The domain and the range of a function/graph/relation are defined as follows:
Domain: set of input values.Range: set of output values.What are the domain and range of a function?The domain of a function is the set that contains all possible input values of the function/relation, hence it is composed by the values of x.The range of a function is the set that contains all possible output values of the function/relation, hence it is composed by the values of y.Missing InformationThe problem is incomplete, hence the concepts of domain and range are presented, and then they are used to obtain the domain and the range.
More can be learned about domain and range at https://brainly.com/question/30348593
#SPJ1
The function, y=-16x^2+32x+48, represents the height, in feet, of a firework x seconds after it is launched.
After how many seconds does the firework hit the ground
x=___seconds
Answer: 3
Step-by-step explanation:
Took the test
can someone explain why 4(8x + 2) = 4(7x + 2 + x)
On solving the provided question, we cans ay that the equation is 4(8x + 2) = 4(7x + 2 + x); when we put x = , LHS = RHS
What is equation?A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.
the equation is
4(8x + 2) = 4(7x + 2 + x)
32x + 8 = 28x + 8 + 8x
36x - 32x = 0
4x = 0
x = 0
when we put x = , LHS = RHS
To know more about equation visit:
brainly.com/question/649785
#SPJ1
Accountants often use the median when studying salaries for various businesses. What is the median of the following salary list: 32019, 21955,27507, 43715,38850,25963
The median of the following salary list is 29763.
What is a median?The median is the average in the centre of a data collection, which means that 50% of the data points have a value less than or equal to the median, and 50% of the data points have a value greater than or equal to the median. For a small data collection, calculate the number of data points (n) and organize them in ascending order.
The middle score in the group is called the median. Begin by sorting all of the data sets from lowest to highest before calculating the median. The median in an odd-numbered set will be the value that falls exactly in the center of the list. You must determine the average of the two middle integers in a set of even numbers.
Arrange in ascending order
21955, 25963, 27507, 32019, 38850, 43715
Take the two mid terms
27507 and 32019
Median = [tex]\dfrac{27507 + 32019}{2}[/tex]
Median = 29763
To know more about median, visit
brainly.com/question/28060453
#SPJ1
convert the following measurement
The value of expression after change its measurement as;
⇒ 3.4 × 10⁻⁴ kg . m²/ s²
What is Measurement unit?A measurement unit is a standard quality used to express a physical quantity. Also it refers to the comparison between the unknown quantity with the known quantity.
Given that;
The expression is,
⇒ 3.4 × 10⁵ g . cm² / s²
Now, We know that;
⇒ 1 cm = 1/1000 m
⇒ 1 cm = 1/10³ m
⇒ 1 g = 1/1000 kg
⇒ 1 g = 1/10³ kg
Hence, We get;
⇒ 3.4 × 10⁵ g . cm² / s²
⇒ 3.4 × 10⁵ (1/10³) kg . (1/10³)² m²/ s²
⇒ 3.4 × 10⁵ × 10⁻³ × 10⁻⁶ kg . m²/ s²
⇒ 3.4 × 10⁻⁴ kg . m²/ s²
Learn more about the measurement unit visit:
https://brainly.com/question/777464
#SPJ1
Everyone should have free Internet access to education, news, jobs, and more.
The graph plots education and news on the x-axis and other goods and services on the y-axis.
Draw the economy's PPF before the Internet and label it PPF0.
Draw the PPF after the arrival of the Internet if the effect on education and news is greater than on other goods and services. Label it PPF1.
From the provided graph, Due to the greater impact of the internet on education and news, PPF on the x-axis (education and news axis) moves more than the shift on the y-axis.
What is graphs?Mathematicians use graphs to lοgically convey facts or values using visual representations or charts. A graph pοint will typically reflect a relationship between two or more things. Nοdes, or vertices, and edges make form a graph, a nοn-linear data structure. Glue together the nodes, often referred tο as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5), (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representatiοns of expοnential growth. a lοgarithmic graph in the shape of a triangle.
