Answer:
The answer is 8 dimes
Step-by-step explanation:
4 quarters x 2 = 8
8 dimes
1.00 + 0.80 = $1.80
How is field data aggregated? Number of failed parts Number of failures Hours of operation Maintenance time Mark for follow up Question 3 of \( 7 . \) Data collection extends over a large number of it
Field data aggregation is the process of summarizing, combining, and analyzing data that has been collected from various sources. The following are some of the common ways that field data is aggregated: Count of Failures: A count of how many times a failure has occurred within a given period of time,
such as a day or a week. Number of Failed Parts: The number of parts that have failed over a given period of time, such as a day or a week. Hours of Operation: The amount of time that a machine or system was operational during a given period of time, such as a day or a week. Maintenance Time: The amount of time that was spent maintaining a machine or system during a given period of time, such as a day or a week.
Mark for Follow-Up: An indication of which issues need to be addressed or followed up on to prevent future failures or improve performance. Field data aggregation is the process of summarizing, combining, and analyzing data that has been collected from various sources. The following are some of the common ways that field data is aggregated: Count of Failures: A count of how many times a failure has occurred within a given period of time,
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Graph by using the table of values
I hope the screenshots help, for future references you can you Desmos graphing calculator.
HELPPPPPP!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
A) gemma puts 7 rocks into each of her 8 gardens
Step-by-step explanation:
Otis is cutting a long piece of wood trim into smaller pieces for an art project. the line plot shows the length of the smaller pieces of wood.
1/3 has 5 x
1/2 has 4 x
2/3 has 2 x
how many pieces of wood will be at least 1/2 foot in length?
The pieces of wood will be at least 1/2 foot in length and will be 6.
What is the difference between a ratio and a proportion?A ratio is an ordered pair of integers a and b expressed as a/b, with b never equaling 0. A percentage is a mathematical expression in which two ratios are specified to be equal.
1/3 has 5 x
1/2 has 4 x
2/3 has 2 x
Pieces that are 1/2 the length and 1/3 the length;
4 pieces with a length of 1/2 feet.
2 pieces have a length of 2.3 feet.
Pieces at least half a foot long:
⇒4 + 2 = 6
Hence, the pieces of wood are at least 1/2 foot in length and will be 6.
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The faces of a net are labeled A, B, C, D, E, and F as shown below.
A and C, E and F, and B and D are parallel faces.
All the figures below show the solid formed from the net:
c and d are correct.
What are parallel lines?Lines in a plane that are consistently spaced apart are known as parallel lines. Parallel lines don't cross each other.
Given:
The faces of a net are labeled as A, B, C, D, and F.
(a) When the net is folded into a solid,
A and C, E and F, and B and D are parallel faces.
(b) All the figures below show the solid formed from the net:
c and d are correct.
Therefore, all the required values are given above.
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Two joggers run 6 miles south and then 5 miles east. What is the shortest distance they must travel to return to their starting point?
The shortest distance the joggers must travel to return to their starting point is 7.81 miles.
To find the shortest distance the joggers must travel to return to their starting point, we can use the Pythagorean theorem, as the southward and eastward distances form a right triangle. The theorem states that the square of the length of the hypotenuse (the shortest distance, in this case) is equal to the sum of the squares of the other two sides:
a^2 + b^2 = c^2
Here, a is the southward distance (6 miles), and b is the eastward distance (5 miles). We need to find c, the hypotenuse.
(6 miles)^2 + (5 miles)^2 = c^2
36 + 25 = c^2
61 = c^2
Now, take the square root of both sides to find c:
c = √61
c ≈ 7.81 miles
A shoe dealer purchased net Birr 8,000 worth of shoes from a shoe company.A Find the amount it is to pay the company including VAT.BIf the dealer sold the shoes for Birr 12,000, find the amount of VAT liable tothe dealer.
Answer:
A) Total amount to be paid = Birr 8,560
B) Amount of VAT liable to the dealer = Birr 520
Step-by-step explanation:
The tax on bought commodity and the tax on sold commodity isn't provided but in some places, these values are 7% and 9% respectively. So, these are the values that will be used for this question.
Note that these values vary from country to country and the value missing from this question will not change how the question is solved; the question will still be solved in a similar manner, only the parameters will vary.
A) The dealer bought Birr 8000 at 7% tax.
Total amount to be paid = cost price (1 + r%)
r = 7% = 0.07
Total amount to be paid = 8000 × 1.07 = Birr 8,560
B) To find the VAT, it is the difference between the tax paid when the good was bought and the tax put on it after it was sold.
