When adding two rational numbers with different signs, you can determine the sign of the sum by comparing the magnitudes of the numbers.
• If the absolute value of the first number is greater than the absolute value of the second number, the sum will have the same sign as the first number.
• If the absolute value of the second number is greater than the absolute value of the first number, the sum will have the same sign as the second number.
To determine whether the sum will be positive or negative, you can also compare the signs of the numbers:
• If one number is positive and the other is negative, the sum will be negative if the positive number is smaller than the negative number and positive if it is greater.
• If the numbers have different signs, the sum will be positive if the numbers have opposite signs and negative if they have the same sign.
• If the sum of the two rational numbers is zero, it means that the two numbers cancel each other out, which happens when the absolute value of the first number is equal to the absolute value of the second number with opposite signs.
It's important to note that if you are adding two rational numbers with different signs, you also have to keep in mind that the order of the numbers matters and you might get different results depending on the order.
I hope this helps :)
The equation of a line in slope intercept form is y=mx+b where m is the slope of the line.
Yes, that's correct. In the slope-intercept form, the equation of a line is given as y = mx + b where m is the slope of the line.
The variable "m" represents the slope of the line, which is a measure of how steep the line is. It is calculated as the ratio of the change in the y-coordinate to the change in the x-coordinate, also known as the rise over the run.
A line with a positive slope will rise as it moves to the right, while a line with a negative slope will fall as it moves to the right. A line with a slope of zero is a horizontal line and one with an infinite slope is a vertical line.
The variable "b" is the y-intercept, which is the point where the line crosses the y-axis. It is the value of y when x = 0.
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The graph represents the increase of the sales of juice. Write an equation for the line in slope-intercept form to represent this situation.
The equation for the line in the slope-intercept form will be y = x/2 + 2.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The linear equation is given as,
x/a + y/b = 1
Where 'a' is the x-intercept of the line and ‘b’ is the y-intercept of the line.
From the graph, the intercepts of the line will be (-4, 0) and (0, 2). Then the equation is given as,
x / (-4) + y / 2 = 1
Convert the equation into a slope-intercept form. Then we have
x / (-4) + y / 2 = 1
- x / 2 + y = 2
y = x/2 + 2
The equation for the line in the slope-intercept form will be y = x/2 + 2.
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A study of a local high school tried to determine the mean amount of money that each student had saved. The study surveyed a random sample of 55 students in the high school and found a mean savings of 2900 dollars with a standard deviation of 1300 dollars. Determine a 95% confidence interval for the mean, rounding all values to the nearest whole number.
A 95% confidence interval for the mean of 3243 dollars.
What is a confidence interval?In statistics, the confidence interval formula is used to express the degree of uncertainty surrounding a sample estimate of a population parameter. It is used to describe the degree of uncertainty surrounding a sampling technique.
Given random sample = 55
mean = $2900
standard deviation = $1300
Confidence Interval = m ± z(SD/√n)
n = Number of terms
m = Sample average
SD = Standard Deviation
z = Value corresponding to confidence interval in z table
value of z for 95% confidence interval is 1.96,
substitute the values in formula,
Confidence Interval = m ± z(SD/√n)
Confidence Interval = 2900 ± 1.96(1300/√55)
Confidence Interval = 2900 ± 343.581
Confidence Interval = 3243.581
Confidence Interval = 3243
Hence the mean is 3243 dollars.
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The Miller family must drive 8 hours to reach their destination. They drive 323 hours before stopping for the first time. Then they drive 235 hours before stopping again. How many more hours will it take the Miller family to reach their destination? Use paper to show your work. Enter your answer in the box.
It will take the Miller family
The number of hours it would take Miller's family to reach their destination is [tex]2\frac{2}{3}[/tex] hours. This can be solved using the concept of fractions.
What is a fraction?A fraction is expressed as p/q, where q ≠ 0. Proper fractions, in which the numerator is less than the denominator, and improper fractions, in which the numerator is higher than the denominator, are the two sorts of fractions.
Given, The Miller family must drive 8 hours to reach their destination.
The first time they stopped after driving hours and again for the second time they stopped after driving hours.
Therefore the total hours they drive is,
= [tex](2\frac{2}{3}+2\frac{2}{3})[/tex] hours.
= (8/3 + 8/3) hours.
= 16/3 hours.
= [tex]5\frac{1}{3}[/tex] hours.