Assume that in the "οld PPF," which existed befοre the internet, equal amounts of news, educatiοn, and other commodities and services are generated.
Due to the greater impact οf the internet on education and news, PPF on the x-axis (education and news axis) moves mοre than the shift on the y-axis.
To know more about graphs visit:
brainly.com/question/11950136
#SPJ1
Based on previous sales, Ron predicted sales of 80 pen sets. He actually sold 100 pen sets. Find the error and absolute error for the pen sets. A 5-column table with 3 rows. Column 1 is labeled Item with entries folders, erasers, pen sets. Column 2 is labeled Approximate Value with entries 25, 220, 80. Column 3 is labeled Exact value with entries 30, 200, 100. Column 4 is labeled Error with entries negative 5, 20, a. Column 5 is labeled Absolute Error with entries 5, 20, b.
The error is 20 and absolute error for the pen sets is also 20. Absolute error is the difference between a quantity's observed or inferred value and its actual value.
What is a absolute error statement?Absolute error is the difference between such a quantity's observed or assumed value and its real value. Because it doesn't indicate the error's magnitude, the absolute inaccuracy is insufficient.
What are absolute and relative error?The difference between a quantity's measured value and its actual value is known as absolute error. The difference between the measurement's absolute error and the quantity's actual value is referred to as relative error.
To know more about absolute error visit;
https://brainly.com/question/11599357
#SPJ1
Answer:
15%
Step-by-step explanation:
flip edge
At Hometown Hospital, the cancer registrar recorded the age (at the time of initial diagnosis) of patients diagnosed with lung cancer. A total of 68 cases were recorded. The ages are ranked from oldest to youngest. 91 86 83 82 81 80 80 79 78 77 76 75 75 74 74 73 73 72 72 72 71 71 70 70 70 70 69 69 68 68 67 67 67 66 66 66 66 66 65 65 65 64 64 63 63 62 62 61 61 61 60 60 59 59 59 58 58 57 57 57 56 56 55 54 53 53 52 51 Complete the frequency distribution table with the following data: All score limit ranges Frequency Cumulative frequency Relative frequency [round to two decimal places] Frequency percentage [should be a whole percentage without decimals]
On solving the provided question, we can say that Frequency Percentage is equal to the relative frequency times one hundred.
what is frequency distribution?In order to make the information easier to understand, frequencies are organized into frequency distributions, which are visual displays. The frequencies displayed in a frequency distribution can be absolute or relative, like ratios or percentages. Both a graph and a table of frequencies can be used to represent a frequency distribution. Both the exact number of observations and the proportion of observations falling within each range can be displayed in a frequency distribution. A relative frequency distribution is the name given to the distribution in the latter scenario. The frequency of an observation is the frequency with which it appears in the data. The frequency of the number 9 in the following list of numbers, for instance, is 5. (because it occurs 5 times). 1, 2, 3, 4, 6, 9, 9, 8, 5, 1, 1, 9.
25–29 is listed as the First Class Group.
Class size is 4 (29-25).
Maintain the same class size for reminders from 89 through 93.
Count the values and record the frequency next to the appropriate class.
Midpoint equals (higher class limit plus lower class limit) / 2.
Relative Frequency is equal to Frequency/total Values.
Cumulative Frequency equals the sum of the past and current frequencies.
Frequency Percentage is equal to the relative frequency times one hundred.
Class Recurrence Point Midway Frequency relative Frequency Added Up percentage of frequency 25-29 0 27 0 0 0.00% 1.25% 1 31 0.0125
%ile Rank for 48 = 12.5
To know more about frequency distribution visit:
https://brainly.com/question/14926605
#SPJ1
Describe in words two ratios from the image that are equivalent.
Two ratios from the image that are equivalent to each other are the oranges shapes and the two smaller green shapes.
What are equivalent ratios ?When we compare two ratios, they are said to be equivalent. To determine whether two or more ratios are equivalent, they can be compared to one another. For instance, the ratios 1: 3 and 2: 6 are equivalent.