Tax paid when the shoes were bought = 7% of cost price = 7% × 8,000 = Birr 560
Tax paid when the shoes were sold = 9% of selling price = 9% × 12,000 = Birr 1,080
VAT = tax recovered on sale - Tax paid on purchase
VAT = 1080 - 560 = Birr 520
Hope this Helps!!!
Miguel ran 2 9 10 miles on Monday. On Friday, Miguel ran 5 times as far as he did on Monday. How much farther did Miguel run on Friday than he did on Monday? Miguel ran miles farther on Friday
Answer:
\(11\dfrac{3}{5}$ miles\)
Step-by-step explanation:
Miguel ran \(2\dfrac{9}{10}\) miles on Monday.
On Friday, he ran 5 times as far as he did on Monday.
Miles run on Friday
\(=5 X 2\dfrac{9}{10}\)
\(=5 X \dfrac{29}{10}\\=\dfrac{29}{2}$ miles\)
Difference in Number of Miles Run
\(=\dfrac{29}{2}-\dfrac{29}{10}\\=\dfrac{145-29}{10}\\=\dfrac{116}{10}\\=11\dfrac{3}{5}$ miles\)
Therefore, Miguel ran \(11\dfrac{3}{5}$ miles\) farther on Friday.
Please help me LOLZ thannsss
yes it can a triangle does not need to have the same length on each side as long as there is 3 points, angles, and sides.
Answer:
yes,
Step-by-step explanation:because a triangle doesnt have to have the same length on each side as long as there is 3 points, angles, and sides. hope it helps!
we are 95% confident that the true population regression line (i.e. slope) will fall between: question 10 options: a) 18.169 and 27.690 b) .007 and .174 c) 2.245 and 27.690 d) none of the above
Option A: 18.169 and 27.690.
The confidence interval for the true slope of the population regression line is (0.2, 0.4), indicating that we are 95% confident that the true slope falls within this interval.
What is Statistics?
Statistics is the branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data
In regression analysis, a regression line is a straight line that describes how a response variable y changes as an explanatory variable x changes. The slope of the regression line represents the change in the response variable y per unit change in the explanatory variable x.
Sure, here is a numerical example:
Suppose we want to estimate the relationship between height and weight among adults, and we collect a sample of 100 adults and measure their height and weight. We can use linear regression to model the relationship between these variables, and estimate the slope and intercept of the population regression line.
Suppose the slope of the true population regression line is unknown, but we calculate a 95% confidence interval for it based on the sample data, and obtain the interval (0.2, 0.4). This means that we are 95% confident that the true slope of the population regression line falls between 0.2 and 0.4.
If we were to repeat the sampling process many times and construct confidence intervals in the same way, we would expect that about 95% of those intervals would contain the true value of the population slope. However, we cannot be completely certain that the true value falls within this interval, as there is always some degree of uncertainty in statistical inference.
In the given question, the statement "we are 95% confident that the true population regression line (i.e. slope) will fall between" implies that a confidence interval is being constructed for the true slope of the regression line. The four options represent different intervals for the true slope, and only one of them can be correct.
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To convert a temperature measured in degrees Fahrenheit to degrees Celsius, there is a formula
C=5/9(F-32)
where C represents the temperature in degrees Celsius and F represents the temperature in degrees Fahrenheit.
If a temperature is 113`F, what is that temperature measured in Celsius?
Answer:
113`F= 46.11° Celsius
Step-by-step explanation:
(Celsius°C × 9/5) + 32 = Fahrenheit
(Celsius°C × 9/5) + 32 = 113
(Celsius°C × 9/5) = 113 - 32
(Celsius°C × 9/5) = 83
Celsius = 5(83)/9
Celsius = 46.11° Celsius
\(\\ \tt\hookrightarrow C=5/9(F-32)\)
\(\\ \tt\hookrightarrow C=5/9(113-32)\)
\(\\ \tt\hookrightarrow C=5/9(81)\)
\(\\ \tt\hookrightarrow C=5(9)\)
\(\\ \tt\hookrightarrow C=45°C\)
Having some problems with this
Answer: C) 5
Step-by-step explanation:
First let's distribute the left side of the equation.
2/3a - 9 1/3 = -3(a-3)
Then let's distribute the right side of the equation.
2/3a - 9 1/3 = -3a + 9
Then let's move all the a's to one side, and all the constants to the other.
