The completion of the trend analysis for sales with 2010 as the base year is as follows:
Trend Analysis of Sales:2013 2012 2011 2010
Sales $ 620,000 $ 580,000 $ 450,000 $ 600,000
Trend Analysis 103% 97% 75% 100%
What is trend analysis?Trend analysis is a technical analysis that uses historical data over some periods to predict and monitor future developments in a particular topic.
To undertake a trend analysis for sales, a base year is chosen and the sales account for the base year is set at 100% and used to check how sales have changed during the review periods.
The other years' results are compared to the base year's by dividing each year's result by the base year's.
Percentages are used to depict trend analysis so that the resulting increases and decreases can be easily compared to the base year.
Sales Trend Analysis:2013 (D) = 103% ($620,000/$600,000 x 100)
2012 (C) 97% ($580,000/$600,000 x 100)
2011 (B) 75% ($450,000/$600,000 x 100)
2010 (A) = 100% ($600,000/$600,000 x 100)
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Find the slope and reduce.
P=(2, 3) Q=(9, 7)
Answer:
[tex]\frac{4}{7}[/tex]
Step-by-step explanation:
Slope = m
m = [tex]\frac{y_{2}- y_{1}}{x_{2}-x_{1}}[/tex]
m = [tex]\frac{7-3}{9-2}[/tex] = [tex]\frac{4}{7}[/tex]
Find all intervals on which the function f(x) = (e^(2x^2+5)/-6x is decreasing.
The function f(x) is decreasing on the interval x∈(1/2,∞) and all the real values.
What is meant by a function?A function from a set X to a set Y in mathematics assigns to each element of X exactly one element of Y. The domain of the function is the set X, and the codomain of the function is the set Y.
The first known approximation to the concept of function is attributed to the Persian mathematicians Al-Biruni and Sharaf al-Din al-Tusi. Functions were originally idealistic representations of how one variable quantity depended on another. The location of a planet, for example, changes throughout time. Historically, the concept was formed with infinitesimal calculus near the end of the 17th century, and the functions that were analyzed were differentiable until the 19th century.
Given function,
f(x)=[tex]e^{2 x^{2} +5}[/tex]/-6x
f'(x)=-1/6x([tex]e^{2 x^{2} +5}[/tex])(4x)+[tex]e^{2 x^{2} +5}[/tex](1/6x²)
=[tex]e^{2 x^{2} +5}[/tex]/6x((1/x)-4x)
f'(x)=0
((1/x)-4x)=0
1-4x²=0
4x²=1
x=±1/4
Given that, f(x) is decreasing function then,
f'(x)<0
((1/x)-4x)<0
(1-4x²)/x<0
1-4x²<0
1<4x²
1/4<4x²
x²>1/4
x>1/2
x∈(1/2,∞)
Hence, f(x) is decreasing on the interval x∈(1/2,∞)
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One hundred eight Americans were surveyed to determine the number of hours they spend watching television each month. It was revealed that they watched an average of 151 hours each month with a standard deviation of 32 hours. Assume that the underlying population distribution is normal.
Which distribution should you use for this problem? (Enter your answer in the form z or tdf where df is the degrees of freedom.)
The Z distribution also referred to as the standard normal distribution is the distribution that we would have to use here.
What is the z distribution?A unique type of normal distribution with a mean of 0 and a standard deviation of 1 is known as the standard normal distribution, or z-distribution.
By transforming the values of any normal distribution into z-scores, it is possible to standardize it. Z-scores indicate the number of standard deviations from the mean that each value falls within.
This is the z distribution given that the value of n is more than 30.
We have to make use of z when n which is the number of samples is greater than 30.
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Timothy plans to add a railing parallel to a flight of stairs that goes down to the basement in his house. Each step has the dimensions shown in the sketch.
What will be the length of the railing?
The length of the railing is 105.81 inches.
Given,
The stair has 7 steps
The rise of each step = 8.5 inches
The tread of each step = 12.5 inches
Slope of each step = x
We have to find the length of the railing.
Length of railing = 7x
Then,
Slope of step, x can be determined using Pythagorean theorem.
Let rise be the height of the right angled triangle and tread be the base of the triangle
Then,
Hypotenuse= Slope, x = [tex]\sqrt{Rise^{2} + Tread^{2} }[/tex]
x = [tex]\sqrt{8.5^{2}+ 12.5^{2} }[/tex]
x = [tex]\sqrt{72.25 + 156.25}[/tex]
x = √228.5
x = 15.12 inches
That is,
The slope, x of one step is 15.12 inches
Now,
Length of the railing = 7x = 7 × 15.12 = 105.81 inches
Therefore,
The length of the railing is 105.81 inches.
