A table of values and an equation for C, in terms of t, representing the total cost of using a computer for t minutes at the internet cafe are as follows:
C t
$10.60 1
$11.20 2
$11.80 3
C = 0.60t + 10.
How to write an equation for the total cost?In order to write an equation for the total cost, we would assign variables to the amount of time used and the total cost of using a computer, and then translate the word problem into algebraic equation as follows:
Let the variable C represent the total cost in dollars.Let the variable t represent the amount of time in minutes.Since the cafe has an initial charge of $10 to use a computer and an additional charge of $0.60 for every minute of use, an equation for the total cost is given by:
C = 0.60t + 10
When t = 1, we have:
Total cost, C = 0.60(1) + 10
Total cost, C = $10.60.
When t = 2, we have:
Total cost, C = 0.60(2) + 10
Total cost, C = $11.20.
When t = 3, we have:
Total cost, C = 0.60(3) + 10
Total cost, C = $11.80.
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In a multiple regression problem involving two independent variables, if b1 is computed to be +2.0, it means thatthe estimated mean of Y increases by 2 units for each increase of 1 unit of X1, without regard to X2.the estimated mean of Y increases by 2 units for each increase of 1 unit of X1, holding X2 constantthe estimated mean of Y is 2 when X1 equals zero.the relationship between X1 and Y is significant.
The solution is y will increase by 2 units with every unit increase in x1
What do you mean by multiple regression?A single dependent variable and several independent variables can be analyzed using the statistical technique known as multiple regression. In order to predict the value of the single dependent value, multiple regression analysis uses independent variables whose values are known.
What is the difference between multiple and single regression?X and Y variables are the sole ones in simple linear regression. Two or more x variables and one y variable make up multiple linear regression. For instance, basic linear regression is used when we forecast rent using only square footage.
In the above question:-
Interpretation of b1=2
it means that y will increase every 2 units for every unit increase in x1
holding x2 constant.
Hence option B is the correct answer.
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A partial payment is made on the date indicated. Use the United States rule to determine the balance due on the note at the date of maturity. (The Effective Date is the date the note was written.) Assume the year is not a leap year.Principal Rate Effective Date Partial Payment Maturity Date Amount Date $2000 4% April 1 $1000 May 1 June 1 The balance due on the note at the date of maturity is $nothing.(Round to the nearest cent as needed.)
The balance due on the note at the date of maturity is $1010.13.
What is meant by partial payment?The offering of a payment by cheque for less than the whole amount sought by the creditor is known as partial payment. It is standard practice to grant debt forgiveness in exchange for the tender of a "payment-in-full" check.
Given permission to apply the US rule
In the United States, a year is deemed to have 360 days for the purposes of calculating interest.
Given that the principal is $ 2000,
Interest rate = 4% = 0.04
The effective date is April 1.
The whole amount is $1,000.
May 1 = partial payment
Duration = 30 days (May 1 - April 1)
Therefore, interest = PTR = 2000 * 0.04 * 30/360 = $6.67
So value = $ 2000 + $6.67 = $6.67
Partial payment received = $1,000
As a result, value = $ 1006.67 = $2006.67 - $ 1000
Time T= 31
Interest = PTR * 31/360 * 0.04 = 3.46
So the total value is $1006.67 + $3.47 = $1010.13.
The note's outstanding balance at maturity is $1010.13.
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Calculate how far each of the following travels. A helicopter flies at a speed of 72miles per hour for 10 minutes
Answer:
12 miles
Step-by-step explanation:
72 x [tex]\frac{10}{60}[/tex] = 12
determine the zeros of f(x)=28x^2−7
The zeroes of the function f(x) = 28x² - 7 will be 1/2 and negative 1/2.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The quadratic equation is given as ax² + bx + c = 0. Then the degree of the equation will be 2.
The function is given below.
f(x) = 28x² - 7
For the zeroes of the function, put f(x) = 0, then we have
f(x) = 0
28x² - 7 = 0
x² = 1/4
x = ± 1/2
The zeroes of the function f(x) = 28x² - 7 will be 1/2 and negative 1/2.
