Answer:
Step-by-step explanation:
According to question
[tex]4ax^{2} +9x+c < 0[/tex]
This means that the coefficient of the highest degree term
([tex]4ax^{2}[/tex]) must be positive
And the constant term (c) must be negative
So, the according to condition
4a must be positive,
which means a must be positive
And, c must be negative
[tex]a > 0\\c < 0[/tex]
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You and your friend could go to Theater X and each buy an adult ticket, drink, and popcorn, or you and your friend
could rent a video for $3.50, buy a 2 liter of cola for $1.60, and a bag of microwave popcorn for $1.98.
Which situation costs less and by how much?
The second situation costs less by
$16.92How to know the situation that cost lessThe cost of the first situation is
Adult = 8 * 2 = 16
drink = 2 * 2 = 4
popcorn = 2 * 2 = 4
Total = $24
Second situation
rent a video = $3.50
buy a 2 liter of cola = $1.60
a bag of microwave popcorn = $1.98.
Total = $7.03
The second situation costs less by
$24 - $7.03
= $16.92
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Convert 1000000 seconds to hrs, min and seconds
The value of the conversion is;
16, 666. 67 minutes
277.78 hours
What is conversion of units?Conversion of units is described as the conversion between different units of measurement for the same quantity, using the multiplicative factor.
From the information given, we have;
10⁶ seconds
But, we have to take note of;
60 seconds = 1 min
Then 10⁶ seconds = x min
cross multiply
x = 16, 666. 67 minutes
Also,
60 minutes = 1 hour
Then 16, 666. 67 minutes = x
cross multiply
x = 277.78 hours
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A lemonade recipe calls for 3 cups of water for every 2 cups of mix. This recipe makes 5 cups of lemonade.
If there are 16 cups in a gallon, how many cups of mix will need to be used to make 2 gallons of lemonade?
The number of cups of mix that is needed to be used will be 12.8 cups.
What is the solution to the equation?Any value assigned to a variable that results in equal outcomes, i.e., tends to equalize the Left Hand Side (LHS) and Right Hand Side (RHS) of the formula equal, is a solution to a formula. To solve a problem, you must find the formula's workable answer.
For every 2 cups of mix in a lemonade recipe, there should be 3 cups of water. Lemonade made with this recipe makes 5 cups.
Let 'W' be the amount of water in gallons and 'M' be the amount of mix in gallons.
Then the equations are given as,
W / M = 3 / 2 ...1
W + M = 2 ...2
From equations 1 and 2, then we have
(3/2)M + M = 2
(5/2)M = 2
M = 4/5
M = 0.80 gallons
We know that in one gallon, there are 16 cups. Then we have
M = 0.80 x 16
M = 12.8 cups
The number of cups of mix that is needed to be used will be 12.8 cups.
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Hence, or otherwise, find the two consecutive integers whose squares have a difference of 279
The two consecutive integers whose squares have a difference of 279 is 140 and 139.
What are consecutive integers?The uninterrupted series of integers is represented by consecutive meaning in mathematics. It implies that the numbers are continuously following one another in a series. First, we must comprehend the idea of predecessors and successors in order to comprehend the consecutive meaning of consecutive numbers in mathematics. The number that is written immediately before the number is referred to as the predecessor. As opposed to successors, which refer to the number that follows the number. Think about the range 4, 5, 6, and 7. In this case, 4 comes before 5, while 6 comes after 5.
Let us suppose a number = x.
The consecutive number is given as (x - 1)
Two consecutive integers whose squares have a difference of 279, is given as:
x² - (x - 1)² = 279
x² - x² + 2x - 1 = 279
2x - 1 = 279
2x = 280
x = 140
x - 1 = 140 - 1 = 139
Hence, the two consecutive integers whose squares have a difference of 279 is 140 and 139.
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what is the square root of 378 multiply by the factorial of 1 thousand divided by 10^(10^100)?
