4-unit segment is divided into segments of length 4 and (a - 4), so we can write:
a = 4 + (a - 4)
Simplifying this equation, we get:
a = a
Now we can substitute this expression for a into the previous equation and solve for x:
(x + 6)² = (4 + (a - 4))² + 18²
Expanding and simplifying, we get:
x² + 12x - 36 = 0
Using the quadratic formula, we get:
x = (-12 ± √(12² - 4(1)(-36))) / (2(1))
x = (-12 ± √(288)) / 2
x = -6 ± 6√(2)
Since the length of a segment cannot be negative, we take the positive root:
x = -6 + 6sqrt(2)
x ≈ 1.46
Therefore, the value of x is approximately 1.46 units.
3. Let's denote the length of the hypotenuse as h and the length of the leg adjacent to the angle opposite the 9-unit perpendicular as b. We can then use the Pythagorean theorem to write:
h² = b² + 9²
We are told that the hypotenuse is divided into segments of length x and 6 units, so we can write:
h = x + 6
Substituting this expression into the first equation, we get:
(x + 6)² = b² + 9²
Expanding and simplifying, we get:
x² + 12x - b² = 27
We also know that the length of the leg opposite the 9-unit perpendicular is:
a = √(h² - 9²)
= √((x + 6)² - 9²)
= √(x² + 12x + 27)
Now we can use the fact that the tangent of the angle opposite the 9-unit perpendicular is equal to the ratio of the lengths of the opposite and adjacent sides:
tan(θ) = a / b
Substituting the expressions for a and b, we get:
tan(θ) = √(x² + 12x + 27) / (x + 6)
We also know that the tangent of the angle theta is equal to the ratio of the length of the opposite side to the length of the adjacent side:
tan(θ) = 9 / b
Substituting the expression for b, we get:
tan(θ) = 9 / √(h² - 9²)
Substituting the expression for h, we get:
tan(θ) = 9 / √((x + 6)² - 9²)
Since the tangent function is the same for equal angles, we can set these two expressions for the tangent equal to each other:
√(x² + 12x + 27) / (x + 6) = 9 / √((x + 6)² - 9²)
Squaring both sides, we get:
(x² + 12x + 27) / (x + 6)² = 81 / ((x + 6)² - 81)
Cross-multiplying and simplifying, we get:
x⁴ + 36x³ + 297x² - 1458x - 2916 = 0
Using a numerical method such as the Newton-Raphson method or the bisection method, we can find the approximate solution to this equation:
x ≈ 9.449
Therefore, the value of x is approximately 9.449 units.
4. Let's denote the length of the hypotenuse as h and the length of the leg adjacent to the angle opposite the distance we want to find as b. We can use the Pythagorean theorem to write:
h² = b² + d²
We are told that the hypotenuse is divided into segments of length 9 and 4 units, so we can write:
h = 9 + 4 = 13
Substituting this expression into the first equation, we get:
13² = b² + d²
Simplifying and solving for d, we get:
d = √(13² - b²)
Now, we need to find the value of b. We know that the hypotenuse is divided into segments of length 9 and 4 units, so we can use similar triangles to write:
b / 4 = 9 / 13
Simplifying and solving for b, we get:
b = 36 / 13
Substituting this expression for b into the equation we found earlier for d, we get:
d = √(13² - (36/13)²)
Simplifying and finding a common denominator, we get:
d =√ (169*13 - 36²) / 13²
Simplifying further, we get:
d = √(169169 - 3636) / 169
Calculating this expression, we get:
d ≈ 0.829
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Related Questions
what does -12x +24= equal
Answers
To solve the equation -12x + 24 = 0, we want to get x by itself on one side of the equation.
First, we can subtract 24 from both sides:
- 12x + 24 - 24 = 0 - 24
This simplifies to:
- 12x = -24
Next, we can divide both sides by -12:
- 12x / -12 = -24 / -12
This simplifies to:
x = 2
Therefore, the solution to the equation -12x + 24 = 0 is x = 2.
To solve this equation, we can start by isolating the variable x on one side of the equation, and simplifying the terms on the other side.
First, we can subtract 24 from both sides of the equation to get:
-12x = -24
Next, we can divide both sides of the equation by -12 to get:
x = 2
Therefore, the solution to the equation -12x + 24 = 0 is x = 2.
Determine the slope from the table given below.
Answers
Answer:
m = 6
Step-by-step explanation:
Slope = rise/run or (y2 - y1) / (x2 - x1)
Pick 2 points on the table (4,6) (5,12)
We see the y increase by 6 and the x increase by 1, so the slope is
m = 6
So, the slope is 6
Two cars, one going due east at the rate of 90 km/hr and the other going to south at the rate of 60 km/hr are traveling toward the intersection of two roads. At what rate the two cars approaching each other at the instant when the first car is 0.2 km and the second car is 0.15 km from the intersection ?
