The average speed of the current is 1 mile per hour.
To construct a rational equation that can be solved for the speed of the current, we can use the relationship t = d/r, where t is the time taken, d is the distance traveled, and r is the speed. We can set up two equations using this relationship, one for the upstream journey and one for the downstream journey:
Upstream journey: t = 4/(10-c)
Downstream journey: t = 6/(10+c)
Here, c represents the speed of the current. We use 10-c for the upstream journey because the current is going against the boat's direction, effectively reducing the boat's speed. Conversely, we use 10+c for the downstream journey because the current is aiding the boat's direction, effectively increasing the boat's speed.
Now, we can set these two equations equal to each other and solve for c:
4/(10-c) = 6/(10+c)
Multiplying both sides by (10-c)(10+c), we get:
4(10+c) = 6(10-c)
Simplifying and solving for c, we get:
c = 1
This means that when the boat is traveling with the current, its effective speed is 11 miles per hour, and when it's traveling upstream, its effective speed is 9 miles per hour.
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On Sunday a local hamburger shop sold 356 hamburgers and cheeseburgers. The number of cheeseburgers sold was three times the number of hamburgers sold. How many hamburgers were sold on Sunday
The number of hamburgers sold on Sunday was 89
How many hamburgers were sold on SundayLet's assume that the number of hamburgers sold on Sunday was x.
According to the problem, the number of cheeseburgers sold was three times the number of hamburgers sold.
Therefore, the number of cheeseburgers sold can be expressed as 3x.
The total number of hamburgers and cheeseburgers sold was 356.
Therefore, we can write an equation to represent this information:
x + 3x = 356
Simplifying the left-hand side of the equation, we get:
4x = 356
Dividing both sides by 4, we get:
x = 89
Therefore, the number of hamburgers sold on Sunday was 89, and the number of cheeseburgers sold was 3 times that, or 267.
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in exercises 59-62, find the component form of the sum of u and v with direction angles
The component form of the sum of u and v with direction angles is u + v = (10√2 - 50)i + 10√2 j.
We are given the magnitudes and direction angles of vectors u and v. We need to find the component form of their sum.
Let's first convert the given magnitudes and direction angles to their corresponding components. For vector u:
|u| = 20, θu = 45°
The x-component of u is given by:
ux = |u| cos(θu) = 20 cos(45°) = 10√2
The y-component of u is given by:
uy = |u| sin(θu) = 20 sin(45°) = 10√2
Therefore, the component form of vector u is:
u = 10√2 i + 10√2 j
Similarly, for vector v:
|v| = 50, θv = 180°
The x-component of v is given by:
vx = |v| cos(θv) = -50 cos(180°) = -50
The y-component of v is given by:
vy = |v| sin(θv) = 50 sin(180°) = 0
Therefore, the component form of vector v is:
v = -50 i + 0 j
The component form of the sum of u and v is given by the sum of their x- and y-components:
u + v = (10√2 - 50) i + (10√2 + 0) j
Simplifying, we get:
u + v = (10√2 - 50) i + 10√2 j
Therefore, the component form of the sum of u and v is:
u + v = (10√2 - 50) i + 10√2 j
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The question is -
Find the component form of the sum of u and v with the given magnitudes and direction angles θu and θv.
| | u | | = 20 , θu = 45° | | v | | = 50 , θv = 180°.
pretty please helpppp
Answer: 2(n6)
And true states are
The two operations are mulitplication and substraction
The constants are 2 and 6
The expression is written as 2(n-6)
Step-by-step explanation:
Answer:
A,C,D,E should be correct.
A. Replace “a number” with the variable, n.
C. The two operations are multiplication and subtraction.
D. The constants are 2 and 6.
E. The expression is written as 2(n – 6).
hope this helped!
The function f is given by f(x) = 10x + 3 and the function g is given by g(x) = 2×. For each question, show your reasoning
1. Which function reaches 50 first
2. Which function reaches 100 first?
1. x = 4.7 for f(x) and x = 25 for g(x), f(x) reaches 50 first.
2. x = 9.7 for f(x) and x = 50 for g(x), f(x) reaches 100 first.
