We can say that approximately 4.29 inches of rain fell in 15 minutes.
We can apply a proportion to determine the amount of rain that fell in 15 minutes.
We can calculate the proportion because we know that 12 inches of rain fell in 42 minutes:
x inches in 15 minutes equals 12 inches in 42 minutes.
where x is how much rain fell in 15 minutes.
We can cross-multiply and simplify to find x's value:
42 minutes equals 12 inches times 15 minutes (x inches)
180 = 42x
x = 180 / 42
x = 4.2857...
We may estimate that 4.29 inches of rain, rounded to the nearest hundredth, fell in 15 minutes.
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Which two statements describe the end behavior of the function?
The function values increase in size in a positive direction and decrease in size in a negative direction.
The following two statements can be used to describe how the function in the given graph ultimately behaves:
The function gets closer to positive infinity as x gets closer to negative infinity. This is the case since the graph's left end is pointed upward, showing that as x decreases, the function values increase in size in a positive direction.
The function becomes closer to negative infinity as x gets closer to positive infinity. This is the case since the graph's right end is pointing downward, showing that as x increases in value, the function values decrease.
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Prove for any real number, |x−6|+x>3. Please use proof by cases, explaining each as you go.
The proof of |x−6|+x>3 is shown below.
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Unlike to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Given:
We have |x−6|+x>3.
Now, opening the absolute value
|x−6|+x>3
-(x- 6) + x >3
-x + 6 +x > 3
6 > 3
Thus, |x−6|+x>3 has been proved.
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Dividing integers. The temperature dropped 32° F in 4 hours. Suppose the temperature dropped by an equal amount each hour. What integer describes the change?
Answer:
To find the integer that describes the change in temperature, we can divide the total temperature drop by the number of hours:
32 ÷ 4 = 8
Therefore, the temperature dropped by 8 degrees Fahrenheit each hour. The integer that describes the change is -8, since the temperature decreased.
Answer: To find the integer that describes the change in temperature, we need to divide the total change in temperature (32° F) by the number of hours over which the temperature dropped (4 hours). This will give us the amount that the temperature dropped by each hour.
So, dividing 32 by 4, we get:
32 ÷ 4 = 8
Therefore, the temperature dropped by 8 degrees Fahrenheit each hour.
Step-by-step explanation:
If f(x) = x2-9/x+5, find f(0), f(-1), f(1/k)
Step-by-step explanation:
f(0):
f(0) = (0^2 - 9) / (0 + 5)
= -9/5
f(-1):
f(-1) = ((-1)^2 - 9) / (-1 + 5)
= (-8) / 4
= -2
f(1/k):
f(1/k) = ((1/k)^2 - 9) / (1/k + 5)
= (1/k^2 - 9) / (1/k) + 5
= (1 - 9k^2) / (k^2 + 5k)
Therefore, f(0) = -9/5, f(-1) = -2, and f(1/k) = (1 - 9k^2) / (k^2 + 5k).
Answer:
Step-by-step explanation:
To find the values of f(x) at the given points, we substitute the values of x into the expression for f(x) and simplify:
f(x) = (x^2 - 9)/(x + 5)
a) To find f(0), we substitute 0 for x:
f(0) = (0^2 - 9)/(0 + 5) = -9/5
Therefore, f(0) = -1.8.
b) To find f(-1), we substitute -1 for x:
f(-1) = (-1^2 - 9)/(-1 + 5) = (-10)/4
We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor of 2:
f(-1) = -5/2
Therefore, f(-1) = -2.5.
c) To find f(1/k), we substitute 1/k for x:
f(1/k) = ((1/k)^2 - 9)/(1/k + 5)
We can simplify the numerator by multiplying out the square:
f(1/k) = (1/k^2 - 9)/(1/k + 5)
We can simplify the denominator by multiplying by k/k:
f(1/k) = (1 - 9k^2)/(1 + 5k)
Therefore, f(1/k) = (1 - 9k^2)/(1 + 5k).
y= a(1+r)t
1. The sales of McDonald's for one year is $650,000. Their sales are increasing at a rate of
4% per year. What will be their sales after 5 years?
a=
r=
t =
2. The population of a school is 800 students and is increasing at a rate of 2% per year.
What will be their population after 6 years?
a=
r=
t =
3.There are 70 northern sea otters that are seeing a growth at a rate of 18%.What will their population be after 4 years?
a=
r=
t=
4. Annual sales for a furniture stores are $375,000 and are increasing at a rate of 6.75% each year.What will their sales me after 9 years?
a=
r=
t=
5. The population of Indiana showed an annual growth rate of 0.6%.Their population in 1999 was 273,000,000. What will their population be in 2007?
a=
r=
t=
1) If the sales of McDonald's for one year is $650,000 and increasing at 4% annually (exponential growth), their sales after 5 years will be $790,824.
