At the end of the sale, there were a total of 196 customers in the store for the given function.
What is a function?The earliest known attempt to the notion of function may be traced back to works of Persian mathematicians Al-Biruni and Sharaf al-Din al-Tusi. Functions were initially the idealization of how a variable quantity depended on another quantity.
The total number of shoppers in the store is the number of shoppers present at the start of the sale Plus the number of shoppers who entered the store minus the number of shoppers who left.
Given that there were no shoppers in the store before the sale began, the number of shoppers in the store at the start of the sale is 0.
It is assumed that the number of customers who have entered the store is represented by S(t)=0.5t⁴-16t³+144t².
So, at t=12, the number of shoppers in the store is S(12)=
0.5(12)⁴-16(12)³+144(12)²
S(12)=3456 shoppers.
L(t)= -80+(4400/t²-14t+55)
At t=12,
[tex]\int\limits^{12}_0 {L(t)} \, dt[/tex]=[tex]\int\limits^{12}_0[/tex]( -80+(4400/t²-14t+55))dt
At the end of the sale, there were a total of 196 customers in the store.
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Need help with geometry please !
Answer:
90°
Step-by-step explanation:
Note that the sum of the exterior angles of an octagon is 360°. Therefore we can say:
x+2x+3x+4x+5x+7x+8x+10x=360
40x=360
x=9
10x° is the largest exterior angle and x=9, so 10x°=90°
Hope this helps :)
The bill for two book came to $28. 48. One book cot $7. 44. What wa the cot of the other one
Answer:
Step-by-step explanation:
Ok:
If the two books together costs $28.48 and one of them cost $7.44 Subtract to get the other book's price
2. 28.45-7.44=$21.01
3. Answer: The cost of the other one is $21.01
How to solve Solve 3! what the exclamation point means but it part of the problem
Answer:
3! = 3*2*1 = 6
Step-by-step explanation:
! is factorial meaning that you multiply that number by all of the number below it
9! = 9*8*7*6*5*4*3*2*1
1011 = 1011*1010*1009*1008...3*2*1
please help im suffering right now
Answer:
C
Step-by-step explanation:
If we use the distributive property for 4 (2x + 1), we see that 4 (2x) = 8x and that 4 (1) = 1. That means 4 (2x + 1) = 8x + 4 which is not equivalent to 2x + 4y. So this limits our answer to either C or D. C is the correct answer because if we use the distributive property again here for 4 (2x + y), we see that 4 (2x) = 8x and 4 (y) = 4y. That means that 4 (2x + y) = 8x + 4y which is the answer we're looking for.
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if the mean and mode are 15 and 10, respectively, then determine the potential range of the median for a positively skewed distribution
The median will be greater than 10 and less than 15.
Given,
The mean of the skewed distribution = 15
The mode of the skewed distribution = 10
We have to find the potential range of the median for a positively skewed distribution;
Here,
The empirical relationship between mean, median, and mode for a frequency distribution that is positively skewed is mean > median > mode. Based on this, the range of the median is 15 > median > 10 if the mean is 15 and the mode is 10.
Therefore,
The median will be higher than 10 and lower than 15.
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Please solve this question with proper explanation to this,
thank you
The owner of a landscaping company can determine how much time, on average, his employees spend mowing one lawn by taking hours per lawn.
How do we calculate average?An average is now a single number that is selected to represent a collection of numbers; it is frequently the sum of the numbers divided by the total number of numbers in the collection.Average When calculating the arithmetic mean, a set of numbers is added, their count is divided, and the result is then taken.The median or mode of a statistic, for example, could also be considered an average depending on the circumstance. Since the mean would be artificially inflated if it included the personal incomes of a few billionaires, the median is frequently used to represent the average personal income.The median is the value at or above which half of all personal incomes fall and half of all personal incomes rise.To learn more about average refer :
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Which expression is equivalent to quantity negative three and one fourth times d plus three fifths end quantity minus quantity two and seven eighths times d plus seven tenths end quantity?.
