Answer:
0 :/
Step-by-step explanation:
S(48) = (48/2)(2a+47d),
S(36) = (36/2)(2a+35d).
Now S(48) = 4S(36)
24(2a+47d) = 4*18(2a+35d) = 72(2a+35d).
Then 2a+47d = 3(2a+35d) and
6a +105d -2a -47d = 0,
4a +58d = 0,
2a+29d = 0.
Now S(30) = (30/2)(2a+29d) = (15)(2a+29d)=0
A single die is rolled twice. the 36 equally-likely outcomes are shown to the right. find the probability of getting two numbers whose sum is 3.
There are 30 cans of soda in a refrigerator. This table shows how many cans there are of each type. If you reach in and pull out one can of soda, what is the probability that is it not a cola?
The probability of randomly selecting a can that is not a cola is:
P = 0.8
How to find the probability?We know that there are 30 cans of soda on a refrigerator, such that 6 of these are of cola.
We want to find the probability of randomly selecting a can that is not of cola, to get that probability, we need to take the quotient between the number of cans that are not of cola and the total number of cans.
There are:
30 - 6 = 24 cans that are not of cola.
30 cans in total.
Then the probability is:
P = 24/30 = 0.8
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The sum of four consecutive multiples of 11 is 2046. What is the smaller of those four numbers?
The smallest of the consecutive numbers is 495
How to determine the smallest of the numbersFrom the question, we have the following parameters that can be used in our computation:
Mathematical statement
The mathematical statement is given as
The sum of four consecutive multiples of 11 is 2046
The smallest mulitple of 11 is represented by 11x
Where x is an integer greater than 0
This means that the other numbers are 11(x + 1), 11(x + 2) and 11(x + 3)
When represented as an equation, we have
11x + 11(x + 1) + 11(x + 2) + 11(x + 3) = 2046
Evaluate the like terms
44x = 2046 - 66
So, we have
44x = 1980
Divide through by 44
x = 45
The smallest is then calculated as
Smallest = 11 * 45
Evaluate
Smallest = 485
Hence, the smallest of the numbers is 495
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There are three dials on a combination lock. Each dial can be set to one of the numbers 1, 2, 3, 4, 5 The three digit number 514 is one way the dials can be set as shown in the diagram.
a) Work out the number of different three digit numbers that can be set for the combination lock.
b) How many of the possible three digit numbers have three different digits?
Answer:
a) 125 different numbers
b) 60 numbers with different digits
Step-by-step explanation:
You want to know the number of different combinations you can have with three dials, each having numbers 1–5, and you want to know the number of combinations with three different digits.
a) CombinationsAny of the three dials may be set to any of the five digits, so there are ...
5 × 5 × 5 = 125
possible three digit combinations.
The number of different 3-digit numbers is 125.
b) Different digitsIf the digits are to be different, there can be 5 different first digits, 4 different second digits, and 3 different 3rd digits, for a total of ...
5 × 4 × 3 = 60
possible combinations with different digits.
The number of 3-digit numbers with different digits is 60.
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Leo made a scale drawing of a swimming pool. He used the scale 1 inch: 8 feet. The diving board is 16 feet long in real life. How long is the diving board in the drawing?
Answer:
x = 128
Step-by-step explanation:
A cyclist bikes at a constant speed for 24 miles. He then returns home at the same speed but takes a different route. His return trip takes two hours longer and is 30 miles. Find his speed.
Answer: they are ripped
Step-by-step explanation:
i guessed
Answer:
3 mi / hr
Step-by-step explanation:
It takes the cyclist 2 hours to go 6 miles further ( 30 -24 mi)
6 mi / 2 hr = 3 m/hr
22. A survey was given to 90 high school students. They were asked if they preferred fiction or non-fiction and if they preferred indoor or outdoor activities. Partial survey results are shown in the table.
What percent of students in the survey, to the nearest whole number, prefer outdoor activities given they prefer non-fiction?
