Negative numbers are sometimes rational numbers. As, this statement is only true in all the following statements.
What is numbers ?A number is an arithmetic value that is used to calculate and represent a quantity. Numerical symbols, such as "3," are written to represent numbers. A number system is a logical way of writing numbers that uses digits or symbols to represent them. the system of numbers
Following statements are given,
1. Positive numbers are always rational numbers.
2. Negative numbers are always irrational numbers.
3. Negative numbers are sometimes rational numbers.
4. Negative numbers are always integers.
According to statement Positive numbers are always rational numbers
As this statement is not always true because though √2 is positive, it is not a rational number.
According to statement Negative numbers are always irrational numbers.
This is also not true as always as -4 is negative and it can be expressed in the form of [tex]\frac{-4}{1}[/tex] , hence it is rational.
According to statement Negative numbers are sometimes rational numbers. As it can be both -2 is a negative rational number and -√2 is negative irrational number.
According to statement Negative numbers are always integers.This is not always true because [tex]\frac{-2}{3}[/tex] is a negative number with a fractional part, hence it is not an integer.
Hence, only 3rd statement is true ,
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Am I right or wrong?
Answer:
Step-by-step explanation:
right i think?
Angel simplified both sides of an equation. Both sides of the equation have a variable expression with the same coefficient but different constants. Explain how to determine the number of solutions of the equation.
The number of solutions of the system of equations is given by:
Zero.
How to obtain the number of solutions of the system of equations?The number of solutions of a system of equations is obtained considering the coefficients and the constants of each side of the expression.
If the sides have different coefficients, then it will guarantee that the solution has only one solution, as there will be a division by a term different of zero.
If the sides have the same coefficients and then different constants, as is the case in this problem, the number of solutions is of zero, as a number different of zero will be divided by zero.
If the sides have the same coefficients and the same constants, then the number of solutions is of infinity, as the equivalent solution will be obtained with a division of zero by zero, that can be any value.
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Find the quotient of
4 2/3 divided by 2 2/5
Give your answer as a mixed number in its simplest form
Answer:
1 17/18
Step-by-step explanation:
4 2/3 / 2 2/5 =
= 14/3 / 12/5
= 14/3 × 5/12
= 70/36
= 35/18
= 1 17/18
4 2/3 divided by 2 2/5 results to 35/18.
What is Division?In mathematics, division is the process of dividing a number into equal parts and calculating the maximum number of equal parts that may be formed.
Given:
4 2/3 divided by 2 2/5
So, 14/3 divided by 12/5
= 14/ 3 x 5/ 12
= 7/3 x 5/6
= 35/ 18
Hence, 4 2/3 divided by 2 2/5 results to 35/18.
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Write each equation in slope-intercept form.
9.-10x + 2y = 12
12. 6x-3y=-18
10. 4y + 12x = 16
13.-2x-8y = 24
11. -5x + 15y = -30
14. -4x-10y = -7
Answer:
Step-by-step explanation:
2
Michael and Imani go out to eat for lunch.
Part A
If their food and beverages cost $25.30 and there is an 8% meals tax, how much is the bill? Enter your answer to the nearest cent.
$
Part B
After adding a tip, the total lunch cost was $32.24. What percentage tip did they give? Enter your answer to the nearest percentage.
%
Part A:
After adding the meals tax we get the total bill as $27.32
Part B:
After adding the tip the total lunch cost was 432.24, hence the percentage of tip he gave is 18%
Tax
Meal plus tax = 25.3 + 8/100 * 25.3
Meal plus tax = 25.3 + 2.024 Round later. Find the total.
Meal plus tax = 27.324
Meal plus tax = 27.32 rounded to the nearest cent.
Tip
Total cost = $32.242
tip = 32.242 - 27.324
percentage of tip= 4.918
= 18%
Hence we get the required answers.
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It's a small sentence word problem, I don't understand it though...
The sentence, using the rational root theorem, is completed as follows:
If a polynomial function f has integer coefficients, then every rational solution of f(x) = 0 has the format p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.
What is stated by the rational root theorem?The rational root theorem states that a polynomial with integer coefficients will have every rational solution following the format p/q.
The variables p and q are defined as follows:
Variable p: factor of the constant term, which is the last coefficient of the polynomial function.Variable q: factor of the leading coefficient, which is the first coefficient of the polynomial function.Hence the blanks in this problem are completed, respectively, by:
Constant term and leading coefficent.
