Answer:
The number is 20
Step-by-step explanation:
First we have n, then n/2, then 4n/2, which equals 40. Thus, we have 2n=40, or n=20 which is the number.
Answer:
20
Step-by-step explanation:
whats the mean median mode and range of 75 55 68 44 82 28 19 31 75 36 59 93 48
The mean ,median ,mode and range of 75 55 68 44 82 28 19 31 75 36 59 93 48 are:
mean = 49.7
media = 55
mode=75
Range=74
How can the mean median mode and range be calculated?The concept that can be used here is mean median and mode.
We will need to arrange the value from the lowest to the biggest as :
75 55 68 44 82 28 19 31 75 36 59 93 48
19 28 31 36 44 48 55 59 68 75 75 82 93
The mean can be calculated by adding all numbers in the data set and then dividing by the number of values in the set.
= (19+ 28+ 44 +48+55+ 59+ 68+ 75+ 75+ 82+ 93 )/13 =646/13= 49.7
Median = (n + 1)/2th value
Where n = numner of the given digits which is 13
= (13 + 1)/2th value
= 7th value
=55
Mode = is the number that occurs most often = 75
Range = highest value - lowet value = 93-19 =74
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camila writes down five positive integers. the unique mode of these integers is 2 greater than their median, and the median is 2 greater than their arithmetic mean. what is the least possible value for the mode?
The least possible value for the mode is D=11
Let M be the median
According to the question, the two largest integers are M+2
Let a and b be the two smallest integers such that a<b
Accordingly, the sorted list can be concluded as a,b, M, M+2, M+2
Since the median is 2 greater than their arithmetic mean, we have,
{a+b+M+(M+2)+(M+2)/5 }+2 =M
OR, a+b+14=2M
Note that a+b must be even.
We minimize this sum so that the arithmetic mean, the median, and the unique mode is minimized.
Let a=1 and b=3
from which M=9 and
M+2=11
Therefore, The least possible value for the mode is D=11
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mr. and mrs. zeta want to name their baby zeta so that its monogram (first, middle, and last initials) will be in alphabetical order with no letters repeated. how many such monograms are possible?
Mr. and Mrs. Zeta want to make sure that their baby's monogram, which consists of the first, middle, and last initials, is in alphabetical order with no letters repeated. We may utilize the idea of permutations to determine the number of possible monograms.
A permutation is a way to arrange a group of things in a particular sequence. In this instance, we are examining the alphabet's set of letters (from A to Z), and we are trying to determine how many different ways there are to arrange them so that the monogram is composed entirely of unique letters.
The breakdown of the computation is as follows:
There are 26 different alternatives for the first initial (A to Z).
Since the monogram must be in alphabetical sequence, the letter for the second initial must appear after the first initial. There are so 25 possibilities left (the letters that come after the first initial in the alphabet).
There are 24 possibilities left for the final initial (the remaining letters that come after the second initial in the alphabet).
By multiplying the alternatives for each initial, we can calculate the total number of possible monograms using the basic counting principle:
26 x 25 x 24 = 15,600
Because they must be in alphabetical order and contain no repeating letters, there are 15,600 number of monograms are possible .
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Gabe purchased a razor for $13.99, a refill pack of razor blades for $5.75, shaving cream for $3.29 and lotion for $7.35. He has a $.65 coupon for the shaving cream and a $3.00 rebate for the razor.
Answer:
13.99 + 5.75 + 3.29 + 7.35 = 30.38
30.38 - .65 - 3.00 = 26.73
Step-by-step explanation:
Hope this helps! =D
Answer:
$26.73
Step-by-step explanation:
razor = $13.99 - $3.00(rebate) = $10.99
refill pack of razor blades = $5.75
shaving cream = $3.29 - $0.65(coupon) = $2.64
lotion = $7.35
Triangle ABC is similar to triangle FGH.
What is the value of x in centimeters?
Triangle ABC is similar to triangle FGH.
And the value of the x is 22.5 centimeters.
What are similar triangles?Those triangles that looks the same but different in sizes.