1. Which function reaches 50 first?
To answer this, we need to solve for x in each function when the output is 50:
For f(x): 50 = 10x + 3
47 = 10x
x = 4.7
For g(x): 50 = 2x
x = 25
Since x = 4.7 for f(x) and x = 25 for g(x), f(x) reaches 50 first.
2. Which function reaches 100 first?
Similarly, we'll solve for x in each function when the output is 100:
For f(x): 100 = 10x + 3
97 = 10x
x = 9.7
For g(x): 100 = 2x
x = 50
Since x = 9.7 for f(x) and x = 50 for g(x), f(x) reaches 100 first.
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Katrine’s baby brother weighed 8 pounds and 3 ounces on the day he was born. He gained 5 ounces each week for 12 weeks. How much did Katrine’s baby brother weigh, in ounces, at the end of 12 weeks?”
Answer:
191 ounces at the end of 12 weeks
Step-by-step explanation:
What is the area of this figure?
Answer:
Step-by-step explanation:
first you divide the shape into 3 parts ;a big triangle, and 2 little squares
after that to get the height of the triangle i gotten by adding
3+5+2+6=16yd
area of a triangle =1/2 × b×h
area =1/2×7×16
area=112/2
area=56yd²
small squre 1=
area=5×5
=25yd²
area of small rectangle=
area=LB
=3×2
=6yd²
total area =triangle+square+rectangle
=56+25+6
TA=87yd²
Please help me with this homework
Answer:sasa
Step-by-step explanation:
a sequence is ---select--- sequence when the first differences are all the same nonzero number.
A sequence is arithmetic sequence when the first differences are all the same non-zero number.
An arithmetic sequence is a set of integers where each term is created by multiplying the preceding term by a defined number. The common difference of the series, which is a constant value, is the same for all following pairs of terms.
As a result, a sequence can be said to be arithmetic if its first differences all contain the same non-zero value. For instance, the arithmetic sequence 3, 6, 9, 12, 15,... has a common difference of 3.
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. which one of the following statements is true? a. if you are given a sample percentage of 43%, you would need to know the sample size in order to convert this percentage to a proportion. b. the test statistic is affected by the size of the sample. c. the larger the p-value, the more evidence you have against the null hypothesis. d. we always begin a hypothesis test by assuming that the null hypothesis is false. e. none of the above statements are true.
If you are given a sample percentage of 43%, you would need to know the sample size in order to convert this percentage to a proportion.
The conversion formula is proportion = percentage/100. However, the proportion alone does not give information about the sample size, which is necessary for inference and hypothesis testing. The other statements are not true.
The test statistic is not affected by the sample size, but its value can be used to determine the significance of a hypothesis test. A larger p-value indicates weaker evidence against the null hypothesis, not stronger evidence. Finally, we assume the null hypothesis is true until we have sufficient evidence to reject it.
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Can y’all tell me 4 positive slope equations (y=mx+b)
Answer:
1. y = 4x + 2
2. y = 3x – 7
3. y = 7x + 6
4. y= 2x + 8
Step-by-step explanation:
1. y = 4x + 2
2. y = 3x – 7
3. y = 7x + 6
4. y= 2x + 8
These 4 equations have a positive slope because remember in the equation (y=mx+b) m = slope and since these equations have positive numbers in the m spot the slope of these equations are positive.
A large pizza at a Pizza Palace costs $11.50 plus $0.90 per topping. The cost for a Large pizza at Tasty Pizza costs $13.25 $0.55 per topping. Let n represent the number of toppings. Let c represent the total cost for the pizza.
a) Write a system of equations to model this scenario
b) then solve the system (using the SUBSTITUTION method) to find the number of toppings where the cost is the same. Be sure to **show all work**
Answer:
Step-by-step explanation:
a) The system of equations modeling this scenario is as follows:
C = 11.50 + 0.9n
C = 13.25 + 0.55n.
b) The number of toppings where the cost is the same at either Pizza Palace or Tasty Pizza is 5.
What is a system of equations?
A system of equations is two or more equations solved concurrently.
A system of equations is also called simultaneous equations because the equations are solved at the same time or simultaneously.
Pizza Palace Tasty Pizza
Pizza cost per unit $11.50 $13.25
Topping cost per unit $0.90 $0.55
Let the number of toppings = n
Let the total cost for the pizza at each pizza place = c
Equations:
The total cost at Pizza Palace C = 11.50 + 0.9n... Equation 1
The total cost at Tasty Pizza, C = 13.25 + 0.55n... Equation 2
For the total cost, c, to be the same at the pizza places, Equation 1 must equate Equation 2:
That is, C = C.