2) If the population of a school is 800 students and is increasing at a rate of 2% per year (exponential growth), after 6 years, the population will be 901.
3) With 70 northern sea otters growing at a rate of 18% annually (exponential growth), after 4 years, the population will be 136.
4) If the annual sales for a furniture stores are $375,000 and increasing (exponential growth) at a rate of 6.75% each year, the sales after 9 years will be $675,060.
5) If the population of Indiana showed an annual growth rate of 0.6% (exponential growth) and their population in 1999 was 273,000, the population in 2007 will be 286,383.
What is exponential growth?Exponential growth refers to the consistent increase in quantity over time and at a constant growth rate.
Exponential growths are modeled using the exponential growth function y = a(1+r)^t.
1. McDonalds:
y= a(1+r)^t
Where a = $650,000
r = 0.04 (4%)
t = 5 years
Sales after 5 years, y= a(1+r)^t
= $650,000 (1.04)^5
= $650,000 × 1.2166529
= $790,824
2) School Population:
Current population = 800
Annual increasing rate = 2%
a = 800
r = 2%
t = 6 years
Population after 6 years, y= a(1+r)^t
= 800(1.02)^6
=901
3) Northern Sea Otters:
a = 70
r = 18% or 0.18
t = 4 years
Population after 6 years, y= a(1+r)^t
= 70(1.18)^4
= 136
4) Furniture Stores:
a = $375,000
r = 6.75% or 0.0675
t = 9 years
Sales after 9 years, y = a(1+r)^t
= 375,000(1.0675)^9
= $675,060
5) Indiana Population:
a = 273,000
r = 0.6% or 0.006
t = 8 years (2007 - 1999)
Population after 8 years, y = a(1+r)^t
= 273,000(1.006)^8
= 286,383
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A bookstore needs to sell at least 235 books. The number of books the store sells is described by 745-30b,where is the price per book.
Select the answer choice in each blank to make the statement true.
The range of the (profit per book)
Sold should be
(greater than $30 )
(between $0 and $17)
(greater than $17)
(between $17 and $30)
The parentheses are the choices for the answer.
The choice in the blank to make the statement true will be D. between $17 and $30)
How to explain the informationRevenue = Price per book × Number of books sold = (745 - 30P) b
Since the store needs to sell at least 235 books, we have:
Revenue ≥ 235 × Price per book = 235(745 - 30P)
Simplifying this inequality, we get:
745b - 30Pb ≥ 235 × 745
P ≤ (745/30) - (235/b)
Since we want to find the minimum profit per book sold, we need to maximize the value of (235/b). The maximum value of (235/b) occurs when b is minimized
If we assume that the cost per book is constant, then the profit per book sold will increase as the price per book increases. Therefore, we can say that the minimum profit per book sold that would enable the store to sell at least 235 books is greater than $17.
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please help me with this
The linear function that models the scatter plot is given as follows:
y = 7/8x + 6.
How to define the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
m is the slope, representing the rate of change.b is the intercept, representing the value of y when x = 0.For the equation in this problem, we have that:
The slope is positive, as when x increases, y increases.The intercept is also positive, as the graph is composed only by positive values.Hence the option that satisfies the sign of the slope and the intercept is given as follows:
y = 7/8x + 6.
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Sam is collecting money for an animal shelter. He collects $150.00 each day for 6 days. The shelter will use 35% of the money he collects to buy pet food. The rest of the money will be used to buy cleaning supplies.
How much of the money that Sam collects will be used to buy cleaning supplies?
According to the solving Sam will spend $585.00 of the money he collects on cleaning materials.
What do the percentages mean?%, a relative figure signifying hundredths of any amount. Since one percent (symbolised as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified. percentage. Mathematical percentile is a related topic.