Answers
The two cars are approaching each other at a rate of 36 km/hr at the given instant.
We can solve this problem by using the Pythagorean theorem and differentiating with respect to time. Let's call the distance of the first car from the intersection "x" and the distance of the second car from the intersection "y". We want to find the rate at which the two cars are approaching each other, which we'll call "r".
At any moment, the distance between the two cars is the hypotenuse of a right triangle with legs x and y, so we can use the Pythagorean theorem
r^2 = x^2 + y^2
To find the rates of change of x and y, we differentiate both sides of this equation with respect to time
2r(dr/dt) = 2x(dx/dt) + 2y(dy/dt)
Simplifying and plugging in the given values
dr/dt = (x(dx/dt) + y(dy/dt)) / r
dr/dt = (0.2 x 90 + 0.15 x (-60)) / sqrt((0.2)^2 + (0.15)^2)
dr/dt = (18 - 9) / sqrt(0.04 + 0.0225)
dr/dt = 9 / sqrt(0.0625)
dr/dt ≈ 36 km/hr
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Please answer Full question
Answers
(1) 4y-7z is a binomial.
(2) 8-xy² is a binomial.
(3) ab-a-b can be written as ab - (a + b) which is a binomial.
(4) z²-3z+8 is a trinomial.
What are monomials, binomials and trinomials?In algebra, monomials, binomials, and trinomials are expressions that contain one, two, and three terms, respectively.
A monomial is an algebraic expression with only one term. A monomial can be a number, a variable, or a product of numbers and variables.
A binomial is an algebraic expression with two terms that are connected by a plus or minus sign. For example, 2x + 3y and 4a - 5b are both binomials.
A trinomial is an algebraic expression with three terms that are connected by plus or minus signs.
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Classify into monomials, binomials and trinomials.
(1) 4y-7z
(1) 8-xy²
(v) ab-a-b
(ix) z2-3z+8
please help I know its 9:35 PM I Just need help what this question2.1 × 1.6 =
21
10
×
16
10
= tenths × tenths my parents are gonna kill me help
Answers
The value of the expression 2.1 × 1.6 = 3.36.
What are decimals?Decimals are a collection of numbers falling between integers on a number line. They are only an additional mathematical representation of fractions. Decimals allow us to express quantifiable quantities like length, weight, distance, money, etc. with more accuracy. Integers, also known as whole numbers, are represented to the left of the decimal point, while decimal fractions are shown to the right of the decimal point.
Given that the expression is: 2.1 × 1.6.
2.1 × 1.6 can be written as:
2.1 × 1.6 = 21/10 × 16/10
Multiply the numerator and denominator:
21/10 × 16/10 = 336/100
Covert the fraction into decimal:
336/100 = 3.36
Hence, the value of the expression 2.1 × 1.6 = 3.36.
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p(s) = s³ + 10s
f(s) = 6s - 3
Find p(2)-f(2)
Answers
Answer:
19
Step-by-step explanation:
We are given the following two functions of s
[tex]p(s) = s^3 + 10s\\f(s) = 6s - 3\\\\\text{To find p(2) substitute 2 for s in p(s)}\\p(2) = (2)^3 + 10(2) = 8 + 20 = 28\\\\[/tex]
[tex]\text{To find f(2) substitute 2 for s in f(s)}\\f(2) = 6(2) - 3= 12 - 3= 9\\[/tex]
[tex]p(2) - f(2) = 28 - 9 = 19[/tex]
the value of the given test statistic lies between the given cutoffs -2.58 and 2.58. it falls in acceptance region.
Answers
Here the values -0.94 and 2.12 falls between the points -2.58 and 2.58. The area between is the acceptance region. So we cannot reject the null hypothesis.
The given is an example for two tailed test. A two tailed test is used to determine whether the value is greater than or less than the mean value of the population. It represents the area under both tails or sides on a normal distribution curve.
Here the value of the test statistic lies between -2.58 and 2.58. So the values less than -2.58 and greater than 2.58 fall in the rejection region, where the null hypothesis can be rejected.
a) -0.94 falls between -2.58 and 2.58. So it is in the acceptance region. So null hypothesis is accepted.
b) 2.12 lies between -2.58 and 2.58. It is also in acceptance region. So null hypothesis is accepted.
So in both cases null hypothesis cannot be rejected.
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The complete question is :
f the cutoffs for a z test are -2.58 and 2.58, determine whether you would reject or fail to reject the null hypothesis in each of the following cases and explain why:
a. z = −0.94
b. z = 2.12
A card is pulled from a deck of cards and noted. The card is then replaced, the deck is shuffled, and a second card is pulled and noted. What is the probability that both cards are face cards?