Substituting the values of C:
11.50 + 0.9n = 13.25 + 0.55n
0.35n = 1.75
n = 5
A game requires players to roll a six-sided number cube and spin a spinner, like the one shown below. A circle shaped spinner divided in to 3 equal sections and named green ,blue, red. A needle is shown in center. Then, find the number of outcomes that represent rolling an odd number and landing on blue. What is the answer? 3 4 5 6? Please answer quick!!! I will get you Brainiest!!!
Using probability, there is only one outcome that represents rolling an odd number and landing on blue.
What exactly is probability?
Probability is a measure of the possibility or chance that an event will occur. It is represented by a number between 0 and 1, with 0 representing an improbable occurrence and 1 representing a certain event. A given event's probability is estimated by dividing the number of favourable outcomes by the total number of potential possibilities. Probability theory is frequently used to analyse and forecast the likelihood of occurrences in domains such as statistics, physics, economics, and finance.
Now,
The probability of rolling an odd number is 3/6, which can be simplified to 1/2. The probability of landing on blue= 1/3. Since the events of rolling an odd number and landing on blue are independent, we can multiply the probabilities to find the probability of both events occurring:
(1/2) × (1/3) = 1/6
So, there is only one outcome that represents rolling an odd number and landing on blue. The answer is 1.
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An article on the relation of cholesterol levels in human blood to aging reports that average cholesterol level for women aged 70-74 was found to be 230m/dl. If the standard deviation was 20mg/dl and the distribution normal, what is the probability that a given woman in this age group would have a cholesterol level
a) Less than 200mg/dl
b) More than 200mg/dl
c) Between 190mg/dl and 210mg/dl
d) Write a brief report on the guidance you would give a woman having high cholesterol level in this age group
a) The probability of a given woman in this age group having a cholesterol level less than 200mg/dl is 6.68%.
b) The probability of a given woman in this age group having a cholesterol level more than 200mg/dl is 93.32%.
c) The probability of a given woman in this age group having a cholesterol level between 190mg/dl and 210mg/dl is 15.87%.
d) If a woman in this age group has a cholesterol level higher than 230mg/dl, it is considered high and puts her at risk of heart disease
To calculate the probability of a given woman in this age group having a cholesterol level less than 200mg/dl, we need to find the z-score first. The z-score is the number of standard deviations that a given value is from the mean. The formula to calculate the z-score is:
z = (x - μ) / σ
where x is the given value, μ is the mean, and σ is the standard deviation.
For a cholesterol level of 200mg/dl, the z-score is:
z = (200 - 230) / 20 = -1.5
We can then use a z-table or calculator to find the probability of a z-score being less than -1.5, which is 0.0668 or approximately 6.68%.
Next, to find the probability of a given woman in this age group having a cholesterol level more than 200mg/dl, we can use the same process but subtract the probability of a z-score being less than -1.5 from 1 because the total probability is always 1.
So, the probability of a given woman in this age group having a cholesterol level more than 200mg/dl is:
1 - 0.0668 = 0.9332 or approximately 93.32%.
Finally, to find the probability of a given woman in this age group having a cholesterol level between 190mg/dl and 210mg/dl, we need to find the z-scores for both values.
For a cholesterol level of 190mg/dl, the z-score is:
z = (190 - 230) / 20 = -2
For a cholesterol level of 210mg/dl, the z-score is:
z = (210 - 230) / 20 = -1
We can then use the z-table or calculator to find the probability of a z-score being between -2 and -1, which is 0.1587 or approximately 15.87%.
Finally, a brief report on the guidance that you would give a woman having high cholesterol levels in this age group is:
It is essential to make lifestyle changes such as eating a healthy diet, exercising regularly, quitting smoking, and managing stress to lower cholesterol levels.
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a production manager at a wall clock company wants to test their new wall clocks. the designer claims they have a mean life of 14 years with a variance of 16 . if the claim is true, in a sample of 40 wall clocks, what is the probability that the mean clock life would be less than 13.6 years? round your answer to four decimal places.