The expression "(-3 1/4d + 3/5) - (2 7/8d + 7/10) is equivalent to "negative forty nine over 8 times d minus one tenth" or -49/8d - 1/10.
An algebraic expression is a number, variable, or the combination of both and operational symbols.
To determine the equivalent of the expression "quantity negative three and one fourth times d plus three fifths end quantity minus quantity two and seven eighths times d plus seven tenths end quantity" or simply (-3 1/4d + 3/5) - (2 7/8d + 7/10), combine all like terms and perform the necessary operations.
(-3 1/4d + 3/5) - (2 7/8d + 7/10)
⇒ -3 1/4d + 3/5 - 2 7/8d - 7/10
⇒ (-3 1/4 - 2 7/8)d + 3/5 - 7/10
⇒ (-13/4 - 23/8)d + 6/10 - 7/10
⇒ (-26/8 - 23/8)d - 1/10
⇒ -49/8 d - 1/10
Hence, the equivalent expression is "negative forty nine over 8 times d minus one tenth" or -49/8d - 1/10.
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A mountain climber found that the relationship between his altitude and the surrounding air temperature is linear. The function
represents this relationship, where is the altitude in meters and is the temperature in degrees Fahrenheit. According to this function, by how much is the temperature decreasing for every meter that the mountain climber’s altitude increases?
The temperature decrease for every meter that the mountain climber's altitude increases is given by:
-100 ºF.
What is the temperature decrease?The function that models this situation is a linear function, which has the format defined as follows:
y = mx + b.
In which the coefficients are given as follows:
m is the slope of the function, representing by how much y changes when x is increased by one.b is the y-intercept of the function, representing the numeric value of y when x = 0.In the context of this problem, the function is defined as follows:
f(a) = -100a + 75.
Hence the slope of the function is of:
-100.
Representing the temperature decrease for each meter of altitude increase of the climber.
Missing InformationThe function is defined as:
f(a) = -100a + 75.
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Help I don't know how to do this
Answer:
Step-by-step explanation:
a(n) = a(1) + (n-1)d
a(n) = -9 + (n-1) x (-6-(-9)
a(n) = -9 + (n-1) x (-6 +9)
a(n)= -9 + (n-1) x 3
a(n) = -9 + 3n - 3
a(n) = 3n - 12
a(30) = 3 x 30 - 12
a(30) = 90 - 12
a(30) = 78
Solve for x:
7x(x+1. 8)=0
Need help ASAP.
Answer is not x=-1. 8 or x=0
Answer:
Step-by-step explanation:
x = -9/5 = -1.800 or
x = 0
help meeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeeee!!!!!!!!!!!!!!help meeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeeee!!!!!!!!!!!!!!help meeeeeeeeeeeeeeeeeee pleaseeeeeeeeeeeeeee!!!!!!!!!!!!!!
Answer:
7.9
Step-by-step explanation:
Using the half-life formula, there will be about [tex]30(0.5)^{11000/5730} \approx 7.9[/tex] grams left.
What additional information could be used to prove that ΔXYZ ≅ ΔFEG using ASA or AAS? Check all that apply.
∠Z ≅ ∠G and XZ ≅ FG
∠Z ≅ ∠G and ∠Y ≅ ∠E
XZ ≅ FG and ZY ≅ GE
XY ≅ EF and ZY ≅ FG
∠Z ≅ ∠G and XY ≅ FE
intuitive distortion
The additional information that could be used to prove that ΔXYZ ≅ ΔFEG by ASA or AAS are:
∠Z ≅ ∠G and XZ ≅ FG
∠Z ≅ ∠G and XY ≅ FE .
What is ASA and AAS?The AAS is a theorem that states that we can prove that two triangles are congruent if they have two pairs of congruent angles and a pair of non-included sides.
The SAS is also another theorem that states that we can prove that two triangles are congruent if they have two pairs of congruent sides and a pair of included congruent angles.
From the image attached below, we are only given one pair of congruent angles, which is ∠X ≅ ∠F.