Answers
Answer: There is a 5.32544378% Chance of a face card being pulled twice
Step-by-step explanation: If there is 52 cards in a deck, and 12 of them are face cards, there is roughly a 23% (23.0769%) chance of pulling one in the first draw. Multiply .230769 x .230769 and you get .0532544378 which equals 5.32544378%
if the slope of the line joining the points (2,4) and (5,k) is 2. find the value of k
Answers
10 is the value of k of the slope of the line .
What are slopes called?
Slope, usually referred to as rise over run, is a line's perceived steepness. By dividing the difference between the y-values at two places by the difference between the x-values, we can determine slope.
You may determine a line's slope by looking at how steep it is or how much y grows as x grows. slope categories. When lines are inclined from left to right, they are said to have a positive slope, a negative slope, or a zero slope (when lines are horizontal).
the points (2,4) and (5,k)
formula from slope of two points
slope = y₂ - y₁/x₂ - x₁
substitute the values in formula
slope = 2
slope = k - 4/5- 2
2 =k - 4/3
6 = k - 4
k = 6 + 4
k = 10
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Question content area top
Part 1
Find the future value of an ordinary annuity if payments are made in the amount R and interest is compounded as given. Then determine how much of this value is from contributions and how much is from interest.
R; % interest compounded semiannually for years.
Question content area bottom
Part 1
The future value of the ordinary annuity is $
177,961.83.
(Round to the nearest cent as needed.)
Part 2
The amount from contributions is $
enter your response here and the amount from interest is
$
enter your response here. (Round to the nearest cent as needed.)
Answers
The Amount from contributions = R * n
Define the term future value?The future value refers to the value of an asset or investment at a specified time in the future, based on a specific interest rate or rate of return.
Without knowing the specific values of R, interest rate, and number of years, we cannot calculate the amounts from contributions and interest. However, we can provide the general formula for calculating the future value of an ordinary annuity:
FV = R * [(1 + i)ⁿ - 1] / i
where FV is the future value of the annuity, R is the periodic payment, i is the interest rate per period, and n is the number of periods.
To calculate the amount from contributions, we can multiply the periodic payment R by the number of periods n.
Amount from contributions = R * n
To calculate the amount from interest, we can subtract the amount from contributions from the future value of the annuity.
Amount from interest = FV - R * n
Once the specific values for R, interest rate, and number of years are provided, we can use these formulas to calculate the amounts from contributions and interest.
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Segment AE shown has length of sqrt 20. Which segment is closest in length to sqrt 10?
Answers
Segment C has a length of √10, which is the closest to √10 compared to the other segments.
What is Segment?Segment is a customer data platform (CDP) that enables companies to collect, store, and analyze customer data from multiple sources. It helps companies build customer profiles and create personalized experiences for their customers. Segment allows businesses to track website visits, user actions, and other events in real-time, as well as to create custom events and store customer data in a secure and unified data warehouse. With Segment, companies can create powerful customer segmentation, which allows them to target customers with personalized messages and offers. Segment also integrates with various marketing, analytics, and CRM tools to provide a complete picture of customer behavior. It enables companies to build cohesive customer journeys, run campaigns, and optimize their customer experience.
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Complete Question.
Examine the following graphed systems of linear inequalities. Select the points below that are solutions to each system of inequalities. Select TWO that apply.
1. 2.
(2,3) (0,0)
(4,3) (4,3)
(-7,6) (6,1)
(-2,3) (2-5)
I need help D: pls
Answers
The solution of the graphs are as follows
first graph
(2, 3)(4, 3)second graph
(4, 3)(6, 1)How to find the ordered pair that are solution of the graphThe graphs consist of two sets of equations plotted, each has shade peculiar to the equation.
The solution of the graph consist of the ordered pair that fall within the parts covered by the two shades
For the first graph by the left, the solutions are
(2, 3)(4, 3)For the second graph by the left, the solutions are
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Mr. Chand is one of the landlords of his town. He buys a land for his daughter spanning over a
area of 480m². He fences the dimensions of the land measuring (x+12) mx (x+16) m. Now he
plans to erect a house with a beautiful garden in the ratio 5:3 respectively. A total of Rs. 5,00,000 is estimated as the budget for the expenses.
1)Give the area of the land purchased in linear polynomial form using algebraic expression
2)Mr. Chand's daughter is ready to share 3/5" of the expenses by her earnings. Express the
fraction in amount.
3)Can you solve the linear equation/polynomial of the area into different factors?
Answers
The required answers are 1) [tex]$$A = x^2 + 28x + 192$$[/tex] 2) 300000 3) [tex]$$x^2 + 28x + 192 = (x + 14 - 2\sqrt{19})(x + 14 + 2\sqrt{19})$$[/tex].
