Answer:
yes, each input (x) has only one output (y)
Step-by-step explanation:
A family plans to have 3 children. For each birth, assume that the probability of a boy is the same as the probability of a girl. What is the probability that they will have at least one boy and at least one girl?.
Probability of at least one boy and one girl = [tex]\frac{3}{4}[/tex]
The probability of no of boys = 1/2 ×1/2×1/2= 1/8
The probability of no of girls = 1/2×1/2×1/2= 1/8
Now we have to find the probability of at least one girls
Probability of one boy and one girl = 1 - (1/8 + 1/8)
= 1 - 1/4
= 3/4
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Name the sides of angle 4
The sides of angle 4 will be side CD and side DG.
We are given a ray diagram.
We need to tell the sides or the rays of the angle 4.
an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles formed by two rays lie in the plane that contains the rays. Angles are also formed by the intersection of two planes.
Here, angle 4 has the sides as CD and DG.
Therefore, the sides of angle 4 will be side CD and side DG.
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Three positive integers are (x - 1), x and (x + 1). If their sum is 105, find the numbers.
The three positive integers are 34, 35, 36
Three positive integers are given as (x-1),x and (x+1)
Sum of these three integers are 105,
As we know the total sum of the three positive integers, we can get the value by adding the three integers to the sum value.
Thus,
(x-1) + x + (x+1) = 105
x - 1 + x + x + 1 = 105
3x + 0 = 105
3x = 105
x = 105/3
x = 35
Then, the integers are (35 - 1) , 35 , (35 + 1)
Therefore, the three positive integers are 34, 35, 36
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HLEP NUMBER 3 HELPPOO
Answer:
8.3333333 square & root of 25
Step-by-step explanation:
Kerri got her cell phone bill this month and was charged for her normal plan, but unfortunately she went over her data allowance and was also charged for each gigabyte over her plan limit. Her bill is represented by the following expression: 10x + 65
What does the coefficient represent in this case?
the cost of her normal plan
how many gigabytes she went over
the cost for the gigabytes over her plan
The coefficient in this question represents the cost for the gigabytes over her plan.
What is the coefficient ?A coefficient is a number that is multiplied by a variable. In this question, the coefficient is 10 and the variable is x. 10 here represents the the cost for the gigabytes over her plan.
10x represents the variable cost. Variable cost is the cost that increases with the number of gigabyte used. Fixed cost is the cost that does not change with the gigabyte used. It remains constant regardless of the level of gigabyte used. Total cost is the sum of the fixed cost and the variable cost. The fixed cost is the cost of her normal plan.
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2. If an airplane's speed is 625 miles per hour, what is its speed in feet per second? Round
your answer to the nearest whole number. There are 5,280 feet in a mile.
A.
B.
C.
D.
426 feet per second
917 feet per second
55,000 feet per second
1,188,000 feet per second
Answer: The answer is B
Your grandmother gives your little brother 42 coins. Some are dimes and some are
nickels, but they total to $3.00. How many dimes does your little brother have?
Taking into account the definition of a system of linear equations, you little brother has 6 dimes.
System of linear equationsA system of linear equations is a set of equations that have more than one unknown, appearing in several of the equations but necessarily in all of them. The equations relate the unknowns to each other.
Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. In other words, the values of the unknowns must be sought, with which when replacing, they must give the solution proposed in both equations.
Amount of dimesIn this case, a system of linear equations must be proposed taking into account that:
"d" is the amount of dimes."n" is the amount of nickels.You know that:
Your grandmother gives your little brother 42 coins. Some are dimes and some are nickels, but they total to $3.00.The system of equations to be solved is
[tex]\left \{ {{d+n=42} \atop {0.1d + 0.05n=3}} \right.[/tex]
It is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.
In this case, isolating the variable "n" from the first equation:
n= 42 -d
Replacing this expression in the second equation obtained:
0.1d + 0.05×(42 - d)= 3
Solving:
0.1d + 0.05×42 - 0.05d= 3
0.1d + 2.1 - 0.05d= 3
0.15d + 2.1=3
0.15d= 3 -2.1
0.15d= 0.9
d= 0.9÷0.15
d= 6
Finally, you little brother has 6 dimes.
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The prize money on a game show about collecting tokens is found using the
formula below.
Keelan won £8695. How many tokens did he collect?
p=20x+75
Using given algebraic equation, Keelan collected 431 tokens.
What is an algebraic equation?In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions.
At least one variable and one operation must be present in an algebraic expression (addition, subtraction, multiplication, division). One such algebraic statement is 2(x + 8y).
You must substitute a number for each variable and carry out the arithmetic operations in order to evaluate an algebraic statement. Since 6 + 6 equals 12, the variable x in the example above is equal to 6. If we are aware of the values of our variables, we may substitute those values for the original variables before evaluating the expression.