According to the given information:Sam collects $150.00 each day for 6 days, so the total amount he collects is:
$150.00/day x 6 days = $900.00
The shelter will use 35% of the money he collects to buy pet food. To find out how much money will be used to buy pet food, we can multiply the total amount Sam collects by 35% (or 0.35):
$900.00 x 0.35 = $315.00
So, $315.00 of the money that Sam collects will be used to buy pet food. To find out how much money will be used to buy cleaning supplies, we can subtract the amount used to buy pet food from the total amount collected:
$900.00 - $315.00 = $585.00
$585.00 of the money that Sam collects will be used to buy cleaning supplies.
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If you can please help !! (the question is provided below)
Answer:
The distance between the student and the mirror is 7.5 feet.
Step-by-step explanation:
We can use similar triangles to solve this problem.
Let's call the distance between the student and the mirror "d". We can create a right triangle with the student's height as one leg, the distance "d" as the other leg, and the hypotenuse being the line from the student's eyes to the top of the school. Let's call the length of this line "h".
We can also create a second right triangle with the height of the school as one leg, the distance from the school to the mirror as the other leg, and the hypotenuse being the same line from the student's eyes to the top of the school.
Since these two triangles share an angle (the angle formed by the line from the student's eyes to the top of the school and the ground), they are similar triangles. This means that the ratios of their corresponding sides are equal.
We can set up the following proportion:
(student height) / d = (school height) / (distance from school to mirror)
Plugging in the given values, we get:
4.5 / d = 30 / 50
Simplifying, we get:
4.5 / d = 3 / 5
Cross-multiplying, we get:
3d = 22.5
Dividing by 3, we get:
d = 7.5
Therefore, the distance between the student and the mirror is 7.5 feet.
The distance of the student to the mirror, is 7.5 ft
What are similar triangles?Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion.
Given that, a mirror is placed outside a school the distance from the school to the mirror is 50 ft and the height of the school is 30 ft we need to find the distance of the student to the mirror,
This arrangement is creating two similar triangles, here we will use the properties of the similar triangles, to find the distance of the student to the mirror,
Therefore,
30 / 4.5 = 50 / d
d = 50 x 4.5 / 30
d = 225 / 20
d = 7.5
Hence, the distance of the student to the mirror, is 7.5 ft
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Triangle ABC is shown. Use the graph to answer the question. triangle ABC on a coordinate plane with vertices at negative 8 comma 1, 0 comma 1, negative 4 comma 5 Determine the coordinates of the image if triangle ABC is translated 8 units to the right. A′(−14, 1), B′(−8, 1), C′(−12, 5) A′(−6, 9), B′(0, 9), C′(−4, 13) A′(0, 1), B′(8, 1), C′(4, 5) A′(2, −7), B′(8, −7), C′(4, −3)
The cοοrdinates οf the image if triangle ABC is A′(0, 1), B′(8, 1), C′(4, 5).
What is Triangle?A triangle is a clοsed, twο-dimensiοnal geοmetric figure with three straight sides and three angles. It is οne οf the basic shapes in geοmetry.
A triangle is a pοlygοn with three edges and three vertices. It belοngs tο the basic geοmetric shapes. A triangle with vertices A, B, and C is knοwn as triangle ABC. Any three pοints in Euclidean geοmetry that are nοt cοllinear result in a distinct triangle and a distinct plane.
The cοοrdinates οf the image if triangle ABC is translated 8 units tο the right are:
A′(0, 1), B′(8, 1), C′(4, 5).
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In addition to physical safeguards on all machinery, what else is considered a crucial part of providing safeguard against machine-related hazards
To have an effective safeguarding system, specific and detailed training of workers must also be included.
What constitutes the foundation of the safety system?
Any portion of the operator's body, including the hands, arms, and other body parts, must not come into touch with potentially harmful moving parts.
A strong safety system completely avoids the chance of the operator or another worker putting their bodies in close proximity to dangerous moving parts.
What are the two main sorts of protection strategies?
There are primarily two types of safeguarding: hard guards and safeguarding gadgets. Hard guards act as a physical barrier between workers and moving parts.
Safeguarding devices, however, stop unintentional access to dangers. A machine that needs two hands to operate it, for instance, ensures that neither hand may enter the danger zone.
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If x= 1, solve for y.
y = 3.5x
y = [?]
3.5
you plug in 1 in the x spot then solve
3.5 (1)
which then equals 3.5
that means that's what Y equals
Help due in 30 mins
.