How to deal with area and fractions?area of the land purchased is given as 480m², and the dimensions of the land are (x+12)mx(x+16)m. Therefore, the area of the land can be expressed as:
[tex]$$A = (x+12)(x+16)$$[/tex]
Expanding this expression, we get:
[tex]$$A = x^2 + 28x + 192$$[/tex]
Hence, the area of the land purchased is given by the polynomial expression [tex]$x^2 + 28x + 192$[/tex].
The total budget for the expenses is Rs. 5,00,000. If Mr. Chand's daughter is ready to share 3/5 of the expenses, then the fraction of the expenses she will pay is:
[tex]$\frac{3}{5}=\frac{x}{500000}$$[/tex]
Simplifying this expression, we get:
[tex]$x = \frac{3}{5}\times 500000 = 300000$$[/tex]
Therefore, Mr. Chand's daughter will pay Rs. 3,00,000 towards the expenses.
We can solve the polynomial [tex]$x^2 + 28x + 192$[/tex] into different factors by using the quadratic formula:
[tex]$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$[/tex]
Here, the coefficients of the polynomial are:
[tex]$$a = 1, \quad b = 28, \quad c = 192$$[/tex]
Substituting these values in the quadratic formula, we get:
[tex]$x = \frac{-28 \pm \sqrt{28^2 - 4\times 1 \times 192}}{2\times 1}$$[/tex]
Simplifying this expression, we get:
[tex]$$x = -14 \pm 2\sqrt{19}$$[/tex]
Therefore, the polynomial [tex]$x^2 + 28x + 192$[/tex] can be factored as:
[tex]$$x^2 + 28x + 192 = (x - (-14 + 2\sqrt{19}))(x - (-14 - 2\sqrt{19}))$$[/tex]
or
[tex]$$x^2 + 28x + 192 = (x + 14 - 2\sqrt{19})(x + 14 + 2\sqrt{19})$$[/tex]
So, we have factored the polynomial into two factors.
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Suppose that Y, YS,. … Y n constitute a random sample from a population with probability density function 0, elsewhere. Suggest a suitable statistic to use as an unbiased estim ator for θ.
Answers
The sample mean X is an unbiased estimator for θ.
To find a suitable statistic as an unbiased estimator for θ, we need to find a function of sample Y, YS, ..., Yn whose expected value is equal to θ.
X = (Y + YS + ... + Yn) / n
To show that X is unbiased, we need to calculate its expected value and show that is equal to θ:
E[X] = E[(Y + YS + ... + Yn) / n]
= (1/n) E[Y + YS + ... + Yn]
= (1/n) [E[Y] + E[YS] + ... + E[Yn]]
= (1/n) [nθ] (by the given density function)
= θ
Therefore, sample mean X is an unbiased estimator for θ.
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FAST
Write two expressions to represent the following situation. Then, find the answer.
When Nathan went to bed, the outside temperature was 28°F. When he woke up the next morning, the temperature had decreased to -13°F. By how many degrees did the temperature change during the overnight hours
Answers
The temperature changed by 41°F during the overnight hours, decreasing from 28°F to -13°F.
How is an expression determined?The difference in temperature from 28°F to -13°F can be shown in one of two ways:
Temperature change equals final temperature - The starting temperatureTemperature change: (-13°F) - (28°F)Temperature change: -41°FTemperature change = final temperature minus initial temperature; temperature change = -13°F minus 28°F; temperature change = -41°F; temperature change = 41°F.To calculate the change in temperature, the first exponent equation subtracts the initial temperature from the end temperature. The change in this instance is negative and points to a drop in temperature.
The absolute value function is employed in the second statement to guarantee a positive result regardless of whether the temperature rose or fell. The result is the same as the first expression in this instance, but with a positive sign.
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Each interior angle of a regular polygon is 140 Celcius.How many sides does the polygon have?
Answers
Answer:
9 sides
Step-by-step explanation:
180 - 140 = 40
360 ÷ 40 = 9
What is the slope of the line in the following graph?
Answers
Answer:
1/3
Step-by-step explanation:
using rise over run fron the two dots, we can find 2/6, which simplifies down to 1/3
A survey of 500 music lovers showed that 350 like rock, 300 like country, and 200 like both. How many of the 500 music lovers surveyed dislike both rock and country?
Answers
Answer:
50
Step-by-step explanation:
A Venn diagram is very helpful for this picture and I've included one in the attached.
If we look at the numbers we're given, we see that the numbers do not add up to 500 as 350 + 300 + 200 = 850.
However, we can work through the numbers to find the exact values and eventually the number of people that liked neither rock nor country.
Since 200 people like both rock and country, these people are part of the 350 people that like rock.
We can find the number of people who like rock only by subtracting 200 from 350:
350 - 200 = 150 (Rock only)
Using the same logic from above, we know that the 200 people who like both rock and country are a part of the 300 people who like country.
We can find the number of people who like country only by subtracting 200 from 300:
300 - 200 = 100 (Country only)
Currently, we have 450/500 as 150 + 200 + 100 = 450.
