The speed of the boat in still water is 3 times the speed of the river current.
To find the speed of the boat in still water, we can use the concept of relative motion and the given information about the boat's speed while traveling upstream and downstream.
Let's assume the speed of the boat in still water is "v" km/h, and the speed of the river current is "c" km/h.
When the boat is traveling upstream, it moves against the current, so its effective speed is reduced.
The boat's speed relative to the ground is given by (v - c) km/h.
Similarly, when the boat is traveling downstream, it moves with the current, so its effective speed is increased.
The boat's speed relative to the ground is given by (v + c) km/h.
According to the problem, the boat can travel 40 km upstream in the same time it would take to travel 80 km downstream.
Since time is constant in both cases, we can set up the following equation:
40/(v - c) = 80/(v + c)
To solve this equation, we can cross-multiply and simplify:
40(v + c) = 80(v - c)
40v + 40c = 80v - 80c
40c + 80c = 80v - 40v
120c = 40v
Dividing both sides by 40, we get:
3c = v.
For similar question on speed.
https://brainly.com/question/13262646
#SPJ8
How should the experimental probability compare to the theoretical probability in a trial 10 versus 500
In a trial of 10 versus 500, the experimental probability is expected to be closer to the theoretical probability when there are more trials (500 in this case).
The experimental probability and theoretical probability can be compared in a trial of 10 versus 500 by understanding the concepts behind each type of probability.
Theoretical probability is based on mathematical calculations and is determined by analyzing the possible outcomes of an event. It relies on the assumption that the event is equally likely to occur, and it can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Theoretical probability is often considered the expected or ideal probability.
On the other hand, experimental probability is determined through actual observations or experiments. It involves conducting the event multiple times and recording the outcomes to determine the relative frequency of a specific outcome. The experimental probability is an estimation based on the observed data.
In the given trial of 10 versus 500, we can expect the experimental probability to be closer to the theoretical probability when the number of trials (or repetitions) is larger. In this case, with 500 trials, the experimental probability is likely to be a more accurate representation of the true probability.
When the number of trials is small, such as only 10, the experimental probability may deviate significantly from the theoretical probability. With a smaller sample size, the observed outcomes may not accurately reflect the expected probabilities calculated theoretically.
In summary, in a trial of 10 versus 500, the experimental probability is expected to be closer to the theoretical probability when there are more trials (500 in this case). As the number of trials increases, the observed frequencies are likely to converge towards the expected probabilities calculated theoretically.
for more such question on probability visit
https://brainly.com/question/251701
#SPJ8
if 2540cm is increase by 15%, the result is
Answer:
2921
Step-by-step explanation:
[tex]2540 + 2540 * \frac{15}{100} \\\\= 2540 + 381\\\\= 2921[/tex]
you are a trainer . .you have developed a 5 week training course for 20 trainees that will cost $140,000. what is the cost per trainee
The cost per trainee for the 5-week training course is $7,000.
To find the cost per trainee, we divide the total cost of the training course by the number of trainees.
Total cost of the training course = $140,000
Number of trainees = 20
Cost per trainee = Total cost of the training course / Number of trainees
Cost per trainee = $140,000 / 20
Cost per trainee = $7,000
Therefore, the cost per trainee for the 5-week training course is $7,000.
for such more question on cost
https://brainly.com/question/25109150
#SPJ8
In a sample of 5,000 students , the mean GPA is 2.80 and the standard deviation is 0.35. Assume the distribution to be normal.
How many students score below 2.60?
In a sample of 5000 students, the mean GPA is 2.80 and their standard deviation is 0.35 and 1428 students score below 2.60.
To find the number of students scoring below 2.60, we need to calculate the area under the normal distribution curve to the left of this value.
First, we need to standardize the value of 2.60 using the z-score formula: z = (x - μ) / σ, where x is the value (2.60), μ is the mean (2.80), and σ is the standard deviation (0.35). Plugging in the values, we get z = (2.60 - 2.80) / 0.35 = -0.57.