Enter a number in the box.
P(outdoor | non−fiction)= ______%
Note that the percentage of the students in the survey, to the nearest whole number, that prefer outdoor activities given they prefer non-fiction is: 11%.
What is the rationale for the above response?To get the percentage of those who love outdoor activities as well as non-fiction, we must complete the table.
Given:
Total number of those who love Fiction and Non Fiction but who love indoors = 50
From that list those who love fiction = 24, thus, those who love indoor and non-fiction =
50 - 24 = 26
Total number of those who were served are = 90
If the total number of those who love Fiction and Non-Fiction but who love indoors = 50
Then the total number of those who love Fiction and Non Fiction but who love Outdoors = 90 - 50 = 40
If the total number of those who love outdoor (Fiction and non-fiction) = 40 and those who prefer fiction only from this category is = 30;
Then the total number of those who love Non Fiction but who love Outdoors =
40 -30
= 10
Thus, the percentage of this number against the total number of those surveyed is:
10/90
= 0.1111111111 or 11%
Therefore, the percentage of students in the survey, to the nearest whole number, prefer outdoor activities given they prefer non-fiction is given as 11%. See the full table attached.
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Suppose that 7 boys and 13 girls line up in a row. Let $S$ be the number of places in the row where a boy and a girl are standing next to each other. For example,for the row $GBBGGGBGBGGGBGBGGBGG$ we have $S=12$. If all possible orders of these $20$ people are considered,what is the average value of $S$?
(a) 9 (b) 10 (c) 11 (d) 12 (e) 13
Answer:
[tex]$\boxed{(c) : 11}$[/tex]
Step-by-step explanation:
We can think of this problem as placing $7$ dividers (representing the boys) in $20$ slots (representing the people). Thus, the number of ways to arrange the boys and girls is the number of ways to place the dividers, which is $\binom{20}{7}$.
To find the average value of $S$, we need to find the total number of arrangements where $S = k$ for each possible value of $k$, then divide by the total number of arrangements.
Let's first consider the case where $k=0$. There is only $1$ way to arrange the boys and girls such that there are no boys and girls standing next to each other: BBBBBBBBBBBBBBBBBBBBB.
Next, let's consider the case where $k=1$. There are $\binom{7}{1}\binom{13}{6}$ ways to arrange the boys and girls such that there is exactly $1$ pair of boys and girls standing next to each other. To see this, consider that there are $\binom{7}{1}$ ways to choose the position of the divider that separates a boy and a girl, and $\binom{13}{6}$ ways to arrange the remaining dividers and slots.
We can continue this process to find the total number of arrangements for each possible value of $k$. When we add up all of these arrangements and divide by the total number of arrangements, we get the average value of $S$.
More specifically, the average value of $S$ is equal to
[\frac{1\cdot1+\binom{7}{1}\binom{13}{6}\cdot1+\binom{7}{2}\binom{13}{5}\cdot2+\binom{7}{3}\binom{13}{4}\cdot3+\binom{7}{4}\binom{13}{3}\cdot4+\binom{7}{5}\binom{13}{2}\cdot5+\binom{7}{6}\binom{13}{1}\cdot6+\binom{7}{7}\binom{13}{0}\cdot7}{\binom{20}{7}}.]
Simplifying this expression gives us $\boxed{(c) : 11}$.
Note: This problem MUST be solved using a graphing tool (Desmos, Wolfram
Alpha, graphing calculator). Solutions submitted using logarithms (which is not a
topic taught or assessed in Applied Math) will be given a grade of zero.
Two small towns are adjacent to one another. Town A has a population of 700 people,
while Town B has a population of 1400.
Town A has a population growth rate of 3.5% per year. Town B's annual growth rate is
1.25%.
When will the populations be the same? What will their populations be when they are
the same?
Unless you are instructed differently this assignment is worth 5 marks. Use the
following information to guide your work:
After 31 years the population will be the same. Their populations will be 2072 when they are the same.