Now, we can find the number of people who like neither rock nor country by subtracting 450 from 500:
500 - 450 = 50 (Neither rock nor country)
We can check that the numbers we found equal 500:
Rock only + Both rock and country + Country only + Neither rock nor country = Total amount of music lovers surveyed
150 + 200 + 100 + 50 = 500
500 = 500
(**In the attached Venn diagram, M stands for the total set of music lovers, R stands for rock only, B stands for both, C stands for country only, and N stands for neither)
A farmer needs to water a new potato field. To do so, he builds an irrigation system using 124 plastic pipes and 97 metal pipes. How many pipes does he use?
Answers
Answer:
The farmer uses 221 pipes in total: 124 plastic pipes and 97 metal pipes.
Answer:
To find out how many pipes the farmer used in total, we simply add the number of plastic pipes to the number of metal pipes:
Total pipes = Plastic pipes + Metal pipes
Total pipes = 124 + 97
Total pipes = 221
Therefore, the farmer used a total of 221 pipes for the irrigation system.
PLEASE HELP MEEE
whoever answers right gets brainliest!!!
Answers
Answer:
[tex]30\leq x[/tex] AND [tex]x \leq 106[/tex]
Notice the valid answer is the one with the AND since need to be both at the same time.
Step-by-step explanation:
Is the one is market, you add 6 to each side and you obtain that answer
[tex]24 \leq x-6\leq 100[/tex]
[tex]24 +6\leq x\leq 100+6[/tex]
[tex]30\leq x\leq 106[/tex]
Mariana and her children went into a movie theater and she bought $51.25 worth of candies and pretzels. Each candy costs $4.75 and each pretzel costs $3.25. She bought a total of 13 candies and pretzels altogether. Write a system of equations that could be used to determine the number of candies and the number of pretzels that Mariana bought. Define the variables that you use to write the system.
pls help i have trouble figuring out what equations im suppose to use to solve.
Answers
Answer: 51.25 = 4.75c + 3.25p
Step-by-step explanation:
1. Since she spent $51.25, we can start our equation with this: 51.25=
2. Since she bought candies and pretzels, we can make 2 new variables, c for candies, and p for pretzels.
3. Since she spent $4.75 per candy, we can add this in to our equation:
51.25 = 4.75c +
4. We can do the same for the pretzels, which she spent $3.25 per piece. Adding this into our equation will leave us with: 51.25 = 4.75c + 3.25p.
5. Now we have to find out what c and p are, given the info that she bought 13 altogether.
6. If we c=6 and p=7, (because they add up to 13) we will get: 51.25!
7. Now we know what c and p are.
8. The answers would be 51.25 = 4.75c + 3.25p, or 51.25=28.5+22.75.
1) Pendant la période des soldes, tous les manteaux d'un magasin sont soldés à 15%.
a. Marjorie a repéré un manteau qui coûtait initialement 78€.
Quel est son prix après réduction ?
b. Mélanie veut acheter un manteau dont le prix après réduction est de 55,25€.
Quel était son prix initial ?
2) Manu affirme que sur les étiquettes suivantes, le pourcentage de réduction appliqué au prix
de la montre est supérieur à celui appliqué aux lunettes. A-t-il raison ?
45€→ 35,55€
Réduction
de 20%
Answers
Answer: Zemāk
Step-by-step explanation:
1)
a. Le prix du manteau après la réduction de 15% est:
78€ - (15/100)*78€ = 66,30€
Le prix du manteau après la réduction est de 66,30€.
b. Soit x le prix initial du manteau.
Le prix du manteau après la réduction de 15% est:
x - (15/100)*x = 55,25€
Simplifions cette équation:
0,85x = 55,25€
x = 65€
Le prix initial du manteau était de 65€.
2)
Pour les lunettes, le prix initial est de 45€ et la réduction appliquée est de 20%:
45€ - (20/100)*45€ = 36€
Pour la montre, le prix initial est de 35,55€ et la réduction appliquée est également de 20%:
35,55€ - (20/100)*35,55€ = 28,44€
On constate que le pourcentage de réduction est le même pour les deux articles, donc Manu a tort.
One side of the triangle is 4 cm, and the sum of the other two sides is equal to a whole number of cm. What is the smallest possible perimeter of the triangle?
F. 9 cm
G. 10 cm
H. 11 cm
J. 15 cm
K. 17 cm
Answers
Answer:
9 cm
Step-by-step explanation:
By the Triangle Inequality, any two sides of a triangle must be greater than the remaining side.
In order to minimize the perimeter, we will assume that 4 cm is the longest side.
Thus, the two remaining sides must be greater than 4.
Since we are given that the sum of the two remaining sides is a whole number, the smallest whole number value greater than 4 is 5.
Hence, the smallest perimeter possible 9 cm.