Now, we can use a standard normal distribution table or a statistical calculator to find the area to the left of -0.57. Consulting a standard normal distribution table, we find that the area to the left of -0.57 is approximately 0.2857.
To calculate the number of students scoring below 2.60, we multiply this area by the total number of students in the sample: 0.2857 * 5000 ≈ 1428.5.
Since the number of students must be a whole number, we round down to 1428 students.
Therefore, approximately 1428 students score below 2.60 in the sample of 5000 students, assuming a normal distribution with a mean of 2.80 and a standard deviation of 0.35.
Know more about standard deviation here:
https://brainly.com/question/475676
#SPJ8
Divisores pares de 100
Answer:
2, 4, 10, 20, 50, and 100.
Step-by-step explanation:
Analyzing Wages-Plus-Commission Pay
Maybelle works in the shoe department for a high-end
store. She earns $15 per hour for at least 40 hours per
week. On top of that, she earns 10% commission for each
pair of shoes she sells. She is expected to sell $2,500
worth of shoes every week.
What will Maybelle earn in wages in a typical week?
How much commission will Maybelle earn if she sells
$3,000 of shoes in one week?
v
The next week, customers return $1,000 worth of
shoes. How much money will be deducted from
Maybelle's paycheck?
With an economic downturn, sales slump. As a result,
Maybelle will likely
a)In a typical week, Maybelle will earn a total of: $600 + $250 = $850
b) Her total earnings for the week would be: $600 + $300 = $900
c) Her paycheck will be reduced by $100.
d) Her wage earnings should remain the same assuming she still works at least 40 hours per week.
To calculate Maybelle's earnings in a typical week, we first need to determine the minimum number of hours she works. Since she earns $15 per hour for at least 40 hours per week, her minimum wage earnings are:
$15 x 40 = $600
In addition to her wage earnings, Maybelle earns a commission of 10% for each pair of shoes she sells. Since she is expected to sell $2,500 worth of shoes every week, her commission earnings are:
$2,500 x 0.10 = $250
b) If Maybelle sells $3,000 worth of shoes in one week, her commission earnings would be:
$3,000 x 0.10 = $300
On top of her wage earnings of $600 (based on working at least 40 hours at $15 per hour)
c) If customers return $1,000 worth of shoes the next week, Maybelle's commission earnings will not be affected. However, her wage earnings will be reduced by the amount of the returned shoes, which is $1,000 x 0.10 = $100.
d) With an economic downturn and sales slump, Maybelle's earnings from commission will likely decrease since she will sell fewer shoes. However, her total earnings will likely decrease due to the decrease in commission earnings.
For such more questions on total
https://brainly.com/question/28521601
#SPJ8
Pregunta 1
Resuelve el siguiente problema aplicando las estrategias de solución de problemas.
• El área de un triángulo es de 30 pies cuadrados y la base mide 5 pies. ¿Cuál es la
altura del triángulo en pulgadas?
Answer:
I can't understand the language but try people who can
Q.14 In the figure given below, let the lines 1, and 1, be parallel and t is transversal. Find
the value of x.
J
Answer:
I wish you good luck in finding your answer
Answer: 115
Step-by-step explanation:
HELP THIS QUESTION IS HARD
Answer:
a)
[tex] \frac{1}{( - 7)^{4} } [/tex]
Answer:
[tex](-7)^-^4=\frac{1}{(-7)^4}[/tex]
Step-by-step explanation:
The user aswati already wrote the correct answer, but I wanted to help explain why their answer is correct so that you'll understand.
According to the negative exponent rule, when a base (let's call it m) is raised to a negative exponent (let's call it n), we rewrite it as a fraction where the numerator is 1 and the denominator is the base raised to the same exponent turned positive.
Thus, the negative exponent rule is given as:
[tex]b^-^n=\frac{1}{b^n}[/tex]
Thus, [tex](-7)^-^4[/tex] becomes [tex]\frac{1}{(-7)^4}[/tex]
I need help please!!