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Where is the gap in the data?
Number of Patients Per Hour Who Waited Longer than 15 Minutes
A dot plot going from 0 to 5. 0 has 8 dots, 1 has 6 dots, 2 has 1 dot, 3 has 5 dots, 4 has 0 dots, and 5 has 3 dots.
0
2
4
8
Answer:
4 hours
Step-by-step explanation:
I don’t work with data points too much but I believe the gap is at 4 because it is where no one waited that long and where the date kind of stops and then start back up at 5 hours
Hopes this helps
carla's cell phone company charges $35 a month for phone service plus $0.50 for each text message. carla's bill was $52 this month.
The number of text messages sent by carla in a month is 34.
What is an algebric equation ?
An algebraic equation is a mathematical statement that sets two expressions equal to each other. An algebraic equation is typically made up of a variable, coefficients, and constants.
For given question,
Phone service = $35
For each text message = $0.50
Total bill = $52
Let x be the no. of total text messages.
Equation: 52 = 35 + 0.50x
Solving for x,
52 - 35 = 0.50x
17 / 0.50 = x
34 = x
The number of text messages sent by carla in a month is 34.
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I am thinking of a number. When I divide my number by $7$ and subtract $\dfrac{3}{5},$ I get back my original number. What is my number?
solve the following system of equations. if there is no solution, write dne in each coordinate of the ordered triplet. if there are an infinite number of solution, write each coordinate in terms of z . z. x 7
DNE in each coordinate of the ordered triplet are y is -7 , DNE ,y is-2.
Whais the explanation?1.) 2+3 = y + 12
Make y the formula's subject after adding the LHS.
5 = y + 12
Y = 5 - 12
Y = - 7
The answer to the equation is -7
2.) 2 + 13 = 1 +8
The equation cannot have a solution since there is no unknown variable and the sum of the numbers on the left hand side (LHS) does not equal the sum of the numbers on the right hand side (RHS).
3.) y - 7 = 2 - 11
RHS is added, and y is become the formula's subject.
Y - 7 = -9
Y = -9 + 7
Y = -2
The equation's answer is -2.
The complete question is:Solve the following system of equations. If there is no solution, write DNE in each coordinate of theordered triplet. If there are an infinite number of solution, write each coordinate in terms of z.2+3 = y + 12
2 + 13 = 1 +8
y - 7 = 2 - 11
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Calculate the average rate of change from x = −2 to x = 1 of the function below. f(x) = x2 + 5x − 12 First, find the change in y by evaluating the function at −2 and 1:
The average rate of change over the interval x = -2 and x = 1 is 4
How to determine the average rate of changeThe equation is given as
f(x) = x² + 5x - 12
The interval is given as:
x = -2 to x = 1
Start by calculating the functions f(-2) and f(1)
So, we have
f(-2) = (-2)² + 5(-2) - 12 = -18
f(1) = (1)² + 5(1) - 12 = -6
So, the average rate over these intervals is calculated as:
Average rate = [f(1) - f(-2)]/[1 - -2]
This gives
Average rate = [-6 - -18]/[1 - -2]
Evaluate
Average rate = 4
Hence, the average rate of change is 4
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A study conducted by Norman Hollenberg, professor of medicine at Brigham and Women’s Hospital and Harvard Medical School, involved 27 healthy people aged 18 to 72. Each subject consumed a cocoa beverage containing 900 milligrams of flavonols (a class of flavonoids) daily for five days. Using a finger cuff, blood flow was measured on the first and fifth days of the study. After five days, researchers measured what they called "significant improvement" in blood flow and the function of the cells that line the blood vessels.³³ What flaw in the design of this experiment makes it impossible to say whether the cocoa really caused the improved blood flow? Explain.
There was no control group for comparison answers.
There was no control group to compare the results to change in blood flow could have been caused by something else .
What is meant by blood flow ?The movement of blood through the vessels from arteries to capillaries and then into veins is referred to as blood flow.