The probability that the mean clock life would be less than 13.6 years in a sample of 40 wall clocks is 0.1337
The probability that the mean clock life would be less than 13.6 years in a sample of 40 wall clocks can be calculated using the t-distribution since the population variance is unknown. The formula for t-distribution is:
t = (x-bar - μ) / (s / √n)
where x-bar is the sample mean, μ is the hypothesized population mean (14 years), s is the sample standard deviation (the square root of the sample variance), and n is the sample size (40).
Using the given variance, we can calculate the sample standard deviation as √16 = 4. Plugging in the values, we get:
t = (13.6 - 14) / (4 / √40) = -1.118
Using a t-distribution table with degrees of freedom (df) = n - 1 = 39, we find that the probability of getting a t-value less than -1.118 is 0.1337. Therefore, the probability that the mean clock life would be less than 13.6 years in a sample of 40 wall clocks is 0.1337 (rounded to four decimal places).
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∠A=6x−2
∘
start color #11accd, angle, A, end color #11accd, equals, start color #11accd, 6, x, minus, 2, degrees, end color #11accd \qquad \green{\angle B} = \green{4x +48^\circ}∠B=4x+48
∘
, angle, B, equals, start color #28ae7b, 4, x, plus, 48, degrees, end color #28ae7b
Solve for xxx and then find the measure of \blueD{\angle A}∠Astart color #11accd, angle, A, end color #11accd:
The given information describes the measures of two angles, A and B. Angle A is represented as ∠A and has a measure of 6x-2 degrees. Angle B is represented as ∠B and has a measure of 4x+48 degrees. These measures are respectively shown in the colors #11accd and #28ae7b.
The question gives us two equations, one for angle A and one for angle B, in terms of x. We will have to solve for x and then find the measure of angle A.
To solve for x, we can set the expressions for ∠A and ∠B equal to each other and solve for x
∠A = ∠B
6x - 2 = 4x + 48
Subtracting 4x from both sides we get
2x - 2 = 48
Adding 2 to both sides we get
2x = 50
Dividing by 2 we get
x = 25
Now that we have found the value of x, we can substitute it into the expression for ∠A
∠A = 6x - 2
∠A = 6(25) - 2
By multiplying 6 with 25 we get
∠A = 150 - 2
By Subtracting we get
∠A = 148
Hence, the measure of angle A is 148 degrees.
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The area of (V is 624.36 square meters. The area of sector
SVT is 64.17 square meters. Find the indicated measure.
1. The radius of V is approximately 14.04 meters.2.The circumference of V is approximately 88.24 meters. 3.mST arc is 26.85 degrees. 4.the length of ST arc is approximately 6.61 meters. 5.34.69 meters. 6.88.24m.
Describe Sector?In geometry, a sector is a part of a circle enclosed by two radii and an arc. Essentially, a sector is a slice of a circle. The two radii that form the sector are equal in length and share a common endpoint, which is the center of the circle. The arc of the sector is a portion of the circumference of the circle and its length is proportional to the measure of the central angle that it subtends.
We can use the given information to solve for the following:
1. Radius of V:
The area of a circle is given by the formula A = πr². We are given the area of V as 624.36 square meters, so we can solve for the radius r as:
A = πr²
624.36 = πr²
r² = 624.36/π
r ≈ 14.04 meters
Therefore, the radius of V is approximately 14.04 meters.
2. Circumference of V:
The circumference of a circle is given by the formula C = 2πr. Using the radius we just found, we can solve for the circumference of V as:
C = 2πr
C = 2π(14.04)
C ≈ 88.24 meters
Therefore, the circumference of V is approximately 88.24 meters.
3. mST arc:
The area of the sector SVT is given as 64.17 square meters. The area of a sector is given by the formula A = (θ/360)πr², where θ is the central angle of the sector in degrees. We are not given the value of θ, but we can solve for it as:
A = (θ/360)πr²
64.17 = (θ/360)π(14.04)²
θ ≈ 26.85 degrees
Therefore, the central angle of the sector SVT is approximately 26.85 degrees, and mST arc is also 26.85 degrees.
