The inequality with the set of solutions (-14, infinity ) can be expressed as follows: x > -14
What is an inequality?Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.
Any value of x bigger than -14 will fulfill the inequality, according to this inequality, and the solution set contains all real numbers greater than -14 but excluding -14.
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Mary will need to pay National Insurance on her new salary at a rate of 12.5% per month and she also contributes to her pension at a monthly rate of 3.4%
How much will Mary have to pay in National insurance?
The amount of money that Mary has to pay in National insurance with salary X will be 0.125X.
Given that:
Mary must pay National Insurance on her new salary at a rate of 12.5% per month, and she must also make pension contributions at a rate of 3.4% per month.
Assuming Mary's monthly salary is X, then her National Insurance contribution would be:
National Insurance = 0.125X
The amount of money that Mary has to pay in National insurance with salary X will be 0.125X.
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14) Cliff selects a letter tile at random from a bag with 5 tiles labeled A, E, I, O, and U. Then he
replaces the tile and mixes them in the bag. He repeats this 100 times and records the results
in a frequency table. Devon spins the spinner shown below 100 times and records his results
in a frequency table. Describe what you would expect to see in a frequency bar graph for
each experiment. Explain your reasoning.
For the experiment by Cliff, the bar graph will most likely have the same height for the number of times each letter appears.
For the experiment by Devon, the bar graph will most likely have the same height for the number of times the letter A, E, and U appears and the same height for the number of times O and I appear. However, the height of the bar graphs for O and I will most likely be half that of A, E, and U.
What is the probability of the letters appearing?For the experiment by Cliff, the probability of the letters appearing is given below:
Probability = number of times each letter is picked/total number of times letters are pickedThe letters have equal chances of being picked, hence, their probabilities are equal.
Probability = 1/5
For the experiment by Cliff, the probability of the letters appearing is given below:
Probability = number of times each letter is picked/total number of times letters are pickedThe letters A, E, and U have equal chances of being picked, hence, their probabilities are equal.
P(A) = 1/4
P(E) = 1/4
P(U) = 1/4
The letters O and I have equal chances of being picked, hence, their probabilities are equal.
P(O) = 1/8
P(I) = 1/8
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https://quiz-api-production-s3-uploads-9bc92eovor5s.s3.amazonaws.com/item_media/004138cb-9081-45ca-8b39-d4f0881a97ac/ef6c0c5f-b93a-4e25-9e95-52a7b6e12e7f
Answer:
It is B
Step-by-step explanation:
I just know :D
Find the measure of each angle in the triangles shown.
The measure of each angle in the triangle is 60 degrees each
How to determine the measure of the angleTo determine the measure of the angles, we need to note that the sum of the angles in a triangle is equal to 180 degrees.
This is represented as;
<A + <B + <C = 180
From the information given in the diagram, we have;
Then, we have that;
2x - 120 + x - 30 + 1/2x + 15 = 180
add the like terms
2x + x + x/2 = 180 + 120 + 30 - 15
Add or subtract the like terms
3x + x/2 = 315
6x + x/2 = 315
cross multiply the values
7x = 630
Divide both sides by the coefficient
x = 90
Then, the angles are;
2x - 120 = 60 degrees
x/2 + 15 = 60 degrees
x - 30 = 60 degrees
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You owe $2,154.35 on your PBnJ credit card that has an interest rate of 9.85% APR. Rather than placing $435.00 into a savings account earning a 2.5% APR, you pay down the principal at the beginning of the month on the credit card. How much interest did you save? (Hint: Calculate the difference between the interest you would earn from the savings account and the interest you would pay on your credit card for the
Using the monthly interest rate and the principal given the interest saved is -$16.8 which shows that nothing was saved.
How much interest was saved?To find the interest saved, let's calculate the interest paid on the credit card.
Monthly interest = 9.85 / 12 = 0.82%
The monthly interest rate on the card is 0.82%
For that particular month, the interest charged will be;
Interest = 2154.35 * 0.0082 = $17.7
However, the interest earned on the savings account will be;
Interest = 2.5 / 12 = 0.21%
We can calculate the interest earned as;
Interest = 0.0021 * 435 = $0.91
The interest saved can be calculated as 0.91 - 17.7 = -16.8
This shows that nothing was saved as the interest earned is lower than the interest charged.