Answer:
(r q)(-3) = -3
(q r)(-3) = -3
Step-by-step explanation:
let x = 1
q(1) = -1 +2 = 1
r(1) = 1² = 1
(r q)(-3) = ?
(1×1)(-3) = -3
(q r)(-3) = ?
(1×1)(-3) = -3
What number completes the sequence below? Enter your answer in the input
box at the bottom.
8——-4
16——8
24——12
32——?
Answer:
16
Step-by-step explanation:
the numbers on the right of the arrow are half the value of the corresponding numbers on the left, then
32 → [tex]\frac{1}{2}[/tex] (32)
32 → 16
15. A landscaper uses a wheelbarrow to move soil to a certain region of the garden. A
wheelbarrow can hold approximately 6 cubic feet of soil. The soil is damped out into a pile
that makes the shape of a cone. The landscaper calculates that once the pille has a diameter
of 13 foet and a height of 3 feet, there will be sufficient soil for the project How maty
wheelbarrow loads of soil are needed for this project?
The number of wheelbarrow loads of soil required for this project is 71.
The landscaper uses a wheelbarrow to transport soil to a particular region of the garden. A wheelbarrow can accommodate roughly 6 cubic feet of soil. Once the pile has a diameter of 13 feet and a height of 3 feet, the landscaper determines that there will be enough soil for the project.
Area of a cone =1/3πr²hwhere r = 13/2 feet and h = 3 feet.
Substituting the given values to find the area of the cone.1/3 x 3.14 x (6.5)² x 3 = 422.55 cubic feet.Then, divide the total amount of soil required by the volume of soil that a wheelbarrow can hold to determine the number of wheelbarrow loads required.
Number of wheelbarrow loads = (Volume of soil needed) / (Volume of one wheelbarrow)Volume of one wheelbarrow = 6 cubic feet.The total volume of soil required is 422.55 cubic feet.
Therefore, the number of wheelbarrow loads required is:Number of wheelbarrow loads = (422.55) / (6) = 70.42 ≈ 71 wheelbarrow loads, which is the final answer.
For more such questions on soil, click on:
https://brainly.com/question/1286340
#SPJ8
Evaluate leaving your answer in a standard form 0.0048*0.81 /0.027*0.04
Step-by-step explanation:
When we simplify the expression, we get:
0.0048 * 0.81 / 0.027 * 0.04 = (0.0048 / 0.027) * (0.81 / 0.04)
Using a calculator to evaluate the two fractions separately, we get:
0.0048 / 0.027 ≈ 0.1778
0.81 / 0.04 = 20.25
Substituting these values back into the original expression, we get:
(0.0048 / 0.027) * (0.81 / 0.04) ≈ 0.1778 * 20.25
Multiplying these two values together, we get:
0.1778 * 20.25 ≈ 3.59715
To express the answer in standard form, we need to write it as a number between 1 and 10 multiplied by a power of 10. We can do this by moving the decimal point three places to the left, since there are three digits to the right of the decimal point:
3.59715 ≈ 3.59715 × 10^(-3)
Therefore, the final answer in standard form is approximately 3.59715 × 10^(-3).
Steven earns extra money babysitting. He charges $31.00 for 4 hours and $62.00 for 8 hours.
Enter an equation to represent the relationship. Let x represent the number of hours Steven babysits and y represent the amount he charges.
The equation is y = 7.75x, where x is the number of hours Steven babysits and y is the amount he charges.
To represent the relationship between the number of hours Steven babysits (x) and the amount he charges (y), we can use a linear equation in the form of y = mx + b, where m is the slope and b is the y-intercept.
From the given information, we can identify two data points:
(4, 31.00) and (8, 62.00)
Using these points, we can calculate the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
m = (62.00 - 31.00) / (8 - 4)
m = 31.00 / 4
m = 7.75
Now, we can substitute one of the points and the slope into the equation to find the y-intercept (b).
Using the point (4, 31.00):
31.00 = 7.75(4) + b
31.00 = 31.00 + b
b = 0
Therefore, the equation that represents the relationship between the number of hours Steven babysits (x) and the amount he charges (y) is:
y = 7.75x
The equation is y = 7.75x, where x is the number of hours Steven babysits and y is the amount he charges.
for such more question on equation
https://brainly.com/question/17482667
#SPJ8
Write the equation of the trigonometric graph.