4. Length of ST arc:
The length of an arc of a circle is given by the formula L = (θ/360)C, where θ is the central angle of the arc in degrees, and C is the circumference of the circle. We can use the values we have already calculated to solve for the length of ST arc as:
L = (θ/360)C
L = (26.85/360)(88.24)
L ≈ 6.61 meters
Therefore, the length of ST arc is approximately 6.61 meters.
5. Perimeter of shaded region (sector):
The perimeter of a sector is the sum of the length of the arc and the lengths of the two radii that form the sector. Using the values we have already calculated, we can solve for the perimeter of the shaded sector as:
Perimeter = L + 2r
Perimeter = 6.61 + 2(14.04)
Perimeter ≈ 34.69 meters
Therefore, the perimeter of the shaded region (sector) is approximately 34.69 meters.
6. Perimeter of unshaded region (remaining circle part):
The perimeter of a circle is given by the formula C = 2πr. Using the radius we previously calculated, we can solve for the perimeter of the unshaded region as:
Perimeter = 2πr
Perimeter = 2π(14.04)
Perimeter ≈ 88.24 meters
Therefore, the perimeter of the unshaded region (remaining circle part) is approximately 88.24 meters.
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An equation is shown:
0.35v+0.40v+1.2+0.05v=7.12
What is the value of v?
To solve for x, we can combine like terms on the left side of the equation:
0.35x + 0.40x + 0.05x + 1.2 = 7.12
0.8x + 1.2 = 7.12
Subtracting 1.2 from both sides:
0.8x = 5.92
Dividing both sides by 0.8, we get:
x = 7.4
Therefore, the value of x is actually 7.4
the manager of a supermarket tracked the amount of time needed for customers to be served by the cashier. after checking with his statistics professor, he concluded that the checkout times are exponentially distributed with a mean of 5.5 minutes. what propotion of customers require more than 12 minutes to check out?
Approximately 0.357 or 35.7% of customers require more than 12 minutes to check out.
Since the checkout times are exponentially distributed with a mean of 5.5 minutes, we can use the exponential distribution formula to find the probability that a customer will take more than 12 minutes to check out:
P(X > 12) = 1 - P(X ≤ 12)
where X is the checkout time.
To find P(X ≤ 12), we can use the cumulative distribution function (CDF) of the exponential distribution, which is:
F(x) = 1 - e^(-λx)
where λ is the rate parameter of the distribution. For an exponential distribution with mean μ, the rate parameter λ is equal to 1/μ.
So, in our case, λ = 1/5.5 = 0.1818, and we can calculate P(X ≤ 12) as:
P(X ≤ 12) = F(12) = 1 - e^(-0.1818 × 12) ≈ 0.643
Therefore, the probability that a customer will take more than 12 minutes to check out is:
P(X > 12) = 1 - P(X ≤ 12) ≈ 1 - 0.643 ≈ 0.357
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What is the most upper (+3) or (-7)? Help please
Answer: Of the two numbers you provided, +3 is greater than -7. So, +3 is the most upper of the two numbers.
Answer: +3
Step-by-step explanation: Positive 3 is greater than negative 7. Therefore, +3 is the greater value.
Find the volume
of the figure below:
Step-by-step explanation:
Use Pythagorean theorem to find the base of the right triangle
221^2 = 195^2 + b^2
b = 104 km
triangle area = 1/2 base * height = 1/2 * 104 * 195 = 10140 km^2
Now multiply by the height to find volume
10140 km^2 * 15 km = 152100 km^3
assume that the class has 50 students and that the examination period is 90 minutes in length. how many students do you expect will be unable to complete the exam in the allotted time? (round your answer up to the nearest integer.) students
The number of students that would be expected to be unable to complete the exam in the allotted time is 8 students.
To find the number of students who would be unable to complete the exam in the allotted time, we need to calculate the number of students who take more than 90 minutes to complete the exam.
First, we calculate the z-score for the cutoff point of 90 minutes:
z = (90 - 80) / 10 = 1
Using a standard normal distribution table, we find that the probability of a student taking more than 90 minutes is approximately 0.1587.
Therefore, the expected number of students who would be unable to complete the exam in the allotted time is:
0.1587 x 50 = 7.935
Rounding up to the nearest integer, we can expect 8 students to be unable to complete the exam in the allotted time.