What is the equation for a cosecant function with vertical asymptotes found at x equals pi over 2 plus pi over 2 times n comma such that n is an integer?
f (x) = 2cscx
g(x) = 4csc2x
h(x) = 4csc3x
j of x is equal to 2 times cosecant of the quantity x over 2 end quantity
Answers
The equation for a cosecant function with vertical asymptotes found at x equals pi over 2 plus pi over 2 times n, where n is an integer, is [tex]f(x) = csc(x - \pi/2)[/tex] .
What is the cosecant function ?
The cosecant function is a trigonometric function that is defined as the reciprocal of the sine function. It is denoted as csc(x) and is defined for all values of x except where sin(x) is equal to zero. The graph of the cosecant function shows a series of vertical lines where the function is undefined, called vertical asymptotes. The value of the cosecant function oscillates between positive and negative infinity as it approaches these asymptotes. The cosecant function is used in trigonometry and calculus to model periodic phenomena such as sound and light waves.
Determining the equation for a cosecant function with vertical asymptotes :
The cosecant function has vertical asymptotes at the zeros of the sine function, which are given by
[tex]x = \pi/2 + n\times\pi[/tex], where n is an integer.
To shift the graph of the cosecant function horizontally by [tex]\pi/2[/tex] units to the right, we subtract [tex]\pi/2[/tex] from the input variable x, so the equation becomes [tex]f(x) = csc(x - \pi/2)[/tex].
[tex]f(x) = csc(x - \pi/2)[/tex] is the equation for a cosecant function with vertical asymptotes found at [tex]x = \pi/2 + n\pi[/tex], where n is an integer.
[tex]g(x) = 4csc(2x)[/tex] is the equation for a cosecant function with period pi, amplitude 4, and vertical asymptotes found at [tex]x = \pi/2 + n\pi[/tex], where n is an integer.
[tex]h(x) = 4csc(3x)[/tex] is the equation for a cosecant function with period [tex]2\pi/3[/tex], amplitude 4, and vertical asymptotes found at [tex]x = \pi/6 + n\pi,[/tex] where n is an integer.
[tex]j(x) = 2csc(x/2)[/tex] is the equation for a cosecant function with period 4pi, amplitude 2, and vertical asymptotes found at [tex]x = 2n\pi[/tex], where n is an integer.
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Por favor, necesito ayuda con esto es de estadística. Muchas gracias
Las calificaciones de 20 alumnos que presentaron exámen de admisión a cierta facultad, utilizando la escala de 0 a 100, fueron:
83 64 51 46 82 91 73 82 65 61 74 64 75 81 94 65 42 81 56 61 72 65 54 39 70 93 42 46 54 72
•Elaborar: diagrama de tallo y hoja
•Calcular: coeficiente de variación
•Realizar un diagrama de caja
•Percentil 85, decil 2
Answers
Therefore, the coefficient of variation for the given data is approximately 24.71%.
What is box plot?A box plot, also known as a box-and-whisker plot, is a graphical representation of a data set that shows the distribution of the data using quartiles. It is a standardized way of displaying the distribution of data based on the five-number summary: minimum, first quartile, median, third quartile, and maximum. The box represents the middle 50% of the data, with the median marked by a line inside the box. The whiskers extend from the box to the minimum and maximum values, or to a certain range if there are outliers. Box plots are useful for comparing the distributions of different data sets and identifying potential outliers.
Here,
1. Stem-and-Leaf Plot:
A stem-and-leaf plot is a way to display data that separates the tens digit of each number from the ones digit. Here is the stem-and-leaf plot for the given data:
3 | 9 9
4 | 2 2 6 6
5 | 1 4 4 6
6 | 1 4 5 5 5 5 5 5
7 | 0 2 3 4
8 | 1 2 2 3 5
9 | 3 4
In this plot, the stem represents the tens digit and the leaves represent the ones digit.
2. Coefficient of Variation:
The coefficient of variation is a measure of the relative variability of a data set. It is calculated as the ratio of the standard deviation to the mean, expressed as a percentage. Here is how to calculate the coefficient of variation for the given data:
Calculate the mean of the data:
Mean = (83+64+51+46+82+91+73+82+65+61+74+64+75+81+94+65+42+81+56+61+72+65+54+39+70+93+42+46+54+72)/20 = 68.25
Calculate the standard deviation of the data:
Standard deviation = sqrt((1/20) * ((83-68.25)^2 + (64-68.25)^2 + ... + (72-68.25)^2))
Standard deviation ≈ 16.88
Calculate the coefficient of variation:
Coefficient of variation = (Standard deviation / Mean) * 100
Coefficient of variation ≈ 24.71%
3. Box Plot:
A box plot is a way to visualize the distribution of data. It displays the minimum value, first quartile (Q1), median, third quartile (Q3), and maximum value of the data. Here is the box plot for the given data:
| +----------+
94 | |
| +----------+
93 | |
| +-----+-----+
82 | | |
| | |
81 | | |
| +-----+ |
80 | | |
| | |
79 | | |
| | |
78 | | |
| | |
77 | | |
| | |
76 | | |
| | |
75 | | |
| | |
74 | | |
| | |
73 | | |
| | |
72 | +-----------------+
|
+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
In this plot, the horizontal line inside the box represents the median, the bottom and top edges of the box represent the first and third quartiles (Q1 and Q3), respectively, and the vertical lines extending from the box represent the minimum and maximum values, excluding outliers.