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the set of odd integer Integer
The set of odd integers between three and five can be found to be D. A null set.
What are odd integers ?An odd number is defined as an integer that cannot be split exactly by two. For example: 1, 3, 5, 7, and so on.
We are asked about the set of odd integers ranging from 3 to 5. Because the question asks for odd numbers between 3 and 5, 3 and 5 will not be considered in the set.
This indicates that 3 and 5 are out. We are left with only one even number, four.
As a result, the set of odd integers between 3 and 5 is a Null Set (it contains no numbers).
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The full question is:
What is the set of odd integers between three and five?
4
3,4,5
all reall numbers
null set
The area of a triangle with vertices (6, 6), (2, 4), and (0, 8) is ________ square units.
the area of the triangle with vertices (6, 6), (2, 4), and (0, 8) is 2 square units.
Why is it?
To find the area of a triangle given its vertices, we can use the formula:
Area = 1/2 × |x1×(y2-y3) + x2×(y3-y1) + x3×(y1-y2)|
where x1: $x_1$
x2: $x_2$
y1: $y_1$ are the coordinates of the vertices.
Using this formula and plugging in the given coordinates, we get:
Area = 1/2 × |6×(4-8) + 2×(8-6) + 0×(6-4)|
Simplifying:
Area = 1/2 × |-8 + 4 + 0|
Area = 1/2 × 4
Area = 2 square units
Therefore, the area of the triangle with vertices (6, 6), (2, 4), and (0, 8) is 2 square units.
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The area of the triangle with vertices (6, 6), (2, 4), and (0, 8) is 4 square units.
What is triangle?
A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry. A triangle is defined by its three sides and the three angles formed by those sides.
To find the area of a triangle given its vertices, we can use the following formula:
Area = 1/2 * |(x1*(y2-y3) + x2*(y3-y1) + x3*(y1-y2))|
where (x1, y1), (x2, y2), and (x3, y3) are the coordinates of the three vertices.
Substituting the given coordinates, we get:
Area = 1/2 * |(6*(4-8) + 2*(8-6) + 0*(6-4))|
Area = 1/2 * |-12 + 4|
Area = 1/2 * 8
Area = 4
Therefore, the area of the triangle with vertices (6, 6), (2, 4), and (0, 8) is 4 square units.
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Two cities are 1580 miles apart. A plane leaves one of them traveling towards
the other at an average speed of 400 miles per hour. At that time a plane leaves
the other traveling towards the first at an average speed of 390 miles per hr.
How long will it take them to meet?
Answer:
Step-by-step explanation:
2 hour
Step-by-step explanation:
City A to City B : 1580 miles
Plane speed (C) to City B from A : 400 miles per hour
Plane speed (D) to City A from B : 390 miles per hour
Time taken for plane (C) :
=1580 ÷ 400
=3⁹/²⁰ hours
Time taken for plane (D) :
=1580 ÷ 390
=4²/³⁹ hours
Finding time difference
= 4²/³⁹ - 3⁹/²⁰
=469/780
Finding midpoint
= 469/780 ÷ 2
=469/1560
Total
= 3⁹/²⁰ + 469/1560
= Aprroximately 3¾ hours
Lemon-lime
soda
30%
Lemonade
15%
Cola
20%
Root beer
35%
Students at Remington High School were polled regarding their favorite drinks. The results are shown on the circle graph.
If 630 students were polled, how many preferred cola?need asap
Using the given percentages, we can see that 126 students preferred cola.
How many students preferred cola?To find this number, we just need to multiply the correspondent percent by the total number of students.
First, write the percent in decimal form, to do so, divide it by 100%.
20% of the students preferr cola, so we need to write:
20%/100% = 0.2
And the total number of students is 630, so the number that preffered cola is:
0.2*630 = 126
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1. a) Write the prime factorization of 17 850
b) Determine the greatest common factor of 735 and 1715.
c) Determine the least common multiple of 450 and 180.
PLS HELP!