So, The number of hours they still need to drive is,
= (8 - 16/3) hours.
= (2⁴ - 16)/3 hours.
= 8/3 hours.
= [tex]2\frac{2}{3}[/tex] hours.
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Find the perimeter of the figure
Answer: 30
Step-by-step explanation: 6 + 4 + 4 + 9.5 + 6 + 6.5 = 30
Elise is working out 20% of 600 kg.
÷
She types 600 20 into her
calculator.
Elise writes down the answer: 30 kg
What is Elise's mistake?
Think of 20% as 20/100 = 0.20
Then we multiply, not divide, this value with 600
0.20*600 = 120 is the answer.
Answer: She divided it by 2 which is incorrect, instead she should multiply 20% by 600kg to get 20% of 600
[tex]\frac{20}{100}[/tex] x 600 (the answer will be 120kg)
What is the difference between the lateral and total surface areas of the prism sitting on its base?
Check the picture below.
well, firstly let's find out the areas, and then let's get their difference
[tex]\stackrel{\textit{\LARGE total surface area}}{\stackrel{\textit{top and bottom}}{2(14.5)(6)}~~ + ~~\stackrel{\textit{left and right}}{2(6)(8.5)}~~ + ~~\stackrel{\textit{front and back}}{2(14.5)(8.5)}}\implies 522.5~ft^2 \\\\\\ ~\hspace{8em}\stackrel{\textit{\LARGE lateral area}}{\stackrel{\textit{left and right}}{2(6)(8.5)}~~ + ~~\stackrel{\textit{front and back}}{2(14.5)(8.5)}}\implies 348.5~ft^2 \\\\[-0.35em] ~\dotfill\\\\ 522.5~~ - ~~348.5\implies \text{\LARGE 174}~ft^2[/tex]
Avelina and half as much as Gus if Gus are in 125 how much did Avelina earn
By solving a simple equation, we will see that Avelina earns $62.50
How much did Avelina earn?Here we know that Avelina earns half as much as Gus, then if we define the variables:
A = amount that Avelina earns.
G = amount that Gus earns.
Then we can write the equation:
A = G/2
That says that Avelina earns half as much as Gus.
We know that Gus earns $125. then we can replace that in the equation above:
A = $125/2
A = $62.50
Avelina earns 62.50 dollars.
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PLS DO NUMBER 10 WILL MARK BRAINLY AND ALSO GIVE AN ADDITIONAL 100 PTS IF CORRECT PLS HURRY. THANK YOU
Answer:
Step-by-step explanation:
the whole one or only one of them?
Answer:
i d k
Step-by-step explanation:
According to a recent poll, 27% of adults in a certain area have high levels of cholesterol. They report that such elevated levels "could be financially devastating to the regions healthcare system" and are a major concern to health insurance providers. Assume the standard deviation from the recent studies is accurate and known. According to recent studies, cholesterol levels in healthy adults from the area average about 210 mg/dL, with a standard deviation of 30 about mg/dL, and are roughly Normally distributed. If the cholesterol levels of a sample of48 healthy adults from the region is taken,
What is the probability that the mean cholesterol level of the sample will be no more than 210?
The probability of 50% shows that the mean cholesterol level of the sample will be no more than 210 for the given mean and standard deviation.
As given in the question,
Area average represents the mean ' μ ' = 210 mg /dL
Standard deviation 'σ ' = 30 mg /dL
Sample 'n' = 48
Normal distribution 's' = σ /√n
= 30 /√48
= 4.35
Probability so that mean of the given sample not more than 210
By using central limit theorem we have,
Z = ( X - μ ) /s
= ( 210 - 210 )/ 4.35
= 0
When Z = 0 it has p-value equals to 0.5.
0.5 = 50%
Therefore, the probability of 50% shows that the mean cholesterol level of the sample will be no more than 210.
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Solve the system of linear equations by substitution.
-5x+6y=-11
6y=x+5
The solution set to the given system of equation is -
x = 4 & y = 1.5.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the system of linear equations as -.
- 5x + 6y = - 11
6y = x + 5
In mathematics, a system of linear equations is a collection of one or more linear equations involving the same variables.