In this case, the two orange shapes are equivalent because they are the same size seeing as they both occupied the same portions of the green and white shapes. The smaller green shapes are also equivalent as they have the same length and width.
Find out more on equivalent ratios at https://brainly.com/question/13513438
#SPJ1
Miss brown butt the following items to make a cake for her daughter's 13th birthday party quantity for flower is 5LB the unit costs $2.74 per LB the total cost is $6.54The next item is sugar free for the sugar is 2 1⁄2 LB the unit costs $1.70 per LB the total cost is $1.60 the other item is butter quantity for the butter is 2LBP The next item is sugar free for the sugar is 2 1⁄2 LB the unit costs $1.70 per LB the total cost is $1.60 the other item is butter quantity for the butter is 2LBP that you need to cost is $7.49 per lb the total cost is $4.49Miss brown also needed to buy some eggs exhaust sole 6 for $4.85 and she needs to buy 1⁄2 dozen eggs calculate the cost of eggs calculated her total bill for the 4 items there is a 5% discount if you spend $50 on how much more money will she need to spend to get the discounts which is the best deal spent $50 And get the 5% Discounts Or purchase the four tems ?explain your reasoning.
The total cost of the ingredient to make the cake and the comparison to the percentage discount to get the best deal indicates that we get;
The total cost of the ingredient for the cake is $37.78The best deal is to purchase the 4 items and minimize spendingWhat is a percentage?A percentage is the representation of a proportion of an item per 100 of a set of items.
Quantity of flour = 5 lb
Unit cost for the flour = $2.74 per lb
Quantity of sugar = 2 1/2 lb
Unit cost of the sugar = $1.70 per lb
Quantity of butter = 2 lb
Unit cost of the butter = $7.49 per lb
Quantity of eggs required = 1/2 dozen
Cost of six eggs = $4.85
Miss Brown's total bill for the four items, C, is therefore;
C = 5 × 2.74 + (2 1/2) × 1.7 + 2 × 7.49 + 4.85 = 37.78
Her total cost for the four items, C = $37.78The discount available for purchases of $50 or more = 5% discount on the purchase
The amount of more money she will have to spend to get the 5% discount is therefore;
$50 - $37.78 = $12.22
Miss Brown will have to spend $12.22 extra to get the 5% discount
The 5% discount indicates that spending $50, Miss Brown only has to pay $50 - $50 × 5% = $47.5
Therefore, in order to get the discount, the total amount spent on the purchase is increase by $47.5 - $37.78 = $9.72, and the amount saved from the discount is $2.5, therefore;
Miss Brown should purchase the four itemsLearn more on percentage discount here: https://brainly.com/question/26950456
#SPJ1
help with this geometry please!
no fake answers :)
The value of x in the given set triangles are:
1) x=17.5
2) x=48
3) x= 8
4) 24.5
5) x=11
6) x=9
What is Triangle Proportionality Theorem?
If a line parallel to one side of a triangle contacts the other two sides of the triangle, the line proportionally splits these two sides.
1) According to Triangle Proportionality Theorem,
from given fig 1,
[tex]\frac{14}{12} =\frac{x}{15} \\\\\frac{7}{6} =\frac{x}{15} \\\\x= 17.5[/tex]
2) From fig 2,
[tex]\frac{x}{18} =\frac{56}{21} \\\\x=48[/tex]
3) From fig 3,
[tex]\frac{x}{36} =\frac{10}{45} \\\\\frac{x}{36} =\frac{2}{9} \\\\x=8[/tex]
4) From fig 4,
[tex]\frac{6}{21}=\frac{7}{x} \\\\6x=7*21\\\\x=24.5[/tex]
5) From fig 5,
[tex]\frac{30}{x+7} =\frac{25}{15} \\\\\frac{30}{x+7} =\frac{5}{3} \\\\x=11[/tex]
6) From fig 6,
[tex]\frac{6}{21}=\frac{x-1}{3x+1} \\\\ 18xx+6=21x-21\\\\3x=27\\\\x=9[/tex]
To know more about Triangle Proportionality Theorem visit,
https://brainly.com/question/8160153
#SPJ1
Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions. If the system has one solution, name it.
y=x-2
y=x-1
The system of equations are parallel lines and they do not intersect. Thus, the system has no solution.