There are two blood circulatory systems in the human body, which are linked: The systemic circulation transports blood to organs, tissues, and cells, supplying them with oxygen and other vital substances. The pulmonary circulation is where fresh oxygen enters the bloodstream.
As the heart beats, blood is pumped through a network of blood vessels known as the circulatory system. The vessels are flexible tubes that transport blood to all parts of the body.
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2 and 2/3 simplified
[tex]\stackrel{mixed}{2\frac{2}{3}}\implies \cfrac{2\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{8}{3}}[/tex]
Drew's grandmother is 72 years old. Drew's mother is y years younger than Drew's grandmother, and she is 45 years old. Write an equation using subtraction that represents this situation.
A right triangle is formed in the first quadrant by the x- and y-axes and a line through the point.
The area of the triangle as the function of x is [tex]x^2[/tex] / 2x - 4 and the domain of the function is x∈(2, ∞)
The point on the line = (2, 1)
The give three points are (0, y), (2, 1) and (x, 0)
The slope of the line is the change in y coordinates with respect to the change in x coordinates of the line
Consider the point (0, y) and (2, 1)
Slope = (1-y) / (2-0)
= (1-y) /2
Consider the point (2, 1) and (x, 0)
Slope = (0-1) / (x-2)
= -1/x-2
Both slopes are equal
(1-y) /2 = -1/x-2
(1-y) = -2 / (x-2)
y = 1 + (2/(x-2))
y = x / (x-2)
The area of the triangle = (1/2)bh
Where b is the base
h is the height
The area of the triangle = (1/2) × x × (x / (x-2))
= [tex]x^2[/tex] / 2x - 4
The domain is x∈(2, ∞)
Hence, the area of the triangle is [tex]x^2[/tex] / 2x - 4 and the domain of the function is x∈(2, ∞)
The complete question is
A right triangle is formed in the first quadrant by the x- and y-axes and a line through the point (2,1). Write the area of the triangle as a function of x, and determine the domain of the function.
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simetrico de [tex]\frac{8}{4}[/tex]
The symmetric fraction to 8/4 is given as follows:
1/2.
How to obtain the symmetric fraction?A fraction is a numerical representation of the division of the two terms, symbolized x and y, as follows:
Fraction = x/y.
The technical terms of x and y are given as follows:
The top term x of the fraction is the numerator of the fraction.The bottom term x of the fraction is the denominator of the fraction.The symmetric fraction is obtained exchanging the numerator and the denominator, hence it is of:
Symmetric fraction = y/x.
The fraction in this problem is given by:
8/4.
Hence the symmetric fraction is of:
4/8 = 1/2.
(as both 4 and 8 are divisible by 4).
TranslationThe problem asks for the symmetric fraction to 8/4.
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In the diagram, A and B are points
on the circle AC and BC are
tangents to the circle and meet
at C. Work out the angle ACB.
The angle ACB would be 80 degrees.
What is tangent to a circle?
The tangent always makes a single-point contact with the circle. It never intersects the circle twice. Tangents from an external point to a circle have the same length.
In the given figure,
angle AOB = 40.
So angle OBA = 40.
Then the angle AOB = 180 - 40 -40
AOB = 100.
By the theorem of circles,
AOB + ACB = 180
100 + ACB = 180
ACB = 80.
Hence, the angle ACB would be 80 degrees.
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Determine which integers in the set S: {−2, −3, −4, −5} will make the inequality 2p − 8 < 5p + 4 true.
S:{−2, −3}
S:{−3, −4}
S:{−4, −5}
S:{−2, −5}
Answer:
[tex]S=\{-2,-3\}[/tex]
Step-by-step explanation:
Required integers are: -2 and -3
(2x² + 3x − 9)
Factor
The sum of three numbers is 23.
Three times the smallest is 4 less than the largest, while the sum of the largest
and smallest is 16. Use a linear system in three variables to find the three numbers.
The three numbers are __ , __
and __
Answer:
The three numbers are 3, 7 and 13
Step-by-step explanation:
Considering the 3 numbers: x, y and z
x + z = 16
z=16-x
3x=z-4
3x=16-x-4
4x=12
x=3
3+z=16
z=16-3
z=13
3+13+y=23
y=23-13-3
y=7
Hope this helps :)
Write an equation of the line that passes through (18, 2) and is parallel to the line 3y−x=−12.