And in the similar triangle,
the corresponding sides in proportion to each other and corresponding angles are equal to each other.
Given:
Triangle ABC is similar to triangle FGH.
That means, the corresponding sides of the triangles are in proportion to each other.
That means,
13.5/9 = 18/12 = x/15
Now,
18/12 = x/15
x = 270/12
x =22.5 centimeters
Therefore, the value of the x is 22.5 centimeters.
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an element in a ring is called an idempotent if . prove that the only idempotents in an integral domain are and . find a ring with a idempotent not equal to 0 or 1.
A ring with a idempotent not equal to 0 or 1 is 3 and 4.
Make (R,+) a domain that is integral.
As a commutative ring with two elements, R, ab = 0 when either an or b are equal to zero.
If a ∈ R is an idempotent element, then a ≠ 0,a ≠ 1 will result.
[tex]a^{2}[/tex] = a
We can take multiple of 1 because the same number return if we multiply 1 to any number.
[tex]a^{2}[/tex] = a·1
Subtract a·1 on both side, we get
[tex]a^{2}[/tex] - a·1 = 0
Taking a common
a(a -1) = 0
(a -1) = 0 or a =0
R has no zero divisors.
So, a = 1 or a = 0
As a result, the only idempotent elements in the integral domain R are 0 and 1.
A ring that is not equal to 0 or 1 and is idempotent.
A ring with respect to addition and multiplication is the set R = 0 through 5.
Let 3 ∈ R,
[tex]3^{2}[/tex] = 6+3 = 0+3 = 3
Let 4 ∈ R.
[tex]4^{2}[/tex] = 16 = 12+4 = 2
Hence, 3 and 4 are idempotent elements other than 0 and 1
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The complete question is:
An element x in a ring is called an idempotent if [tex]x^2[/tex] = x. Prove that the only idempotents in an integral domain are 0 and 1. Find a ring with an idempotent x not equal to 0 or 1.
Evaluate: 3(x+4)(x+1) / (x+2)(x-2) for x = 4
A.10/3
B.10
C.-10/3
D.-10
a spherical balloon is inflated so that its volume is increasing at the rate 6 cm^3/min. at what rate is the radius increasing when the radius is 3 cm
The radius is increasing at rate of [tex]\frac{10}{36\pi } \\[/tex]
What is volume ?
Volume' is a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface.
As we know Volume of sphere V=
[tex]V=\frac{4}{3} \pi r^3\\dv/dt=6\\Given\\radius=3cm\\[/tex]
so, we need to find dr/dt
Since there is no t in our equation. So differentiate using chain rule
[tex]\frac{dv}{dt} =\frac{dv}{dr} *\frac{dr}{dt} \\[/tex]
Since, in question it is given dv/dt=6
[tex]6=\frac{dv}{dr} .\frac{dr}{dt} \\[/tex]
To find dv/dr differentiate
[tex]4/3\pi r^3\\dv/dr(\frac{4}{3} \pi r^3)=4\pi r^2\\6=4\pi r^2\frac{dr}{dt} \\[/tex]
Dividing
[tex]\frac{10}{4\pi (3)^2} =dr/dt\\dr/dt=\frac{10}{36\pi } \\[/tex]
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The radius is increasing at rate of 10/36π
What is volume ?
Volume' is a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface.
As we know Volume of sphere V= 4/3 πr³
dv/dt =6
Given r = 3 cm.
so, we need to find dr/dt
Since there is not in our equation. So differentiate using chain rule
dv/dt =dv/dr * dr/dt
Since, in question it is given dv/dt=6
6 =dv/dr * dr/dt
To find dv/dr differentiate
dv/dr (4/3πr³) = 4πr²
6 = 4πr² dr/dt
Finally,
dv/dt = 10/36π
Hence, The radius is increasing at rate of 10/36π
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Lat year, Kaitlin opened an invetment account with $5200 . At the end of the year, the amount in the account ha decreaed by 7% . How much i thi decreae in dollar? How much money wa in her account at the end of lat year?