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a square sheet of cardboard, 18 inches on a side, is used to make an open box by cutting squares of equal size from the corners and folding up the sides. what size squares should be cut to obtain a box with largest possible volume?
The dimensions of the box are (S-2x)by(S-2x)byS = 2S/3 by 2S/3 S by S/6 to obtain a box with largest possible volume
What are dimensions ?In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coordinate is needed to specify a point on it – for example, the point at 5 on a number line. A surface, such as the boundary of a cylinder or sphere, has a dimension of two (2D) because two coordinates are needed to specify a point on it – for example, both a latitude and longitude are required to locate a point on the surface of a sphere. A two-dimensional Euclidean space is a two-dimensional space on the plane. The inside of a cube, a cylinder or a sphere is three-dimensional (3D) because three coordinates are needed to locate a point within these spaces.
CalculationLet S = length of the sides of the square cardboard sheet. Let x = the side of each square cut from the corners. The volume, V, of the box when the sheet is folded up is:
V = (S-2x)(S-2x)x = 4x3 - 4Sx2 + S2x
To find the maximum value, take the derivative of V wrt x, set it to zero, and solve for x:
V ' = dV/dx = 12x2 - 8Sx + S2
0 = 12x2 - 8Sx + S2
0 = (6x-S)(2x-S)
x = S/6 and S/2
To determine which is the max and which is the min, take the second derivative of V wrt x.
V'' = d2V/dx2 = 24x - 8S
At x = S/2, V'' = 24(S/2) - 8s = 4S. Since S>0, the point x=S/2 is a minimum. This makes sense because you have cut away the entire cardboard square.
At x = S/6, V'' = 24(S/6) - 8S = -4S < 0, so x = S/6 is the maximum
The dimensions of the box are (S-2x)by(S-2x)byS = 2S/3 by 2S/3 S by S/6
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Pocahontas weighs 8.5 kg. Her brother is 3 times as heavy. How
31
4
much does her brother weigh?
Your answer is in bold below!
8.5 x 3 = 25.5
Answer: Her brother is 25.5 kg.
Step-by-step explanation:
If her brother is 3 times as heavy, we need to multiply 8.5 kg by 3.
8.5 kg times 3 is 25.5 kg.
if the individual outcomes of a phenomenon are uncertain, but there is nonetheless a regular distribution of outcomes in a large number of repetitions, we say the phenomenon is
If the individual outcomes of a phenomenon are uncertain, but there is nonetheless a regular distribution of outcomes in a large number of repetitions, this phenomenon is called random phenomenon.
A phenomenon is random if individual outcomes are uncertain, but there is in spite of that, a regular distribution of outcomes in a great number of repetitions.
The probability of any outcome of a random phenomenon can be
described as the proportion of times the outcome would happen in a very lengthy chain of repetitions.
The outcome of any individual coin toss is random. But the outcome over many tosses is foreseeable, as long as the trials are individualistic (i.e., the outcome of a new coin flip is not impacted by the outcome of the preceding flip).
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The screen of a tablet is shaped like
a rectangle. Find the area of the screen by
A = bh, when b = 7 in and
A h = 11 in.
The screen of a tablet is shaped like a rectangle. then the area of the screen is 77 square inches.
What is the area of a rectangle?
If the length of the rectangle is 'l' and the breadth of the rectangle is 'b', then the area of the rectangle can be calculated as
Area = Length * Breadth
The length of the screen is 11 in. and the breadth of the screen is 7 in.
Then the area of the screen,
Area = length * breadth
= 11 * 7
= 77 square inches.
Hence, the screen of a tablet is shaped like a rectangle. then the area of the screen is 77 square inches.
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solve 1/3 x= -4/5
-2 2/5
4/15
2 2/5
-4/15
solve 1/3 x= -4/5
1/3 * -4/5 = -4/15
-2 2/5
4/15
2 2/5
-4/15
Answer:
first option
Step-by-step explanation:
[tex]\frac{1}{3}[/tex] x = - [tex]\frac{4}{5}[/tex]
multiply both sides by 15 ( the LCM of 3 and 5 ) to clear the fractions
5x = - 12 ( divide both sides by 5 )
x = - [tex]\frac{12}{5}[/tex] = - 2 [tex]\frac{2}{5}[/tex]
Three students share 8 blocks of clay equally How much clay does each student get? 8+3= Each student's share is blocks of clay
Answer:
11?
Step-by-step explanation:
since 8+3 = 11 won't each student get 11 because they equally share it and in total 11 x 8 = 88 so they have to share 11 blocks of clay.