Answer: No solution
Step-by-step explanation:
3y - x = (3 * 2 - 18) = 6 - 18 = -12
3y - x = -12
x - 3y = 12
since parallel lines, by definition, have NO point of intersection, there is no solution.
HELP ANSWERpleaseeee im timed
The percentage of the campers that are participating in a nature hike that are females is 57.1% (first option)
What is the percentage?
Percentage is the fraction out of an amount expressed as a number out of hundred. The sign that is used to represent percentage is %. In order to convert a number to percentage, multiply the number by 100. Percentage is a measure of frequency.
Percentage of the campers that are participating in a nature hike that are females = (number of females in the nature hike / total number of campers in the nature hike) x 100
Total number of campers in the nature hike = 20 + 15 = 35
Percentage of the campers that are participating in a nature hike that are females = (20 / 35) X 100 = 57.1%
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What i the value of x in the equation 0. 2(x 1) 0. 5x = –0. 3(x – 4)?
Negative even-halve
–1
1
Seven-halve
The value of x for the given equation is 1.
What is solving an equation?
A General Rule for Equation Solving
Remove parentheses from each side of the equation and combine similar phrases to make it simpler.
To separate the variable term on one side of the equation, use addition or subtraction.
To find the variable, use division or multiplication.
Consider the given expression
0.2(x + 1) + 0.5x = -0.3(x - 4)
Simplifying,
0.2x + 0.2 + 0.5x = -0.3x + 1.2
0.7x + 0.2 = -0.3x + 1.2
Add 0.3x on both sides,
0.7x + 0.2 + 0.3x = -0.3x + 1.2 + 0.3x
x + 0.2 = 1.2
Subtract 0.2 from both sides,
x + 0.2 - 0.2 = 1.2 - 0.2
x = 1
Hence, the value of x for the given expression is, 1.
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What is irrational number and is 4/3 a irrational number??
Answer: 4/3 is not irrational, it is rational
Explanation:
A rational number is a ratio, or fraction, of two integers. The denominator cannot be zero.
4/3 is rational since it's the ratio of the integers 4 over 3.
Since it is rational, it is not irrational. The term "irrational" literally means "not rational". Therefore, a real number is either of those options, but not both simultaneously.
A famous example of an irrational number is [tex]\pi \approx 3.14...[/tex] because it cannot be written as a fraction of two integers. We can get approximations like 22/7, but never manage to capture the full value of [tex]\pi[/tex] with a single fraction.
Another example of an irrational number is [tex]\sqrt{2}[/tex]
[tex]\displaystyle\\Answer: \ \frac{4}{3} \ isn`t\ an\ irrational\ number[/tex]
Step-by-step explanation:
An irrational number is an infinite non-periodic fraction
[tex]\displaystyle\\\frac{4}{3}=1\frac{1}{3} \\\\\frac{4}{3} =1.333333...\\\\\frac{4}{3}=1.(3)[/tex]
1.(3) - is an infinite periodic fraction
[tex]\displaystyle\\Hence,\ \frac{4}{3} \ isn`t\ an\ irrational\ number[/tex]
!!50 Points!! Pls help ASAP!!!
Simplify
[tex](3\sqrt{-5} + 2)(4\sqrt{-12} - 1)[/tex]
The simplification of the expression (3√-5 + 2)(4√-5 -1) gives 5√-5 - 62
How to simplify numbers and expressions?Simplification is a way of determining an answer for a complex calculation that may involve numbers on division, multiplication, square roots, cube roots, plus and minus, etc.