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h.
Week 5
Day 5
Date: 21/10/2022
A bag of garri weighs 12kg 104g. Find the weight of 6
such bags.
Answer:
72.624 kg
Step-by-step explanation:
1g = 0.001 kg
104g = 0.104kg
weight of 1 bag = 12.104kg
weight of 6 bags = 12.104 x 6
weight of 6 bags = 72.624kg
(7x-7)
63°
(3x +45)
(9-4)
Find x and y
Answer:
x+7=4/3x-1/3 One solution was found : x = 22 Rearrange: Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : ... 3x-9/4x-12: correct answer right here
Step-by-step explanation:
a recipe for fizzy grape juice, the ratio of cups of sparkling water to cups of grape
ice concentrate is 3 to 1.
a. Find two more ratios of cups of sparkling water to cups of juice concentrate that
would make a mixture that tastes the same as this recipe.
b. Describe another mixture of sparkling water and grape juice that would taste
different than this recipe.
Lesson 3 Practice Problem
Answer:
3:2
Step-by-step explanation:
You need to find two more equivalent ratio of cups of sparkling water to cups of juice concentrate that would make a mixture that tastes the same as this recipe.
Another mixture of sparkling water and grape juice that would taste different than this recipe is 3 : 2 of cups of sparkling water to cups of juice concentrate
Ratio of cups of sparkling water to cups of grape juice concentrate is 3 to 1
ratio of cups of sparkling water : cups of grape juice concentrate = 3 : 1
Equivalent ratio to 3 : 1 are
6 : 2,
9 : 3,
12 : 4
15 : 5
21 : 7
Non equivalent ratio of 3 : 1 are
3 : 2
4 : 2
5 : 5
6 : 4
Therefore, another mixture of sparkling water and grape juice that would taste different than this recipe is 3 : 2 of cups of sparkling water to cups of juice concentrate
I need the answer:’)
Answer:
its D
Step-by-step explanation:
calculator
Cp when Sp is 5625 and profit is 25%
4500 is the Cost price.
What do you mean by price at cost?
Cost price is the total sum of money that it costs a manufacturer to make a particular good or offer a particular service.The cost price of an item is the price at which it is produced or the price at which it is purchased. C.P. stands for "cost price." Selling Price: A product's selling price is the cost at which it is sold.SP = 5625
Profit = 25%
CP = ?
CP = 5625/125 * 100
= 45 * 100
= 4500
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A restaurant manager recorded the number of people in different age groups who attended their food festival. They created the following histogram:
Histogram with title Food Festival Participants, horizontal axis labeled Age Group (year) with bins 0 to 19, 20 to 39, 40 to 59, and 60 to 79, and vertical axis labeled Number of People with values from 0 to 60 at intervals of 10. The first bin goes to 20, the second goes to 40, the third goes to 60, and the last goes to 50.
What percentage of the participants are ages 40 to 59? Round to the nearest whole percent.
20%
35%
60%
100%
According to the histogram, the percentage of participants aged 40 to 59, who attended the restaurant's food festival, is 35%.
What is a histogram?A histogram approximately represents a distribution of grouped data with numerical values.
A histogram uses rectangular bars to show the frequency of data items in successive numerical intervals of equal sizes.
Age Group (year) Number of People
0 to 19 20
20 to 39 40
40 to 59 60
60 to 79 50
Total 170
Percentage of ages 40 to 59 = 60/170 x 100 = 35.29%
Thus, using the histogram, we can assure the restaurant manager that 35% of the festival participants are between 40 and 59 years old.
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Here's a brain teaser.
(I already know the answer)
1=5
2=10
3=15
4=20
5=?
Answer:
5 = 1
or
5 = 25
Step-by-step explanation:
I've seen two answers to this.
1. Since we are told 1 = 5, then 5 = 1.
One answer is 1 = 5
2. Since each number on the right is 5 times the number on the left, then 25 corresponds to 5, and 5 = 25.
Answer: 5=1 (The correct answer) 5=25 (The answer that makes sense but is not correct).
Step-by-step explanation:
Explanation for answer 1: It say's that 1 = 5.
Explanation for answer 2: If we follow the pattern of adding 5 each time we go up a number then 5 would equal 25.
Select the correct answer.
Which set of absolute values is compared correctly?
A. -71 <181<|9|<1-10|
B.1-41 <1-3/<13<|4|
C. 1211-51> |-7|>1-81
D. 1-41>19> |-31 >|-10|
Answer: A
Step-by-step explanation:
The absolute value of a number is its relative distance from zero, so it doesn't matter if it is negative. For example, -3 and 3 are both 3 units away from zero on the number line.