Therefore, for both triangles to be congruent by AAS or SAS, the additional information needed are:
∠Z ≅ ∠G and XZ ≅ FG or ∠Z ≅ ∠G and XY ≅ FE .
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A construction company in Florida is struggling to sell condominiums. The company believes that it will be able to get an average sale price of $210,000. Let the price of these condominiums in the next quarter be normally distributed with a standard deviation of $15,000. [You may find it useful to reference the z table.]a. What is the probability that the condominium will sell at a price (i) below $200,000? (ii) above $240,000? (Round your final answers to 4 decimal places.)b. The company is also trying to sell an artist’s condo. Potential buyers will find the unusual features of this condo either pleasing or objectionable. The manager expects the average sale price of this condo to be the same as others at $210,000, but with a higher standard deviation of $20,000. What is the probability that this condo will sell at a price (i) Below $200,000? (ii) Above $240,000? (Round your answers to 4 decimal places.)
At a standard deviation of $15,000, the probability that the condominium will sell at a price below $200,000 is 0.2525 and above $240,000 is 0.02. At a standard deviation of $20,000, the probability that the condominium will sell at a price below $200,000 is 0.3085 and above $240,000 is 0.0668.
From the given question;
Let the average sale price(μ)=210,000
Standard Deviation(σ)=$15,000
(a) We have to find the probability that the condominium will sell at a price.
(i) below $200,000, i.e. P(x<200,000)
Z=(x−μ)/σ
Z=(200,000−210,000)/15,000
Z= −10,000/15000
Z= −0.67
Now finding P(x<200,000) is same as finding P(Z<−0.67) using the standard table of z.
P(Z<−0.67) = 0.2525
(ii) above $240,000, i.e. P(x>240,000)
Z=(x−μ)/σ
Z=(240,000−210,000)/15,000
Z= 30,000/15000
Z= 2
Now finding P(x>240,000) is same as finding P(Z>2) using the standard table of z.
P(Z>240,000)=P(Z>2)
P(Z>240,000)=1−P(Z<2)
P(z>240,000)=1−0.98
P(z>240,000)=0.02
(b) Now the average sale price(μ)=210,000
Standard Deviation(σ)=$20,000
We have to find the probability that the condominium will sell at a price.
(i) below $200,000, i.e. P(x<200,000)
Z=(x−μ)/σ
Z=(200,000−210,000)/20,000
Z= −10,000/20000
Z= −0.5
Now finding P(x<200,000) is same as finding P(Z<−0.5) using the standard table of z.
P(Z<−0.5) = 0.2085
(ii) above $240,000, i.e. P(x>240,000)
Z=(x−μ)/σ
Z=(240,000−210,000)/20,000
Z= 30,000/20000
Z= 1.5
Now finding P(x>240,000) is same as finding P(Z>1.5) using the standard table of z.
P(Z>240,000)=P(Z>1.5)
P(Z>240,000)=1−P(Z<1.5)
P(z>240,000)=1−0.93319
P(z>240,000)=0.0668
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Identify the sampling technique used in the given scenario. The English department is interested in overall performance in its entry-level 101 course. The department chair selects every tenth student's final grade from a list of all students enrolled in the course and calculates the average final grade.
The sampling technique used in the given scenario is Systematic sampling technique.
Systematic sampling technique
Systematic sampling is a probability sampling technique in which researchers randomly choose individuals of a population at regular intervals. The sampling interval, or fixed periodic interval, is calculated by dividing the population size by the required sample size.
Types of Systematic sampling technique
A systematic sample can be generated in three ways:
Systematic random sampling: The most common type of systematic sampling in which the subject is chosen at a predefined interval.
Linear systematic sampling: Instead of picking the sample interval at random, a skip pattern is constructed by following a linear path.
Circular systematic sampling: It occurs when a sample begins from the same spot where it ends.
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It cost $255 for 30 students to see the musical. How much will it cost 85 students to see the
play? Write and solve a proportion to answer the question.