Answer:
[tex]y=\boxed{2}\:\cos \left(\boxed{1}\;x\right)+\boxed{3}[/tex]
Step-by-step explanation:
The graph of the solid black line is the cosine parent function, y = cos(x).
The standard form of a cosine function is:
[tex]\boxed{y = A \cos(B(x + C)) + D}[/tex]
where:
A is the amplitude (height from the mid-line to the peak).2π/B is the period (horizontal distance between consecutive peaks).C is the phase shift (horizontal shift - positive is to the left).D is the vertical shift (the mid-line is y = D).From inspection of the graph, the x-values of the turning points (peaks and troughs) of the parent function and the new function are the same. Therefore, the period of both functions is the same, and there has been no horizontal shift. So, B = 1 and C = 0.
The mid-line of the new function is y = 3. Therefore, D = 3.
The y-value of the peaks is y = 5. The amplitude is the distance from the mid-line to the peak. Therefore, A = 2.
Substituting these values into the standard formula we get:
[tex]y = 2 \cos(1(x + 0)) + 3[/tex]
[tex]y=2 \cos (1(x))+3[/tex]
[tex]y= 2 \cos(x) + 3[/tex]
Therefore, the equation of the trigonometric graph is:
[tex]y=\boxed{2}\:\cos \left(\boxed{1}\;x\right)+\boxed{3}[/tex]
10 donuts cost $2.99 how much 1 cost?
If a turtle travels 1/12 of a mile per hour how long will it take to get to a pond 5/6 of a mile away
Answer:
Step-by-step explanation:
To find the time it takes for the turtle to reach the pond, we can use the formula:
Time = Distance / Speed
Given that the turtle travels at a speed of 1/12 mile per hour and the distance to the pond is 5/6 mile, we can substitute these values into the formula:
Time = (5/6) / (1/12)
To simplify this, we can multiply the numerator by the reciprocal of the denominator:
Time = (5/6) * (12/1) = (5 * 12) / 6 = 60 / 6 = 10
Therefore, it will take the turtle 10 hours to reach the pond.
Find the equations of the asymptotes of the hyperbola defined by the equation shown below. If necessary, round to the nearest tenth. 100pts
The equations of the asymptotes of the hyperbola are y = (5/9)x - 79/9 and y = -(5/9)x + 79/9.
To find the equations of the asymptotes of the hyperbola defined by the equation:
[tex]-25x^2 + 81y^2 + 100x + 1134y + 1844 = 0[/tex]
We can rewrite the equation in the standard form by isolating the x and y terms:
[tex]-25x^2 + 100x + 81y^2 + 1134y + 1844 = 0[/tex]
Rearranging the terms:
[tex]-25x^2 + 100x + 81y^2 + 1134y = -1844[/tex]
Next, let's complete the square for both the x and y terms:
[tex]-25(x^2 - 4x) + 81(y^2 + 14y) = -1844\\-25(x^2 - 4x + 4 - 4) + 81(y^2 + 14y + 49 - 49) = -1844\\-25((x - 2)^2 - 4) + 81((y + 7)^2 - 49) = -1844[/tex]
Expanding and simplify
[tex]-25(x - 2)^2 + 100 - 81(y + 7)^2 + 3969 = -1844\\-25(x - 2)^2 - 81(y + 7)^2 = -1844 - 100 - 3969\\-25(x - 2)^2 - 81(y + 7)^2 = -4913[/tex]
Dividing both sides by -4913:
[tex](x - 2)^2/(-4913/25) - (y + 7)^2/(-4913/81) = 1[/tex]
Comparing this equation to the standard form of a hyperbola:
[tex](x - h)^2/a^2 - (y - k)^2/b^2 = 1[/tex]
We can determine that the center of the hyperbola is (h, k) = (2, -7). The value of [tex]a^2[/tex] is (-4913/25), and the value of [tex]b^2[/tex] is (-4913/81).