Given: the expression (3√-5 + 2)(4√-5 -1)
(3√-5 + 2)(4√-5 -1)
Clear the parenthesis:
(3√-5 + 2)(4√-5 -1) = 3√-5(4√-5) + 3√-5 (-1) + 2(4√-5) + 2(-1)
= -60 - 3√-5 + 8√-5 -2
= 5√-5 - 62
Therefore, the expression (3√-5 + 2)(4√-5 -1) simplifies to 5√-5 - 62
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slope=6 y-intercept=-3
The equation of the line with a slope of 6 and a y-intercept of -3, is y = 6x - 3
Determining the equation of a line with slope and interceptFrom the question, we are to determine the equation of the line that has the given slope and y-intercept
From the slope-intercept form of the equation of a straight line, we have that
y = mx + b
Where m is the slope
and b is the y-intercept
From the given information,
The slope of the line is 6
and
The y-intercept is -3
That is,
m = 6
b = -3
Substitute the values into the equation
y = mx + b
y = 6(x) + (-3)
Simplify
y = 6x - 3
Hence, the equation is y = 6x - 3
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5. If g = -2 and h = -3 find the value of
a) 7g - 2h
b) 3gh - 4h
c) 2g²-4h²
Answer: a
Step-by-step explanation:
PLEASE HELP ASAP!!
Geometry Help!!
5) <OSL
Vertical pair angles are equal angles formed by intersecting lines
6) <MSN (or <LOS)
Supplementary angles are angles that add up to 180 degrees
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
3
6
5
The expression above can also be written in the form
a
b
c
.
For this expression, a = , b = , and c = .
From knowledge of numerals the answer to the given Question is: a = 3 b = 6 c = 5
What are Numerals?
Numerals are symbols or numerals used to represent numbers. They are used in math and other fields to represent quantities and measurements. Numerals can be written in different forms, such as Arabic numerals (1, 2, 3, etc.) or Roman numerals (I, II, III, etc.). Numerals are also used to label items, such as dates (e.g. May 4th, 2020), addresses (e.g. 1234 Main Street), and telephone numbers (e.g. 555-123-4567). Numerals are an important part of our everyday lives, used to count, measure, and express amounts.
Numerals are just a combination of digits that we know
for example if 0,1,2,3,4,5,6.....9
are the fundamental digits then numbers from these like
12,34,668,389,23,39 etc are called numerals
We can also conclude that all numbers have originated from numerals itself and numerals are basic unit of formation of numbers
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In a school there are 1,970 pupils. If there are 799 boys, how many more girls are there than boys?.
If in the school of 1970 pupils, there are 799 boys, there are 372 girls more than the boys.
What do you understand by linear equation?A linear equation is an equation with the maximum degree of one. No variable in a linear equation, thus, has an exponent greater than 1. The graph of a linear equation is always a straight line.
Both linear equations with one variable and those with two variables exist. This is already taught in schools. Let's use the examples below to understand how to distinguish between linear and non-linear equations.
y = 8x - 9 Linear
y = x2 - 7 Non-Linear, the power of the variable x is 2
√y + x = 6 Non-Linear, the power of the variable y is 1/2
y + 3x - 1 = 0 Linear
How to solve?
total number of pupils = 1970
number of boys = 799
number of girls = 1970 - 799 = 1171
number of girls more than the boys = 1171 - 799 = 372
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Alex and Debbie took an afternoon walk through the city. Alex practiced his map making skills along the way, and drew an accurate picture of each turn they took. When he got home, he measured the angles of their turns with a protractor. His drawings are shown below. If they started their walk going north, what direction did they end up facing?
Answer:
connect with a tour
Step-by-step explanation:
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Fill in the blank with an appropriate word, phrase, or symbol(s). Measures of dispersion are used to indicate the spread or _ of the data.
Measures of dispersion are used to indicate the spread or variability of the data.
What is measure of dispersion?Measures of dispersion are crucial for representing the spread of the data, or its fluctuation around a central value, whereas measures of central tendency are used to assess a dataset's "normal" values.
The four main measure of dispersion include
Range Standard deviationInterquartile rangeVarianceThe range in statistics refers to the distribution of data between the lowest and greatest value in the distribution. It is a widely used indicator of variation.
The standard deviation deals with how much the data is away from the mean
The variance is standard deviation squared
These measures the spread, variability or distribution of data
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