The square root of 378 is 19.4422
The square root of a number is a value that, when multiplied by itself, gives the original number. The symbol used to denote the square root is √, and it is placed in front of the number for which we are looking for the square root.
First, let's define what factorial means. The factorial of a non-negative integer is the product of all positive integers less than or equal to that number.
Next, we have to compute the square root of 378, which is a much simpler task. The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 25 is 5 because 5 x 5 = 25. Using a calculator, we can find that the square root of 378 is approximately 19.4422.
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Complete Question:
What is the square root of 378?
Y less than 9 in algebra expression
Answer:
9 - y
Step-by-step explanation:
less than means Subtraction
3. Zaidi says the table does not represent a function because all of the inputs have the same output 20. Is Zaidi correct?
From the table, the conclusion can be made that for any value of the input, the value of the output remains the same. Then the correct option is C.
What is a function?A function is an argument, concept, or regulation that demonstrates an association between two variables. Functions may be located throughout mathematics and are necessary for the expansion of significant linkages.
If the number of values of the variable 'y' is more than one for a given value of 'x', then it is not a function.
The table is given below.
x y
- 5 20
0 20
5 20
10 20
From the table, the conclusion can be made that for any value of the input, the value of the output remains the same. Then the correct option is C.
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The complete question is attached below.
The seats in a theater are arranged in rows with an equal number of seats in each row. The graph shows the relationship between the number of rows and the total number of seats. How many seats are in each row (The variables can only be positive numbers.)
The number of seats in each raw by the given graph is 30.
How do we make graph of a function?Suppose the considered function whose graph is to be made is
f(x)
The values of 'x' (also called input variable, or independent variable) are usually plotted on horizontal axis, and the output values
f(x)
are plotted on the vertical axis.
They are together plotted on the point
(x,y) = (x, f(x))
This is why we usually write the functions as:
y = f(x)
Let the number of rows in the original arrangement be x. Then, the number of seats in each row in original arrangement = x
Total number of seats = x x x = x²
From the given information,
2x(x-10)= x²+ 300
2x²-20x = x²+300
x²-20x-3000
(x-30) (x+10) = 0
x = 30, -10
Since, by the function number of rows or seats cannot be negative. So, x = 30.
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suppose you believe that stress causes headaches. what is the hypothesis? explain why we would use an experiment study to test this hypothesis. identify the independent and dependent variables. explain the treatments for the experimental and control groups. make sure all parts of your potential experiment are defined and labeled
If the presented hypothesis is confirmed, it can be assumed that individuals in the experimental group suffer from headaches more frequently than those in the control group.
The study examines how stress affects headaches. The theory can be stated as follows: People who encounter stress episodes more than twice per day would feel headaches more frequently than people who do not experience stress. This question concerns a cause and effect analysis, which can be done with reliable results when using an experimental investigation. Therefore, it is advised to use an experimental design for dealing with headaches brought on by stress. Stress events are the only unchanging factor in our study, however they do cause changes in the frequency of headaches. The degree of headaches, which fluctuates when the independent variable is changed, can be thought of as the dependent variable. Here, the technique can be applied as follows: Informed consent is obtained from a sample of 400 persons, all of whom fall within the age range of 25 to 40 (to lessen the impact of any auxiliary variables on the results). The volunteers are divided into two groups at random, one of which is the experimental group and the other the control group (double-blind design to avoid any potential biases). Three times a day, participants in the experimental group are exposed to a show that is heavy on the negative feelings that can lead to stress; in contrast, individuals in the control group are not exposed to any of the shows mentioned above. Then, the presence of headaches is assessed in both groups' members.
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The redwood national park is home to some of the largest trees in the world hyperion is the tallest tree in the park with a heigt of approximately 379 feet tom wants to find the height of the tree in yards
Using the unit conversions, the height of the tree in yards is 126.33 yd
Let h be the height of the tree.
It is given that the Height of the tree is 379 feet and we need to find the height of the tree in yards.