The decrease in Kaitlin's investment account is 7%, which is calculated by multiplying the initial $5200 by 0.07.
This gives a decrease of $364. The amount in her account at the end of the year is the initial $5200 minus the decrease of $364, which equals $4836.
This can be expressed algebraically as:
Let x = amount in Kaitlin's account at the end of the year
Initial Amount (x) = 5200
Decrease (%) = 0.07
Decrease in Dollars = x * 0.07
Decrease in Dollars = 5200 * 0.07
Decrease in Dollars = 364
Amount in Account at the End of the Year = 5200 - 364
Amount in Account at the End of the Year = 4836
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Complete the table to combine like terms when adding Expression One and Expression Two. Expression One Expression Two 14−3a 7a−9
The addition of the two expression is 4a + 23
The term called expression in math is defined as the mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Here we know that the following expression are known.
=> 14 - 3a
=> 7a - 9
Now, we have to perform the addition operation on it.
Then the expression can be written as
=> (14 - 3a) + (7a + 9)
Now, we have to combine the similar term of the expressions, then we get,
=> (14 + 9) + (-3a + 7a)
When we simplify this one then we get,
=> 23 + 4a
When we write it as the standard form, then we get,
=> 4a + 23.
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In 1957 an earthquake in Alaska
measured about 9.0 on the Richter
scale. An earthquake with magnitude 6.0 occurred in Japan in early 2007. How many times more intense was the earthquake in Alaska than the one in Japan?
The answer is that the earthquake in Alaska was 1.5 times or 1000 times more intense than the one in Japan.
How much more intense the earthquake in Alaska and find ratio of amplitude?To determine how much more intense the earthquake in Alaska was than the one in Japan, we can use the formula:(magnitude of Alaska earthquake / magnitude of Japan earthquake) = (9.0 / 6.0) = 1.5This means that the earthquake in Alaska was 1.5 times more intense than the one in Japan.Alternatively, we can use the logarithmic relationship of the Richter scale to calculate the ratio of amplitude.(10^(magnitude of Alaska earthquake)/10^(magnitude of Japan earthquake)) = (10^9.0/10^6.0) = (1000000000/1000000) = 1000This means that the amplitude of the earthquake in Alaska was 1000 times greater than the one in Japan.So the answer is that the earthquake in Alaska was 1.5 times or 1000 times more intense than the one in Japan.To learn more about ratio of amplitude refer:
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A mountain has a snow line at an elevation of 9000 feet which runs parallel to its base. The mountain is a triangle, the length of the snow line is 2. 4 times the height of the snow covered part of the mountain. If the snow covers 1,200,000 square feet of part of the mountain, how high is the mountain?
The height of the mountain is 10000ft.
Now, According to the question:
A mountain has a snow line at an elevation of 9000 feet which runs parallel to its base.
The snow covers 1,200,000 square feet of part of the mountain.
We know that:
Area of triangle = 1/2 × base × height
Area of a triangle = 1/2 × 2.4 h × h
1200000 = 2.4[tex]h^2[/tex]/2
cross multiply
1200000 × 2 = 2.4[tex]h^2[/tex]
2400000 = 2.4[tex]h^2[/tex]
Divide both sides by 2.4
[tex]h^2[/tex] = 2400000/2.4
[tex]h^2[/tex] = 1000000
h = √1000000
h = 1000 ft.
The height of the mountain = 1000 ft. + 9000 ft. = 10000 ft.
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Taylan i elling platic and wooden frame. He old 7 total frame. The number of platic frame Taylan old wa 5 le than twice the number of wooden frame. How many of each type of frame did Taylan ell?
Taylan sold 3 wooden frames and 5 plastic frames. the number of plastic frames is less than twice the number of wooden frames, we can set up an inequality equation
Given: Taylan sold 7 total frames, with the number of plastic frames being less than twice the number of wooden frames
Let x = number of wooden frames
Since the number of plastic frames is less than twice the number of wooden frames, we can set up an inequality equation to represent this:
x + (x * 2) < 7
2x < 7
x < 7/2
x = 3
Therefore, Taylan sold 3 wooden frames and 5 plastic frames.
