the confidence interval for the mean amount of money spent per household on internet service
each month is $47.45 to $72.45. what is the estimated mean?
internet each
The estimated mean amount of money spent per household on internet service each month is $59.95 with confidence interval.
To calculate the estimated mean amount of money spent per household on internet service each month, we first need to find the lower and upper bounds of the confidence interval. The lower bound is $47.45 and the upper bound is $72.45. We then take the average of these two numbers to get the estimated mean. The average of $47.45 and $72.45 is
($47.45 + $72.45) / 2
= $59.95.
Therefore, the estimated mean amount of money spent per household on internet service each month is $59.95.
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You sold your car for $1,000 which had cost $1,450. How much did you lose expressed as a %?.
Answer:
45%
Step-by-step explanation:
1,450 - 1,000 = 450
the 450 becomes 0.45
to make 0.45 a percent, we multiply it by 100
0.45 x 100 = 45
45%
Find the sum of the first 8 terms of the following series, to the nearest integer.
12, 36, 108, ...
Answer:
The sum of the first 8 terms is 39360
Step-by-step explanation:
A geometric series is a series of numbers that have a common ratio. The series given to us is the following: 12, 36, 108,... We can see that there is a common ratio of 3 (108/36 = 36/12 = 3). Therefore, this series is a geometric series. Since we know that, we can use the sum of geometric series formula to find the sum of the first 8 terms:
\(S_n=\frac{a_1(1-r^n)}{1-r}\)
In this formula, \(S_n\) is the sum of the first n terms of the series (in our case, n would be 8). \(a_1\) is the first term in the series, which is 12 in our case. r is the common ratio between the terms (which is 3). Finally, n is the number of terms, and since we know we are looking for the sum of the first 8 terms, n is 8. Now, we can plug in our known quantities and solve:
\(S_n=\frac{a_1(1-r^n)}{1-r}\\\\S_8=\frac{12(1-3^8)}{1-3}\\\\S_8=\frac{12(1-6561)}{-2}\\\\S_8=-6(-6560)\\\\S_8=39360\)
Therefore, the sum of the first 8 terms is 39360
If p varies inversely as q and p =8 when q=10,find p when q=4
Answer:
20
Step-by-step explanation:
When two numbers vary inversely, they always multiply to the same product, in this case, it is 80, because it is 8 x 10(product of two known values of p and q). This means, for q = 4, we can write:
p * 4 = 80
This means that p is equal to 20.
The value of p is 20 when q=4
What is directly proportional and inversely proportional relationship?Let there are two variables p and q
Then, p and q are said to be directly proportional to each other if
p = kq
where k is some constant number called constant of proportionality.
When two numbers vary inversely, then the will always multiply to the same product,
Here it is 80, because it is 8 x 10
Then product of two known values of p and q).
This means, for q = 4, we can write:
p x 4 = 80
This means that p is 20.
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if a third plane could be drawn which contains both lines a and b .
Answer:
must be parallel
Step-by-step explanation:
They must be parallel.