Answer:
$722.5
Step-by-step explanation:
Since $225 is 30 students we can do 85/30 and multiply 225 by that.
For the proportion, it would be: 255/30=x/85
85/30=2.8 1/3
2.8 1/3*255=722.5
So it would be $722.5 for 85 students
Answer:
$722.5
Step-by-step explanation:
$255/ 30= 8.5
8.5* 85= $722.5
jadaa maake 55 ccups of blueberry jam and divided the jam equally amoung 4 containers how much jam went in each container a 2t third of a cup b 1 cup c 3over 2 of a cup and d 24 cups
When the denominator is bigger than the numerator, a fraction is expressed as one with a numerator and a denominator. 55 cups of jam divided equally into 4 containers yields 13.75 cups per container. 13.75 cups of jam are contained in each container.
What is a fraction?When the denominator of a fraction is greater than the numerator, the fraction is expressed as a pair of numbers. A fraction is a piece of the entire. In mathematics, the number is represented as a quotient, where the numerator and denominator are divided. Both are integers in a straightforward fraction. In the numerator or denominator of a complex fraction is a fraction. A proper fraction has a numerator that is lower than its denominator. Example: 1/2, 1/3 is a fraction.We have,
55 cups of blueberry jam were produced by Jada, who then evenly distributed the jam across 4 containers.
jam content of each container.
= 55 cups / 4 container
= 13.75 cups / 1 container
This indicates that there are 13.75 cups of jam in each container.
55 cups of jam are divided into 4 equal containers in this manner.
13.75 cups / 1 container
The amount of jam in each container is 13.75 cups of jams.
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A hall can accommodate 600 chairs arranged in rows Each row has the same number of chairs The chairs are rearranged such that the number of row is increased by 5 but the number of chairs per row is decreased by 6 a) Find the original number of rows of chairs in the hall b) After the re-arrangement 450 people were seated in the hall leaving the same number of empty chairs in each row. Calculate the number of empty chairs per row.
The 600 chairs capacity of the hall and the arrangement such that an increase in the number of rows by 5 decreases the number of chairs per row by 6 is a word problem that indicates;
(a) There are originally 20 rows of chairs in the hall
(b) The number of empty chairs per row is 6 empty chairs
What is a mathematics word problem?A word problem is a question in which the information required to find the solution and the description of the situation is provided using sentences, or regular verbal statements rather that symbols, expressions or operators.
(a) The number of chairs the hall can accommodate = 600
Let x represent the number of rows of chairs, therefore;
The number of chairs per row = 600/x
When the number of rows is increased by and the number of shares per row is decreased by 6, we get;
New number of rows = x + 5
New number of chairs per row = (600/x) -6
The equation for the number of chairs in the hall becomes;
(x + 5) × ((600/x) - 6) = 600
600·x + 6·x² - 570·x - 3000 = 0
6·x² + 30·x - 3000 = 0
x² + 5·x - 500 = 0
(x + 25)·(x - 20) = 0
x = -25 and x = 20
The number of rows is a positive number, therefore;
The original number of rows, x = 20(b) After re-arrangement, the number of rows, x = 20
The new number of chairs per rows = (600/20) - 6 = 24
The new number of rows = 20 + 5 = 25
Let E represent the number of empty chairs, the number of people in each row becomes 24 - E, which indicates;
25 × (24 - E) = 450
450 ÷ 25 = 18 = 24 - E
E = 24 - 18 = 6
The number of empty chairs per row, E = 6
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12. A rectangle is drawn so that the base lies on thex-axis, and the top corners are on the curvey=48−x 2. Draw a diagram. Find the maximum area of such a rectangle.
the maximum area of such a rectangle will be 144 unit²
What is a rectangle?
Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral, A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason.
Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel.