The types of systems of linear equations are as follows:
Dependent : The system has infinitely many solutions. The graphs of the equations represent the same lines. ...Independent : The system has exactly one solution. The graphs of the equations intersect at a single point. ...Inconsistent : The system has no solution.The system of linear equations is -
- 5x + 6y = - 11
6y = x + 5
We can write -
6y = x + 5
x = 6y - 5
Now, we can write -
- 5(6y - 5) + 6y = - 11
- 30y + 25 + 6y = - 11
- 24y = - 11 - 25
- 24y = - 36
y = 36/24
y = 9/6
y = 3/2
y = 1.5
Then, we can write -
x = 6 x 3/2 - 5
x = 9 - 5
x = 4
Therefore, the solution set to the given system of equation is -
x = 4 & y = 1.5.
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What is the domain of f 3 x − 2?
The domain of f(x) = 3x - 2 is (-∞, +∞) or the set of all real numbers.
The domain of a function is the set of all input values (x-values) for which the function produces a valid output (y-value). For f(x) = 3x - 2, the domain is all real numbers.
In other words, for any value of x, whether it is a whole number, a fraction, a decimal or a negative number, we can substitute it into the function and find the corresponding output. Therefore, the domain of f(x) = 3x - 2 is (-∞, +∞) or the set of all real numbers.
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Match the solution to its expression.
Answer: Numbers 3, and 1
Step-by-step explanation:
1. (3/7)/(1/2) = 3/7 * 2 = 6/7 = Number 3
2. 3/4 * 1/4 = 3/4*4 = 3/16 = Number 1
What is 3 3/4 x 2 1/2 as a fraction?
Answer:
3 3/4 * 2 1/2 = 758 = 9 38 = 9.375. Spelled result in words is seventy-five eighths (or nine and three eighths).
Long division
7/55
Pls help ASAP
Answer:55/7= 8
Step-by-step explanation:
It’s division
Answer:
7 with a remainder of 4
Step-by-step explanation:
Open the picture and look how i did.
Your Best Friend
s183960
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For what values of k the vectors are linearly independent?
A collection of vectors v 1, v 2, …, v r from R n is linearly independent if the only scalars that satisfy are k 1 = k 2 = ⃛ = k r = 0.
What are vectors?A quantity or phenomena with both magnitude and direction being independent of one another is called a vector. Additionally, the phrase designates how such a quantity is represented mathematically or geometrically. Velocity, momentum, force, electromagnetic fields, and weight are some natural examples of vectors. Mathematically speaking, a vector is a quantity that has magnitude and direction but not position. Velocity and acceleration are two examples of such variables.If only the scalars k 1 = k 2 = = k r = 0 satisfy, then a set of vectors from R n, v 1, v 2,..., v r, is linearly independent. The trivial linear combination refers to this. However, if a nontrivial linear combination occurs that results in the zero vector, the vectors are dependent.Trivial solutions are those to some equations with a straightforward structure. Despite being of less importance, they must be included for the purpose of completeness. In other terms, a trivial solution to an equation is one that is straightforward.To learn more about trivial linear combination refer to:
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A local restaurant serves 8 entrees for every 5
desserts. Which combination of entrees and
desserts does the restaurant serve?
The combination of entrees and desserts that the restaurant serve will be:
A. The restaurant could serve 40 entrees and 25 deserts.
E. The restaurant could serve 64 entrees and 40 deserts.
How to calculate the combination of entrees?The word problem in mathematics refers to a question that is written as a sentence which requires an individual to use his or her mathematics knowledge.
In this case, the local restaurant serves 8 entrees for every 5 desserts.
In this case it should be noted that:
40 / 25 = 8 / 5
64 / 40 = 8 / 5
The correct options are A and E.
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Is natural log positive or negative?
The natural logarithm function gradually increases as x rises to positive infinity and gradually decreases as x approaches zero. Only for x>0 is the natural logarithm function ln(x) defined. Therefore, it is unknown what a negative number's natural logarithm is.
A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.
After that, the definition of the natural logarithm can be expanded to include logarithm values for all non-zero complex numbers as well as negative numbers, albeit this results in a multi-valued function.
When seen as a real-valued function of a positive real variable, the natural logarithm function is the exponential function's inverse. Not just e, but any positive base other than 1, logarithms can be defined.
However, compared to the natural logarithm, logarithms in other bases only differ by a fixed multiplier.
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an underground storage tank has been in place for 15 years. what is its remaining useful life, on average?