From the given statement, Hyperion is the tallest tree in the park, with a height of approximately 379 feet,
We need to convert the height of the tree from feet to yards. So, We divide the height of the tree by three for the yard.
So, for one foot: h = (1/3) yd
For, 379 feet: h = 379/3 yd
= 126.33 yd
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14 units up of f(x)= – 2x–4.
Answer:
-2x + 10
Step-by-step explanation:
When you add units you affect the y axis.
Knowing this you can translate it 14 units up by adding 14 + (-4).
Add twice the weight in kilograms to the volume in litres and multiply the result by one thousandth of the distance the parcel is sent in kilometres (1 litre equals 1000 cubic centimetres).
This gives the postal cost in dollars.
A customer wishes to post a parcel which measures 50cm x 50cm x 20cm and weighs 40kg to a city 200km away. How much will it cost?
The postal cost is $26
What is volume?
In three-dimensional space, volume is the area occupied by an object within its borders. Another name for it is an object's capacity.
twice the weight = 2(40) = 80 kg
volume = 50cm x 50cm x 20cm = 50,000 cm³ = 50 litres
80 + 50 = 130
distance = 200 km
one thousandth = 0.001
one thousandth of the distance = 0.001 * 200 = 0.2
Multiply 130 by 0.2 as given
130*0.2 = 26
The postal cost is $26
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$500 is deposited into a savings account that pays 7% interest compounded annually. Find the amount of money in the account after 2 years
The amount of money in the account after 2 years is $573.04.
What is compound interest?
Compound interest is the interest earned on an initial principal deposit as well as on the accumulated interest from previous periods. In other words, it is interest on interest.
To calculate the amount of money in the account after 2 years, we can use the formula for compound interest:
A = P(1 + r/n)ⁿᵗ
where A is the final amount, P is the principal amount (the initial deposit), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time period (in years).
In this case, P = $500, r = 0.07 (7%), n = 1 (compounded annually), and t = 2.
Plugging these values into the formula, we get:
A = 500(1 + 0.07/1[tex])^{(1 \times 2)}[/tex]
A = 500(1.07)²
A = $573.04
Therefore, the amount of money in the account after 2 years is $573.04.
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if the expression x^(-3/4)y^-(-4/3)∜16x^2y^4 is written in the form ax^by^c, then what is the product of a, b and c?
The value of a, b, and c will be 2, -1/4, and 7/3, respectively. Then the product of a, b, and c will be - 7/6.
What is an equivalent?The equivalent is the expression that is in different forms but is equal to the same value.
The meaning of straightforwardness is simplifying something to accomplish or get a handle on while likewise making it somewhat less troublesome.
The expression is given below.
[tex]\rm \rightarrow x^{-3/4 } \cdot y ^{-(-4/3)} \cdot \sqrt[4]{16x^2y^4}[/tex]
Simplify the expression, then we have
[tex]\rm \rightarrow x^{-3/4 } \cdot y ^{-(-4/3)} \cdot \sqrt[4]{16x^2y^4}\\\\\rightarrow x^{-3/4 } \cdot y ^{(4/3)} \cdot (16x^2y^4)^{1/4}\\\\\rightarrow x^{-3/4 } \cdot y ^{4/3} \cdot 2x^{1/2}y\\\\\rightarrow 2 x^{1/2 - 3/4} \cdot y^{4/3 + 1} \\\\\rightarrow 2x^{-1/4} \ \cdot y^{7/3}[/tex]
The given expression is [tex]\rm ax^by^c[/tex]. Compare the expression with given expressions, then we have
a = 2, b = - 1/4, and c = 7/3
Then the product of a, b, and c is given as,
⇒ 2 x (-1/4) x (7/3)
⇒ - 7/6
The value of a, b, and c will be 2, -1/4, and 7/3, respectively. Then the product of a, b, and c will be - 7/6.