The area of rectangle is A = a*b
A = 2x*(48-x²) = 96x - 2x³
We are asked to maximize the Area as changes so hopefully, we can identify a critical point of
It an associated with a maximum, So we need to find [tex]\frac{dA}{dx}[/tex] = 0
96 - 6x² = 0
x² =96/6 = 16
x = ±6
So the width = 12
Height = 48 - 36 = 12
So the area = 144 unit²
Hence the maximum area of such a rectangle will be 144 unit²
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Which properties are present in a table that represents a logarithmic function in the form y = logo when b>
1. The y-values are always increasing or always decreasing.
II. The point (0, 1) exists in the table.
III. The y-values will decrease rapidly as the x-values approach zero.
IV. There will only be one x-value in the table with a y-value of zero.
O
O
O
O
I only
I and II only
1, 111, and IV
II and III only
Mark this and return
Save and Ex
Submit
Answer:
Step-by-step explanation:
i think its 1
Write the equation of the line that passes through the points (4, -8) and (7,-8) fully reduced PLEASE HELP
The equation of the line that passes through the points (4, -8) and (7,-8) is 5.33x + y = 13.22.
What is linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.
Given two points,
(x1 = 4 ,y1 = -8) and (x2 = 7, y2 = -8)
The equation's general form will be written first:
y = mx + c
We may compute the slope of the equation (m) as follows:
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m = \frac{-8-8}{7-4}[/tex]
m = -16/3
m = -5.33
equation is y = -5.33x + c.
By entering the values of the x and y coordinates, we can now determine the value of the y-intercept (c):
For the point (4,-8),
-8 = -5.33(4) + c
-8 = -21.32 + c
c = 13.32
So the equation become ;
y = -5.33x + 13.32
or, 5.33x + y = 13.22
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Can walk 4 miles in one hour and can run 8 miles in one hour what percent of average running speed is her average walking speed 
Answer: 50% of her average running speed is her average walking speed
Step-by-step explanation:
60 ÷ 4 = 15
60 ÷ 8 = 7.5
7.5 is half of 15, making it 50% of her running speed.
can anyone help ? No links please worth a lot of points! I also need a explaination and the answer for Z
Answer:
11.66
Step-by-step explanation:
10^2 + 6^2 = Z^2
100 + 36 = Z^2
136 = Z^2
sqrt(136) = Z
sqrt 136 = 11.66
Need help ASAP
2^7x2^-2 +2^9/2^4 +2^3/2^-2
Show that C = a×2^b where a and b are two integers to be determined
The problem is based on laws of exponents and answer to this Question is a = 2 and b = 14
What are laws of exponents?
Laws which are used to solve the problems including the exponents are called laws of exponents
Solution:
As we can clearly see in whole expression 2 is present in every term
By laws of Exponents we can take 2 common out and we can easily express this thing in given form that a multiplied 2 rays to power b
When we solve this expression we get
this expression equal to 2^15
which we can write 2×2^14
hence on comparing we get a = 2 and b = 14
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Rewrite the expression with rational exponents as a radical expression by extending the properties of integer exponents:
three to the one third power all over three to the one sixth power
A. the square root of three to the one sixth power
B. the ninth root of three squared
C. the square root of three to the sixth power
D. the sixth root of three
Answer:
D. The sixth root of three
Step-by-step explanation:
Translate from words to math symbols:
three to the one third power all over three to the one sixth power
[tex]\frac{3^{\frac{1}{3} } }{3^{\frac{1}{6} } } \\[/tex]
Rewrite the expression with rational exponents as a radical expression by extending the properties of integer exponents:
[tex]\frac{\sqrt[3]{3} }{\sqrt[6]{3} }[/tex]
Simplify:
[tex]\frac{\sqrt[3]{3} }{\sqrt[6]{3} } = \frac{\sqrt[3]{3} }{\sqrt[6]{3} } * \frac{\sqrt[6]{3^{5} } }{\sqrt[6]{3^{5} } } = \frac{\sqrt[3]{3} *\sqrt[6]{3^{5} } }{\sqrt[6]{3^{6} } } = \frac{3^{\frac{1}{3} }*3^{\frac{5}{6} } }{3^{\frac{6}{6} } } = \frac{3^{(\frac{1}{3} +\frac{5}{6} )} }{3} = \frac{3^{(\frac{2}{6} +\frac{5}{6} )} }{3} = \frac{3^{\frac{7}{6} } }{3} = \frac{3^{\frac{1}{6} } *3}{3} = \\\\3^{\frac{1}{6} } = \sqrt[6]{3}[/tex]
Answer:
[tex]\sqrt[6]{3}[/tex]
D. the sixth root of three
8
Rachel works at 'Best Price Cars' and earns $9 per hour plus 4% commission on every car she sales. She worked 40 hours last week and sold 36,000 in cars. What
was Rachel's total income last week?