The equations of the asymptotes can be found using the formula:
y - k = ±(b/a)(x - h)
Substituting the values we found:
y + 7 = ±(√(-4913/81) / √(-4913/25))(x - 2)
Simplifying:
y + 7 = ±(√(4913) / √(81)) × √(25/4913) × (x - 2)
y + 7 = ±(√(4913) / 9) × √(25/4913) × (x - 2)
Rationalizing the denominators and simplifying:
y + 7 = ±(5/9) ×(x - 2)
Finally, rearranging the equation to isolate y:
y = ±(5/9)x - 10/9 - 7
Simplifying further:
y = ±(5/9)x - 79/9
In light of this, the equations for the hyperbola's asymptotes are y = (5/9)x - 79/9 and y = -(5/9)x + 79/9.
for such more question on hyperbola
https://brainly.com/question/16454195
#SPJ8
Answer:
[tex]\boxed{y=\dfrac{5}{9}x-\dfrac{73}{9}}\;\; \textsf{and} \;\;\boxed{ y=-\dfrac{5}{9}x-\dfrac{53}{9}}[/tex]
Step-by-step explanation:
First, rewrite the given equation in the standard form of a hyperbola by completing the square.
Given equation:
[tex]-25x^2+81y^2+100x+1134y+1844=0[/tex]
Arrange the equation so all the terms with variables are on the left side and the constant is on the right side:
[tex]-25x^2+100x+81y^2+1134y=-1844[/tex]
Factor out the coefficient of the x² term and the coefficient of the y² term:
[tex]-25(x^2-4x)+81(y^2+14y)=-1844[/tex]
Add the square of half the coefficient of x and y inside the parentheses of the left side, and add the distributed values to the right side:
[tex]-25(x^2-4x+4)+81(y^2+14y+49)=-1844-25(4)+81(49)[/tex]
Factor the two perfect trinomials on the left side and simplify the right side:
[tex]-25(x-2)^2+81(y+7)^2=2025[/tex]
Divide both sides by the number of the right side so the right side equals 1:
[tex]\dfrac{-25(x-2)^2}{2025}+\dfrac{81(y+7)^2}{2025}=\dfrac{2025}{2025}[/tex]
[tex]\dfrac{-(x-2)^2}{81}+\dfrac{(y+7)^2}{25}=1[/tex]
[tex]\dfrac{(y+7)^2}{25}-\dfrac{(x-2)^2}{81}=1[/tex]
As the y²-term is positive, the hyperbola is vertical (opening up and down).
The standard equation of a vertical hyperbola is:
[tex]\boxed{\dfrac{(y-k)^2}{a^2}-\dfrac{(x-h)^2}{b^2}=1}[/tex]
Therefore, comparing this with the rewritten equation:
h = 2k = -7a² = 25 ⇒ a = 5b² = 81 ⇒ b = 9The formula for the equations of the asymptotes of a vertical hyperbola is:
[tex]\boxed{y=\pm \dfrac{a}{b}(x-h)+k}[/tex]
Substitute the values of h, k, a and b into the formula:
[tex]y=\pm \dfrac{5}{9}(x-2)-7[/tex]
Therefore, the equations for the asymptotes are:
[tex]\boxed{y=\dfrac{5}{9}x-\dfrac{73}{9}}\;\; \textsf{and} \;\;\boxed{ y=-\dfrac{5}{9}x-\dfrac{53}{9}}[/tex]
Question 2 (1 point)
Which one of the following is true of the mean?
1) one of the less common averages
2) equals some whole number
observations must be ordered from least to most before calculating the
3)
mean
4) equals the sum of all observations divided by the number of observations
The correct statement about the mean is:
The mean equals the sum of all observations divided by the number of observations.
The mean is a commonly used measure of central tendency. It is calculated by summing up all the observations and then dividing the sum by the total number of observations. It provides an average value that represents the typical value of the data set.