At the Jackson Zoo, 1/2 of the animals are primates. Of the primates, 1/2 are monkeys. What fraction of the animals at the Jackson Zoo are monkeys?
The fraction 1/4th of the animals at the Jackson Zoo are monkeys.
What is a fraction?
If the numerator is bigger, it is referred to as an improper fraction and can also be expressed as a mixed number, which is a whole-number quotient with a proper-fraction remainder.
Any fraction can be expressed in decimal form by dividing it by its denominator. One or more digits may continue to repeat indefinitely or the result may come to a stop at some point.
At the Jackson Zoo, 1/2 of the animals are primates
So if x is the total animals in that zoo, total primates are x/2.
Now out of them, 1/2 are monkeys i.e 1/2 of x/2
= x/4.
Hence 1/4 th fraction of the animals at the Jackson Zoo are monkeys.
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When the product of 6 and the square of a number is increased by 5 times the number, the result is 4. Select all of the values that the number could be. 2.
The answer to the given question is -4/3 or 1/2
The product of 6 and the square of a number is increased by 5 times the number, the result is 4.
Firstly, let's write the algebraic expression for the above statement and represent the number as x.
The algebraic expression can be written as:
(6 x x²) + 5x = 4
6x² + 5x = 4
The other expression can also be written as:
6x² + 5x - 4 = 0
Secondly, we must factorize the algebraic expression to solve for x.
6x² - 3x + 8x - 4 = 0
3x (2x - 1) + 4 (2x + 1) = 0
(3x + 4)(2x - 1) = 0
Thirdly, we need to solve for x.
3x + 4 = 0
3x = -4
Now, we need to divide both sides by 3.
3x/3 = -4/3
x = -4/3
or
2x - 1 = 0
2x = 1
Now, we need to divide both sides by 2.
2x/2 = 1/2
x = 1/2
Hence, the values that the number could be is -4/3 or 1/2.
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Multiply. Write your answer as a fraction or as a whole or mixed number.
7 ×
5
6
Answer:210
Step-by-step explanation:
Which set of coordinates represents Figure MNOP reflected across the x-axis?
The set of coordinates after the reflection is (c) M' = (-3, -4) N' = (2, -3) O' = (1, -1) P' = (-2, -2)
How to determine the coordinates after the reflection?The graph represents the given parameter
On the graph, we have the following coordinate points
M = (-3, 4)
N = (2, 3)
O = (1, 1)
P = (-2, 2)
The rule of the reflection is given as:
Reflection across the x-axis
Mathematically, this is represented as
(x, y) ⇒ (x, -y)
When this is applied to the points, we have the following representation
M' = (-3, -4)
N' = (2, -3)
O' = (1, -1)
P' = (-2, -2)
Hence, the set of coordinates is (c)
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Find the value of each angle
Answer:
15° and 75°----------------------------
Given is the right triangle.
The two angles are complementary, so their sum is 90°:
p - 10 + p + 50 = 902p + 40 = 902p = 50p = 25The angles are:
p - 10 = 25 - 10 = 15°p + 50 = 25 + 50 = 75°Answer:
p - 10° = 15° p + 50° = 75°Step-by-step explanation:
Now we have to,
→ find the value of each angle.
Forming the equation,
→ 90° + (p - 10°) + (p + 50°) = 180°
Now the value of p will be,
→ 90° + (p - 10°) + (p + 50°) = 180°
→ (90° - 10° + 50°) + (p + p) = 180°
→ 130° + 2p = 180°
→ 2p = 180° - 130°
→ p = 50°/2
→ [ p = 25° ]
Then the value of other angle is,
→ p - 10° || → p + 50°
→ 25° - 10° || → 25° + 50°
→ 15° || → 75°
Hence, these are the angles.
Which theorem or postulate justifies this statement?
/8 = /10
O linear pair postulate
O alternate exterior angles theorem
O vertical angles theorem
O alternate interior angles theorem
O corresponding angles postulate
Answer: 3)
Could you please mark me as "Brainliest"
4. At an amusement park, the cost for an adult admission is a, and for a child the cost is c. For a group of six
that included two children, the cost was $325.94. For a group of five that included three children, the cost was
$256.95. All ticket prices include tax. Write a system of equations, in terms of a and c, that models this
situation. Use a system of equations to determine the exact cost of each type of ticket algebraically.