What are parallel lines?Parallel lines are any two or more lines that all lie in the same plane and never cross one another. They are equally spaced apart and have the same incline.
No matter how far we extend a parallel line, it will never meet another parallel line.
Given that,
y=x-2
y=x-1
For x = 1:
y = x - 2 = 1 -2 = -1
y = x - 1 = 1 - 1 = 0
For x = 2:
y = 2- 2 = 0
y = 2 -1 = 1
Plot the graph using the points.
The two lines have the same slope hence they are parallel lines.
Since, the two lines are parallel the system has no solutions.
Learn more about system of equations here:
https://brainly.com/question/90105
#SPJ1
In the diagram below, AD EB, m/ABD = 115° and m/D = 27°.
Find m < ABE
The value of angle ABE is 52°
What are interior angle of a triangle ?A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted by triangle ABC.
The interior angles of a triangle are the inside angles formed where two sides of the triangle meet.
The sum of interior angle in a triangle is 180°
Angle EBD = 180-(90+27)
= 180-117
= 63°
angle ABE + EBD = ABD
ABE = ABD - EBD
ABE = 115-63
= 52°
Therefore the value of angle ABE is 52°
learn more about interior angle of triangle from
https://brainly.com/question/25215131
#SPJ1
HELP ASAP TIMED!! hurry
Answer:
3rd choice (x + 8)² + (y - 11)² = 4
Step-by-step explanation:
(x - -8)² + (y - 11)² = 2²
(x + 8)² + (y - 11)² = 4
Step-by-step explanation:
(x - h)² + (y - k)² = r²
h = -8
k = 11
r = 2
(x + 8)² + (y - 11)² = 2²
(x + 8)² + (y - 11)² = 4
The answer is C. (x+8)² + (y-11)² = 4
The Leswaygo Times is a newspaper in the imaginary country Leswaygo. You read in one of its online articles that the people are unhappy with their new king. He is making changes to make Leswaygo more modern. He believes this will benefit the country, but the people do not agree. They are demanding a change in the law to have a voice in any major decisions through voting. If the king allows this, it will change the Leswaygo form of government to
communism
democracy
autocracy
socialism
Since they are demanding a change in the law to have a voice in any major decisions through voting. If the king allows this, it will change the Leswaygo form of government to: B. democracy.
What is democracy?In Government, democracy can be defined as a type of government that is established by the people and generally for the people. This ultimately implies that, a democracy refers to a type of government that accords all the power to the people.
This simply means that, that the form of power that is exercised through the people is generally referred to as democracy. Additionally, all the people living in a country that practice democracy are expected to elect legislators at large and have a voice in any major decisions through voting.
In this context, we can infer and logically deduce that Leswaygo form of government would be changed to democracy.
Read more on democracy here: https://brainly.com/question/2990635
#SPJ1
Answer:
I took the quiz it was B democracy
Step-by-step explanation:
It was democracy because that is the strongest form of government
How likely is it for Bryson to choose a number greater than 4?
The probability of Bryson choosing a number greater than 4 is given as follows:
Amount of numbers that are greater than 4 / Total amount of numbers.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.
For this problem, the outcomes are given as follows:
Desired: numbers greater than 4.Total: all the numbers.Missing InformationThe problem is incomplete, hence the procedure to obtain the probability was described.
More can be learned about probability at https://brainly.com/question/24756209
#SPJ1
Answer:
The answer is likely
Step-by-step explanation:
How to I arrive at this number using a common factor?
The common factor is 6[tex]e^{6x}[/tex] (2x - 5)⁸.
What is a common factor?
These are the "common factors" when we determine the factors of two or more numbers and discover some of those factors are the same (or "common").
Given that
d/dx[[tex]e^{6x}[/tex](2x - 5)⁹]
The formula of the product rule is d/dx(uv) = uv' + vu'.