What is the growth rate?Growth rates are calculated by dividing the difference between the ending and beginning values for the period under consideration by the starting value. The most common time periods for growth rates are annually, quarterly, monthly, and weekly.
The formula for the growth of the population is:
A = P(1+r)^n
A is the total number population after n years.
P is the initial number of population
r is rate of interest.
For town A,
The initial population is 700. The growth rate is 3.5% = 0.035.
The population of town A after t year is y = 700(1+0.035)^t
For town B,
The initial population is 1400. The growth rate is 1.25% = 0.0125.
The population of town A after t year is y = 1400(1+ 0.0125)^t
The system of equations is:
y = 700(1+0.035)^t
y = 1400(1+ 0.0125)^t
The intersection point is (31.537,2071.432).
After 31 years the populations will be the same.
their populations will be 2072 when they are the same
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Line WY is dilated to create line W'Y' using point Q as the center of dilation.
What is the scale factor?
The scale factor of dilation from WY to W'Y' is 2.75
How to determine the scale factor of dilationFrom the question, we have the following parameters that can be used in our computation:
The length of WY is 1.5
The length of W'Y' is 4.125
From the complete question, we understand that:
Line WY is dilated to create line W'Y'The point Q as the center of dilationDilation changes the size of the shape that is being dilated.
This means that
Scale factor = The length of W'Y'/The length of WY
Substitute the known values in the above equation, so, we have the following representation
Scale factor = 4.125/1.5
Evaluate the quotient
Scale factor = 2.75
Hence, the scale factor is 2.75
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Complete question
Line WY is dilated to create line W'Y' using point Q as the center of dilation.
What is the scale factor?
Given that The length of WY is 1.5 and the length of W'Y' is 4.125
What is the name of the line of reflection for the pair of figures?
Enter your answer in the box.
Line {m} is the line of reflection for the given geometry.
What is reflection of graph?Reflections of graphs involve reflecting a graph over a specific line.Reflecting functions are functions whose graphs are reflections of each otherGiven is a pair of heart shaped geometrical figures as shown.
It can be seen clearly that the line {m} forms the line of reflection for the given figure.
Therefore, line {m} is the line of reflection for the given geometry.
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I need help on this one 5 1/2 + 4 1/3
Answer:
9 5/6
Step-by-step explanation:
Add the whole numbers and the fractions separately
(5 + 4) + (1/2 + 1/3)
Add
9 + 5/6
Write as a mixed number
9 5/6
Answer:
9 and 5/6
Step-by-step explanation:
We can start by adding 5 + 4 which equals 9
Then we add 1/2 to 1/3
Both these numbers can be changed to one with the same denominator
So, 1/2 = 3/6 and 1/3 = 2/6
= 3/6 + 2/6
= 5/6
Add 5/6 back to the 9 we got earlier, we get 9 5/6
I have to write a proof
URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100
POINTS!!!
Step-by-step explanation:
I attached the image of answer
Solve 8 sin² (x) - 2 sin(x) - 3 = 0 for all solutions 0 < x < 2π
On solving the provided question we can say that - here in trigonometry [tex]v^2x - 2u - 3 = 0[/tex] = (u-3)(u+1)
what is trigonometry?The area of mathematics known as trigonometry examines the correlation between triangle side lengths and angles. The area first appeared in the Hellenistic era, around the third century BC. from the use of geometry in astronomical study. The area of mathematics known as exact methods deals with specific trigonometric functions and how they might be used in calculations. There are six popular trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their respective names and acronyms (csc). Studying the characteristics of triangles, particularly right triangles, is called trigonometry. The study of geometry, however, is the characteristics of all geometric figures.