Draw a rough sketch of a quadrilateral KLMN. State, (a) two pairs of opposite sides, (b) two pairs of opposite angles, (c) two pairs of adjacent sides, (d) two pairs of adjacent angles. please draw the answer
Answer:
Please find attached the drawing of quadrilateral KLMN created with MS Whiteboard using the Ink to Shape command
(a) Two pairs of opposite sides are \(\overline {KN}\), \(\overline {LM}\) and \(\overline {KL}\), \(\overline {NM}\)
(b) Two pairs of opposite angles are ∠LKN, ∠LMN, and ∠KLM and ∠KNM
(c) Two pairs of adjacent sides are \(\overline {KN}\), \(\overline {NM}\) and \(\overline {KL}\), \(\overline {LM}\)
(d) Two pairs of adjacent angles are ∠LKN, ∠KLM and ∠LMN, ∠KNM
Step-by-step explanation:
We collect the impact strength of five pieces of steel. Let "X" be their strengths in foot-pound/inch. Table 1: Impact Strength (ft-lb/in) 1 1 2 3 4 5 5 Point Values 55 56 55 50 46 O pt x-X 2.6 ✓ 3.6 2.6 -2.4 -6.4 0.5 pt each 0.5 pt cach 6.76 12.96 6.76 5.76 40.96 Note: Carry at least 5 decimal precision for any intermediate calculations. Then, for all numeric entries, round your answer to 3 decimal precision - Leading Os don't count : 3 Part 1: (a) Fill in the missing table cells. (b) The Sum of Squares equals: 73.2 C) This variance equals: 18.3 D) The standard deviation equals: 4.278 E) The deviation for the first observations equals: 2.6 F) The Z-score for the fifth observation equals: -1.4961 Z- Part 2: We wish to convert from foot-pound/in to l/m, so let y be the strength in J/m. There is 1 ft-lb/in for every 53.35 J/m. Note that if Y = a*X+b, then y = a*x + b and sy = 32*sx G) - H) s2y = I) Sy = J) The Z-score for the fifth transformed observation is:
Part 1:
(a) Fill in the missing table cells:
Table 1: Impact Strength (ft-lb/in)
1 1 2 3 4 5 5
Point Values
55 56 55 50 46
(b) The Sum of Squares equals: 73.2
(c) This variance equals: 18.3
(d) The standard deviation equals: 4.278
(e) The deviation for the first observation equals: 2.6
(f) The Z-score for the fifth observation equals: -1.4961
Part 2:
We wish to convert from foot-pound/in to J/m, so let y be the strength in J/m. There is 1 ft-lb/in for every 53.35 J/m.
G) -
H) s2y =
I) Sy =
J) The Z-score for the fifth transformed observation is:
Part 1:
(a) The missing table cells are not provided in the question.
(b) The Sum of Squares is calculated by summing the squares of the deviations of each data point from the mean. Since the values are not provided, we cannot calculate the Sum of Squares.
(c) Variance is the average of the squared deviations from the mean. It is calculated by dividing the Sum of Squares by the number of data points. In this case, the variance is given as 18.3.
(d) Standard deviation is the square root of the variance. It is calculated as the square root of the variance. In this case, the standard deviation is given as 4.278.
(e) The deviation for the first observation is provided as 2.6. It represents the difference between the first observation and the mean.
(f) The Z-score for an observation is a measure of how many standard deviations it is away from the mean. The Z-score for the fifth observation is given as -1.4961.
Part 2:
In order to convert from foot-pound/in to J/m, we need to use the conversion factor of 1 ft-lb/in = 53.35 J/m.
G) - The missing value is not provided in the question.
H) The variance of the transformed variable, y, can be calculated by multiplying the variance of the original variable, x, by the square of the conversion factor (a^2). However, since the variance of x is not provided, we cannot calculate s2y.
I) The standard deviation of the transformed variable, y, can be calculated by multiplying the standard deviation of the original variable, x, by the absolute value of the conversion factor (|a|). However, since the standard deviation of x is not provided, we cannot calculate Sy.
J) The Z-score for the fifth transformed observation can be calculated by subtracting the mean of the transformed variable from the fifth transformed observation and then dividing it by the standard deviation of the transformed variable.
However, since the mean and standard deviation of the transformed variable are not provided, we cannot calculate the Z-score.
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Approximate the area under the
function between a and b using a
left-hand sum with the given
number of intervals.
f(x) = x² + 2
a = 0
b= 6
6 intervals
Answer:
67 square units
Step-by-step explanation:
The area using the left-hand sum is the sum of products of the function value at the left side of the interval and the width of the interval.
AreaThe attachment shows a table of the x-value at the left side of each interval, and the corresponding function value there. The interval width is 1 unit in every case, so the desired area is simply the sum of the function values.
The approximate area is 67 square units.
Split up the interval [0, 6] into 6 equally spaced subintervals of length \(\Delta x = \frac{6-0}6 = 1\). So we have the partition
[0, 1] U [1, 2] U [2, 3] U [3, 4] U [4, 5] U [5, 6]
where the left endpoint of the \(i\)-th interval is
\(\ell_i = i - 1\)
with \(i\in\{1,2,3,4,5,6\}\).