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Write the polynomial below in factored form.
y = x³ - 3x² - 4x
Answer: y = x(x+1)(x-4)
Step-by-step explanation:
Answer:
Step-by-step explanation:
Given,y=x^3-3x^2-4x
taking x commonly
y=x(x^2-3x-4)
y=x(x^2+x-4x-4)
y=x[x(x+1)-4(x+1)]
y=x(x+1)(x-4)
megan wants to test her assumption on the amount of sleep students are getting. she decides to focus her efforts on examining if students are getting less than eight hours of sleep. what should megan state for the null hypothesis and alternative hypothesis? a.) null hypothesis: alternative hypothesis: b.) null hypothesis: alternative hypothesis: c.) null hypothesis: alternative hypothesis: d.) null hypothesis: alternative hypothesis:
To state the null hypothesis and alternative hypothesis for Megan's test, we need to know what type of data she will be collecting and what type of test she will be conducting.
Assuming she will be collecting data on the number of hours of sleep students are getting and conducting a one-tailed hypothesis test, the following are possible null and alternative hypotheses:
a.) Null hypothesis: The average amount of sleep students are getting is equal to or greater than eight hours per night.
Alternative hypothesis: The average amount of sleep students are getting is less than eight hours per night.
b.) Null hypothesis: Less than or equal to 50% of students are getting less than eight hours of sleep per night.
Alternative hypothesis: More than 50% of students are getting less than eight hours of sleep per night.
c.) Null hypothesis: There is no difference in the proportion of students getting less than eight hours of sleep between two groups (e.g., males vs. females, freshmen vs. seniors, etc.).
Alternative hypothesis: There is a difference in the proportion of students getting less than eight hours of sleep between two groups.
d.) Null hypothesis: The number of students getting less than eight hours of sleep is equal to or greater than a certain value (e.g., 30%).
Alternative hypothesis: The number of students getting less than eight hours of sleep is less than the specified value.
Note that in each case, the null hypothesis represents the status quo or the default assumption, while the alternative hypothesis represents Megan's research question or hypothesis. The choice of null and alternative hypotheses depends on the research question, the data being collected, and the type of hypothesis test being conducted.
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) explain in words how the math is supposed to work for calculating the number of scenarios. (b) show the arithmetic behind calculating the final value. (c) why is it important to be able to estimate the number of scenarios before beginning your full assessment?
a) The connection of the literacy principle to assessments created and used by preceptors and others directly involved in classrooms is fairly straightforward. Less egregious is the connection of the principle to assessments created and assessed by parties outside the classroom. Tradition has allowed and indeed encouraged some assessments to serve responsibility or monitoring purposes without sufficient regard for their impact on pupil literacy.
b) To satisfy the literacy principle, assessment must change in ways consonant with the current changes in tutoring, literacy, and class. In the history, pupil literacy was frequently viewed as a unresistant process whereby scholars flashed back what preceptors told them to flash back . harmonious with this view, assessment was frequently allowed of as the end of literacy. The pupil was assessed on commodity tutored preliminarily to see if he or she flashed back it. also, the mathematics class was seen as a fractured collection of information given meaning by the schoolteacher.
c) The alternate chance gave scholars the occasion not simply to redo the questions on which they were unprofitable in the first stage but, more importantly, to give lesser attention to the essay questions they had little time to address. similar two- stage testing basically formalizes what numerous preceptors of writing do in their courses, giving scholars an occasion to revise their work after the schoolteacher or other scholars have read it and offered suggestions.
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PLS HELP FAST ONLY TEN MIN LIFT WILL GIVE BRIANLIEST IF RIGHT
LOTS OF POINTS
Answer:
lol
Step-by-step explanation:
that sucks
Here are the hottest recorded temperatures (ln^ F) for eight cities throughout North America. Complete the grouped frequency distribution for the data. In the distribution, the frequency of a class is the number of temperatures that class. (Note that we are using a class width of 5.)
The frequency of each class interval 103 - 107, 108 - 112 and 113 - 117 are 2, 2 and 4 respectively.
What is meant by Grouped Frequency Distribution?A grouped frequency distribution is the distribution of data into various classes with equal width with the frequency being the number of outcomes in that class.