The cost of a Boston Red Sox baseball cap is $24.00. The local sporting goods store sells it for 30.00, Find the markup rate?
Answer:
25%
Step-by-step explanation:
$30-$24 =$6
$6×100
________ =25 percent
24
a broker invested 1,600 in a particular stock. the table shows the value og the stock and the number of weeks since the investment. wgich function best models the value of the stock v(n), in dollars, m weeks since the investment for the given period?
The exponential function that best models the value of the stock after n weeks is given as follows:
v(n) = 1600(1 + r)^n.
How to define the exponential function?The standard definition of an exponential function is given as follows:
y = a(b)^x.
In which:
a is the value of y when x = 0.b is the rate of change.The initial investment was of 1600, hence the parameter a is given as follows:
a = 1600.
The rate of change is obtained multiplying two consecutive values on the table, and will have the following format:
b = 1 + r.
In which r is the growth rate.
Missing InformationThe problem is incomplete, hence the general procedure to obtain the function is presented.
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4. Emma Kishketon recently sold 300 shares of stock in a fast food company for
$46.54 per share plus a commission of $49.95 plus 24 per share. She purchased the
stock for $39.22 plus a 1 percent commission.
Emma's profit from selling the stock is $743.44.
To find out Emma's profit from selling the stock, we need to calculate the total cost of purchasing the stock and the total revenue from selling the stock. Then we can subtract the total cost from the total revenue to get the profit.
Total cost of purchasing the stock:
Emma bought 300 shares of the stock for $39.22 per share plus a 1 percent commission.
Commission = 1% of (300 x $39.22) = $117.66
Total cost = (300 x $39.22) + $117.66 = $11,871.66
Total revenue from selling the stock:
Emma sold 300 shares of the stock for $46.54 per share plus a commission of $49.95 plus $24 per share.
Commission = $49.95 + (300 x $24) = $7,449.95
Total revenue = (300 x $46.54) - $7,449.95 = $12,665.05
Profit:
Profit = Total revenue - Total cost - Commission
Profit = $12,665.05 - $11,871.66 - $49.95 = $743.44
Therefore, Emma's profit from selling the stock is $743.44.
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Emma received $6,512.05 after selling the 300 shares of stock in the fast food company.
What is an algebraic expression?
An algebraic expression is a mathematical phrase that contains variables, constants, and mathematical operations. It may also include exponents and/or roots. Algebraic expressions are used to represent quantities and relationships between quantities in mathematical situations, often in the context of problem-solving.
To calculate the total amount Emma paid for the stock, we first need to calculate the commission she paid when she purchased it:
1% commission = 0.01 * 39.22 = 0.3922
Total cost per share = 39.22 + 0.3922 = 39.6122
So, Emma paid $39.6122 per share when she bought the stock.
To calculate the total amount she received for selling the 300 shares, we need to first calculate the commission she paid for selling it:
Commission per share = 24
Total commission = 300 * 24 + 49.95 = 7,449.95
The total amount she received for selling the shares is:
300 * 46.54 = 13,962
Therefore, the total amount of money Emma received after selling the shares and paying the commission is:
13,962 - 7,449.95 = 6,512.05
Therefore, emma received $6,512.05 after selling the 300 shares of stock in the fast food company.
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4(1 + 9x) theres alot lol
Answer:
4 + 36x
Step-by-step explanation:
4(1 + 9x)
= 4 + 36x
So, the answer is 4 + 36x
The mean score on the Stats exam
was 75 points with a standard deviation of 5 points,
and Gregor's z-score was -2. How many points did he
score?
Gregor scored 65 points on the Stats exam.
How to determine the number of points he scoredWe can use the formula for calculating z-score:
z = (x - μ) / σ
Where
z is the z-score,x is the raw score, μ is the population meanσ is the population standard deviation.We are given that the population mean (μ) is 75 and the population standard deviation (σ) is 5.
We are also given that Gregor's z-score (z) is -2.