To calculate the mean, it is not necessary to order the observations from least to most. The order of the observations does not affect the mean calculation.
The mean is not necessarily a whole number. It can be a decimal or a fraction, depending on the data set and the values of the observations. The mean represents the balance point of the data set and can take on any real number value.
for such more question on mean
https://brainly.com/question/14532771
#SPJ8
Select the correct answer.
The number of hours that 20 people spent watching television per day, in relation to age, is graphed. This quadratic equation represents the model
for the set of data.
y = 0.004z²0.314z + 7.5
Based on the model, approximately how much time does an 18-year-old spend watching television each day?
O A.
OB.
O C.
O D.
3 hours
2 hours
7.5 hours
0.5 hour
Based on the quadratic function, an 18 year old would spend 3 hours watching television.
Using the quadratic function given :
y = 0.004z²-0.314z + 7.5The age is represented as the variable , 'z'
substitute z = 18 into the equation
y = (0.004*18²) - 0.314(18) + 7.5
y = 3.144
y = 3 hours approximately
Hence, an 18 year old spend approximately 18 hours watching television.
Learn more on Quadratic functions:https://brainly.com/question/30164833
#SPJ1
Which system of linear inequalities is represented by the graph?
y > x – 2 and y < x + 1
y < x – 2 and y > x + 1
y < x – 2 and y > x + 1
y > x – 2 and y < x + 1
Answer:
The system of linear inequalities represented by the graph is:
y > x - 2 and y < x + 1
This system of inequalities indicates that y is greater than x - 2, which represents the upper boundary of the shaded region in the graph. Additionally, y is less than x + 1, which represents the lower boundary of the shaded region. The intersection of these two conditions is the region between the lines, satisfying both inequalities.
Which of these situations can be represented by the opposite of −5? Use pencil and paper. Describe two more situations that can be represented by the opposite of −5.
The opposite of -5 can be represented by situations such as a temperature increase of 5 degrees and a financial gain of $5. Additionally, it can also represent a distance traveled of 5 miles and a weight gain of 5 pounds.
The opposite of -5 is 5. The opposite of a number represents the number with the opposite sign. Here are three situations that can be represented by the opposite of -5:
Situation 1: Temperature Change
If the temperature is currently -5 degrees Celsius and it undergoes a change in the opposite direction, it means it increases by 5 degrees. Therefore, the opposite of -5 represents a temperature increase of 5 degrees.
Situation 2: Financial Gain
Suppose you owe someone $5, and you receive the opposite of that amount. The opposite of owing $5 would be gaining $5. So, the opposite of -5 represents a financial gain of $5.
Additional situations that can be represented by the opposite of -5:
Situation 3: Distance Traveled
If a car has traveled -5 miles, indicating it has moved in the opposite direction, the opposite of that distance would be 5 miles. So, the opposite of -5 represents a distance traveled of 5 miles.
Situation 4: Weight Gain
Imagine someone loses 5 pounds (which can be represented as -5). The opposite of losing 5 pounds would be gaining 5 pounds. Thus, the opposite of -5 represents a weight gain of 5 pounds.
In each of these situations, the opposite of -5 denotes a change in the opposite direction or the reverse of the initial value.