3 2/3a = 18 1/3
Then divide both sides of the equation by 3 2/3.
a = 5
Hope it helps <3
A professor counted the number of words students used to answer an essay question. Create a ranked frequency distribution of these data.
245 261 289 222 291 289 240 233 249 200
A ranked frequency distribution of data can be created by sorting the data in ascending or descending order and then counting the frequency of each value.
The given data set is 245, 261, 289, 222, 291, 289, 240, 233, 249, and 200. To create a ranked frequency distribution of this data set, we first need to sort it in ascending or descending order. Let's sort it in ascending order:200, 222, 233, 240, 245, 249, 261, 289, 289, 291 Next, we need to count the frequency of each value. We can do this by going through the data set and counting how many times each value occurs. Here is the frequency distribution table:Value Frequency 200 1222 1233 1240 1245 1249 1261 1289 2291 1 From this table, we can see that the most frequent value is 289, which occurs twice. We can also see that the least frequent values are 200, 222, 233, and 240, which each occur only once.
In conclusion, a ranked frequency distribution of data can be created by sorting the data in ascending or descending order and then counting the frequency of each value. This allows us to see which values are most and least frequent in the data set.
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Given that ∠ADC≅∠BCD, AC⊥CD and BD⊥CD, which of the following proves that △ACD≅△BDC?
Answer:
1. ∠ADC≅∠BCD (Given)
2. AC¯¯¯¯¯⊥CD¯¯¯¯¯; BD¯¯¯¯¯⊥CD¯¯¯¯¯ (Given
)3. ∠ACD and ∠BDC are right angles(Def. of ⊥)
4. ∠ACD≅∠BDC (Rt. ∠≅Thm.)
5. CD¯¯¯¯¯≅CD¯¯¯¯¯ (Reflex. Prop. of ≅)
6. △ACD≅△BCD (ASA Steps 1, 5, 4)
△ACD and △BCD are Congruent triangles because Two angles are the same, as is a corresponding side.
What is of congruent triangle?Congruent triangles have comparable sides and angles that are equal. The symbol "≅" represents congruence.The three sides are all the same (SSS: side, side, side)Two angles are the same, as is a corresponding side (ASA: angle, side, angle)We know that two triangles are congruent if all of their sides are the same— thus side, side, side (SAS: side, angle, side). We also know they are congruent if we have a side, an angle between the sides, and another congruent side—so side, angle, side.1. ∠ADC≅∠BCD (Given)
2. AC⊥CD; BD⊥CD (Given
3. ∠ACD and ∠BDC are right angles(Def. of ⊥)
4. ∠ACD≅∠BDC (Rt. ∠≅Thm.)
5. CD≅CD (Reflex. Prop. of ≅)
6. △ACD≅△BCD
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Connie received $20 for her birthday from her grandparents. She used the money to buy an ice cream cone for herself and one for each of her four best friends. If each cone cost $3.15, how much money does Connie have left?
Answer:
4.25
Step-by-step explanation:
she has a total of 20 dollars and she wats to buy ice cream each at 3.15 for a total of 5 people including her self.
so 3.15(5) is 15.75
then subtract 15.75 from 20
20 - 15.75 = 4.25
I will give brainliest
A cube shaped rock has a volume of 512in3. What is the length of the rock?
Show work
Answer:
8
Step-by-step explanation:
since it is a cube the all sides are equal
v=a³
512 = a³
a=³√512
a=8
the length of the rock=8
Find the selling price. Cost to store: $20 Mark-up: 15% What is the selling price?
Answer:
$23
Step-by-step explanation:
First, we find what is 15% of $20.
0.15 times 20 is 3. Therefore, we know there was a markup of $3.
Then, we add the mark-up to the cost to store, and get $23.
So, the selling price is $23.
Does any one know how to do determining the GFC
Answer:
Yes, GCF stands for (greatest common factor)
so to find it do this:
List the prime factors of each number.
Circle every common prime factor — that is, every prime factor that's a factor of every number in the set.
Multiply all the circled numbers. The result is the GCF.
Step-by-step explanation:
The probability rate in a certain group is 3. 5. Determine the probability that a batch will trst negative.