The area under \(f(x)=x^2+2\) on the interval [0, 6] is then given by the definite integral and approximated by the Riemann sum,
\(\displaystyle \int_0^6 f(x) \, dx \approx \sum_{i=1}^6 f(\ell_i) \Delta x \\\\ ~~~~~~~~ = \sum_{i=1}^6 \bigg((i-1)^2 + 2\bigg) \\\\ ~~~~~~~~ = \sum_{i=1}^6 \bigg(i^2 - 2i + 3\bigg) \\\\ ~~~~~~~~ = \frac{6\cdot7\cdot13}6 - 6\cdot7 + 3\cdot6 = \boxed{67}\)
where we use the well-known sums,
\(\displaystyle \sum_{i=1}^n 1 = \underbrace{1 + 1 + \cdots + 1}_{n\,\rm times} = n\)
\(\displaystyle \sum_{i=1}^n i = 1 + 2 + \cdots + n = \frac{n(n+1)}2\)
\(\displaystyle \sum_{i=1}^n i^2 = 1 + 4 + \cdots + n^2 = \frac{n(n+1)(2n+1)}6\)
You have 30 chocolate candy but Jayna has 10 more chocolate candy than you and Amy has A what does A equal to ?
Answer:
40
Step-by-step explanation:
so it is just like a regular equation like 30+10=40 but your just finding what A means so 40 yea
E probability of observing the experiment result, a sample mean, for example, or something more unusual just by chance if the null hypothesis is true is the definition of _____________.
The probability of observing the experiment result, a sample mean, for example, or something more unusual just by chance if the null hypothesis is true is the definition of "P-Value."
What is null hypothesis?A null hypothesis is a sort of statistical hypothesis which asserts that there is no statistical significance in a particular set of observations.
Using sample data, hypothesis testing is performed to determine the believability of a theory. It really is expressed as H0 and is also known to simply as "null."
Some key features regarding null hypothesis are-
A null hypothesis is a statistical conjecture that claims there is no variation between particular qualities of a population and data-generating process.The alternate hypothesis asserts the existence of a distinction.Hypothesis testing allows you to reject the null hypothesis with a particular level of confidence.If the null hypothesis can be rejected, it lends support to the alternative hypothesis.The notion of falsity in science is founded on null hypothesis testing.To know more about null hypothesis, here
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7 Given APHS = ACNF, find the values of x, y, and z.F(3y - 1)H (6x - 290°S36°Р115°fc(4z - 32)N
Here, we have two congruent triangles
Since they are congruent, they have similar and equal angles.
From the diagram, we can see that;
6x - 29 = 115 (They are both topmost angles of both triangles)
Solving this, we have;
6x = 115 + 29
6x = 144
divide both sides by 6
x = 144/6
x = 24°
Furthermore, we can see that;
4z - 32 = 36
4z = 36 + 32
4z = 68
z = 68/4
z = 17°
And lastly;
(3y-1) + 115 + (4z-32) = 180 ( sum of angles in a triangle)
Since z = 17, 4z - 32 will be 4(17)-32 = 68 - 32 = 36
Thus;
3y - 1 + 115 + 36 = 180
3y + 150 = 180
3y = 180 -150
3y = 30
divide both sides by 3
y = 30/3
y = 10°
x = 24° , y = 10° and z = 17°
write an equation in slope intercept form of the line that passes through tge points (0,-1) and (5,6)
Answer:
y = 7/5x + -1
Step-by-step explanation:
First let's find the slope. To do that you find the difference between the given coordinate points. The slope I got was 7/5.
Then plug in the x and y values in the formula y = mx + b
6 = 7/5(5) + b
6 = 7 + b
-1 = b
If the y-intercept (b) is -1 we can complete the equation now.
y = 7/5x + -1
Hope that helps and have a great day!
Average room rate for a motel is $80.00. Occupancy is 60% percent. The motel has 80 rooms. Double occupancy rate is 50%. Spread between single and double rates is $5.00. Average single rate is:
To find the average single rate, we need to first calculate the average double rate. The average single rate is $75.00.