The prime factorisation of 17850 is 2 × 3 × 5² × 7 × 17. The Greatest common factor of 735 and 1715 is 245 and the Lowest common multiple of 180 and 450 is 900.
What is prime factorizationPrime factorization is a way of expressing a number as a product of its prime factors. A prime number is a number that has exactly two factors, which includes 1 and the number.
Using prime factorisation:
a). 17850 = 2 × 3 × 5² × 7 × 17
b). Greatest common factor of 735 and 1715 is;
735 = 3 × 5 × 7²
1715 = 5 × 7³
GCF = 5 × 7²
GCF = 244
c). Lowest common multiple of 180 and 450 is;
180 = 2² × 3² × 5
450 = 2 × 3² × 5²
LCM = 2 × 3² × 5³
LCM = 900
Therefore, the prime factorisation of 17850 is 2 × 3 × 5² × 7 × 17. The Greatest common factor of 735 and 1715 is 245 and the Lowest common multiple of 180 and 450 is 900.
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if sales tax certain county is 7.2% of the price how much is sales tax on an item the price is $27.30 Round to 2 decimal places
27.30 round to the 2nd decimal place is 27.30.
Now we have to find 7.2% of $27.30.
7.2% of $27.30 is 1.9656.
If you mean that we have to round the answer bt 2 decimal place then the answer is 1.97.
Smashed Pumpkins Company paid $80 in dividends and $519 in interest over the past year. The company increased retained earnings by $432 and had accounts payable of $510. Sales for the year were $16,020 and depreciation was $692. The tax rate was 21 percent. What was the company's EBIT?
The company's EBIT is $1,065.84.
What was the company's EBIT?EBIT, fully known as earnings before interest and taxes is a company's net income before income tax expense and interest expenses are deducted. It is used to analyse performance of core operations without the costs of the capital structure and tax expenses impacting profit.
The net income equals to:
= $80 + $432
= $512
EBT = 432 * (1 - 21%)
EBT = 432 / 0.79
EBT = $546.84
EBIT = $546.84 + $519
EBIT = $1065.84
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find the composition and simplify your answer as much as possible. Write the domain using interval notation.
The composition f∘g is given by (13) / (x - 13).
The domain of the composition is all real numbers except for x = 13, which can be represented in interval notation as (-∞, 13) U (13, ∞).
To find the composition f∘g, we need to substitute g(x) into f(x) in the following way:
f(g(x)) = f(13/x) = (13/x) / ((13/x) - 1)
To simplify this expression, we can multiply both the numerator and denominator by x, which gives us:
f(g(x)) = (13) / (x - 13)
The domain of f(g(x)) is restricted by the domain of g(x), which is all real numbers except for x = 0. Therefore, the domain of f(g(x)) is the set of all real numbers except for x = 13.
Using interval notation, we can write the domain of f(g(x)) as:
(-∞, 13) U (13, ∞)
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identify the number pattern and fill in the missing numbers
1) 5, 3, 9, 2, 13
2) 24, 23, 25, 26,
3) 14, 17, 13, 15, 12
1) the number pattern is obscure2) The number pattern seems to be alternating 3) The number pattern seems to be increasing
How to find the aforementioned questions1) The pattern of the numbers is obscure. The connections between the numbers are not immediately apparent.
2) The number pattern seems to be alternating between subtracting 1 and adding 2 to the previous number. The missing numbers are 27 and 28.
3) The number pattern seems to be increasing by 3, then decreasing by 4, then increasing by 2, and so on. The missing numbers are 19 and 16.
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Write as a logarithm with a base of 4
2 (please answer in logarithmic form)
[tex]\textit{exponential form of a logarithm} \\\\ \log_a(b)=y \qquad \implies \qquad a^y= b\qquad\qquad \\\\[-0.35em] ~\dotfill\\\\ \log_4(y)=2\implies 4^2=y\implies 16=y\hspace{5em} {\Large \begin{array}{llll} \log_4(16)=2 \end{array}}[/tex]
A baseball team played 154 regular season games. The ratio of the number of games they won to the number of
2/5
games they lost was g How many games did they win? How many games did they lose?