[tex]sin^2x - 2 sinx - 3 = 0\\u= sinx\\u^2 = sin^2x\\v^2x - 2u - 3 = 0\\\\[/tex]
factors are = -3 and 1
(u-3)(u+1)
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Jim is calculating the probability of flipping a coin multiple time. Jim decides to
flip a coin three times.
a. Make a systematic list for the possible outcomes of flipping the coin three times
b. Find the probability of each of the following events occurring. Be sure to show your thinking clearly:
P (all three heads)
il.
P (at least one tail)
a) The list with all the possible outcomes is given as follows:
Heads, Heads, Heads.Heads, Heads, Tails.Heads, Tails, Heads.Heads, Tails, Tails.Tails, Heads, Heads.Tails, Heads, Tails.Tails, Tails, Heads.Tails, Tails, Tails.b) The probabilities are given as follows:
P(all three heads) = 1/8.P(at least one tail) = 7/8.How to obtain a probability?A probability is calculated as the division of the number of desired outcomes by the number of total outcomes.
Of the 2³ = 8 outcomes, only one result in three heads, hence the probability is given as follows:
p = 1/8.
At least one tail is complementary to three heads, hence it's probability is given as follows:
p = 1 - 1/8 = 8/8 - 1/8 = 7/8.
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There are 75 national monuments in a particular country.
Fifty-seven of these monuments are located in state A.
c. Write the fraction of national monuments found in states other
than state A
Answer:
idek
Step-by-step explanation:
If f(x) = 3x² - x, Find f( -2)
options
14
10
38
Answer: 14
Step-by-step explanation:
f(-2) means x is -2, so we can solve for when x = -2 by plugging -2 into the equation.
[tex]f(-2) = 3(-2^{2}) - (-2)\\=3(4) + 2\\=12+2\\=14[/tex]
Answer:
Step-by-step explanation:
So what you start with is the variable "x" in 3 different places. When you are changing the x variable, you need to plug it into every variable in the equation. Start by doing that and the problem will look like: f (-2) = 3 (-2)^2 - (-2) Now you can start with either the 3 (-2)^2 or the - (-2), but it is better to go from left to right.
Your Best
Elina
Select the two sequences of transformations that would show that triangles ABC and AED are similar.
The two sequences of transformations that would show that triangles ABC and AED are similar are:
Dilating ΔABC by scale factor 1/2 and reflect A'B'C' over AD.
Reflect AED over line AB and Dilate A'E'D' by scale factor 2.
What is Similarity?Two triangles are said to be comparable if their two sides are in the same ratio as the two sides of another triangle and their two sides' angles inscribed in both triangles are equal.
Given:
as, From the Figure we have to dilate the sides of ΔABC by scale factor 1/2.
Then, sides of Δ will be Similar with equal side ratio.
Then we can have,
Dilating ΔABC by scale factor 1/2 and reflect A'B'C' over AD.
or, Reflect AED over line AB and Dilate A'E'D' by scale factor 2.
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Evaluate the expression when a = 1/4 and b = 6 16a^2 - 4b
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{16a^2 - 4b}[/tex]
[tex]\mathsf{= 16(\dfrac{1}{4})^2 - 4(6)}[/tex]
[tex]\mathsf{= 16(\dfrac{1}{4} \times \dfrac{1}{4}) - 4(6)}[/tex]
[tex]\mathsf{= 16\times \dfrac{1(1)}{4(4)} - 4(6)}[/tex]
[tex]\mathsf{= 16(\dfrac{1}{16}) - 4(6)}[/tex]
[tex]\mathsf{= \dfrac{16}{1}(\dfrac{1}{16}) - 4(6)}[/tex]
[tex]\mathsf{= \dfrac{16(1)}{1(16)} - 4(6)}[/tex]
[tex]\mathsf{= \dfrac{16}{1} - \dfrac{4(6)}{1}}[/tex]
[tex]\mathsf{= 1 - 4(6)}[/tex]
[tex]\mathsf{= 1 - 24}[/tex]
[tex]\mathsf{= -23}[/tex]
[tex]\huge\text{Therefore, your answer should be: }[/tex]
[tex]\huge\boxed{\mathsf{-23}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
What inequality is represented here?