The system of equation for each condition will be; 2a + 3c = 325.94 and
2a + c = 162.97 and exact cost of each type of ticket is a = $57.99 and
c = $46.99
What is linear equation?A linear equation is an algebraic equation of the form y = mx+b. involving only a constant and a first-order term, where m is the slope and b is the y-intercept.
At an amusement park, the cost for an adult admission is a and for a child the cost is c. For a group of six that included two children, the cost was $325.94. For a group of five that included three children, the cost was $256.95 and all ticket prices include tax.
According to question,
2a + 3c = $325.94
4a + 2c = $256.95
2a + c = $162.97
Solving the equation by using elimination method, we get,
a = $57.99 and c = $46.99
Hence, The system of equation for each condition will be; 2a + 3c = 325.94 and 2a + c = 162.97 and exact cost of each type of ticket is a = $57.99 and c = $46.99
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write an explanation comparing constant percentage change to constant rate of change. 2. what are some key words in a verbal description that indicate an exponential function can be used to model the situation? what is meant by such words?'
Percentage Change = (ΔV/IV₁I) × 100
Constant rate of Change = (y₂ - y₁)/ (x₂ - x₁)
Constant Percentage Change:
This means that after t period the something has grown to [tex]g^{t} = 1.10^{t}[/tex] it original value .
percentage change formula equals the change in value divided by the absolute value of the original value multiplied by 100.
Constant rate of Change:
In which the rate does not change between different points in the function. in short, constant rate of change refers to the comparison of the way two quantities changes. in equation, the constant rate of change can be seen as a slope.
An exponential function is a function that changes at a constant percentage rate.
An exponential function y of t is characterized by the following property:
when t increases by 1 to find the new value of y the current value by the base.
y- value for t +1 = Base of y - value for t
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what is the probability that the lifetime of at least one component exceeds 2? (do not round intermediate values. round your answer to three decimal places.)
The probability that the lifetime of at least one component exceeds 2 is 0.135.
Given that the joint pdf is f(x,y)=xe^(-x(1+y)) for x≥0, y≥0 and 0 otherwise as shown in attached image.
We want to find the probability that the lifetime of at least one component exceeds 2.
The probability that the lifetime of at least one component exceeds 2 is P(X>2).
[tex]\begin{aligned}P(X > 2)&=\int_{x=2}^{\infty}\int_{y=0}^{\infty}f(x,y)dydx\end[/tex]
Now, we will substitute the given function, we get
[tex]\begin{aligned}P(X > 2)&=\int_{x=2}^{\infty}\int_{y=0}^{\infty}xe^{-x(1+y)}dydx\end[/tex]
Further, we will simplify this, we get
[tex]\begin{aligned}P(X > 2)&=\int_{x=2}^{\infty}\left[-e^{-x(1+y)\right]_{0}^{\infty}dx\\ &=\int_{x=2}^{\infty}e^{-x}dx\\ &=\left[-e^{-x}\right]_{2}^{\infty}\\ &=e^{-2}\\ &=0.135\end[/tex]
Hence, the probability that the lifetime of at least one component exceeds 2 for the joint pdf is f(x,y)=xe^(-x(1+y)) for x≥0, y≥0 and 0 otherwise as shown in attached image is 0.135.
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Chitchat wireless charges $0. 30 per minute plus a monthly base fee. In september, maggie used 120 minutes and her bill was $51. Write and solve an equation that best represents the scenario.
The equation is 51 = x + 120 × 0.30 that can find the monthly base fee charged by Chitchat wireless.
The equation representing the scenario will be formed through following components.
Total bill = monthly base fee + number of minutes × cost per minute
In the above mentioned equation, let us assume the monthly base fee to be x. Now, keep the values in formula to find the value of x.
51 = x + 120 × 0.30
Performing multiplication on Right Hand Side of the equation
51 = x + 36
Rewriting the equation according to x
x = 51 - 36
Performing subtraction on Right Hand Side of the equation
x = 15
Thus, the monthly base fee is $15.
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What is 3860 rounded to
Step-by-step explanation:
3900 if by hundreds
If by thousands 4000
Part A
Steve buys 2 lb of grapefruit and 3 lb of oranges for $7.20. Kennedy buys 4 lb of grapefruit and 2 lb of oranges for $8.80. Let x represent the price per pound for grapefruit, and let y represent the price per pound for oranges. Choose the system of equations that models the situation.