Double occupancy rate = 50%
So, the number of double occupancy rooms = 80 x 50% = 40
Occupancy rate = 60%
So, the number of single occupancy rooms = 80 x (100% - 60%) = 32
Total occupancy = number of single occupancy rooms + number of double occupancy rooms = 32 + 40 = 72
Total revenue generated from room rates = average room rate x total occupancy
Total revenue = $80.00 x 72 = $5,760.00
Let the average double rate be x.
Then, the average single rate would be (x - $5.00)
Total revenue from double occupancy rooms = 40 x x = $40x
Total revenue from single occupancy rooms = 32 x (x - $5.00) = $32x - $160.00
Total revenue from room rates = Total revenue from double occupancy rooms + Total revenue from single occupancy rooms
$5,760.00 = $40x + $32x - $160.00
$5,920.00 = $72x
x = $82.22 (rounded to two decimal places)
So, the average double rate is $82.22, and the average single rate would be $77.22 (i.e. $82.22 - $5.00).
To find the average single rate, we'll follow these steps:
1. Calculate the total revenue from the motel rooms.
2. Calculate the revenue from double occupancy rooms.
3. Calculate the revenue from single occupancy rooms.
4. Determine the number of single occupancy rooms.
5. Divide the single occupancy room revenue by the number of single occupancy rooms to find the average single rate.
Step 1: Total revenue
Average room rate = $80.00
Occupancy rate = 60%
Total rooms = 80
Total occupied rooms = 80 * 60% = 48 rooms
Total revenue = 48 rooms * $80.00 = $3,840
Step 2: Double occupancy revenue
Double occupancy rate = 50%
Number of double occupancy rooms = 48 rooms * 50% = 24 rooms
Double occupancy room rate = $80.00 + $5.00 (spread) = $85.00
Double occupancy revenue = 24 rooms * $85.00 = $2,040
Step 3: Single occupancy revenue
Total revenue - Double occupancy revenue = Single occupancy revenue
$3,840 - $2,040 = $1,800
Step 4: Number of single occupancy rooms
Total occupied rooms - Double occupancy rooms = Single occupancy rooms
48 rooms - 24 rooms = 24 rooms
Step 5: Average single rate
Single occupancy revenue ÷ Number of single occupancy rooms = Average single rate
$1,800 ÷ 24 rooms = $75.00
So, the average single rate is $75.00.
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11. Sara borrowed *60,000 from a money lender at 15% rate of interest per annum. What is
the interest she paid after 4 years?
Answer:
36000
Step-by-step explanation:
Given the following
Principal = 60,000
Rate = 15%
Time = 4years
Using the simple interest formula
SI = PRT/100
SI = 60000*15*4/100
SI = 600 * 60
SI = 36,000
Hence the interest paid after 4 years is 36000
plz help asap im being timed and i only have 20 minutes left
Answer:
first question is B
second F
third C
fourth pretty sure its C
last C
Step-by-step explanation:
How do I find the value of h(13)-f(-1) with h(x)= |2-4x| ???
Answer:
72600
Step-by-step explanation:
thats it calculator lng yan
I don't understand how to solve this, please help!
Answer:
x+1 , x<-1
x²-bx-4 , -1≤x≤4
1/2 x +a
substitute x=-1 , continuous everywhere
x+1=x²-bx-4 when x=-1
-1+1=-1²-b-4
1+b-4=0 ⇒ +b-3 ⇒ b=3then for :
x²-bx-4=1/2 x +a for x=4
4²-4b-4=1/2x+a
16-4(3)-4=4/2+a
16-12-4-2=a
a=-2the equations will be :
x+1
x²-3x-4
1/2x-2
I hope this help
Consider what you know about the sampling distribution of the sample proportion. This sampling distribution will become more variable as the sample size increases. O will be Normal in shape only if the sample size is at least 100. O will have a center equal to the population proportion, or p
O has a shape that is skewed to the right, regardless of sample size. O is a collection of the parameters of all possible samples of a particular size taken from a particular populatio
As per the sampling technique, Let us consider what you know about the sampling distribution of the sample proportion. this sampling distribution will have a center equal to the population proportion, or p.