Given,
p=20x+75
p = 8695
8695 = 20x + 75
x = 8695 - 75 / 20
x = 431
Therefore Keelan collected 431 tokens.
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The angle below measures _____ degrees.
Find the 18th term of the arithmetic sequence whose common difference is d=-5 and whose first term is a₁ = 20.
=================================================
Explanation:
First let's find the nth term denoted as [tex]a_n[/tex]
[tex]a_n = a_1 + d(n-1) \ \text{ ... formula for arithmetic sequences}\\\\a_n = 20 + (-5)(n-1) \\\\a_n = 20 -5n+5 \\\\a_n = -5n+25 \\\\[/tex]
Now we can find the 18th term by plugging in n = 18
[tex]a_n = -5n+25 \\\\a_{18} = -5(18)+25 \\\\a_{18} = -90+25 \\\\a_{18} = \boldsymbol{-65} \\\\[/tex]
The 18th term is -65Answer:
-65
The 18th term in the sequence is -65.
Step-by-step explanation:
an=a1+(n-1)d
d=-5
a1=20
n=18
a18=20+(18-1)(-5)
Simplify.
a18=20+(17)(-5)
a18=20-85
a18=-65
The 18th term in the sequence is -65.
Hope this helps!
Please mark as brainliest if correct!
Find any points of discontinuity for each rational function. y= x²-x-2 / 3 x²-7 x+2
The point of discontinuity for y= x²-x-2 / 3 x²-7 x+2 is x= 1/3 and x= 2.
What is discontinuous function?
Mathematics, functions, and applications all place a premium on continuous functions. But not every function is continuous. A function is said to have a discontinuity there if it is not continuous at that point in its domain.
Given,
y = x²-x-2 / 3 x²-7 x+2
It can be expressed in the form of -
⇒ y = (x-2) (x+1) / (3x-1) (x-2)
The function will be undefined if the denominator will be 0
⇒ 3x-1 = 0
⇒ x = 1/3
⇒ x-2 = 0
⇒x = 2
So, we can conclude that the given function will be having points of discontinuity as x = 2, 1/3
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Work out (7 x 10°) (2 × 10²) 4 Give your answer in standard form.
Answer:
[tex] {1.4 \times 10}^{3} | [/tex]
Step-by-step explanation:
*winks and runs off ;)*
What are the solutions of each equation? Check your answers.
(a) ln x=2
According to the question, the solution for the equation [tex]ln(x)=2[/tex] is [tex]e^{2}[/tex]. And the procedure for the given equation is as follows:
Expression: [tex]ln(x)=2[/tex]
Removing logarithmic function from the equation, equate it to exponential. Therefore, the expression can be re-written as:
[tex]ln(x)=2\\(x)=e^{2}[/tex]
Therefore, the solution for the equation is :[tex]x=e^{2}[/tex].
What is logarithmic function?
In terms of mathematics, the logarithmic function can be defined as the inverse of exponential function. It is always on the positive side of the ordinate axis.
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What is the rate of change seen in the graph below?
Answer: There is none
Step-by-step explanation:
Nicholas received 100$ for his birthday he decides to spend 20$ per day on whatever he wants
Answer: He would use the money in 5 days.
Step-by-step explanation: 100 divided by 20 is 5.
A hot air balloon rises from the ground to 150 feet elevation. But the wind is too strong, so the pilot ascends another 75 feet
Answer: 225
Step-by-step explanation:
I may not be right but I’m taking that ascends is basically adding up the height so 150+75=225
In 1812, an earthquake of magnitude 7.9 shook New Madrid, Missouri. Compare the intensity level of that earthquake to the intensity level of each earthquake below.
magnitude 7.7 in San Francisco, California, in 1906
1) The earthquake at New Madrid was of greater intensity than earthquake at San Francisco.
2) The earthquake at New Madrid was of lesser intensity than earthquake at Valdivia.
3) The earthquake at New Madrid was of greater intensity than earthquake at Charlottesville.
4) The earthquake at New Madrid was of greater intensity than earthquake at Kobe.
In mathematics, the greater than sign is a basic mathematical notation used to represent an inequality between two values. The symbol used to denote greater inequality is “>”. It is the commonly accepted mathematical notation of two strokes of equal length that meet at an acute right angle. A typical use of the greater than sign is to compare two values, where the first is greater than the second, or one is greater than the other. The greater than sign is an approximation of a closing square bracket.Learn more about greater sign here
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The question is incomplete. The complete question is
In 1812, an earthquake of magnitude 7.9 shook New Madrid, Missouri. Compare the intensity level of that earthquake to the intensity level of each earthquake below.