Given: Gross sales, $170,000; sales returns and allowances, $9,000; beginning inventory, $8,000; net purchases, $18,000; ending inventory, $5,000; and operating expenses, $56,000. a. Calculate net sales. b. Calculate cost of merchandise (goods) sold. c. Calculate gross profit from sales. d. Calculate net income.
The calculation of the following income statement figures are as follows:
a) Net Sales are $161,000.b) Cost of goods sold is $21,000.c) The gross profit from sales is $140,000.d) The net income is $84,000.What is the income statement?The income statement is the first financial statement that summarizes the revenues and expenses for a business period to arrive at different profit points.
One of the profit points is the gross profit, which is the difference between the sales revenue and the cost of goods sold.
The other profit points include the operating income, income before tax, and net income.
Income StatementGross sales $170,000
Sales returns and allowances 9,000
Net Sales $161,000
Cost of goods sold:
Beginning inventory $8,000
Net purchases 18,000
Ending inventory (5,000) $21,000
Gross profit $140,000
Operating expenses (56,000)
Net Income $84,000
Thus, the calculation of the income statement figures shows a net income of $84,000.
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Question 2 (1 point)
Determine the sequence and the common difference.
9, 14, 19, 24
Answer:
5 is added each time. the next numbers are, 29, 34 and 39
Step-by-step explanation:
9+5 = 14 14+5=19 19+5=24
Annie's mother asked Annie to go buy oranges, dog food, and bug spray. Each square's side length is 1 block. How many blocks will Annie have to walk
in all if she visits the fruit stand, the pet store, and the supermarket, in that order, before returning home?
A. 14 blocks
B. 18 blocks
C. 20 blocks
D. 32 blocks
We can learn from the graph that ANNIE is required to walk 14 blocks.
What is a graph?a diagram that shows how a variable varies in relation to one or more other variables (such as a collection of points, lines, line segments, curves, or regions).: a grouping of all points whose coordinates meet a specific relation (such as a function): a group of edges and vertices connecting pairs of verticesHow to solve a graph.-
TO GRAPHICALLY SOLVE A SYSTEM OF LINEAR EQUATIONSThe first equation is graphed.Using the same rectangular coordinate system, graph the second equation.Identify whether the lines are parallel, intersect, or are one and the same line.Determine the system's remedy. Find the intersection if the lines do indeed meet.acc to the question-
fruit vendor=(-3,7)
pet store-=(-1,6)
supermarket=(1,5)
annie's house=(1,4)
Hence,We can learn from the graph that ANNIE is required to walk 14 blocks.
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which function has the greater y-intercept?
y=-x+6 x: -1, 0, 1, 2, 3
y: 7,6,5,4,3
y=2x-3 x: -1, 0, 1, 2, 3
y: -5, -3, -1, 1, 3
By evaluating in x = 0, we can see that the function with the greater y-intercept is the first one:
y=-x+6
Which function has the greater y-intercept?
For any function y = f(x), we define the y-intercept as the value that y takes when we evaluate the function in x = 0.
For the first function:
y = -x + 6
The y-intercept is:
y = -0 + 6 = 6
While for the second function:
y = 2x - 3
Evaluating in 0 we get:
y = 2*0 - 3 = -3
So the y-intercept of the first function is 6, and the one of the second function is -3.
Then the first function has the greater y-intercept.
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Find two z values so that the middle 67% of the area is bounded by them.
The two z values that the middle 67% of the area is bounded by them are -3.999 and 3.999.
What is a standard normal distribution?In all continuous probability distributions, it is possible to calculate the percentiles, which are defined as the value of the random variable that leaves an area equal to the percentile to the left of the distribution. When it comes to a central percentile, the area is distributed and the percentile is determined using a table of values or technology.
The area between the two boundaries is 0.67and the remaining area is 0.33 (= 1-0.56) , which is to the left of it.
Look into the z table to find the area between z=-x and mean and z=x and mean. According to z score table z=0.44 has 0.67 of the area to the left of (below) it. That means z=-0.44 has 0.67 of the area to the right of (above) it.
Therefore, the two z values are 0.44 and -0.44.
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The two z values that the middle 67% of the area is bounded by them are -3.999 and 3.999.
What is a standard normal distribution?In all continuous probability distributions, it is possible to calculate the percentiles, which are defined as the value of the random variable that leaves an area equal to the percentile to the left of the distribution. When it comes to a central percentile, the area is distributed and the percentile is determined using a table of values or technology.