Answer:
y ≥ x + 1
Step-by-step explanation:
The slope is 1. Rise over run 1/1 = 1
The y-intercept is 1. Where the line crosses the y axis. The shaded part is above the line so that would be greater than or equal to.
Answer:
y >= x+1
Step-by-step explanation:
The Slope is x + 1 and the shaded area plus the solid line is the inequality. The shaded area represents y so y >= x+1.
Hope this helps!
By selling a bicycle for Rs. 2,850, a shopkeeper gains 14%. If the profit is
reduced to 8%, then the selling price will be:
Answer:
Rs.2700
Step-by-step explanation:
14% profit means 100% +14% more=114% profit
then to make into decimal 114% divided by 100 to give 1.14
then divide 2850 by 1.14 to find original selling price of bicycle
which will be Rs.2,500
next, a 8% profit means 100%+8% which equals 108% and then make into decimal which is 1.08
then multiply the original selling price (Rs.2,500) by 1.08 to give your final selling price after the 8% profit of ...
Rs.2,700
two less than the product of negative six and 5 eights
The value of two less than the product of negative six and 5 eights will be -5 3/4.
How to calculate the expression?An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.
In this case, some of the mathematical operations that are illustrated in this case include addition, subtraction, etc. The value of two less than the product of negative six and 5 eights will be:
= (-6 × 5/8) - 2
= -3 3/4 - 2
= - 5 3/4
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Caleb has a part-time job at an ice skating rink selling hot cocoa. He decided to plot
the number of hot cocoas he sold relative to the day's high temperature and then
draw the line of best fit. Based on the line of best fit, how many hot cocoas would you
predict Caleb to sell if the day's high temperature were 12°F?
Hot Cocoas Sold
Therefore , As a result 5, 10, and 15 make up the reasonable domain for the function 2 (l + w) = 64..
The definition of functionA connection between a group of sources and one output for each input is referred to as a function. A function is, to put it simply, a collection of equation connected to a single, unique output. In mathematics, a function is a statement, rule, or law that describes the connection between two variables (the dependent variable). One input leads to one output when a rule of this type is used. by Alex Federspiel, the photographer. This statement gives an example of y=x2. There is just one output for y from any input for x. According to our definition, y is a function of x since x is the input value.
We must determine the length and breadth values necessary to make the rectangle's perimeter 64.
l + w = 32
The possible widths are 5, 10, 15, 20, and 25.
Now,
[tex]l + 5 = 32\\l = 27\\l + 10 = 32\\l = 22\\l + 15 = 32\\l = 17\\l + 20 = 32\\l = 12\\l + 25 = 32\\l = 7[/tex]
The domain has widths of 5, 10, 15, 20, and 25.
The range for length is: 27, 22, 17, 12, and 7.
The following is the reasonable domain for the aforementioned situation:
5, 10, 15, 20, and 25
Below is a graph of the function 2 (l + w) = 64.
Therefore , As a result, 5, 10, and 15 make up the reasonable domain for the function 2 (l + w) = 64.
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1:What is the name of the shape to the left?
2:Draw a net of the figure to the left
On solving the provided question we can say that - Pythagorean Theorem triangle [tex]5^2+x^2=10^2 = > x²=100−25=75[/tex]x=√75=√3×25=5√3
What is triangle?Three sides and three vertices make up a triangle, which is a polygon. It is among the fundamental forms in geometry. Triangle ABC is the name given to a triangle with vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are found. A triangle is a polygon that has three sides and three corners. The spots where the three sides join end to end make up the triangle's corners. Three triangle angles added together equal 180 degrees.