4. To find the 85th percentile, we need to arrange the data in order from smallest to largest:
39, 42, 42, 46, 46, 51, 54, 56, 61, 61, 64, 64, 65, 65, 65, 70, 72, 72, 73, 74, 75, 81, 81, 82, 82, 83, 91, 93, 94
There are a total of 20 scores, so the 85th percentile would be the score at the 0.85(20) = 17th position:
85th percentile = 72
To find the 2nd decile, we first need to calculate the number of scores in each decile. Since there are 20 scores, each decile would have 2 scores. The 2nd decile would be the score at the 0.2(20) = 4th position:
2nd decile = 46
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Complete question:
Please, I need help with this, it's about statistics. Thank you very much. The grades of 20 students who took an admission exam to a certain faculty, using a scale of 0 to 100, were: 83 64 51 46 82 91 73 82 65 61 74 64 75 81 94 65 42 81 56 61 72 65 54 39 70 93 42 46 54 72
• Make: stem-and-leaf plot
• Calculate: coefficient of variation
• Create a box plot
• 85th percentile, 2nd decile.
find the closed formula for 3,6,11,18 by relating them to a well known sequence. assume the first term given is
Answers
The closed formula for this particular sequence is an = n² + 2.
Take note that the odd numbers 3, 5, 7, 9, and 11 are separate consecutive terms. This shows that the first n odd numbers can be added to the initial term, az, to get the nth term. Hence, the following is how we may represent the nth term a = az + 1 + 3 + 5 + ... + (2n-3) (2n-3). We may utilize the formula for the sum of an arithmetic series to make the sum of odd integers simpler that is 1 + 3 + 5 + ... + (2n-3) = n².
As a result, we get a = az + n^2 - 1. In conclusion, the equation for the series (an)n21, where a1 = az and an is the result of adding the first n odd numbers to az, is as a = az + n^2 - 1. We have the following for the given series where a1 = az = 3.
So, the closed formula for this particular sequence is an = n² + 2.
To learn more about arithmetic sequences, refer to:
Your question is incomplete. The complete question is:
Find the closed formula for the sequence (an)n21. Assume the first term given is az. an = 3, 6, 11, 18, 27... Hint: Think about the perfect squares.
Between 11pm and midnight on Thursday night Mystery pizza gets an average of 4.2 telephone orders per hour
A. Find the probability that at least 3 minutes will elapse before the next telephone order
B. Find the probability that less then 15 minutes will elapse
C. Find the probability that between 15 and 30 minutes will elapse
Answer all please URGENT
Answers
The probability that at least 3 minutes will elapse before the next telephone order is 0.797.
The probability that less than 15 minutes will elapse between orders is 0.677.
The probability that between 15 and 30 minutes will elapse between orders is 0.2275
Using Poisson distribution:To solve the following problem, we need to use the Poisson distribution, which is a probability distribution that describes the number of events that occur in a fixed interval of time or space, given the average rate of occurrence of those events.
The Poisson distribution has the following formula:
[tex]P(X = k) = (\lambda\times ex^{-\lambda}) / k![/tex]
Where:
P(X = k) is the probability that there are exactly k events in the interval
λ is the average rate of occurrence of events in the interval
e is the mathematical constant e (approximately 2.71828)
k! is the factorial of k (i.e., k * (k-1) * (k-2) * ... * 2 * 1)
Here we have
Between 11 pm and midnight on Thursday night Mystery pizza gets an average of 4.2 telephone orders per hour
A. The probability that at least 3 minutes will elapse before the next telephone order, using the complement rule:
=> P(at least 3 minutes) = 1 - P(less than 3 minutes)
Assume that the time between telephone orders follows an exponential distribution with a mean of 1/4.2 = 0.2381 hours (or 14.28 minutes).
Therefore, the Poisson distribution is λ = 1/0.2381 = 4.2/1.0 = 4.2.
Using the exponential distribution, we can find the probability of less than 3 minutes elapsing between orders as follows:
P(less than 3 minutes) = [tex]1 - e ^{(-\lambda \times t) }[/tex]
Where t = 3/60 = 0.05 hours
P(less than 3 minutes) = [tex]1 - e^{(-4.2\times 0.05) } = 0.203[/tex]
Therefore,
P(at least 3 minutes) = 1 - 0.203 = 0.797
The probability that at least 3 minutes will elapse before the next telephone order is 0.797.