The area between the two boundaries is 0.67and the remaining area is 0.33 (= 1-0.56) , which is to the left of it.
Look into the z table to find the area between z=-x and mean and z=x and mean. According to z score table z=0.44 has 0.67 of the area to the left of (below) it. That means z=-0.44 has 0.67 of the area to the right of (above) it.
Therefore, the two z values are 0.44 and -0.44.
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Which number can each term of the equation be multiplied by to eliminate the fractions before solving?
6-3x+=x+5
4
2
6
12
10
If you multiply by 12 you will get rid of all your fractions.
What are linear equations?In mathematics, a linear equation is one that may be written in the form where the variables are alphabets, and the coefficients are frequently real integers. An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
It is rather simple to locate both intercepts when an equation is stated in this way (x and y).
The given linear equation is
6 - (3/4)x + (1/3) = (1/2)x + 5
In this equation the fractions are
(3/4), (1/3) and (1/2)
Take the LCM of 4, 3, and 2
LCM(4, 3, 2) = 12
So, if we multiply the equation with the number 12 we can eliminate the fractions.
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Captain scores 120 points on Space Invaders. Tyger scores 10% more points than Captain. How many points does Tyger score?
The number of points scored by Tyger will be 132 points.
What is the number of points?From the information, Captain scores 120 points on Space Invaders. Tyger scores 10% more points than Captain.
Therefore, the number of points scored by Tyger will be:
= Points scored by Captain + (Percentage × Captain point)
= 120 + (10% × 120)
= 120 + 12
= 132
Tyger scored 132 points.
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The number of points scored by Tyger will be 132 points.
What is the number of points?From the information, Captain scores 120 points on Space Invaders. Tyger scores 10% more points than Captain.
Therefore, the number of points scored by Tyger will be:
= Points scored by Captain + (Percentage × Captain point)
= 120 + (10% × 120)
= 120 + 12
= 132
Tyger scored 132 points.
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The ratio of teachers to students on a field trip is 2:13. If there are 132 more students than adults on the field trip, how many adults are there and how many students are there?
There are 284 number of students and 152 number of adults.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
The ratio of teachers to students on a field trip is 2:13
Let x be the number of adults
If there are 132 more students than adults on the field trip, then 132+x
To find the number of adults and number of students formulate a equation as below
2/13=(x+132)/x
Apply cross multiplication
2x=13(x+132)
Apply distributive law on RHS
2x=13x+1716
11x=1716
Divide both sides by 11
x=152
x+132=152+132=284
Hence there are 284 number of students and 152 number of adults.
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some help me pls with this
Solve the equation: r - 535 = 175
Step-by-step explanation:
r - 535 = 175
r = 175 + 535 = 710
Answer:
take - 535 to the other side (over equal to side)
which makes it +535
r = 175 + 535
r = 710
Use the Product Rule of Logarithms to write the completely expanded expression equivalent to log4 (6(5 + 2x)). Make sure
to use parenthesis around your logarithm functions log(x + y).
[tex]log_{4}(2) + log_{4}(3)+ log_{4}(5+2x)[/tex] is the completely expanded logarithmic expression .
What are logarithms ?Logarithm, an exponent or power that must be raised to obtain a particular number. Mathematically, if bx = n then x = logb n then x is the logarithm of n to base b. Example: 23 = 8; so 3 is the base 2 logarithm of 8, or 3 = log2 8.
The most common types of logarithms are the base 10 common logarithm, the base 2 binary logarithm, and the base e ≈ 2.71828 natural logarithm.
Calculationsthe product rule for logarithms is
[tex]log_{b}(MN) = log_{b}(M) + log_{b}(N)[/tex] for b > 0
now ,
[tex]log_{4}(6(5 + 2x)) \\\\log_{4}(6) + log_{4}(5 + 2x)\\ \\ log_{4}(2.3) + log_{4}(5 + 2x) \\\\ log_{4}(2) + log_{4}(3)+ log_{4}(5 +2x)[/tex]
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The base of a triangle is one half of its height. If the area of the triangle is 196 square millimeters,
find its base and height.
Step-by-step explanation:
the area of a triangle is
base × height / 2
in our case
base × height / 2 = 196 mm²
base × height = 392
base = height / 2
so, using that in our main equation :
(height / 2) × height = 392
height² = 784
height = sqrt(784) = 28 mm
base = height / 2 = 28/2 = 14 mm
Anika earns $5 a week for doing all of her chores around the house. Which graph below represents this relationship between x, the number of weeks she has been doing chores, and y, the amount of money she has earned?