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The complete question is :
If a class of 50 students has an examination period of 90 minutes, and the average time a student takes to complete the exam is 80 minutes with a standard deviation of 10 minutes, how many students would be expected to be unable to complete the exam in the allotted time?
Answer this question pls due soon
The height of the monitor using Pythagoras theorem is: 13.3 inches
How to use Pythagoras theorem?Pythagoras Theorem is defined as the way in which you can find the missing length of a right angled triangle.
The triangle has three sides, the hypotenuse (which is always the longest), Opposite (which doesn't touch the hypotenuse) and the adjacent (which is between the opposite and the hypotenuse).
Pythagoras is in the form of;
a² + b² = c²
We are given:
Diagonal = 27 inches
Length = 23.5 inches
Thus:
Height is:
h = √(27² - 23.5²)
h = 13.3 inches
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Area of Triangle::
8m
Area of Rectangle (without missing triangle):;
Area of shaded region:
The area of the rectangle is 104 m², area of the triangle is 15 m², and area of the shaded region is equal to 74 m².
How to evaluate for the shaded regionThe shaded region is the remaining area in the rectangle which is outside the triangle, so it is derived by subtracting the area of the triangle from the area of the rectangle as follows:
area of the rectangle = 13 m × 8 m
area of the rectangle = 104 m²
area of the triangle = 1/2 × 5 m × 6 m
area of the triangle = 15 m²
area of the shaded region = 104 m² - 15 m²
area of the shaded region = 89 m²
Therefore, the area of the rectangle is 104 m², area of the triangle is 15 m², and area of the shaded region is equal to 74 m².
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Need answer by 11:45am
Question 8(Multiple Choice Worth 2 points)
(Creating Graphical Representations MC)
The number of milligrams of Vitamin C from 100 different gummy vitamins sold in the world was collected.
Which graphical representation would be most appropriate for the data, and why?
Box plot, because the median can easily be determined from the large set of data
Stem-and-leaf plot, because you can see the shape of the data
Histogram, because it shows each individual data point
Bar chart, because the data is categorical
Unlocked badge showing an astronaut’s boot touching down on the moon
See what the community says and unlock a badge
The graphical representation that is best and most appropriate for the data is Box plot, because the median can easily be determined from the large set of data. That is option A.
What is a box plot ?The box plot is a type of graphical representation of data that gIves more than one detail about the data set such as;
minimum, first quartile, median, third quartile, and maximum.Box plots allow you to compare multiple data sets better than others dues to the above listed features that it has.
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what will increase the width of a confidence interval? increase confidence level. b) increase number in sample c) decrease confidence level. d) decrease variance
Increasing the width of a confidence interval can be achieved by:
a) Increasing the confidence level: A higher confidence level requires a wider interval to capture the true population parameter with greater certainty.
b) Decreasing the number in the sample: A smaller sample size results in less precision and a wider confidence interval due to increased sampling variability.
c) Increasing the variance: A larger variance implies greater dispersion in the data, which requires a wider confidence interval to accommodate the increased uncertainty.
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Increasing the confidence level or decreasing the sample size would increase the width of a confidence interval. c
Conversely, decreasing the confidence level or increasing the sample size would decrease the width of the confidence interval.
Decreasing the variance of the data would also decrease the width of the confidence interval.
As it would make the data points more tightly clustered around the mean, reducing the uncertainty of the estimate.
On the other hand, a smaller confidence level or a larger sample size would result in a narrower confidence interval.
The breadth of the confidence interval would be reduced if the data's volatility was reduced.
The data points would become more closely packed around the mean, lowering the estimate's level of uncertainty.
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The table shows the results for spinning the spinner 50 times. What is the relative frequency for the event "spin a 1"?
Outcome. | 1 | 2| 3 |4
Frequency|16| 16|16|2
Number of trials
50
The relative frequency for the event "spin a 1" is
The relative frequency of spinning a 1 is 0.32 or 32%.
The given table shows the results of spinning a spinner 50 times. The outcomes of the spins are listed in the first column, and the frequencies are listed in the second column. To find the relative frequency of spinning a 1, we need to divide the frequency of spinning a 1 by the total number of trials (50).