We can plug these values into the formula and solve for x:
-2 = (x - 75) / 5
Multiplying both sides by 5, we get:
-10 = x - 75
Adding 75 to both sides, we get:
x = 65
Hence, the score is 65 points
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Which expression has the same value as
-4 - (-5)
F. -4 + (-5)
G. -4 +5
H. -5 + (-4)
J. -5-(-4)
Answer:
G. -4 +5Step-by-step explanation:
Let's simplify - 4 - (-5):-
[tex]\tt -4 - (-5)[/tex]
[tex]\tt -4+5[/tex]
[tex]\tt 1[/tex]
Now, let's see which expression has the same value:-
F. -4 + (-5)
[tex]\tt -4 + (-5)[/tex]
[tex]\tt -4-5[/tex]
[tex]\boxed{\tt -9}[/tex]
________________
G. -4 +5
[tex]\tt -4 +5[/tex]
[tex]\boxed{\tt 1}[/tex]
_________________
H. -5 + (-4)
[tex]\tt -5 + (-4)[/tex]
[tex]\tt -5-4[/tex]
[tex]\boxed{\tt -9}[/tex]
_________________
J. -5-(-4)
[tex]\tt -5-(-4)[/tex]
[tex]\tt -5+4[/tex]
[tex]\boxed{-1}[/tex]
Therefore, we can say that G. -4 +5 has a similar value as
-4 - (-5).
________________________
Hope this helps! :)
Write an inequality that represents 12more than w is at least 45?
Answer:
The inequality that represents the given statement is:
12 + w ≥ 45
Step-by-step explanation:
3. Colin is painting his basement floor. The dimensions are shown on the diagram below:
If one can of paint will cover 3.5 m², and each can costs $15.25, what is the total cost including 13% HST.
2.3 m
2.5 m
32m
1.8 m
The total cost of painting his basement floor is $51.70.
How to calculate total cost ?To find the total cost of the paint including HST, we first need to calculate the total area of the basement floor that needs to be painted. We can do this by multiplying the length by the width:
Area of basement floor = length x width
Area of basement floor = 2.5 m x 2.3 m + 1.8 m x 2.3 m
Area of basement floor = 5.75 m² + 4.14 m²
Area of basement floor = 9.89 m²
Now, we can calculate the number of cans of paint needed:
Number of cans = Area of basement floor / Area covered by each can
Number of cans = 9.89 m² / 3.5 m²
Number of cans = 2.8257
Number of cans = 3
The total cost of the paint without HST would be:
Total cost = Number of cans x Cost per can
Total cost = 3 x $15.25
Total cost = $45.75
To calculate the HST, we need to multiply the total cost by the HST rate (13% or 0.13):
HST = Total cost x HST rate
HST = $45.75 x 0.13
HST = $5.95 (rounded to two decimal places)
Finally, we can find the total cost including HST by adding the total cost and the HST:
Total cost including HST = Total cost + HST
Total cost including HST = $45.75 + $5.95
Total cost including HST = $51.70
Therefore, the total cost of the paint including 13% HST is $51.70.
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the following data gives the amount in thousand spend s on feeding by fourty
household in ibadan in febuary 2023
32,22,19,18,43,42,40,43,18,21,31,26,22,25,47,40,26,32,34,22,35,38,34,41,36,25,22,45,48,26,28,38,35,19,47,28,26,35,38,35.
( a) construct a frequency distribution using class interver
(b) hence compute the (1) class mark for each class (2)class boundary for each class (3) cummulate frequency of the distribution (4) relative frequency of the classes (5) relative cummulative frequency.
The frequency distribution is calculated below
How to construct the frequency distributionThe dataset is given as
32,22,19,18,43,42,40,43,18,21,31,26,22,25,47,40,26,32,34,22,35,38,34,41,36,25,22,45,48,26,28,38,35,19,47,28,26,35,38,35.
To construct a frequency distribution using class intervals, we calculate the class width as follows:
Class width = Range / Number of intervals
So, we have
Class width = (48 - 18)/5 = 6
Now we can construct the frequency distribution table:
Class Interval Frequency
18 - 23 9
24 - 29 8
30 - 35 9
36 - 41 7
42 - 47 6
48 - 53 1
The class mark for each class can be calculated as:
Class mark = (Lower limit + Upper limit) / 2
For the class boundaries, we use the following formula
Lower boundary = Lower limit - 0.5
Upper boundary = Upper limit + 0.5
For the cumulative frequency of the distribution, we need to add up the frequencies of each class and all the preceding classes.