Here we have to find what you know about the sampling distribution of the sample proportion. This sampling distribution will become more variable as the sample size increases.
Here for the given question, let us check all the given statements in the options
Here we know that the shape is approximately normal. Then the given option will be false.
Next, it is collection of all samples taken from the population, So the given option will be false
Now, we have to check as the sample size increases, the value of n increases. here n is the value on the denominator of the equation of standard deviation.
Therefore, due to an increase in the value of n, then there will be decreases in the standard deviation.
Then the less standard deviation means a small variance.
Therefore, as a result, as the sample size grows, the variation will be minimal.
So, the center is the same as the sample proportion p.
Therefore, this is correct.
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Determine whether the stated conclusion is valid based on the given information. If not, write invalid. Explain your reasoning.Given: If Elan stays up late, he will be tired the next day. Elan is tired.
Conclusion: Elan stayed up late.
Based on the explanation below, the conclusion that Elan is tired because Elan stayed up late is invalid.
How do we use reasoning to determine a conclusion?In the question, it is stated that if Elan stays up late, he will be tired the next day.
However, staying up late is not the only thing that could make Elan get tired.
This implies that there are so many other things than can make Elan get tired such as working for long hours.
It is possible that Elan was tired because Elans worked long hours.
By implication, the conclusion is invalid.
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Please help! (look at the image below!!)
The numbers arranged in order from least to greatest is: √146, 12.39, 12.62, 12⅝, and 12¾. The third option is correct.
What is ordering of numbersThe ordering of numbers refers to arranging numbers in a specific sequence based on their magnitude or value. The ordering of numbers is determined by their relative values. Comparisons are made between numbers to determine their position in the order.
12⅝ = 101/8 = 12.645
12.62 = 12.62
√146 = 12.0830
12.39 = 12.39
12¾ = 51/4 = 12.75
Therefore, the numbers arranged in order from least to greatest is: √146, 12.39, 12.62, 12⅝, and 12¾.
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pls pls pls pls help me istg ill be your best friend and give you brianliest and all the points i can give and ill love you forvever pls pls pls pls
a. The chart did not maintain consistent scaling
b. The graph is not the appropriate graph type to display such data
c. The display had inaccurate or distorted visual representations
How do we explain?When the actual data may not support it, changing the scales on the axes might give the appearance of big changes or differences.
The visual effect of data can be exaggerated or minimized, for instance, by adopting a non-linear scale or deleting specific sections of the axis.
So it important to Choose appropriate graph type that best represents the data and the relationship you want to convey.
It also advisable to make use of clear and accurate labeling with descriptive titles and units of measurement.
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You are on a fishing trip with your friends. The diagram shows the location of the river, fishing hole, campsite, and bait store. The campsite is located 200 feet from the fishing hole. The bait store is located 110 feet from the fishing hole. How wide is the river?.
the width of the river is approximately 64.03 feet.
To determine the width of the river, we can use the concept of triangle similarity.
Let's assume that the river width is represented by the variable "x".
From the information given, we have a right triangle formed by the river, the fishing hole, and the campsite. The campsite is located 200 feet from the fishing hole, and the river width is the unknown side.
Using the Pythagorean theorem, we can set up the equation:
x^2 + 200^2 = (200 + 110)^2
Simplifying the equation:
x^2 + 40000 = 44100
x^2 = 44100 - 40000
x^2 = 4100
Taking the square root of both sides:
x = sqrt(4100)
x ≈ 64.03 feet
Therefore, the width of the river is approximately 64.03 feet.
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There are three square gardens whose lengths of the sides are 3 ft, 7ft, and 2 ft respectively. Find the total area of the three gardens in square feet.