for such more question on situations
https://brainly.com/question/7890421
#SPJ8
solve this system of equations by using the elimination method x-5y=16 4x-2y=-8
Answer:
(- 4, - 4 )
Step-by-step explanation:
x - 5y = 16 → (1)
4x - 2y = - 8 → (2)
multiplying (1) by - 4 and adding to (2) will eliminate x
- 4x + 20y = - 64 → (3)
add (2) and (3) term by term to eliminate x
(4x - 4x) + (- 2y + 20y) = - 8 - 64
0 + 18y = - 72
18y = - 72 ( divide both sides by 18 )
y = - 4
substitute y = - 4 into either of the 2 equations and solve for x
substituting into (1)
x - 5(- 4) = 16
x + 20 = 16 ( subtract 20 from both sides )
x = - 4
solution is (- 4, - 4 )
Sin(theta)=2/3 and theta is in quadrant II, find cos theta
Answer: Choice C. [tex]\displaystyle \boldsymbol{-\frac{\sqrt{5}}{3}}[/tex]
===================================================
Work Shown:
Part 1
[tex]\sin^2(\theta)+\cos^2(\theta) = 1\\\\\cos^2(\theta) = 1-\sin^2(\theta)\\\\\cos(\theta) = -\sqrt{1-\sin^2(\theta)} \ \ \text{ ..... cosine is negative in Q2}\\\\\cos(\theta) = -\sqrt{1-\left(\frac{2}{3}\right)^2}\\\\\\cos(\theta) = -\sqrt{1-\frac{4}{9}}\\\\[/tex]
Part 2
[tex]\cos(\theta) = -\sqrt{\frac{9}{9}-\frac{4}{9}}\\\\\cos(\theta) = -\sqrt{\frac{9-4}{9}}\\\\\cos(\theta) = -\sqrt{\frac{5}{9}}\\\\\cos(\theta) = -\frac{\sqrt{5}}{\sqrt{9}}\\\\\cos(\theta) = -\frac{\sqrt{5}}{3}\\\\[/tex]
anna rolled a pair of number cubes what is the probability of getting even number on both sides PLSSS HELP ME
It is best to draw a table of outcomes and list all the possible outcomes when you roll a pair of numbered cubes. As follows:
1 2 3 4 5 6
1 ( 1 , 1 ) ( 1 , 2 ) ( 1 , 3 ) ( 1 , 4 ) ( 1 , 5 ) ( 1 , 6 )
2 ( 2 , 1 ) ( 2, 2 ) ( 2 , 3 ) ( 2 , 4 ) ( 2 , 5 ) ( 2 , 6 )
3 ( 3 , 1 ) ( 3 , 2 ) ( 3 , 3 ) ( 3 , 4 ) ( 3 , 5 ) ( 3 , 6 )
4 ( 4 , 1 ) ( 4 , 2 ) ( 4 , 3 ) ( 4 , 4 ) ( 4 , 5 ) ( 4 , 6 )
5 ( 5 , 1 ) ( 5 , 2 ) ( 5 , 3 ) ( 5 , 4 ) ( 5 , 5 ) ( 5 , 6 )
6 ( 6 , 1 ) ( 6 , 2 ) ( 6 , 3 ) ( 6 , 4 ) ( 6 , 5 ) ( 6 , 6 )
- Each cube has 6 faces, Hence, 6 numbers for each are expressed as row and column for first and second cube respectively.
- Now locate and highlight all the even pairs shown in bold.
- The total number of even pairs outcomes are = 9.
- The total possibilities are = 36.
- The probability of getting even pairs as favorable outcome can be expressed as:
P ( Even pairs ) = Favorable outcomes / Total outcomes
P ( Even pairs ) = 9 / 36
P ( Even pairs ) = 1 / 4.
- So the probability of getting an even pair when a pair of number cubes are rolled is 1/4
Para tener una sucesión es imprescindible que los números que lo forman :
A: sean infinitos
B: tengan una ley de formación C:estén ordenados
For a collection of numbers to be considered a sequence, it is essential that they have a law of formation, are ordered in a specific manner, and can be either finite or infinite.
B: They have a law of formation:
A sequence is a set of numbers arranged in a specific order according to a rule or pattern. The numbers in a sequence are not random but follow a specific law of formation.
This law can be a mathematical formula, a recursive relationship, or any other systematic pattern that determines the values of the sequence. Without a well-defined law of formation, a collection of numbers cannot be considered a sequence.
C: They are ordered:
In a sequence, the numbers are arranged in a specific order or sequence. The order of the numbers is crucial and defines the pattern and structure of the sequence.
Each number in the sequence has a unique position or index that determines its place in the sequence. The order of the numbers allows us to identify the next number or predict the pattern of the sequence. Without the concept of order, the numbers would simply be a set of unrelated elements and not a sequence.
A: They may or may not be infinite:
Sequences can be finite or infinite. A finite sequence has a specific number of terms, and once the pattern or rule is established, the sequence ends.