On average, an underground storage tank has a remaining useful life of between 10-20 years depending on the construction, maintenance, and environment it is in. The tank's remaining useful life is also dependent on the type of material used in its construction.
Tanks constructed from steel or fiberglass have a life span of around 15-20 years, while concrete tanks have a longer life expectancy of up to 25 years. In this case, the tank has been in place for 15 years, which puts it at the midpoint of its expected life expectancy.
Depending on the maintenance and environment that the tank has been subjected to, it is not unlikely that it could last longer than its expected life, but it is recommended to inspect the tank periodically to ensure that it is still in good condition. If the tank is not properly maintained, the remaining useful life may be significantly shorter.
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Honeybees beat their wings at very fast rates. In 9 seconds a honeybee can beat its wings 1917 times. In 23 seconds a honeybee can beat its wings 4899 times. Question Complete the table to show ratios that are equivalent to the ratio of time to number of wing beats for a honeybee. Enter a number in each box.
Answer: To complete the table, we need to find ratios that are equivalent to the ratio of time to number of wing beats for a honeybee.
We can start by finding the ratio of time to number of wing beats for the first data point:
9 seconds / 1917 wing beats = 9/1917
And the second data point:
23 seconds / 4899 wing beats = 23/4899
To find equivalent ratios, we can multiply or divide both parts of the ratio by the same number, without changing the value of the ratio. For example, we can divide both parts of the ratio by 9 to get:
9/1917 = (9/9) / (1917/9) = 1 / 213
We can also divide both parts of the ratio by 23 to get:
23/4899 = (23/23) / (4899/23) = 1/213
We can use this same method to find equivalent ratios for other values of time and number of wing beats.
Time (s) Number of wing beats Ratio
9 1917 9/1917 or 1/213
23 4899 23/4899 or 1/213
So, the ratio of time to a number of wing beats for a honeybee is equivalent to 1/213, regardless of the specific values of time and number of wing beats.
Step-by-step explanation:
How do you know if a quadratic function can be factored?
If the discriminant is a perfect square then it represents that quadratic function is factored.
As given in the question,
Standard quadratic function is expressed as :
ax² + bx + c = 0
Quadratic function can be factored by two methods :
1. Splitting of the middle term.
By splitting method it can be expressed as a product of linear function
A( x - u )( x -r )
2. By using quadratic formula : x = ( -b ± √b² -4ac ) /2a
Here discriminant = √b² -4ac
If the discriminant is a perfect square it is possible to factored quadratic equation.
Therefore, the value of discriminant is perfect square it represents that quadratic function is possible to factored.
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Help me with this quick please and quick
Now that we additionally know the point (3, -1) through which the new line should pass, we may express a line using the point-slope form: y = - 5 / 3 x + 4.
How to find the calculation?The line we are attempting to analyze must have the same slope as this given line because it is parallel to the one provided by the common equation 5x + 3y = 6. Using slope-intercept notation, let's solve this equation to determine the slope:5x + 3y = 6
3y = -5x + 6
y = -5/3x + 6 / 3
y = - 5 / 3x + 2
If our line is to be parallel to the supplied line, its slope must likewise be "-5/3."Now that we additionally know the point (3, -1) through which the new line should pass, we may express a line using the point-slope form:y - y0 = m(x - x0)
y - (-1) = -5 / 3 (x - 3)
y + 1 = -5 / 3 x + 5
y = - 5 / 3 + 4.
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What is the Volume of the sphere? Round to the nearest tenth place.
Which inequality matches the graph?
X, Y graph. X range is negative 10 to 10, and y range is negative 10 to 10. Solid line on graph has positive slope and runs through negative 9, negative 10 and negative 3, negative 1 and 3, 8. Above line is shaded.
−2x + 3y > 7
2x − 3y < 7
−3x + 2y ≥ 7
3x − 2y ≤ 7
The solid line on the graph has a positive slope that will be 2y - 3x ≥ 7. Then the correct option is C.
What is the equation of a line passing through two points?Let the equation of the line pass through (x₁, y₁) and (x₂, y₂).
Then the equation of the line is given as,
\rm (y - y_2) = \left (\dfrac{y_2 - y_1}{x_2 - x_1} \right ) (x - x_2)
The points that are on the line are given below.