65
60
62
64
Answer:
62
Step-by-step explanation:
1. To find the total area, we must find the area of the three individual gardens and sum them together
2. Since the gardens are square, the area is equal to the side length squared
3. Therefore, square the sides and sum:
3^2 = 9
7^2 = 49
2^2 = 4
4+9+49 = 62
a salad dressing is made by mixing yoghurt and mayonnaise in the ratio 3 : 5
karolina makes 800 ml of the salad dressing
how much yoghurt does she use?
give your answer in mililetres (ml)
Answer:
Step-by-step explanation:
The amount of yogurt that Karolina used when making 800 ml of salad is 300 ml.
A salad dressing is made by mixing yoghurt and mayonnaise in the ratio
3:5. For 800 ml of salad:
Amount of yoghurt = (3 / (3 + 5)) * 800 ml = 300 ml
The amount of yoghurt that Karolina used when making 800 ml of salad is 300 ml.
Which of the following is a quadratic function?
A)f(x)=2-7x^2
B)f(x)=4^x
C)f(x)=0x^2+7x-4
D)f(x)=3x+8
Answer:
A.
Step-by-step explanation:
A quadratic equation is raised to a degree of 2. Because there is an \(x^{2}\) term, it is considered a quadratic equation.
Answer:
The curve will touch the x-axis at x = 2, but not pass through it.
Step-by-step explanation:
I got it right on my test.
Suppose that you have 9 coins: 2 dimes, 2 quarters, and 5 nickels. Two coins are selected at random. What is the probability that you choose exactly 30 cents
The probability that you choose exactly 30 cents is 1/3.
What is the probability?To find the probability of choosing exactly 30 cents, we would first find the probability of choosing just a quarter and a nickel. This would be gotten this way:
4/9 * 3/8
= 12/72
= 1/6
The probability of choosing a nickel and a quarter would be:
3/9 * 4/8
= 12/72
= 1/6
Now we add up the probabilities to get the chance of choosing exactly 30 cents and this is:
1/6 + 1/6
= 2/6
=1/3
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The average driving distance (yards) and driving accuracy (percent of drives that land in the fairway) for 8 golfers are recorded in the table to the right. Complete parts a through e below.
Player Distance (yards) Accuracy (%)
1 316.4 46.2
2 303.8 56.9
3 310.7 51.8
4 312.2 53.2
5 295.5 61.8
6 290.8 66.1
7 295.1 60.4
8 295.9 61.6
a. Write the equation of a straight-line model relating driving accuracy (y) to driving distance (x). Choose the correct answer
below.
A. y = β1x2 + β0
B. y = β0 + β1x + ε
C. y = β1x + ε
D. y = β1x
b. Fit the model, part a, to the data using simple linear regression. Give the least squares prediction equation.
^y = (1)________ + (2) __________x
(1) a. 232.4 b. 258.2 c. 271.1 d. 296.9 (2) a.− 0.7639 b. − 0.6975 c. − 0.5979 d. − 0.6643
c. Interpret the estimated y-intercept of the line. Choose the correct answer below.
A. Since a drive with distance 0 yards is outside the range of the sample data, the y-intercept has no practical interpretation.
B. For each additional percentage in accuracy, the distance is estimated to change by the value of the y-intercept.
C. Since a drive with 0% accuracy is outside the range of the sample data, the y-intercept has no practical interpretation.
D. For each additional yard in distance, the accuracy is estimated to change by the value of the y-intercept.
d. Interpret the estimated slope of the line. Choose the correct answer below.
A. Since a drive with distance 0 yards is outside the range of the sample data, the slope has no practical interpretation.
B. For each additional yard in distance, the accuracy is estimated to change by the value of the slope.
C. For each additional percentage in accuracy, the distance is estimated to change by the value of the slope.
D. Since a drive with 0% accuracy is outside the range of the sample data, the slope has no practical interpretation.
e. A golfer is practicing a new swing to increase her average driving distance. If the golfer is concerned that her driving accuracy will be lower, which of the two estimates, y-intercept or slope, will help determine if the golfer's concern is valid?
The (3)_____________ will help determine if the golfer's concern is valid because the (4)________________ determines whether the accuracy increases or decreases with distance.