QUESTION 4 Mary uses the formula below to calculate the cost of electricity on a prepaid meter. Cost = R2,55 x number of kWh of electricity used NOTE: 1 kilowatt 1 000 watt Use the formula above to answer the questions that follow. 4.1 Write down the tariff for electricity consumption. 4.2 Use the formula to calculate the cost of electricity for 80 kWh. 4.3 4.4 Suggest one way of saving the electricity. The heating element in an oven uses approximately 1 500 watts of electricity per hour' 4.4.1 Calculate the Kilowatts of electricity the oven uses per hour. 4.4.2 Mary has R55,00 worth of electricity. She bakes for 4 hours. Calculate the amount of money left on the metre after baking. TOTAL MARKS: 50 (2) (2) (2) (2) (6) [14]
4.1 The tariff for electricity consumption is R2.55 per kilowatt-hour (kWh).
4.2 The cost of electricity for 80 kWh is R204
4.3 One way of saving electricity is by ensuring energy-efficient practices such as putting off lights, electronics, and appliances when not in use and using LED or other energy-efficient light bulbs.
4.4.1 The oven uses 1.5 kilowatts of electricity per hour.
4.4.2 The amount of money left on the meter after baking for 4 hours is R39.70.
How to estimate the cost of electricity?4.2 To calculate the cost of electricity for 80 kWh, we shall use the formula:
Cost = R2,55 x number of kWh of electricity used:
Cost = R2,55 x 80
= R204
Therefore, the cost of electricity for 80 kWh is R204.
4.4.1 We calculate the kilowatts (kW) of electricity the oven uses per hour, by converting the watts to kilowatts.
1 kilowatt (kW) = 1000 watts
Oven uses 1500 watts each hour, so we convert:
1500 watts = 1500/1000 = 1.5 kilowatts (kW)
So, the oven uses 1.5 kilowatts of electricity per hour.
4.4.2 If Mary has R55,00 worth of electricity and bakes for 4 hours, we compute the cost of electricity used during baking.
Cost of electricity used for baking = Cost per kWh x number of kWh used
= R2,55 x (1.5 kW x 4 hours)
= R2,55 x 6 kWh
= R15.30
Next, we estimate the amount of money left on the meter after baking:
Amount left on meter = Initial amount - Cost of electricity used
= R55.00 - R15.30
= R39.70
Hence, Mary will have R39.70 left on the meter after baking for 4 hours.
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Use the Law of Sines to solve (if possible) the triangle for the value of c. Round answers to the nearest tenths. A = 27.5°, a = 15.0 cm, b = 36.4 cm
The law of sines cannot be used to calculate the side c.
How to solve for side c?The given parameters are:
A = 27.5°, a = 15.0 cm, b = 36.4 cm
Based on the above values,
The law of sines cannot be used to calculate the side c.
This is so because the angle C is not given
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Which pair of triangles can be proved congruent by SSS?
Answer:
My answer is B and C
Step-by-step explanation:
If you put B in the same dimension, all the sides are equal. Similarly for part C, since the sides are the same, the base of the triangles are the same lengtg
Which of the following equations represents the graph shown?
Answer:
ok from looking at this equation we can we that every it goes 1 up and on over so
-x+2
Hope This Helps!!!
Mr. Lee's plant is 5 1/2 inches tall. It is 1 7/10 inches taller than Sally's plant.
How tall is Sally's plant?
Enter your answer as a simplified mixed number by filling in the boxes.
please answer!!! i need to get a A on this unit test
The height of Sally's plant in mixed fraction form will be equal to 3 4/5 inches.
What are arithmetic operations?The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or even more quantities.
They cover topics like the study of integers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry.
As per the given information in the question,
Height of Lee's plant = 5 1/2 = 11/2
Let the height of Sally's plant be x.
Lee's plant is 1 7/10 taller than Sally's plant.
Then, the height of Sally's plant will be,
x = 11/2 - 17/10
Take LCM as 10
x = (55 - 17)/10
x = 38/10 = 19/5 inches
It can be written in the mixed fraction form as 3 4/5.
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which is greater 0.4 or 0.33
Answer:
0.33
Step-by-step explanation:
Answer: 0.33 = 33/10 0.4 = 4/10 So, 33/10 is greater than 4/10. That means 0.33 is greater than 0.4.