B. To find the probability that less than 15 minutes will elapse between orders, we can use the same exponential distribution as before and set t = 15/60 = 0.25 hours:
P(less than 15 minutes) = [tex]1 - e ^{(-\lambda \times t) }[/tex]
P(less than 15 minutes) = [tex]1 - e^{(-4.2 \times 0.25)} = 0.677[/tex]
Hence, The probability that less than 15 minutes will elapse between orders is 0.677.
C. To find the probability that between 15 and 30 minutes will elapse between orders, we can subtract the probabilities found in less than 15 minutes and less than 30 minutes.
P(15 to 30 minutes) = P(less than 15 minutes) - P(less than 30 minutes) -
P(15 to 30 minutes) = [tex]e^{ (-\lambda0.5)} - e^{ (-\lambda 0.25)}[/tex]
= 0.3499 - 0.1224 = 0.2275
Therefore,
The probability that at least 3 minutes will elapse before the next telephone order is 0.797.
The probability that less than 15 minutes will elapse between orders is 0.677.
The probability that between 15 and 30 minutes will elapse between orders is 0.2275
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Ignacio makes a display shelf from 4 wooden boards. All angles formed by the
boards are right angles. Ignacio plans to stain all faces of the shelf, except the
back face, which will be against the wall. What is the total area Ignacio will
stain? Show your work.
512
7 in.
1
2
32 in.
30 in.
72
17
56
9 in.
4 in.
512
24
A
329-30.7
72
Answers
Answer:
shelf area = 19018.33 square inches
Step-by-step explanation:
shelf area calculation:
Ignacio makes a display shelf from 4 wooden boards. All angles formed by the boards are right angles. Ignacio plans to stain all faces of the shelf, except the back face, which will be against the wall. What is the total area Ignacio will stain? Show your work. 512 7 in. 1 2 32 in. 30 in. 72 17 56 9 in. 4 in. 512 24 A 329-30.7 72
To find the total area that Ignacio will stain, we first need to determine the area of each face that will be stained.
Let's label the boards as follows:
Board 1: 512 in x 7 in
Board 2: 12 in x 32 in
Board 3: 30 in x 72 in
Board 4: 17 56/9 in x 4 in
For each board, we need to find the total area of all the faces that will be stained.
Board 1 has two faces that will be stained: the top face and the two side faces. The area of the top face is 512 in x 7 in = 3584 in^2. The area of each side face is 512 in x 12 in = 6144 in^2. So the total area of all three faces is 3584 in^2 + 2 x 6144 in^2 = 15872 in^2.
Board 2 has three faces that will be stained: the top face and the two side faces. The area of the top face is 12 in x 32 in = 384 in^2. The area of each side face is 12 in x 4 in = 48 in^2. So the total area of all three faces is 384 in^2 + 2 x 48 in^2 = 480 in^2.
Board 3 has three faces that will be stained: the top face and the two side faces. The area of the top face is 30 in x 72 in = 2160 in^2. The area of each side face is 72 in x 4 in = 288 in^2. So the total area of all three faces is 2160 in^2 + 2 x 288 in^2 = 2736 in^2.
Board 4 has two faces that will be stained: the top face and the side face. The area of the top face is 17 56/9 in x 4 in = 71 2/3 in^2. The area of the side face is 17 56/9 in x 9 in = 158 2/3 in^2. So the total area of both faces is 71 2/3 in^2 + 158 2/3 in^2 = 230 1/3 in^2.
To find the total area that Ignacio will stain, we just need to add up the areas of all the faces that will be stained:
15872 in^2 + 480 in^2 + 2736 in^2 + 230 1/3 in^2 = 19018 1/3 in^2
Therefore, the total area that Ignacio will stain is approximately 19018.33 square inches.
original question :
Ignacio makes a display shelf from 4 wooden boards. All angles formed by the boards are right angles. Ignacio plans to stain all faces of the shelf, except the back face, which will be against the wall. What is the total area Ignacio will stain? Show your work. 512 7 in. 1 2 32 in. 30 in. 72 17 56 9 in. 4 in. 512 24 A 329-30.7 72
chatgpt
He has 2 pens. His friend gives him 2 more pens. How many pens he has?
Answers
Step-by-step explanation:
4 i guess... sry i m not good at maths
Question 6 (2 points)
A wire costs $3 per foot. How much will 18 inches of wire cost?
$1.50
$3.00
$4.50
$9
Answers
Answer:
$4.50
Step-by-step explanation:
There are 12 inches in a foot. 18 inches is 1.5 feet.
1 foot of wire is $3.00 and a half of foot should be $1.50.
1.5 feet of wire should cost $4.50
1.5 ft × $3/ft
= $4.50