=(2x - 5)⁹d/dx([tex]e^{6x}[/tex]) + [tex]e^{6x}[/tex]d/dx(2x - 5)⁹
Now applying the formula d/dx(x^n) = nx^(n-1), d/dx e^(mx) = m e^(mx)
=(2x - 5)⁹ 6[tex]e^{6x}[/tex] + [tex]e^{6x}[/tex]×2×9 × (2x - 5)⁸
= 6[tex]e^{6x}[/tex] (2x - 5)⁹ + 18[tex]e^{6x}[/tex](2x - 5)⁸
Now taking common 6[tex]e^{6x}[/tex] (2x - 5)⁸
= 6[tex]e^{6x}[/tex] (2x - 5)⁸ [(2x - 5) + 3]
= 6[tex]e^{6x}[/tex] (2x - 5)⁸ [2x - 5 + 3]
= 6[tex]e^{6x}[/tex] (2x - 5)⁸(2x - 2)
To learn more about derivatives, click on the below link:
https://brainly.com/question/25324584
#SPJ1
Find dy/dx by implicit different iation xy^2= 4.
The value of after differentiation dy/dx will be ( 4 - y² ) / ( 2xy ).
What is differentiation by parts?By using the concept of differentiation by parts the differential will be done in two parts. In the first part, it is done with respect to y and in the second part the differentiation is done for x.
Given function is xy²= 4. The given expression will be different as below,
dy / dx ( xy² ) - 4 = 0
2xy( dy / dx) + y² = 0
dy / dx = -y / 2x
Therefore, the value of dy/dx upon differentiation will be (4 - y2) / ( 2xy ).
To know more about differentiation follow
https://brainly.com/question/16644382
#SPJ9
Jim vende perritos calientes a $2.95 cada uno y sándwiches de bistec a $9.95 cada uno en su carrito de comida. Durante un ajetreado festival al aire libre, vendió un total de 985 artículos por $7343,75. ¿Cuántos sándwiches de bistec vendió?
De acuerdo con la información, se puede inferir que Jim vendió 634 sándwiches de bistec y 351 perritos calientes.
¿Cómo identificar cuántos perros y sándwiches vendió Jim?Para identificar cuántos perros y sandwiches vendió Jim durante la feria debemos comprobar con diferentes números hasta encontrar el número correcto. En este caso, debemos multiplicar el valor de cada producto por un número específico e ir ajustado los valores hasta obtener el número total de productos.
En este caso, la cantidad de sándwiches vendidos por Jim sería 634 y perritos 351.
351 * 2.95 = 1,035.45634 * 9.95 = 6,308,36,308.3 + 1,035.45 = $7343,75Aprenda más sobre comidas en: https://brainly.com/question/7729754
#SPJ1
Assuming that the relationship is exponential, which equation best represents the curve of best fit for this set of data?
The equation that best represents the curve of best fit for this set of data is y = ae^{bx}, where a and b are constants to be determined by the data points.
What is Equation?An equation is a mathematical expression that uses symbols, such as numbers and variables, to represent a relationship between two or more values or quantities. Equations are used to describe physical laws, solve problems and to make predictions. Equations are fundamental to all areas of mathematics and science, and their use is essential for understanding and exploring the natural world.
This equation is an example of an exponential function, which is used to model data that increase or decrease at an increasing rate. The constants a and b can be determined using a least-squares regression to find the line of best fit. The equation can then be used to extrapolate future values from the data points.
To know more about Equation click-
https://brainly.com/question/26408808
#SPJ1
(Q) John has 25 red marbles, 15 blue marbles and 10 yellow marbles. He wants to make similar groups using all the marbles.
(a) Work out the highest number of groups he can make.
(b) Also work out how many, of each color marble, will be in each group.
Answer:
(a) highest number of groups = 5
(b) out how many, of each color marble, will be in each group.