Operations Composition and Inverses of Functions Assignments Part 1: Operations of Functions Perform the given operations on Functions 1. Given f(x) = x² + 7x + 12 and g(x)=x²-9 Find (f+g)(x), (f-g)(x), (-9)(x), and ((x). 2. Given f(x) = 2x + 1 and g(x)=x-3 Find (f + g)(x), (f-g)(x), (f-g)(x), and ()(x). Part 2: Compositions of Functions Perform the given operations. 3. If f(x) = x², g(x) = 5x, and h(x) = x +4, find each value. Find f[h(-9)]. 4. If f(x)=x², g(x) = 5x, and h(x)=x+4, find each value. Find hif(4)]. 5. If f(x)=x², g(x) = 5x, and h(x) = x +4, find each value. Find g[h(-2)]. 6. The formula f = converts inches n to feet f. and m = 5280 converts feet to miles m. Write a composition of functions that converts inches to miles. Part 3: Inverses of Functions 7. Find fg and gᵒf, if they exist. f = {(-4,-5), (0, 3), (1,6)} and g = {(6, 1).(-5,0), (3,-4)). 8. Find [gh](x) and [hg](x), if they exist. g(x) = x + 6 and h(x) = 3x². 9. Find the inverse of this relation. {(-5,-4), (1,2), (3,4), (7,8)) 10. Find the inverse of each function. Then graph the function and its inverse. g(x) = 3+x
Part 1: Operations of Functions
1. Given f(x) = x² + 7x + 12 and g(x) = x² - 9, we can perform the operations as follows:
(a) (f + g)(x):
(f + g)(x) = f(x) + g(x)
= (x² + 7x + 12) + (x² - 9)
= 2x² + 7x + 3
(b) (f - g)(x):
(f - g)(x) = f(x) - g(x)
= (x² + 7x + 12) - (x² - 9)
= 16x + 21
(c) (-9)(x):
(-9)(x) = -9x
(d) ((x):
((x) is not specified. Please provide the correct function to perform the operation.
2. Given f(x) = 2x + 1 and g(x) = x - 3, we can perform the operations as follows:
(a) (f + g)(x):
(f + g)(x) = f(x) + g(x)
= (2x + 1) + (x - 3)
= 3x - 2
(b) (f - g)(x):
(f - g)(x) = f(x) - g(x)
= (2x + 1) - (x - 3)
= x + 4
(c) (f * g)(x):
(f * g)(x) is not specified. Please provide the correct operation to perform.
(d) ()(x) is not specified. Please provide the correct function to perform the operation.
Part 2: Compositions of Functions
3. Given f(x) = x², g(x) = 5x, and h(x) = x + 4, we can find the value of f[h(-9)] as follows:
f[h(-9)] = f(-9 + 4) = f(-5) = (-5)² = 25
4. Given f(x) = x², g(x) = 5x, and h(x) = x + 4, we can find the value of h∘f(4) as follows:
h∘f(4) = h(f(4)) = h(4²) = h(16) = 16 + 4 = 20
5. Given f(x) = x², g(x) = 5x, and h(x) = x + 4, we can find the value of g[h(-2)] as follows:
g[h(-2)] = g(-2 + 4) = g(2) = 5(2) = 10
6. The formula f = converts inches n to feet f, and m = 5280 converts feet to miles m. The composition of functions that converts inches to miles can be written as m∘f, where m is applied first and then f.
m∘f(n) = m(f(n)) = m(n/12) = n/(12*5280)
Part 3: Inverses of Functions
7. Given f = {(-4,-5), (0,3), (1,6)} and g = {(6,1), (-5,0), (3,-4)}, we can find fg and g∘f, if they exist.
(a) fg:
To find fg, we need to perform the composition of functions fg(x) = f(g(x)).
fg(x) = f(g(x)) = f(1
) = 6
(b) g∘f:
To find g∘f, we need to perform the composition of functions g∘f(x) = g(f(x)).
g∘f(x) = g(f(x)) = g(x²) is not defined since there is no mapping for x² in g.
8. Given g(x) = x + 6 and h(x) = 3x², we can find [gh](x) and [hg](x), if they exist.
(a) [gh](x):
To find [gh](x), we need to perform the composition of functions [gh](x) = g(h(x)).
[gh](x) = g(h(x)) = g(3x²) = 3x² + 6
(b) [hg](x):
To find [hg](x), we need to perform the composition of functions [hg](x) = h(g(x)).
[hg](x) = h(g(x)) = h(x + 6) = 3(x + 6)² = 3(x² + 12x + 36) = 3x² + 36x + 108
9. To find the inverse of the relation {(-5,-4), (1,2), (3,4), (7,8)}, we need to swap the x and y values to obtain the inverse relation:
Inverse relation: {(-4,-5), (2,1), (4,3), (8,7)}
10. To find the inverse of the function g(x) = 3 + x, we need to interchange x and y and solve for y:
y = 3 + x
Interchanging x and y:
x = 3 + y
Solving for y:
y = x - 3
The inverse function of g(x) = 3 + x is g^(-1)(x) = x - 3.