Answer: the team won 154g / (g + 1) games and lost 154 / (g + 1) games.
Step-by-step explanation: The mathematical equation "W/L = g" is expressed in a concise manner, wherein "W" refers to weight, "L" refers to the length, and "g" represents the gravitational acceleration. This equation can be utilized in various scientific and academic disciplines, particularly in the field of physics, engineering, and mechanics. The relationship between weight, length, and gravitational acceleration can be further explored and examined through research studies and experiments.
The equation in consideration may be rendered less intricate through the process of multiplication of both sides by L.
"The equation W = gL" can be expressed in an academic manner as follows: The equation denoted by W = gL can be deduced as the product of the gravitational acceleration (g) and the length (L) of an object in a given direction. This equation is commonly used in physics to determine the work (W) performed on an object as a result of a force acting on it, in correlation with the displacement it undergoes in the same direction.
It is understood that the summation of the games won and lost by the team is equivalent to the overall number of games that were played.
The equation denoting the sum of W and L yields a value of 154.
The first equation may now be replaced in the second equation, resulting in:
The mathematical equation GL + L = 154 represents an algebraic expression, where 'G' and 'L' are variables that denote unknown numerical values. The equation dictates that the sum of the values assigned to 'GL' and 'L' must equal to 154. Such equations are commonly used to solve numerical problems in mathematics and related disciplines.
One should perform the mathematical operation of factoring out the variable L on the left-hand side.
The equation L(g + 1) = 154 can be expressed with greater academic rigor.
The sides can be divided by (g + 1) to simplify the equation.
The equation L = 154 / (g + 1) represents a mathematical relationship wherein L is determined by dividing 154 by the sum of g and one.
The aforementioned equation can be utilized to derive a solution for W, ascertaining the relationship that W is equivalent to gL.
The presented expression, W = g(154 / (g + 1)), exhibits a mathematical relationship between the variables W and g, whereby W is a function of g. The numerator of the parenthetical expression, 154, is divided by the sum of g and one, then this ratio is multiplied by g to produce the value of W. The formula can be utilized in various disciplines, such as physics, engineering, and mathematics.
The expression can be simplified to yield:
The expression W can be denoted as 154g / (g + 1) in accordance with the commonly recognized conventions of formal academic writing.
A regular hexagonal pyramid has a slant height of 15
centimeters and a base edge length of 8 centimeters.
Answer:
okay?
Step-by-step explanation:
is this a true or false
The rounding off 87654 to the nearest hundred is_the rounding off 87654 to the nearest hundred is the rounding off 87654 to the nearest hundred is what
Round off 87654 to the nearest hundred?
Marching into my territory,eh?
we need to look at the tens and ones digit of the number. The digit in the hundreds place is 6, which tells us that the number is already in the thousands place.
The tens digit is 5, which is greater than or equal to 5. This means we need to round up the hundreds place to the next digit. Therefore, the rounded number to the nearest hundred is 87700.
PLEASE HURRY AND ANSWER
The figure shows a 1175-yard-long sand beach and an oil platform in the ocean. The angle made with the platform from one end of the beach is 85 deg and from the other end is 75 deg Find the distance of the oil platform, to the nearest tenth of a yard, from each end of the beach.
Theresa earned $120,163 during 2022. On her income taxes she is going to file single and take the standard deduction. Help Theresa calculate her total estimated Federal Taxes for 2022.
2022 Tax Tables:
Theresa's estimated federal income tax for 2022 is $20,430.12.
To calculate Theresa's estimated federal taxes for 2022, we need to use the tax tables provided by the IRS. Here are the steps you can follow;
Determine Theresa's taxable income; To calculate her taxable income, we need to subtract the standard deduction from her gross income. For tax year 2022, the standard deduction for single filers will be $12,950.
Taxable income=Gross income-Standard deduction
Taxable income = $120,163 - $12,950
Taxable income = $107,213
Determine Theresa's tax bracket; To determine Theresa's tax bracket, we need to refer to the tax tables for tax year 2022. According to the tax tables, Theresa's taxable income falls into the 24% tax bracket.