1. magnitude 7.7 in San Francisco, California, in 1906
2. magnitude 9.5 in Valdivia, Chile, in 1960
3. magnitude 3.2 in Charlottesville, in 2001
4. magnitude 6.9 in Kobe, Japan, in 1995
you're playing the lottery, and you buy a ticket with randomly generated numbers. the first three numbers you get are 5, 10, and 15. thus, the next number you get should be 20.
The given statement is of Inductive Reasoning as "the next number you get should be 20" is just a generalization, there is nothing conclusive.
In the Inductive reasoning , if the statements are true then it does not mean that the conclusion will also be true.
In the Deductive reasoning , if the statements are true then the conclusion need to be true.
In the given question ,
We are playing a lottery and buy tickets with randomly generated numbers.
As the numbers are randomly generated we cannot conclude anything concrete/logically about the next number.
It is random that we have found the pattern and found the next number to be 20.
It is just a mere coincidence that the next number is 20 .
There is nothing Logical for the next number to be 20 as the numbers are randomly generated.
Since in this situation we have made a generalization after observing the pattern , "the next number you get should be 20" is mere generalization and thus, it represents Inductive Reasoning .
Therefore , this case is the case of Inductive Reasoning , the correct option is (a) Inductive.
The given question is incomplete , the complete question is
you're playing the lottery, and you buy a ticket with randomly generated numbers. the first three numbers you get are 5, 10, and 15. thus, the next number you get should be 20.
Which type of reasoning does this statement represent ?
(a)Inductive
(b)Deductive
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A car travels at a rate of 45 m iles per hour for 5 hours. Let y be the distance in miles that a car travels for a
given amount of time, x, in hours. The situtation can be modeleAndd by a function. Which of these describes how their
domain of the function?
Answer:477.47 revolutions
Step-by-step explanation:
Evaluate each expression to four decimal places.
e³/₂
The value of e³/₂ is 4.4758
e in here is considered as Euler's number. Euler's number is a numerical constant which is often used in mathematical calculations. the value of e can be taken into consideration as 2.71828.
The given expression e⁽³÷²⁾ can also be written as √e³. First the cube of e is calculated which is then followed by finding the square root of the calculated value.e⁽³÷²⁾ = √e³. The value of e³ when calculated is 2.7182 x 2.7182 x 2.7182 = 20.0855
Now taking the square root of the calculated value is √20.0855 is 4.4816
Therefore the value of e⁽³÷²⁾ up to four decimal places is 4.4816
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Under his cell phone plan, Ian pays a flat cost of $44.50 per month and $5 per gigabyte. He wants to keep his bill at $61 per month. Which equation could be used to determine xx, the number of gigabytes of data Ian can use while staying within his budget?
Answer:
x<2.1
Step-by-step explanation:
5x<70-59.5
5x<10.5
X<10.5/5
X<2.1
–7.64 + 8d = 14.21 + 17.5d
Is it no solution, one solution, or infinite solution? Please Help
Answer:
This equation has one solution I believe if you substitute the variable 68.3375
Step-by-step explanation:
A rocket is launched in the air. Its height, in meters above sea level, as a function of time, in seconds, is given by h(t) =-4.9t^2 + 229t + 234. Find the maximum height the rocket attains.
Check the picture below, that one shows the imperial units, however is pretty much the same curve for a metric one, namely using metres, so the maximum point is at the vertex y-coordinate.
[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ h(t)=\stackrel{\stackrel{a}{\downarrow }}{-4.9}t^2\stackrel{\stackrel{b}{\downarrow }}{+229}t\stackrel{\stackrel{c}{\downarrow }}{+234} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)[/tex]
[tex]\left(-\cfrac{ 229}{2(-4.9)}~~~~ ,~~~~ 234-\cfrac{ (229)^2}{4(-4.9)}\right) \implies \left( - \cfrac{ 229 }{ -9.8 }~~,~~234 - \cfrac{ 52441 }{ -19.6 } \right) \\\\\\ \left(\cfrac{1145}{49}~~,~~ 234+\cfrac{262205}{98} \right)\qquad \approx\qquad (\stackrel{seconds}{23.37}~~,~~\underset{\bigtriangleup}{\stackrel{meters}{2909.56}})[/tex]
Find the perimeter of the polygon with the given vertices:
U (-1,4)
V (3, 4)
W (3, 1)
The perimeter of the polygon = ?
I need help with this
The perimeter of the polygon is 12.
The perimeter of a closed figure is the sum of the lengths of its outermost sides. It is the sum of the lengths of a polygon's sides. All sides add up to the perimeter.
The distance between the two points A(x, y) and B(x₁, y₁ ).
AB = √ [ (x₁ - x)² + (y₁ - y)² ]
Consider the vertices U ( -1, 4), V (3, 4), W (3, 1).