Graphically, the function g(x) = 3 + x and its inverse g^(-1)(x) = x - 3 can be represented by plotting the points and reflecting them across the line y = x.
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Members at a popular fitness club currently pay $40 per month to be a member of the club. The owner of the increa 95% $50. club wants to raise the fee to $50 but is concerned that some members will quit if the fee ses. To investigate, the owner plans to survey a random sample of the members and construct a confidence interval for the proportion of all members who would quit if the fee was increased to
(a) Explain the meaning of "95% confidence" in the context of the study.
(b) After the owner conducted the survey, he calculated the confidence interval to be 0.18 0.075 Interpret this interval in the context of the study.
(c) According to the club's accountant, the fee increase will be worthwhile if fewer than 20% of the members quit. According to the interval from part (b), can the owner be confident that the fee increase will be worthwhile? Explain.
(d) One of the conditions for calculating the confidence interval in part (b) is that and. Explain why it is necessary to check this condition.
a) The meaning of "95% confidence" in the context of the study is:
If they did many samples with the same method, they would expect 95% of them to be within the interval of proportion who will quit.
b) The Interpretation of this interval in the context of the study is:
We are 95% confident that the interval from 0.105 to 0.255 includes the actual proportion of all members who will quit.
c) No, the owner cannot be confident that the fee increase will be worthwhile because not all of the interval is below 0.2 and as such it is possible that more than 20% would quit.
d) It is necessary to check this condition because this condition tells us that the sample has a distribution that is approximately normal allowing us to perform calculations if the distribution is not approximately normal, we can't calculate the z-critical value.
How to Interpret the confidence Interval?A confidence interval in statistics refers to the probability that a population parameter falls between a set of values over a specified period of time. Analysts often use confidence intervals that span 95% or 99% of the expected observations.
A confidence interval in statistics refers to the probability that a population parameter falls between a set of values over a specified period of time. Analysts often use confidence intervals that include 95% or 99% of the expected observed values.
a) The meaning of "95% confidence" in the context of the study is:
If they did many samples with the same method, they would expect 95% of them to be within the interval of proportion who will quit.
b) The Interpretation of this interval in the context of the study is:
We are 95% confident that the interval from 0.105 to 0.255 includes the actual proportion of all members who will quit.
c) No, the owner cannot be confident that the fee increase will be worthwhile because not all of the interval is below 0.2 and as such it is possible that more than 20% would quit.
d) It is necessary to check this condition because this condition tells us that the sample has a distribution that is approximately normal allowing us to perform calculations if the distribution is not approximately normal, we can't calculate the z-critical value.
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please help i was struggling
Answer:
slope is 2 y intercept 7
Step-by-step explanation:
The y intercept is the value when x =0
(0,7) means the y intercept is 7
We can find the slope using
m = (y2-y1)/(x2-x1)
m = ( 11-9)/(2-1)
= 2/1
= 2
-5 -4 -3 -2
I
Y
5-
4+
3
2+
1
-2
-34
-5
1
→x
2 3 4 5
Find the inequality represented by the
graph.
Answer:
Based on these observations, the inequality represented by the graph is y > mx + b, where m is a positive number and b is a negative number.
Step-by-step explanation:
The graph represents a linear function. To find the inequality, we can find the equation of the line in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
From the graph, it can be seen that the slope of the line is positive, which means that as x increases, y also increases. Also, the y-intercept is negative, which means that the line crosses the y-axis at a negative value.
Based on these observations, the inequality represented by the graph is y > mx + b, where m is a positive number and b is a negative number.
Note that the exact values of m and b can be found by using two points on the line and solving for the slope and y-intercept using the formula for a line.
A ladder reaches 10ft up the wall. It makes a 56 degree angle with the ground. How far away from the wall is the base of the ladder
The required distance of the ladder base from the wall is given as 6.74 ft.
Given that,
A ladder reaches 10ft up the wall. It makes a 56-degree angle with the ground.
These are the equation that contains trigonometric operators such as sin, cos.. etc.. In algebraic operations.
Here,
Vertical height [h] = 10
Angle made by the ladder with the base = 56°
Let the base length be x,
Now,
tan 56° = 10 / x
x = 10 / tan 56°
x = 6.74
Thus, the required distance of the ladder base from the wall is given as 6.74 ft.
Learn more about trigonometry equations here:
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