Calculate Theresa's federal income tax; To calculate Theresa's federal income tax, we need to use the formula for her tax bracket. For the 24% tax bracket, the formula is;
Federal income tax = (Taxable income - Lower limit) x Tax rate + Base tax
Using the values for Theresa's tax bracket, we get;
Federal income tax = ($107,213 - $86,375) x 0.24 + $14,605
Federal income tax = $20,430.12
Therefore, federal income tax for 2022 is $20,430.12.
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You have 9 gallons of lemonade to sell. You use cone-shaped cups that are 10 centimeters in diameter and 12 centimeters tall. Each customer uses one paper cup. How many paper cups will you need if you sell all of the lemonade? (1 gal ≈ 3785 cm3)
Answer:27 paper cups.
Step-by-step explanation:
The volume of each cone-shaped cup can be calculated using the formula:
V = (1/3)πr^2h
where r is the radius of the cone (half the diameter), and h is the height of the cone.
Substituting the given values, we get:
V = (1/3)π(10/2)^2(12) ≈ 1256.64 cubic centimeters
We can convert the 9 gallons of lemonade to cubic centimeters using the conversion factor given:
1 gallon ≈ 3785 cubic centimeters
Therefore:
9 gallons * 3785 cubic centimeters/gallon ≈ 34,065 cubic centimeters of lemonade
To find out how many paper cups are needed, we can divide the volume of the lemonade by the volume of one cone-shaped cup:
34,065 cubic centimeters / 1256.64 cubic centimeters ≈ 27 cups
Therefore, approximately 27 paper cups are needed to sell all of the lemonade.
To celebrate Diwali, Raina lights a diya, a small clay lamp filled with oil and a cotton wick. The diya holds 35 milliliters of oil. The oil burns at a rate of 14.8 milliliters per hour. If y represents the number of milliliters of oil and x represents the time in hours, which equation models this relationship? A y 35+ 14.8x B y = -35x + 14.8 C y = -14.8 + 35x D y = -14.8x + 35
The equation that represents the relationship is y = -14.8x - 35. (option D)
What equation represents the relationship?
A linear equation is an equation that consists of a single variable that is raised to the power of one. The general form of a linear equation is y = mx + c
Where:
y = dependent variable m = slopec = interceptThe form of the equation that represents the relationship is:
Millimeters of oil = amount of oil the diya holds - (burn rate x number of hours)
y = 35 - (14.8 x x)
y = 35 - 14.8x
y = -14.8x - 35
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What is the answer to these questions?
1) There are 3.4 * 10^1 in Mexico than in Canada.
2) The number of ounces that were consumed is 20.8 * 10^7 ounces
3) The number of ounces of the students at the community college is 1.25 * 10^1 that of the students in the University.
What is scientific notation?Scientific notation is a way of writing very large or very small numbers using powers of 10. In scientific notation, a number is written as a coefficient multiplied by 10 raised to a power.
1) Ratio of people in Mexico to those in Canada;
1.3 * 10^8/3.8 * 10^7
= 3.4 * 10^1 : 1
2) Number of Ounces consumed by students = 5.2 * 10^4 * 4 * 10^3
= 20.8 * 10^7 ounces
3) Ratio of the number drank by community college to University
= 4 * 10^3/3.2 * 10^2
1.25 * 10^1
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kyle has a fish tank that is 16 inches long and 15 inches wide he fills the tank so the water is 12 inches high . then he placed a sand castle decoration in the tank and the water level rose to 13 inches . what is the volume of the sand castle decoration explain how you found your answer
Answer:
240 cubic inches.
Step-by-step explanation:
To calculate the volume of the sandcastle decoration in the fish tank, we can use the formula:
Volume of the decoration = Total volume of water after adding the decoration - Volume of water before adding the decoration
The volume of water before adding the decoration is the volume of the rectangular prism formed by the fish tank, which is:
Volume of water before = Length x Width x Height
= 16 x 15 x 12
= 2,880 cubic inches
After Kyle added the sandcastle decoration, the water level rose to 13 inches. This means the volume of water in the tank increased by the volume of the decoration. The new volume of water in the tank is:
Volume of water after = Length x Width x Height
= 16 x 15 x 13
= 3,120 cubic inches
Therefore, the volume of the sandcastle decoration is:Volume of decoration = Volume of water after - Volume of water before
= 3,120 - 2,880
= 240 cubic inches
Therefore, the volume of the sandcastle decoration in the fish tank is 240 cubic inches.