On solving the provided question, we can say that the value of x = 5√3
values of x and y
Pythagorean theorem,
The trigonometric ratio: soh-cah-toa, and
According to the given question:
Using the table of trig values, we find that
sin30°=1/2
So, this gives us:
[tex]1/2 = sin 30° = 5/y\\1/2 = 5/y\\(1xy)/2 = 5\\y= 2×5 =10\\[/tex]
Pythagorean Theorem
[tex]5²+x²=10²\\x²=100−25=75\\[/tex]
x=√75=√3×25=5√3
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Helppp . I rlly need help.
Laila should make use of the "box plot" to represent the dataset because it would display the median, minimum, and maximum clearly.
What is the dot plot?A dot plot, sometimes known as a dot chart, is a sort of basic histogram-like graphic used in statistics for very small data sets with discrete values.
Laila wants to create a data display that clearly shows the median salary, highest salary, and lowest salary of her company's 685 employees.
A sample of the data is shown below.
$25,745; $26,512; $27,322; $27,750; $29,820; $32,500; $35,448; $52,020; $63,485; $87,167
She can easily determine the lowest and highest salaries using the three tools (dot plot, box plot, and histogram).
The box plot, on the other hand, makes determining the median easier.
This is because the box plot expresses the quartiles (including the median) of the dataset it represents using a rectangle.
Hence, she should make use of the box plot to represent the data.
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find the absolute value
l-1l
Question 1 Part A: (4 Points): A researcher is following the growth of a particular type of flower. She writes the given equation to show the height of the flower g(n), in inches, and n days.
Complete the inequality below by dragging and dropping the answers on the left into the given boxes
Answer:
0 ≤ n ≤ 5
Step-by-step explanation:
We have the function for growth as
[tex]g(n) = 10(1.02)^n[/tex]
We also know that after a specific n days, the flower has grown to 11.04 inches
Since g(n) represents the height of the flower, we can substitute 11.04 for g(n) and solve for n
∴We get
[tex]11.04 = 10(1.02)^n[/tex]
Switching sides we get
[tex]10(1.02)^n = 11.04[/tex]
Divide both sides by 10 to get
[tex]1.02^n = 1.104[/tex]
Take log on both sides
[tex]\log(1.02^n) = \log(1.104)[/tex]
[tex]\log(x^a) = a \log(x)[/tex]
So
[tex]\log(1.02^n) = n \log(1.02)[/tex]
Therefore
[tex]n \log(1.02) = \log(1.104)[/tex]
[tex]n = \dfrac{\log(1.104)}{\log(1.02)}[/tex]
Using a calculator this works out to
[tex]n = 4.9963[/tex]
Therefore it takes at least these many days for the flower to reach 11.04 inches
Rounding number of days to 5, we get the right side of the inequality as n ≤ 5
n cannot be negative so it starts of with a value of 0 so on the right side of the inequality we get n ≥ 0 which can be rewritten as 0 ≤ n
Together the domain of n can be represented as
0 ≤ n ≤ 5
Hope that helps
Bobby is 3 more than 7 times Jada's age. Bobby is 94 years old. Write and solve an equation to find Jada's age. Pll help due now
Answer:
13 years old.
Step-by-step explanation:
Solution to QuestionLet x be the age of Jada
Given from the question:
Bobby's Age: 7x + 3 years old
Jada's Age: x years old
7x + 3 = 94
7x = 94 - 3
7x = 91
x = [tex]\frac{91}{7}[/tex]
x = 13
Therefore Jada is 13 years old.
Which quantitly is greater than 3 meters A 9ft B 120in C 3.2yd D 0.002km
The quantity that is greater than 3 meters is 120 inches. Option B
What is the conversion factor?
We know that the conversion factor has to do with the manner in which we can be able to convert one value to the other. In this case, we have the fact that the central length that we are considering has been given in the unit of meters.
Now;
We know that;
39.37 inches = 1 meter
120 inches would now be given as;
120 inches * 1 meter/ 39.37 inches
= 3.05 meters
Thus, 120 inches would have more value in meters than 3 meters.
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