(3) a.slope b. y-intercept (4) a. sign of the slope b. sign of the y-intercept c. magnitude of the slope d. magnitude of the y-intercept
A. The equation of the straight-line model relating driving accuracy to driving distance is y = β0 + β1x, where y represents driving accuracy, x represents driving distance, β0 represents the y-intercept, and β1 represents the slope.
B. Using the least squares method, the prediction equation for the given data is ^y = 232.4 - 0.7639x, where ^y represents the predicted accuracy for a given distance x.
C. The estimated y-intercept has no practical interpretation since a drive with 0% accuracy is outside the range of the sample data.
D. The estimated slope indicates that for each additional yard in distance, the accuracy is estimated to decrease by 0.7639%.
E. The slope will help determine if the golfer's concern is valid since the sign of the slope determines whether the accuracy increases or decreases with distance.
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HELP ASAP PLEASS
Jane graded an assignment from all the students in one class. She graded a total of 324problems. Find Jane's daily gross earnings.
1-100 problems $0.02 each.
101-200 problems $0.08 each.
over 200 problems $0.12each.
Answer:
I'm assuming #2 but just wanted to make sure.
Step-by-step explanation:
Possibility 1:
100 * 0.02 = 2.00
100 * 0.08 = 8.00
124 * 0.12 = +14.88
$24.88
Possibility 2:
324 * 0.12 = $38.88
The rule of the derivative of a function is given. Find the location of all points of inflection of the function f.
f'(x) = (x - 2)(x-4)(x - 5) a. 2,4,5 b. 3.67 c. 4 d. 11- √7/3 + 11+ √7/3
The location of all points of inflection of the function f'(x) = (x - 2)(x-4)(x - 5) are option (d) 11- √7/3, 11+ √7/3.
To find the points of inflection of the function f, we need to find its second derivative and set it equal to zero, and then solve for x. If the second derivative changes sign at x, then x is a point of inflection.
Taking the derivative of f'(x), we get
f''(x) = 3x^2 - 22x + 32
Setting f''(x) = 0, we get
3x^2 - 22x + 32 = 0
We can solve this quadratic equation using the quadratic formula
x = [22 ± sqrt(22^2 - 4(3)(32))] / (2*3)
x = [22 ± sqrt(244)] / 6
x = (11 ± sqrt(61))/3
Therefore, the points of inflection of the function f are
x = (11 - sqrt(61))/3 ≈ 0.207
x = (11 + sqrt(61))/3 ≈ 3.793
So the answer is (d) 11- √7/3, 11+ √7/3.
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The location of all points of inflection of the function f'(x) = (x - 2)(x-4)(x - 5) are option (d) 11- √7/3, 11+ √7/3.
To find the points of inflection of the function f, we need to find its second derivative and set it equal to zero, and then solve for x. If the second derivative changes sign at x, then x is a point of inflection.
Taking the derivative of f'(x), we get
f''(x) = 3x^2 - 22x + 32
Setting f''(x) = 0, we get
3x^2 - 22x + 32 = 0
We can solve this quadratic equation using the quadratic formula
x = [22 ± sqrt(22^2 - 4(3)(32))] / (2*3)
x = [22 ± sqrt(244)] / 6
x = (11 ± sqrt(61))/3
Therefore, the points of inflection of the function f are
x = (11 - sqrt(61))/3 ≈ 0.207
x = (11 + sqrt(61))/3 ≈ 3.793
So the answer is (d) 11- √7/3, 11+ √7/3.
Learn more about points of inflection here
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A coin is tossed three times. what is the probability that the coin will land heads at least twice?
The probability that the coin will land heads at least twice when tossed three times is 3/8.
The question is asking for the probability that a coin will land heads at least twice when tossed three times.
To find this probability, we can use the concept of binomial probability.
Determine the total number of possible outcomes when tossing a coin three times. Since each toss has two possible outcomes (heads or tails), the total number of possible outcomes is \(2^3\) = 8.
Determine the number of favorable outcomes where the coin lands heads at least twice. There are three possible scenarios where the coin can land heads at least twice: HH, HHT, HTH, where H represents heads and T represents tails. So, there are 3 favorable outcomes.
Calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes. Probability = favorable outcomes / total outcomes = 3 / 8.
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