Type your answer...
I need the answers
Rachel's total income is $13320.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
Rachel works at 'Best Price Cars' and earns $9 per hour plus 4% commission on every car she sales.
Commission = 9 x 0.04 = $0.36
Commission on 36000 cars = $12960
By working 40 hours he earn = 9 x 40 = $360
Hence, the total income = 360+ 12960 = $13320
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Given that z=x + i y, find the values of real numbers x and y such that z - 4iz' + 3 = 0, when z' is the conjugate of z.
THANKS IN ADVANCE!!!
The value of z = 0 + 0i
What is complex numbers ?
A complex number can be represented in the form a + bi, where a and b are real numbers. A complex number is a part of a number system that extends the real numbers by adding an element designated by the symbol I sometimes known as the imaginary unit, and meeting the equation displaystyle i2=-1.
( x + iy ) - 4i ( x - iy ) = 0
x + iy - 4ix + 4i²y = 0
x + i (-4x + y ) + 4y = 0
x + 4y + ( - 4x + y )i = 0
Now two complex numbers are equal if both the real and imaginary parts are equal, which gives you the system of equation
x + 4y = 0 ⇒(1)
-4x + y = 0 ⇒ (2)
Multiplying equation (1) with 4
4x + 16y = 0
Solving the equations
4x + 16 y = 0
-4x + y = 0
17 y = 0
y = 0
Putting the value of y in (1)
x + 4(0) = 0
x = 0
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The table shows the ingredients for one batch of barbecue sauce. Anne has 9 cups of ketchup and makes the greatest number of whole batches of barbecue sauce possible. How much ketchup remains?
Answer:
hi do you mind making the question a bit clear? where is the table?
Step-by-step explanation:
Evaluate the expression when b=9
4b+10-b
Group of answer choices
37
47
27
17
Answer:
37
Step-by-step explanation:
4b+10-b = 3b + 10 = 3(9) + 10 = 27 + 10 = 37
Dan buys a car for £700.
It depreciates at a rate of 5.5% per year.
How much will it be worth in 6 years?
Give your answer to the nearest penny where appropriate.
The value of car after 6 years is £498.53
Define Modeling Exponential Decay
A model for decay of a quantity for which the rate of decay is directly proportional to the amount present.A(1 - r)^tA = Present value , r = rate, t = timeGiven that,
Dan buys a car = £700
Depreciates at a rate of = 5.5% per year
The value after 6 years = 700 (1 - 5.5 / 100) ^6
= 498.527 or 498.53
Therefore, the value of car after 6 years is £498.53
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If the lowest price in the past year occurred 35 days ago, find the approximate average change per day since then. a. $2.08 b. $2.64 c. $0.90 d. $2.99
The approximate change per day since the lowest price occurred 35 days ago, is a. $2.08.
How to find the approximate average change?The approximate average change can be found by the formula :
= ( Current price of stock - Lowest price ) / Number of days since lowest price
Current price of Dagofi Radar stock = $ 130. 58 closing price
Lowest price = $ 57. 71
The approximate average change is:
= ( 130. 58 - 57. 71) / 35
= 72. 87 / 35
= $ 2.08
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Missing part of question:
Consider today's stock listing for Dagofi Radar, shown below.
52 wk High
52 wk Low
Symbol
Div.
Close
Net Change
162.22
57.71
DFR
9.75
130.58
-2.64