5 red
3 blue
2 yellow
Step-by-step explanation:
The GCF of 25, 15, 10 gives you the greatest number of groups you can form with those numbers
GCF of 25, 15 and 10 can be found as follows by finding factors of each number:
25 = 5 x5
15 = 5 x 3
10 = 5 x 2
Choose the highest number that is common in each group and this is 5
So John can make a maximum number of 5 groups
Divide each number by the GCF to find how may in each group
25/ 5 = 5 red marbles
15/5 = 3 blue marbles
10/5 = 2 yellow marbles
So there are 5 groups max possible each group containing 5 red, 3 blue and 2 yellow marbles
-5-
5
3
24
or to w
4
(0)4
23 45 X
900
Which function represents g(x), a reflection of f(x) = //
(10)* across the x-axis?
O g(x) = -(10)*
Og(x) = -
O g(x) =
5 10
10
g(x) = (10)*
The reflected function across the {x} - axis would be -
g(x) = -2/5 (10)ˣ.
What is the resultant function when f(x) is reflected across the {x} - axis?If the function f(x) is reflected across the {x} - axis, then the new function g(x) becomes -
g(x) = - f(x)
Given is the function as -
f(x) = 2/5 (10)ˣ
We can write the reflected function as -
g(x) = - f(x)
g(x) = - {2/5 (10)ˣ}
g(x) = -2/5 (10)ˣ
Therefore, the reflected function across the {x} - axis would be -
g(x) = -2/5 (10)ˣ.
To solve more questions on reflections, visit the link -
brainly.com/question/30098550
#SPJ1
A quadratic function has a vertex at the point (-1, 3) and passes through the point (-4, -6).
The quadratic function is of the given question is f(x) = [tex]-2x^{2}[/tex] + 10x + 1.
What is quadratic equation?When a, b, and c are constants and x is an unknown variable, the equation has the form [tex]ax^{2}[/tex] + bx + c = 0, which is known as a quadratic equation. The unknown variable x is solved for using the quadratic equation.
The largest power of the variable in a quadratic equation is two. The variable is now squared, but it may also have a coefficient, often known as a multiplier, in front of it. Two more components in the equation are made up of a constant and a variable with an exponent of 1.
In the given question,
The equation of the quadratic function with a vertex at (-1, 3) and passing through (-4, -6) can be written as:
y = [tex]a(x + 1)^{2}[/tex] + 3
Where a is a constant that determines the shape of the function. To find the value of a we can substitute the coordinates of the vertex and the point into the equation and solve for a.
Substituting (x, y) = (-1, 3) into the equation:
3 = [tex]a(-1 + 1)^{2}[/tex] + 3
Simplifying:
3 = [tex]a(0)^{2}[/tex] + 3
3 = 3
Since both sides are equal, a = 1.
Substituting (x, y) = (-4, -6) into the equation:
-6 = [tex]a(-4 + 1)^{2}[/tex] + 3
Simplifying:
-6 = [tex]a(-3)^{2}[/tex] + 3
-6 = 9a + 3
-9 = 9a
Divide each side by 9:
-1 = a
Since both values of a are equal, a = -1.
Therefore, the equation of the quadratic function with a vertex at (-1, 3) and passing through (-4, -6) is:
y = [tex]-(x + 1)^{2}[/tex] + 3
To know about the quadratic function, visit
brainly.com/question/18958913
#SPJ1
Given the following square, solve for x.
(7x+13) °
Answer:
x = 11
Step-by-step explanation:
square = a plane figure with four equal straight sides and four right angles.
so
7x + 13 = 90
7x = 90 - 13
7x = 77
x = 77 : 7
x = 11
------------------------
check
7 x 11 + 13 = 90
90 = 90
the answer is good
Graph the following system of inequalities below and shade the feasible region.
y > -1
y≥ x²+ 1
(x-1)²+(y-1)² ≤ 16
(4marks)
The graph of the system of the equation y > -1, y≥ x²+ 1, and (x-1)²+(y-1)² ≤ 16 is attached with the feasible region of each part shaded
How to identify the graphs
The equation y > -1 is a horizontal line drawn at point y = -1 and shaded above the line because the sign is greater than. the line is dashed line line since the equation is not "greater than or equal to".