Given are the hottest recorded temperatures (in °F) for eight cities throughout North America.
113 110 108 104 117 116 113 103
The class intervals are 103 - 107, 108 - 112 and 113 - 117.
In the distribution, the frequency of a class is the number of temperatures that class.
The temperatures in the class 103 - 107 are 103 and 104.
Frequency of 103 - 107 = 2
The temperatures in the class 108 - 112 are 108 and 110.
Frequency of 108 - 112 = 2
The temperatures in the class 113 - 117 are 113, 113, 116 and 117.
Frequency of 113 - 117 = 4
Hence the frequency are 2, 2 and 4 for the intervals 103 - 107, 108 - 112 and 113 - 117 respectively.
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In a triangle ABC, AB = 5cm , BC = 7cm and CA = 8cm. Id D and E are reep mid points of AB and BC, find the length of DE.
The measured length of DE will be 4 cm.
What is the similarity?Two objects are said to be comparable if they have the same shape. Therefore, two figures are said to be comparable in mathematics if they share the same shapes, lines, or angles.
Given that AB is 5 cm, BC is 7 cm, and CA is 8 cm in the triangle ABC. The reep midpoints of AB and BC are Ids D and E.
The two triangles ABC and ADE will be similar to each other. The measure of the length DE will be calculated as:-
AC = DE = 7 / 3.5
DE = AC / 2
DE = 8 / 2
DE = 4 cm
Hence, the value of the side DE will be 4 cm.
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HELP!!! MEEE ITS URGENT
Answer:
C = 3.14
Step-by-step explanation:
Center of the circle is (h, k)
h = 4, k = 1
Use the equation of a circle and the given point (4, -4) to find r:
r² = (x-h)² + (y-k)² = (4-4)² + (-4-1)² = 0 + (-5)² = 25
r = √25 = 5
Find circumference, C:
C = 2πr = 2π(5) = 31.4
Brainly doesn't provide drawing tools, but you can easily draw this circle. Just plot the center point (4, 1), then draw a circle with a radius of 5 around it. You'll see that this circle passes through the point (4, -4).
Grayson and his friends are ordering a pizza to share. They want one vegetable topping and one meat topping. The vegetable toppings are mushrooms, broccoli, green peppers, olives, and onions. The meat toppings are pepperoni, salami, sausage, chicken, and ground beef. They can pick thick, hand-tossed, or deep-dish crust. They can also pick garlic, tomato, ranch, pesto, or barbecue sauce. Given these choices, how many different combinations can Grayson and his friends create?\
375 different combinations of pizza Grayson and his friends can create.
What is a combination?Combinations are selections made by taking some or all of a number of objects, irrespective of their arrangements. The number of combinations of n different things taken r at a time, denoted by nCr and it is given by, nCr=n!/r!(n−r)!,where 0 ≤ r ≤ n.
The vegetable toppings are mushrooms, broccoli, green peppers, olives, and onions.
Here, n=5 r=1
So, C(n, r) = 5!/1!(5-1)!
= 5
The meat toppings are pepperoni, salami, sausage, chicken, and ground beef.
Here, n=5 r=1
So, C(n, r) = 5!/1!(5-1)!
= 5
They can pick thick, hand-tossed, or deep-dish crust.
Here, n=3 r=1
So, C(n, r) = 3!/1!(3-1)!
= 3
They can also pick garlic, tomato, ranch, pesto, or barbecue sauce.
Here, n=5 r=1
So, C(n, r) = 5!/1!(5-1)!
= 5
Number of ways = 5×5×3×5
= 375
Hence, in 375 ways they can choose pizza.
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What is the slope of the line that passes
through the points (10, 3) and (7,0)?
Write your answer in simplest form.
Answer:
0.75
Step-by-step explanation:
The slope-intercept form is one way to write a linear equation (the equation of a line). The slope-intercept form is written as y = mx+b, where m is the slope and b is the y-intercept (the point where the line crosses the y-axis).