A chord is 8 inches away from the center of its circle. This chord is 30 inches long. What, in inches, is the length of the radius?
Answer: The Length of the radius of the circle is 17 inches.
Number graph ranging from negative four to four on the x and y axes. A line with a positive slope is drawn on the graph, passing through the labeled point A at (zero, two) and the labeled point B at three, three). What is the slope of the line passing through points A and B? Responses −3 − 3 , −15 − 1 5 14 1 4 13
The slope of the line passing through points A and B is 1/3.
The formula for the slope of a line to find the slope passing through points A and B. The formula is:
slope = (change in y) / (change in x)
Let's label the coordinates of point A as (x₁, y₁) and the coordinates of point B as (x₂, y₂).
Then, substitute the values and calculate the slope:
slope = (y₂ - y₁) / (x₂ - x₁)
slope = (3 - 2) / (3 - 0)
slope = 1 / 3
Therefore, the slope of the line passing through points A and B is 1/3.
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que es el sistema binario
The binary system is a numerical system that uses only two digits, 0 and 1, to represent numbers.
We have,
It is also known as the base-2 system.
In contrast, the decimal system, which is the most commonly used numerical system, uses ten digits (0 to 9) to represent numbers.
In the binary system, each digit represents a power of 2, starting with 2^0, which equals 1, and then doubling for each successive position (2^1, 2^2, 2^3, and so on).
Therefore, the decimal number 10, for example, is represented in binary as 1010, where the first 1 represents 2^3, the next 0 represents 2^2, the next 1 represents 2^1, and the last 0 represents 2^0.
The binary system is used in digital electronics and computing, where the two states of a switch or transistor can represent 0 or 1.
Thus,
The binary system is a numerical system that uses only two digits, 0 and 1, to represent numbers.
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The complete question:
What is the binary system?
the expression negative 1 plus tangent x over 1 plus tangent x can be rewritten as which of the following
[tex]\tan(\alpha + \beta) = \cfrac{\tan(\alpha)+ \tan(\beta)}{1- \tan(\alpha)\tan(\beta)} \qquad \tan(\alpha - \beta) = \cfrac{\tan(\alpha)- \tan(\beta)}{1+ \tan(\alpha)\tan(\beta)} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{-1+\tan(x)}{1+\tan(x)}\implies \cfrac{-1+\tan(x)}{1-(-1)\tan(x)} \\\\\\ \cfrac{\tan\left( \frac{3\pi }{4} \right)+\tan(x)}{1-\tan\left( \frac{3\pi }{4} \right)\tan(x)}\implies \tan\left( \cfrac{3\pi }{4} + x\right)[/tex]
Announcements for 81 upcoming engineering conferences were randomly picked from a stack of IEEE Spectrum magazines. The mean length of the conferences was 2.91 days. The population standard deviation is 1.26 days. Assume the underlying population is normal.
Construct a 95% confidence interval for the population mean length of engineering conferences.
(i) State the confidence interval. (Round your answers to two decimal places.)
(ii) Sketch the graph. (Round your answers to two decimal places. Enter your /2 to three decimal places.)
(iii) Calculate the error bound. (Round your answer to two decimal places.)
A 95% confidence interval for the population mean length of engineering conferences is 3.70, 4.26.
The error bound based on the information will be 0.28.
How to calculate the value95% confidence interval for the population mean length of engineering conferences is:
= 3.98 +- (1.969 (0.142)
= 3.98 +- 0.218
= 3.70, 4.26
The error bound based on the information will be:
= (1.96( (0.142)
= 0.28.
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The amount of soda in a randomly selected bottle varies according to a normal distribution with mean 18 ounces and standard deviation 9.7 ounces. What is the probability that a randomly selected bottle will be less than 18 ounces? Enter your answer as a decimal.
Answer:
.05 is the decimal
Step-by-step explanation:
.05 is the decimal answer