The equation y ≥ x²+ 1 is a parabolic equation
The equality sign attached to the greater than makes the line a solid line and because it is greater than the shading is inside the curve.
The equation (x - 1)² + (y - 1)² ≤ 16 is a equation of a circle
The equality sign attached to the greater than ("greater than or equal to") makes the line a solid line and because it is greater than the shading is inside the circle
Learn more about inequality graphs at:
https://brainly.com/question/24372553
#SPJ1
solve. a certain phone call costs 75 cents for the first 3 minutes plus 15 cents for each additional minute. if the call lated x minutes and x is an integer greater than 3, what is cost in dollars
(1) The cost of the phone call was less than $4.16
(2) The cost of the phone call was greater than $3.35
While this is a seemingly simple min/max problem, I was wondering if there is a faster way to deal with decimals—as it took me ~4mins to arrive at the solution.
The cost of a certain phone call was $0.75 for the first 3 minutes and $0.20 for each additional minute after the first 3 minutes. Did the phone call last longer than 15 minutes
According to the above the cost for n minutes, where n>3, is 75 + (n−3)∗20=20n+15
cents. W need to find whether n>15. The cost for 15 minutes is 20n+15=20∗15+15=315
, so we need to find whether the cost is greater than 315 cents.
(1) The cost of the phone call was less than $4.16. Not sufficient.
(2) The cost of the phone call was greater than $3.35. Sufficient.
Learn more about equation formation at:
https://brainly.com/question/2088661
#SPJ1
Amelia and Lucas' son Weights 38.3 pounds. one kilogram is equal to approximately 2.2 pounds Convert their son's weight to kilograms.
Amelia and Lucas' son's weight is 17.41 kilograms.
What is unit conversion?It is the conversion of one unit to another unit with its standard conversion.
Example:
1 hour = 60 minutes
1 km = 1000 m
We have,
Amelia and Lucas' son's Weight = 38.3 pounds.
1 kilogram = 2.2 pounds
Multiply 38.3/2.2 on both sides.
17.41 kilograms = 38.3 pounds
Thus,
Amelia and Lucas' son's weight is 17.41 kilograms.
Learn more about unit conversion here:
https://brainly.com/question/13899873
#SPJ9
Two draws are made at random without replacement from a box containing the following five tickets:
1 2 3 4 3
What is the probability that the sum of the tickets is 5?
in %
The probability that the sum of the ticket is 5, expressed as a percentage is 30%
What is the probability that an event will occur?The probability that an event will occur can be found by the ratio of the number of times the event occurs to the number of all possible events.
The five tickets in the box = 1, 2, 3, 4, 3
The tickets that sum to 5 are; 1 and 4, 2 and 3
The probability that the first ticket picked is 1 = 1/5
The probability that the next ticket picked is a 4 = 1/(5-1) = 1/4
Therefore, the probability of picking a 1 and 4 = (1/5) × (1/4) = 1/20
Similarly, the probability of picking a 4 and then a 1 is 1/20
The probability of picking tickets with numbers 1 and 4 in either order therefore = 2 × 1/20 = 1/10
The probability that the first ticket drawn is 2 = 1/5
The probability that the next ticket picked is a 3 = 2/(5-1) = 1/2
Therefore, the probability to draw a 2 and 3 = (1/5) × (1/2) = 1/10
The probability that the first ticket picked is 3 = 2/5
The probability that the next ticket picked is a 2 = 1/(5-1) = 1/4
Therefore, the probability of picking a 3 and 2 = (2/5) × (1/4) = 2/20 = 1/10
The probability of picking a 2 and a 3 in either order is therefore;
1/10 + 1/10 = 2/10 = 1/5
The probability that the sum of the ticket is 5, is the sum of the probabilities of picking a 1 and a 4 and the probability of picking a 2 and a 3, which is; 1/10 + 1/5 = 3/10 = 0.3
The probability that the sum of the ticket is 5, therefore is 0.3 × 100 % = 30%Learn more on probabilities here: https://brainly.com/question/17082285
#SPJ1
The compression ratio in a certain engine is 7.5 to 1. If the expanded volume of a cylinder is 15 cu in., what is the compressed volume?