Which step is NOT performed in the process of solving n²
A
B
C
D
Add 10 to each side
Add 36 to each side
Factor ² 12n 100
Take the square root of each side
12n 100 by completing the square?
A step that is not performed in the process of solving n² - 12n - 10 = 0 by completing the square is: C. Factor n² - 12n - 10 = 0.
How to solve the quadratic equation?In order to solve the given quadratic equation, we would use the completing the square method as follows;
n² - 12n - 10 = 0
By keeping x terms on the left-hand side of the quadratic equation, we would move the constant term to the right-hand side of the quadratic equation by adding 10 on both sides as follows;
n² - 12n - 10 + 10 = 0 + 10
n² - 12n = 10
In order to complete the square, we would have to add (half the coefficient of the x-term)² to both sides of the quadratic equation as follows:
n² - 12n + (12/2)² = 10 + (12/2)²
n² - 12n + 36 = 10 + 36
n² - 12n + 36 = 46
(n - 6)² = 46
By taking the square root of each side, we have:
n - 6 = ±46
n = 6 ±46
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Complete Question:
Which step is NOT performed in the process of solving n² - 12n - 10 = 0 by completing the square?
Add 10 to each side
Add 36 to each side
Factor n² - 12n - 10 = 0
Take the square root of each side
What is the value of c in the equation?
15.3 = Start Fraction c Over 2.1 End -Fraction
statistics is a rigorous branch of mathematics that deals with group of answer choices data mining visualization understanding data linear regression all of the above
Statistics is a rigorous field that provides a set of tools and techniques for understanding and making decisions based on data. Correct option is C.
Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. Statistics is used in a wide range of fields, from business and finance to social sciences, engineering, and healthcare.
One of the key goals of statistics is to summarize and make sense of complex data, and this is often done through the use of visualization techniques such as histograms, scatterplots, and box plots.
Statistics also involves techniques such as data mining, which involves the use of algorithms and computational methods to analyze large data sets, and linear regression, which is a technique for modeling the relationship between two variables.
In addition to its practical applications, statistics is also important for understanding the world around us. It can be used to test hypotheses, evaluate the reliability of data, and make predictions about future events. Overall, statistics plays a vital role in modern society by helping us make sense of the vast amounts of data that we encounter every day.
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Complete question is:
Statistics is a rigorous branch of mathematics that deals with
group of answer choices
A. data mining
B. visualization
C. understanding data
D. linear regression
E. all of the above
given 20 people, what is the probability that, among the 12 months in the year, there are 4 months containing exactly 2 birthdays and 4 containing exactly 3 birthdays?
the probability of having 4 months containing exactly 2 birthdays and 4 months containing exactly 3 birthdays among 20 people is approximately 0.000008, or about 0.0008%
The problem of calculating the probability of a certain pattern of birthdays among a group of people can be approached using the techniques of combinatorics and probability. To calculate the probability of having 4 months containing exactly 2 birthdays and 4 months containing exactly 3 birthdays among 20 people, we can use the following steps: First, we need to choose which 4 months will have exactly 2 birthdays and which 4 months will have exactly 3 birthdays. There are 12 months to choose from, so the number of ways to make these choices is given by the binomial coefficient: C(12, 4) × C(8, 4). This is the number of ways to choose 4 months out of 12 to have exactly 2 birthdays, multiplied by the number of ways to choose 4 months out of the remaining 8 to have exactly 3 birthdays. Next, we need to assign the people to the months. To do this, we can use the principle of inclusion-exclusion, which states that the number of ways to assign the people to the months so that each of the chosen months has the correct number of birthdays is: N = (20!/(2!²× 3!⁴)) × (4¹² - 6 × 3¹² + 4 × 2¹²). This expression counts the number of ways to distribute the 20 people among the 12 months so that the chosen months have the correct number of birthdays, and subtracts the cases where one or more of the chosen months have too many or too few birthdays. The factor (20!/(2!⁸ × 3!⁴)) accounts for the fact that we are counting distinguishable arrangements of people. Finally, we can calculate the probability of the desired pattern of birthdays by dividing the number of favorable outcomes (N) by the total number of possible outcomes, which is simply the total number of ways to assign the people to the months, given by: 12²⁰. Putting it all together, we get: P(4 months with 2 birthdays, 4 months with 3 birthdays) = N / 12²⁰. Evaluating this expression gives: P(4 months with 2 birthdays, 4 months with 3 birthdays) ≈ 0.000008. Therefore, the probability of having 4 months containing exactly 2 birthdays and 4 months containing exactly 3 birthdays among 20 people is approximately 0.000008, or about 0.0008%.