Lastly, for the relative frequency we divide each frequency by the total frequency (40)
Using the above as a guide, we have
Interval Frequency Boundaries Mark CF
18 - 23 9 17.5 - 23.5 20.5 9
24 - 29 8 23.5 - 29.5 26.5 17
30 - 35 9 29.5 - 35.5 32.5 26
36 - 41 7 35.5 - 41.5 38.5 33
42 - 47 6 41.5 - 47.5 44.5 39
48 - 53 1 47.5 - 53.5 50.5 40
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Find a value of z0 such that for the standard normal random variable z it is true that P(-z0 ≤ z ≤ z0) = 0.98.
P(-2.33 ≤ z ≤ 2.33) = 0.98 for a standard normal random variable Z.
We are aware that the area under the curve between - and - is equal to 1 for a standard normal random variable Z.
The task of finding a number for z0 such that P(-z0 z z0) = 0.98 is given to us.
We can divide the area of 0.98 evenly between the two tails of the distribution since the normal distribution is symmetric around the mean.
(1 - 0.98 / 2) = 0.01 would be the area in each tail.
We can determine the z-score that corresponds to the area of 0.01 by using a calculator or a conventional normal distribution table. An area of 0.01 equates to a z-score of roughly -2.33.
Thus, z0 would have the value:
z0 = -(-2.33) = 2.33
Hence, for a typical normal random variable Z, P(-2.33 z z 2.33) = 0.98.
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Please help geometry question Pythagorean theorem
Therefore , the solution of the given problem of triangle comes out to be L = 3(√(h²) + ((w/2²))) + 3h .
What is a triangle exactly?A triangular is a polygon because it has 2 different or more additional parts. It has a straightforward rectangle form. Only the sides A, B, and C can differentiate a triangle from a parallelogram. When the sides are not exactly collinear, Euclidean geometry results in a singular surface rather than a cube. If a shape has three edges and three angles, it is said to be triangular.
Here,
Given the height and breadth of the top of the frame, we can use the Pythagorean theorem to determine the length of each side of the triangle.
Let's assume the height is h feet and the width of the top of the frame is w feet. The triangle's side lengths can then be calculated as follows:
=> s =√((h²) + ((w/2)²))
We must add up the lengths of all the pipe segments that will be used to build the frame in order to determine the total quantity of steel pipe required.
The following formula can be used to determine how much steel tubing is required:
=> L = 3s + 3h
where h is the height of the frame and s is the length of each edge of the triangle.
Using the method instead of s, we obtain:
=> L = 3(√(h²) + ((w/2²))) + 3h
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K
13
PLAY
STOP
Determine whether the function below is exponential growth or exponential decay, and find the percentage rate of
change.
P(t) = 3.5 (0.91)
A) Exponential decay; 3.5%
B) Exponential decay; 9%
C) Exponential growth; 9%
D) Exponential growth; 3.5%
The function P(t) = 3.5(0.91)^t is an exponential decay and the percentage rate of change is 9%.
option B.
What is the percentage rate of change?The function P(t) = 3.5(0.91)^t is an exponential decay function because the base, 0.91, is between 0 and 1.
To find the percentage rate of change, we need to find the value of r in the exponential function;
P(t) = P(0) (1 + r)^t or
P(t) = P(0) e^(rt)
where;
P(0) is the initial value.In this case, the initial value is 3.5, and the function is P(t) = 3.5 (0.91)^t. Comparing this to the form P(t) = P(0) e^(rt),
we see that P(0) = 3.5 and r = ln(0.91) ≈ -0.094.
Therefore, the percentage rate of change is -9.4%, which means that the value decreases by about 9.4% with each unit of time.
So the correct answer is option B: Exponential decay; 9%.
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The complete question is below:
-Determine whether the function below is exponential growth or exponential decay, and find the percentage rate of
change.
P(t) = 3.5 (0.91)^t
A) Exponential decay; 3.5%
B) Exponential decay; 9%
C) Exponential growth; 9%
D) Exponential growth; 3.5%
in any given month there are at least 20 workdays each week, then how many workdays would roger have in the month if the month starts on a monday ? (hint: Draw a calendar to show how you arrive at your answer)
Roger would have 20 workdays in the month if it starts on a Monday and there are at least 20 workdays each week.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Assuming a month has four weeks, each with at least 20 workdays, we can calculate the total number of workdays in the month starting on a Monday as follows:
Week 1: Monday to Friday = 5 workdays
Week 2: Monday to Friday = 5 workdays
Week 3: Monday to Friday = 5 workdays
Week 4: Monday to Friday = 5 workdays
So the total number of workdays in the month is:
5 + 5 + 5 + 5 = 20
Therefore, Roger would have 20 workdays in the month if it starts on a Monday and there are at least 20 workdays each week.