(-9, -10), (-3, -1), and (3, 8)
The inequality of the line is given as,
(y - 8) ≥ [(8 + 1) / (3 + 3)] (x - 3)
y - 8 ≥ (3/2)(x - 3)
2y - 16 ≥ 3x - 9
2y - 3x ≥ 7
The solid line on the graph has a positive slope that will be 2y - 3x ≥ 7. Then the correct option is C.
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Answer: c
Step-by-step explanation:
The image of the point (0, 7)(0,7) under a translation is (-2, 5)(−2,5). Find the coordinates of the image of the point (5, -2)(5,−2) under the same translation.
The coordinates of the image of point (5, -2) under the same translation is (3, -4)
How to find the coordinates of the image of a point?Translation is a type of transformation that moves a figure or a function in a specific direction and distance without rotating or changing its size.
To solve the given, you can use the equation below:
image = point + translation
So we can say:
translation = image - point
translation = (-2, 5) - (0, 7)
translation = (-2-(0) , 5-7)
translation = (-2, -2)
Under the same translation, the coordinates of the image of the point (5, -2) will be:
image = point + translation
image = (5, -2) + (-2, -2)
image = (5+(-2) , -2+(-2))
image = (3, -4)
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Correct Question
The image of the point (0, 7) under a translation is (−2,5). Find the coordinates of the image of the point (5,−2) under the same translation.
No idea what to do please help
Answer:
1. a = -14 and b = -10
2. c = 12 and d = 1
Step-by-step explanation:
See the attached worksheet. Consolidate like terms, where possible and compare to the rigfht side of the equation,. Assign values to the variables to make both sides equal.
a survey of high school teenagers reported that 96% of those sampled are interested in pursuing a college education. does this statement describe descriptive or inferential statistics?
The statement describes that the survey of high school teenagers reporting that 96% of those sampled are interested in pursuing a college education to be descriptive statistics.
A given data collection, which may be a sample of a population or a representation of the complete population, can be summarised using descriptive statistics, which are concise informational coefficients. Measurements of variability and measures of central tendency make up descriptive statistics (spread). Data are summarised using descriptive statistics.
The statements made by descriptive statistics only apply to the data set from which they were derived; they never extend beyond the data you have. To characterise the fundamental characteristics of the data in a study, descriptive statistics are used. They offer concise summaries of the sample and the measurements. They serve as the foundation for almost all quantitative data analyses, along with straightforward graphical analysis.
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Find the ratio of circles to squares in the diagram below.
OD
O
OOOO
O
Unsimplified ratio of circles to squares:
Just count them a
The ratio of any pair of corresponding sides is the RATIO OF SIMILARITY between any two similar figures. Simply put, when two figures are found to be similar, all of their associated side pairs have the same ratio.
What is a number's ratio?An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls)
Since,
the number of circle in the given figure is 4
the number of squares in the given figure is 16
total number of figures is 20
Ratio is 4/20=1/5
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profit and loss
pls help urgently:)
Answer:
Question 1
₹ [tex]42000[/tex]
Question 2
First table: ₹ [tex]1920[/tex]
Second table ₹ [tex]1200[/tex]
Step-by-step explanation:
Question 1
I will use R and V to denote Ravish and Vineet respectively
Let the original cost of the motorcycle for R be XR sold the bike to V for a loss of 28%Therefore the sales price for the bike to V isQuestion 2
Let the cost of the first table be X and that of the second table be YWe are given the total cost is 3120[tex]X + Y = 3120 \cdots [1][/tex]We are given that the first table was sold for a loss of 15%. A loss of 15% implies that the table was sold for 85% of its original value85% = 0.85So the first table was sold for 0.85XThe second table was sold at a profit of 36%. Profit of 36% implies the table was sold at 136% of its original price136% = 1.36So the second table was sold for 1.36YWe are given both tables were sold for the same priceThereforeSo one table cost ₹1920 and the second table cost ₹1200 ANSWER
What is the domain of the function y â x 5?
The domain of the function y = √(x - 5) is x >= 5, that is [5, ∞).
The domain of the function y = sqrt(x - 5) is the set of all input values (x-values) for which the function is defined.
In this case, the square root function is defined for all non-negative values of x - 5. If x-5 is negative, it would result in an imaginary number, which is not defined. However, since x - 5 cannot be negative, x must be greater than or equal to 5. Therefore, the domain of the function y = √(x - 5) is x >= 5.
--The question is incomplete, answering to the question below--
"What is the domain of the function y = sqrt(x - 5)?"
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