Then,
UV = √ [ ( 3 +1)² + (4 - 4)² ] = √4² = 4
VW = √ [ ( 3 - 3)² + ( 1 - 4)² ] = √(- 3)² = 3
UW = √ [ ( 3 + 1)² + ( 1 - 4)² ] = √ [ ( 4)² + (-3)² ] = √ [ 16 + 9 ] = √25 = 5
Then the perimeter of the polygon will be:
perimeter = UV + VW + UW
perimeter = 4 + 3 + 5 = 12
Hence, the perimeter of the polygon is 12.
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HELP SOMEONE
A 3-quart container of disinfectant costs $13.56. What is the price per cup?
Answer:
I am not sure but I think its is $1.13
There are 12 cups inside a 3-quart container
Step-by-step explanation:
17. The time it takes Sonia to mow 1 acre of land
is shown in the table. If Sonia has to mow
2.5 acres of land with a push mower, how
long does it take her to mow?
Push Mower
1.25 hours per acre
35 minutes per acre
Gas Mower
The time taken by Sonia to mow 2.5 acres of land with push mower is 3.125 hours .
According to the question we have been given that
Time taken by push mower to mow 1 acre land = 1.25 hours
Time taken by Gas mower to mow 1 acre land = 35 minutes
We need to find how many hours Sonia take to mow 2.5 acre of land with push mower.
To find this we will use unitary method. That is
1 acre = 1.25 hours
2.5 acre = 1.25*2.5 hours
= 3.125 hours.
Hence the time taken by Sonia to mow 2.5 acres of land with push mower is 3.125 hours .
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What is the value of x? (hint: use the measure of XYZ) will mark brainliest
The diagram below shows a section of the steel support structure of a roller coaster. Use the diagram for the problem below. Given segment JK is parallel to segment PL, m∠JKL = (10x + 5)° and m∠PLK = (12x - 1)°, what is the measure, in degrees, of ∠JKL and ∠PLK? (HINT: m∠JKL and m∠PLK is not 90 degrees)
The measure of the angles m∠JKL = (10x + 5)° and m∠PLK = (12x - 1)° are 25 degrees and 23 degrees respectively.
What are parallel segments?Parallel segments are defined as lines on a plane that never meets.
The properties of parallel segments include:
The vertically opposite angles are equalThe corresponding angles are equalThe alternate exterior angles are equalThe alternate interior angles are equalGiven the angles;
m∠JKL = (10x + 5)° m∠PLK = (12x - 1)°We can see that the two angles are vertically opposite angles and thus equal.
Then,
m∠JKL = m∠PLK
substitute the values
10x + 5 = 12x - 1
collect like terms
10x - 12x = -1 - 5
-2x = - 6
Make 'x' the subject of formula
x = 3
But:
m∠JKL = (10x + 5)° = 10(2) + 5 = 25°
m∠PLK = (12x - 1)° = 12(2) - 1 = 23°
Thus, the measure of the angles m∠JKL = (10x + 5)° and m∠PLK = (12x - 1)° are 25 degrees and 23 degrees respectively.
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Evaluate each logarithm.
log₂1/4
The answer of the logarithmic form is -2 .
In mathematics, the logarithmic function is the inverse of power. Then the function is given as f(x) = log xThe logarithm base is a. This can be read as the logarithmic base a of x. The two most common bases used in logarithmic functions are base 10 and base e.The logarithm function has several properties that allow the logarithm to be simplified when the input is in the form of products, quotients, or values raised to powers.We have given an equation [tex]log_2\frac{1}{4}[/tex] ..... (1)
Applying the property of logarithm which is given by [tex]log_xy=\frac{log_ay}{loh_ax}[/tex] in equation (1) ,we get
[tex]log_2\frac{1}{4}=\frac{log\frac{1}{4} }{log2}[/tex] ..(2)
[tex]log\frac{1}{4}[/tex] can be written as [tex]log1-log4[/tex] using property [tex]log\frac{a}{b} =loga-logb[/tex] whereas [tex]log1=0[/tex]
Then , the equation (2) becomes
[tex]log_2\frac{1}{4}=\frac{log1-log4 }{log2}\\\\log_2\frac{1}{4}=\frac{0-log4 }{log2}\\\\log_2\frac{1}{4}=\frac{-log4 }{log2}[/tex]
[tex]log4[/tex] can be written as [tex]log2^2[/tex]
The equation (2) becomes
[tex]log_2\frac{1}{4}=\frac{-log2^2 }{log2}[/tex]
using property [tex]loga^b=bloga[/tex]
[tex]log_2\frac{1}{4}=\frac{-2log2 }{log2}\\log_2\frac{1}{4}=-2[/tex]
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What is 1/20 as a percentage
Answer:
1/20 = 5%
Hope this helps with your question :)
Step-by-step explanation:
1. Multiply numerator and denominator by 5 to get 100 in the denominator.
1/20 = 5/100
2. A number over 100 means it is that number on top of 100.
5/100 = 5% out of 100%
3. So final answer is 5%