On the other hand, an infinite sequence continues indefinitely, and its terms extend infinitely in one direction or both directions. Whether a sequence is finite or infinite depends on the context and the specific rule or pattern that governs its formation.
For more such questions on collection visit:
https://brainly.com/question/13458417
#SPJ8
Note: the translated question is:
To have a sequence it is essential that the numbers that form it:
A: be infinite
B: they have a law of formation C: they are ordered
The hip width x of adult females is normally distributed with a mean of 37.6 cm and a standard deviation of 4.36 cm. The maximum width of an aircraft seat that will accommodate 98% of all adult women is about: (Give your answer to one decimal places if necessary.)
Answer:
Step-by-step explanation:
To find the maximum width of an aircraft seat that will accommodate 98% of all adult women, we need to determine the corresponding z-score for the 98th percentile of the normal distribution.
First, we find the z-score corresponding to the 98th percentile using a standard normal distribution table or calculator. The z-score for the 98th percentile is approximately 2.05.
Next, we use the z-score formula to find the corresponding value in the original distribution:
z = (x - μ) / σ
Solving for x (the maximum width of the aircraft seat):
x = z * σ + μ
Substituting the values given:
x = 2.05 * 4.36 + 37.6
x ≈ 45.98
Therefore, the maximum width of an aircraft seat that will accommodate 98% of all adult women is approximately 46 cm (rounded to one decimal place).
Write an inequality and solve.
Negative one hundred eighty three is at least nine more than 24 times a number.
Answer: -8 ≥ x
Step-by-step explanation:
Let x be the number, we set up an inequality:
-183 ≥ 9 + 24x [we use ≥ to present "at least"]
-192 ≥ 24x
-8 ≥ x
Let f(x) = 4x² - 2x +11
The slope of the tangent line to the graph of f(x) at the point (3, 41)
Slope =
M=
B=
Answer:
f(x) = 4x² - 2x + 11
f'(x) = 8x - 2
m = f'(3) = 8(3) - 2 = 24 - 2 = 22
41 = 22(3) + b
41 = 66 + b
b = -25
y = 22x - 25
Find the focus of the parabola defined by the equation 100 points.
Answer : Focus is (0,3)
To find the focus of the parabola defined by the equation (y - 3)² = -8(x - 2), we can compare it with the standard form of a parabolic equation: (y - k)² = 4a(x - h).
In the given equation, we have:
(y - 3)² = -8(x - 2)
Comparing it with the standard form, we can determine the values of h, k, and a:
h = 2
k = 3
4a = -8
Solving for a, we get:
4a = -8
a = -8/4
a = -2
Therefore, the vertex of the parabola is (h, k) = (2, 3), and the value of 'a' is -2.
The focus of the parabola can be found using the formula:
F = (h + a, k)
Substituting the values, we get:
F = (2 + (-2), 3)
F = (0, 3)
Therefore, the focus of the parabola defined by the equation (y - 3)² = -8(x - 2) is at the point (0, 3).
Answer:
Focus = (0, 3)
Step-by-step explanation:
The focus is a fixed point located inside the curve of the parabola.
To find the focus of the given parabola, we first need to find the vertex (h, k) and the focal length "p".
The standard equation for a sideways parabola is:
[tex]\boxed{(y-k)^2=4p(x-h)}[/tex]
where:
Vertex = (h, k)Focus = (h+p, k)If p > 0, the parabola opens to the right, and if p < 0, the parabola opens to the left.
Given equation:
[tex](y-3)^2=-8(x-2)[/tex]
Compare the given equation to the standard equation to determine the values of h, k and p:
h = 2k = 34p = -8 ⇒ p = -2The formula for the focus is (h+p, k).
Substituting the values of h, p and k into the formula, we get:
[tex]\begin{aligned}\textsf{Focus}&=(h+p,k)\\&=(2-2,3)\\&=(0,3)\end{aligned}[/tex]
Therefore, the focus of the parabola is (0, 3).