A. 2x + 3y = 7.20
2x + 4y = 8.80
B. 3x + 2y = 7.20
4x + 2y = 8.80
C. 2x + 3y = 7.20
4x + 2y = 8.80
D. 2x + 3y = 8.80
4x + 2y = 7.20
Part B
Steve buys 2 lb of grapefruit and 3 lb of oranges for $7.20. Kennedy buys 4 lb of grapefruit and 2 lb of oranges for $8.80. Let x represent the price per pound for grapefruit, and let y represent the price per pound for oranges. Use the system of equations from Part A to find the price per pound for oranges.
price: $ ____ per pound
System of equations that models the situation is Option C . 2x+3y = 7.20 , 4x+3y = 8.80 and the price per pound for oranges is $1.40.
Given:
Part A
Steve buys 2 lb of grapefruit and 3 lb of oranges for $7.20. Kennedy buys 4 lb of grapefruit and 2 lb of oranges for $8.80.
Let x represent the price per pound for grapefruit, and let y represent the price per pound for oranges.
2x + 3y = 7.20
4x + 2y = 8.80
Part B
on solving two equations:
2x + 3y = 7.20 and 4x + 2y = 8.80
2(2x + 3y) - 4x - 2y = 2*7.20 - 8.80
4x + 6y - 4x - 2y = 14.40 - 8.80
4y = 5.60
y = 5.60/4
= $1.40
hence price of oranges per pound is $1.40.
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At 10:00 am Han and Tyler both started running toward each other from opposite ends of a 10 mile path along a river. Han runs at a pace of 12 minutes per mile. Tyler runs at a apce of 15 minuttes per mile
The Answer is Han will cover 2.5 miles distance
What is distance ?
Distance is the total path covered by a object or person. As its name implies, any distance formula outputs the distance (the length of the line segment). In coordinate geometry, there is a number of formulas for finding distances, such as the separation between two points, the separation between two parallel lines, the separation between two parallel planes, etc.
Han and Tyler both started running toward each other from opposite ends of a 10 mile path along a river.
We need to find the distance run by Han after a half hour.
Han will cover a distance in 12 minutes=1 mile
Han will cover a distance in 1 minute= 1/12mile
Han runs distance in 30 minutes=30*1/12 miles
Hence, Han runs 2.5 miles after half hour.
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help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The graph of the exponential function f(x) = (3/4)ˣ is attached below and this is also option A in the question given
Graph of Exponential FunctionAn exponential graph is a curve that represents an exponential function. An exponential graph is a curve that has a horizontal asymptote and it either has an increasing slope or a decreasing slope. i.e., it starts as a horizontal line and then it first increases/decreases slowly and then the growth/decay becomes rapid.
In the given function
f(x) = (3/4)ˣ,
we can use a graphing calculator to plot the graph while applying the values from the table of function.
Comparing the graph plotted and the options given, the answer is option A
Kindly find the attached graph below
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Find the area (in cm) of the rectangle shown.
7
3
find ta , the tension in string a. express the tension in string a in terms of g , m1 , l , d , m2 , and x .
The expression for tension in the string is T = [(L/2)×(m1×g) + (x)×(m2×g)]/d.
We are a diagram that shows two blocks with masses m1 and m2.There are two strings, A and B. Everything is in equilibrium. Equilibrium is a condition of rest or balance caused by opposing forces acting equally. We need to find the tension in string A. Let the tension in the strings A and B be denoted by the variables "Ta" and "Tb", respectively. The net torque at point B must be zero as everything is in equilibrium. The diagram is attached below.
Στ(B) = 0
τ(a) + τ(b) + τ(m1) + τ(m2) = 0
τ = r×F×sin(θ)
d×(Ta)×sin(90°) + 0 - (L/2)×(m1×g)×sin(90°) - (x)×(m2×g)×sin(90°) = 0
d×(Ta) - (L/2)×(m1×g) - (x)×(m2×g) = 0
Ta = [(L/2)×(m1×g) + (x)×(m2×g)]/d
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What function is represented in the table? HELP!!!!
Answer:
below
Step-by-step explanation:
y = 3 * 2^x plug in the values of x (first column) to get the values in the second column
g a pair of fair dice is rolled. what is the probability of getting a total on the two dice greater than 10
The probability of getting a sum greater than 10 is 1/12.
From the question, we have
total outcomes = 6 ×6 = 36
Number of events of sum greater than 10: {5, 6}, {6, 5}, {6, 6} = 3
Probability = 3/36
=1/12
The probability of getting a sum greater than 10 is 1/12.
Probability:
Probability refers to possibility. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is.
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