The graph of the linear equation can be seen in the image at the end.
Which graph represents the amount of money Anika has?We start by defining the variables we will use:
x = number of weeks.
y = money that Anika has.
We assume that Anika starts with $0, and then she wins $5 each week, so after x weeks she has:
y = $5*x
To graph this linear equation we need to find two points on the line, if x = 0 we get:
y = $5*0 = $0
So we have the point (0, 0)
if x = 1
y = $5*1 = $5
So we have the point (1, 5)
Now we can graph these two points and connect them with a line, the graph can be seen below.
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What expression has the same value as 2(5x + 2) - (3y)2x – 4x
Answer:
10x+6xy+4
Step-by-step explanation:
2(5x+2)-(3y) 2x-4x
By removing the bracket
10x+4-6xy+12xy
10x+4+6xy
10x+6xy+4
A pet store has 7 cats. Here are their weights (in pounds).
14, 11, 10, 10, 6, 8, 14
Send data to calculator
Find the mean weight of these cats.
If necessary, round your answer to the nearest tenth.
pounds
To find the arithmetic mean (average) of a group of numbers add the numbers and divide by the total number of items we added.
(12+16+10+8+14+15)/6
= 75/6
= 12.5 (answer is already rounded to nearest tenth)
Select the correct answer.
Given that a function, h, has a domain of -3 ≤ x ≤ 11 and a range of 1 ≤ h(x) ≤ 25 and that h(8) = 19 and h(-2) = 2, select the statement that could be true for h.
A.
h(2) = 16
B.
h(-3) = -1
C.
h(8) = 21
D.
h(13) = 18
Option A. The statement that can be said to be true for h is h(2) = 16
How to get the domainIf we look at the domain and range, we can rule out some straight away.
For h - 3 = -1
this is outside of the range of the such that -1 ∉ 1 ≤ hx ≤ 25
When h is 13 = 18
This is also outside of the domain such that 13 ∉ -3 ≤ x ≤ 11
When h is 8 = 21
there is going to be a contradiction with what the question has stated earlier. This is because we are told that h(8) = 19
Therefore on h(2) = 16
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NO LINKS!! Please help me with this one
Answer:
The letter a in an ellipse equation is:
Half of the major axis if a > b and the ellipse is horizontal, orHalf of the minor axis if b > a and the ellipse is vertical.Step-by-step explanation:
General equation of an ellipse
[tex]\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1[/tex]
where:
center = (h, k)Vertices = (h±a, k) and (h, k±b)Foci = (h±c, k) or (h, k±c) where c²=a²−b²If a > b the ellipse is horizontal, a is the major radius, and b is the minor radius.
If b > a the ellipse is vertical, b is the major radius, and a is the minor radius.
The major axis is the longest diameter of an ellipse, so the major radius is one half of the major axis.
The minor axis is the shortest diameter of an ellipse, so the minor radius is one half of the minor axis.
Therefore the letter a in an ellipse equation is:
The major radius (half of the major axis) if a > b and the ellipse is horizontal, orThe minor radius (half of the minor axis) if b > a and the ellipse is vertical.What is the y intercept of the line -3x+2y=6 ?
O
-3
-2
2
3
Answer:
positive 3
Step-by-step explanation:
Steps:
1. first you must get y by itself/isolate it to one side of the equation to get it in the format of y = mx + b
-3x + 2y = 6
+3x +3x add 3x to both sides to get 2y by itself
____________
2y = 3x + 6 -3x+3x cancels out and becomes 0
-------------------------
2 divides both sides by 2 to get y by itself
y = (3/2)x + 3
2. Looking at the equation, we know that 3 is the y-intercept because the "b" in the slope-intercept equation is always the y-intercept.
A plane car fly 300 miles in the same time as it takes a car to go 120 miles. If the car travels 90 mph
slower than the plane, find the speed of the plane.
Using r as your variable to represent the speed of the plane in miles per hour, write an equation
using the information above that can be solved to find the answer to this problem.
Equation:____?
The plane flies___?
The plane flies at a speed of 150mph
A plane can fly 300 miles in the same time as it takes a car to go 120 miles
Let the time taken be t
Let the speed of the plane be x
the car travels 90 mph slower than the plane,
Speed of the car is x - 90
Speed = distance / time
Time taken by plane = time taken by car
300/ x = 120/x - 90
300(x - 90) = 120x
300x - 27000 = 120x
300x - 120x = 27000
180x = 27000
x = 27000/180
x = 150
Therefore, the plane flies at a speed of 150mph
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