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Triangle ABC has angle measures as noted below. Please note this triangle is not drawn to scale, and the longest leg of the figure may not be the longest leg of the actual triangle.
You will need to use the expressions for the angles given below.
m∠A) 3(x + 5)
m∠B) 5x+15
m∠C) 7x
Identify the angle relationship and setup your equation with the given expressions.
What is the value of x? Show your work.
What is the measure of angle A, B, & C? Show your work and make sure to identify which is which.
GIVING 70 POINTS FOR RIGHT ANSWER NEED ASAP (please and ty)
Answer:
m∠A = 45°;m∠B = 65°;m∠C = 70°.-----------------------------------
Recall triangle angle sum property, the sum of three interior angles is 180°.
Add up the three angle measures, then solve the equation for x:
m∠A + m∠B + m∠C = 1803(x + 5) + 5x + 15 + 7x = 1803x + 15 + 12x + 15 = 18015x + 30 = 18015x = 150x = 10Substitute the value of x and find the value of each angle:
m∠A = 3(10 + 5) = 3(15) = 45m∠B = 5*10 + 15 = 50 + 15 = 65m∠C = 7*10 = 703. find the 95% confidence interval for the mean number of hours of tv watched each day by adults in the us. report the upper and lower bounds of the interval:
The lower and upper bounds of the given confidence interval of 95% with sample size= 1,555 , sample mean = 2.938 and standard deviation 2.837 is equal to ( 2.797 , 3.079 ).
Upper and lower bounds of the confidence interval is :
= Sample mean ± Margin of error
And Margin of error is :
= Z-critical × ( σ/√(n ) )
Standard deviation 'σ ' = 2.837
Sample size 'n' = 1,555
Sample mean 'μ' = 2.938
Z-critical for 95% confidence interval
= Zα/2
= 1.96
Margin of error
= 1.96 × (2.837/√1,555)
= 1.96 × (2.837/ 39.43 )
= 0.1410
Confidence interval:
Upper boundary
= 2.938 + 0.1410
= 3.079
Lower boundary
= 2.938 - 0.1410
= 2.797
Therefore, for the given confidence interval of 95% the lower and upper bounds of the interval are ( 2.797 , 3.079 ).
The above question is incomplete , the complete question is:
find the 95% confidence interval for the mean number of hours of tv watched each day by adults in the us. report the upper and lower bounds of the interval:
Sample size Sample mean Standard deviation
1,555 2.938 2.837
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In the graph, y represents a company's profit in thousands of dollars, and x represents the time in years.
(3,4)
(3,2)
per year
x1
At what rate is the company's profit changing?
The company profit is decreasing by 1/3 thousand dollars per year.
What is an equation?An equation is an expression that shows how numbers and variables are related using mathematical operations. Equations can be linear, quadratic, cubic and so on.
The slope intercept form of a linear equation is:
y = mx + b
Where m is the rate of change and b is the initial value of y.
Let y represents a company's profit in thousands of dollars, and x represents the time in years.
From the graph, using the point (-3, 4) and (3, 2):
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)[/tex]
Substituting:
[tex]y-4=\frac{2-4}{3-(-3)} (x-(-3))\\\\y=-\frac{1}{3}x+3[/tex]
The company profit is decreasing by 1/3 thousand dollars per year.
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