On solving the provided question, we can say that inches if a cylinder's enlarged capacity is 45 in3, its compressed volume is 6 in cubic .
what is cylinder?One of the most fundamental curved geometric forms is the cylinder, which is often a three-dimensional solid. It is referred to as a prism with a circle as its base in elementary geometry. Several contemporary fields of geometry and topology also define a cylinder as an indefinitely curved surface. A three-dimensional object known as a "cylinder" consists of curving surfaces with circular tops and bottoms. A cylinder is a three-dimensional solid figure that has two bases that are both identical circles joined by a curving surface at the height of the cylinder, which is determined by the distance between the bases from the center. Examples of cylinders are cold beverage cans and toilet paper wicks.
In a certain engine, the compression ratio is 7.5: 1.
A cylinder's enlarged volume is 45 in3 in.
We must determine the cylinder's compressed volume.
Let v represent the cylinder's compressed volume.
The aforementioned circumstance can be described as
7.5 : 1 = expanded volume : compressed volume
7.5/1 = 45/v
7.5 = 45/v
v = 45/7.5
v = 6 cubic inches .
Therefore, if a cylinder's enlarged capacity is 45 in3, its compressed volume is 6 in cubic .
To know more about cylinder visit:
https://brainly.com/question/16134180
#SPJ1
Please help!! Number 7
Answer:
[tex]x = 9[/tex]
Step-by-step explanation:
Solving For #7
We will use the Angle Bisector Theorem
The angle bisector theorem states that in a triangle, the angle bisector of any angle will divide the opposite side in the ratio of the sides containing the angle.
In the figure provided in #7 we see that QS bisects ∠Q forming two smaller triangles ΔPQS and ΔQRS
According to the angle bisector theorem:
[tex]\dfrac{PQ}{QR} = \dfrac{PS}{RS}\\\\\textrm{Or, alternatively}\\\\\dfrac{QR}{PQ} = \dfrac{RS}{PS}\\[/tex]
Given
[tex]QR = 12.6\\PQ = 7\\RS = x\\PS = 5\\\\[/tex]
[tex]\dfrac{PQ}{QR} = \dfrac{PS}{RS}\\\\\textrm{Or, alternatively}\\\\\dfrac{QR}{PQ} = \dfrac{RS}{PS}\\\\\\\rightarrow \dfrac{12.6}{7} = \dfrac{x}{5}[/tex]
If we multiply by [tex]5[/tex] both sides of the equation we can get rid of the denominator 5 on the right side:
[tex]\rightarrow \dfrac{12.6}{7} \times 5 = x\\\\9 = x\\\\\boxed{x = 9}[/tex]
Select the independent pair(s) of events.
=break your pencil lead while writing, and = feel overly stressed.
=put together a swing set correctly, and =read the directions.
=make an error on your income tax return, and =file Form 1040 long.
=have a salad with dinner, and =work on a home project.
STATS 2332
=break your pencil lead while writing, and = feel overly stressed.
=put together a swing set correctly, and =read the directions.
These are independent events because the occurrence of one event does not affect the occurrence of the other event. Breaking a pencil lead while writing and feeling overly stressed may happen at the same time, but one event does not cause the other. Similarly, putting together a swing set correctly and reading the directions are independent events because one action (reading the directions) does not determine the outcome of the other action (assembling the swing set correctly).
=make an error on your income tax return, and =file Form 1040 long.
These are dependent events because the occurrence of one event (making an error on the tax return) affects the occurrence of the other event (filing Form 1040 long). If you make an error on your tax return, you may need to file a longer form to correct it.
=have a salad with dinner, and =work on a home project.
These are also dependent events because one event (having a salad with dinner) does not determine the outcome of the other event (working on a home project). These events may happen at the same time, but one does not cause the other.