According to the table, the frequency of spinning a 1 is 16. Therefore, the relative frequency of spinning a 1 can be calculated as follows:
Relative frequency of spinning a 1 = (frequency of spinning a 1) / (total number of trials)
Relative frequency of spinning a 1 = 16 / 50
Relative frequency of spinning a 1 = 0.32 or 32%
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Help with algebra 2 homework
The estimated radius of the circular object with an area of 40 cm² is 3.57 cm
Writing the inverse function r(A) and estimating the radius of a circular objectTo find the inverse function r(A), we can start by setting A = πr² and solving for r:
A = πr²
A/π = r²
r = √(A/π)
Therefore, the inverse function is r(A) = √(A/π).
To estimate the radius of a circular object with an area of 40 cm², we can simply substitute A = 40 cm² into the inverse function:
r(40) = √(40/π) ≈ 3.57 cm
Therefore, the estimated radius of the circular object with an area of 40 cm² is approximately 3.57 cm
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A side of the triangle below has been extended to form an exterior angle of 67°. Find the value of xx.
Since a side of the triangle below has been extended to form an exterior angle of 67°, the value of x is equal to 52°.
What is the exterior angle theorem?In Mathematics, the exterior angle theorem or postulate can be defined as a theorem which states that the measure of an exterior angle in a triangle is always equal in magnitude (size) to the sum of the measures of the two remote or opposite interior angles of that triangle.
By applying the exterior angle theorem, we can reasonably infer and logically deduce that the sum of the measure of the two interior remote or opposite angles in the given triangle is equal to the measure of angle x (∠x);
∠y + 67° = 180°
∠y = 180° - 67°
∠y = 113°
∠x = 180° - (15° + 113°)
∠x = 52°
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How do you simplify this.
Answer:
[tex] \sqrt{7y} ( \sqrt{27y} + 5 \sqrt{12y} )[/tex]
[tex] \sqrt{7y} ( \sqrt{9} \sqrt{3y} + 5 \sqrt{4} \sqrt{3y} )[/tex]
[tex] \sqrt{7y} (3 \sqrt{3y} + 10 \sqrt{3y} )[/tex]
[tex]13 \sqrt{7y} \sqrt{3y} [/tex]
[tex]13y \sqrt{21} [/tex]
given that the absolute value of the difference of the two roots of $ax^2 + 5x - 3 = 0$ is $\frac{\sqrt{61}}{3}$, and $a$ is positive, what is the value of $a$?
The value of "a" is approximately 1.83 given that the absolute value of the difference of the two roots of the quadratic equation "ax squared plus 5x minus 3 equals 0" is the square root of 61 divided by 3, and "a" is positive.
We are given that the absolute value of the difference between the two roots of the quadratic equation "ax squared plus 5x minus 3 equals 0" is the square root of 61 divided by 3, and "a" is positive. We need to find the value of "a".
Let the two roots of the equation be r1 and r2, where r1 is not equal to r2. Then, we have:
|r1 - r2| = √(61) / 3
The sum of the roots of the quadratic equation is given by r1 + r2 = -5 / a, and the product of the roots is given by r1 × r2 = -3 / a.
We can express the difference between the roots in terms of the sum and product of the roots as follows:
r1 - r2 = √((r1 + r2)² - 4r1r2)
Substituting the expressions we obtained earlier, we have:
r1 - r2 = √(((-5 / a)²) + (4 × (3 / a)))
Simplifying, we get:
r1 - r2 = √((25 / a²) + (12 / a))
Taking the absolute value of both sides, we get:
|r1 - r2| = √((25 / a²) + (12 / a))
Comparing this with the given expression |r1 - r2| = √(61) / 3, we get:
√((25 / a²) + (12 / a)) = √(61) / 3
Squaring both sides and simplifying, we get:
25 / a² + 12 / a - 61 / 9 = 0
Multiplying both sides by 9a², we get:
225 + 108a - 61a² = 0
Solving this quadratic equation for "a", we get:
a = (108 + √(108² + 4 × 61 × 225)) / (2 × 61)
Since "a" must be positive, we take the positive root:
a = (108 + √(108² + 4 × 61 × 225)) / (2 × 61) ≈ 1.83
Therefore, the value of "a" is approximately 1.83.
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The question is -
Given that the absolute value of the difference of the two roots of the quadratic equation "ax squared plus 5x minus 3 equals 0" is the square root of 61 divided by 3, and "a" is positive, what is the value of "a"?