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Can someone help me with this? As detailed as possible?
F1 = 1167.35N and F2 = 1932.65N are the contact support forces on the beam
How to calculate the contact support forces on the beam?For the torques, let the axis be at support 2 and consider torques and the counterclockwise rotation is positive.
Let m = mass of athlete and M = mass of beam.
Thus, the equilibrium of torques will be:
Mg(1.96) - mg(0.54m) - F1(3.92) = 0
Substitute the values and solve for F1:
(250 * 10 * 1.96) - (60 * 10 * 0.54) - 3.92F1 = 0
3.92F1 = 4900 - 324
3.92F1 = 4576
F1 = 1167.35N
Note: The weight of the beam is acting at the center and the distance from center to axis at support 2 is 1.96m.
Balancing forces in the vertical direction, we have:
F1 + F2 - Mg − mg = 0
1167.35 + F2 - (250 * 10) − (60 * 10) = 0
1167.35 + F2 - 2500 - 600 = 0
F2 = 1932.65N
Note: upward forces (supports) are positive and downward forces are negative.
Thus, the contact support forces on the beam are F1 = 1167.35N and F2 = 1932.65N.
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Marisa wants to buy a home in Atlanta with a 30-year mortgage that has an annual interest rate of 4.9% The house she wants is $250,000 and she will make a $55,000 down payment and borrow the remainder.
a. What is Marisa's monthly mortgage payment to the nearest dollar?
b. How much will the house cost in total after all payments have been made, also include the down payment.
c. How much did Marisa have to spend in interest to borrow this loan?
Answer:
a. Using a mortgage calculator with the given information, Marisa's monthly mortgage payment would be $1,088 to the nearest dollar.
b. The total cost of the house, including the down payment and all payments made over the 30-year mortgage period, would be $453,020. This is calculated by adding the $55,000 down payment to the total amount borrowed ($195,000) and then adding the total interest paid over the 30 years ($203,020) to get $453,020.
c. Marisa will have spent $203,020 in interest over the 30-year mortgage period. This is calculated by subtracting the total amount of the loan ($195,000) from the total amount paid over the 30 years ($398,020), which leaves $203,020 in interest paid.
Solve the system by the addition method.
5x + 6y=5
10x+12y = 10
The solution for the given system of equations is (1,0) using the addition method.
What is addition method?The addition method, also known as the elimination method, is a technique used to solve a system of linear equations by adding the two equations together in such a way that one of the variables is eliminated.
According to question:Multiply the first equation by -2:
-10x - 12y = -10
Add the second equation to the first:
-10x - 12y = -10
10x + 12y = 10
0 + 0 = 0
We can solve one of the original equations for x in terms of y and then replace into the equation to represent the solutions in terms of y. For instance, when we solve the first equation for x, we obtain:
5x + 6y = 5
5x = 5 - 6y
x = (5 - 6y)/5
By substituting this into the second equation, we get:
10x + 12y = 10
10((5 - 6y)/5) + 12y = 10
2(5 - 6y) + 12y = 10
10 - 4y = 10
-4y = 0
y = 0
So the solution to the system is (x, y) = ((5 - 6y)/5, y) = (1, 0)
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Find the cube root of these expression
³√5׳√5׳√5=
We can simplify this expression by multiplying the cube roots together:
³√5 × ³√5 × ³√5 = ³√(5 × 5 × 5)
Simplifying the product inside the cube root, we get:
³√(125)
Therefore, the cube root of 5 × 5 × 5 is equal to:
³√5׳√5׳√5 = ³√125 = 5
A polygon has vertices whose coordinates are A(1, 4), B(4, -1), C(-1, -4), and D(-4, 1). Use the midpoint formula to determine whether or not the diagonals of polygon ABCD bisect each other. In your final answer, include all of your calculations.
Answer:
Step-by-step explanation:
midpoint of AC
[tex]x=\frac{1-1}{2} =0\\y=\frac{4-4}{2} =0\\mid ~point~of~AC=(0,0)[/tex]
midpoint of BD
[tex]x=\frac{4-4}{2} =0\\y=\frac{-1+1}{2} =0\\midpoint ~of~BD=(0,0)[/tex]
so diagonals bisect each other.