Taylan sold 3 wooden frames and 5 plastic frames. the number of plastic frames is less than twice the number of wooden frames, we can set up an inequality equation
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Karen is trying to get to the MRT station, which is 7
10
km away
from where she parked her car. She has already walked for 2
5
km. How much farther does she have to walk to reach the MRT
station?
answer quickly please and please send solution if possible
Answer:
The answer is 685 km hopefully I understood your question and helped you ☻
Step-by-step explanation:
710 km - 25 = 685
imagine that a recent study found that people who eat large amounts of bananas get bitten by mosquitoes on average more often than people who eat smaller amounts of bananas. what causal relationship can we conclude from this study alone?
It is not possible to conclude a causal relationship from this study alone. This is because the study only shows a correlation between eating large amounts of bananas and being bitten by mosquitoes, it does not demonstrate that one causes the other. There could be other factors that are not controlled for in the study that could be the true cause of the relationship, such as people who eat more bananas also spend more time outdoors. To establish a causal relationship, further research would be needed such as a randomized control trial.
Cause and Effect of Bananas and Mosquito BitesTo determine a causal relationship between eating bananas and being bitten by mosquitoes, a randomized controlled trial could be conducted. This type of study would involve randomly assigning participants to two groups: one group would eat a large amount of bananas, while the other group would eat a smaller amount of bananas. The number of mosquito bites each participant receives would be recorded and compared between the two groups.
If the group that ate a large amount of bananas had a significantly higher rate of mosquito bites than the group that ate a smaller amount of bananas, it would suggest that eating bananas may cause an increase in the number of mosquito bites.
Additionally, other variables that could influence the result should be controlled or measured, such as time spent outdoors, skin type, or use of mosquito repellent.
It's important to note that even if the study shows a correlation between eating bananas and being bitten by mosquitoes, it doesn't mean that the banana causes the bites, there could be other factors that are not controlled for in the study that could be the true cause of the relationship.
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Find the length of side x to the nearest tenth.
Considering the figure the side length x is solved to be 6.6
How find the value of xInformation given from the question is interpreted as
√11 = adjacent
x = hypotenuse
The side x is worked using SOH CAH TOA
Sin = opposite / hypotenuse - SOH
Cos = adjacent / hypotenuse - CAH
Tan = opposite / adjacent - TOA
The side x is calculated using cos, CAH
cos 60 = Adjacent / hypotenuse
cos 60 = √11 / x
x = √11 / cos 60
x = 6.633
x = 6.6 to the nearest tenth
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If the perimeter of an equilateral triangle is 36 yards, what is the length of its altitude?
The length of the altitude is 10. 4 yards
How to determine the altitiude of the triangleThe formula for the perimeter of an equilateral triangle is expressed as;
P = 3a
Where;
P is the perimeter of the trianglea is the length of the side of the triangleSubstitute the values
36 = 3a
Divide the value by the coefficient of a
a = 36/3
a = 12 yards
Using the Pythagorean theorem, we get;
12² = h² + 6²
Find the square values
144 = h² + 36
collect like terms
h² = 108
Find the square root
h = 10. 4 yards
Hence, the value is 10. 4 yards
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Solve the system of equations x+3y=5 and -3x-2y=20 by combining the equations
The value of x and y is -10 and 5 respectively in the given equations.
What is a linear equation?
A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.
The first linear equation is - x + 3y = 5
The second linear equation is - -3x - 2y = 20
On evaluating individually the equation obtained is -
-3x - 2y + x + 3y = 20 + 5
-2x + y = 25
Multiply equation (1) with 3 -
3(x + 3y) = 5 × 3
3x + 9y = 15.....(3)
Adding equation (3) and (2) -
-3x - 2y + (3x + 9y) = 20 + 15
-3x - 2y + 3x + 9y = 35
-2y + 9y = 35
7y = 35
y = 35/7
y = 5
Substituting the value of y in equation (1) -
x + 3y = 5
x + 3(5) = 5
x + 15 = 5
x = 5 - 15
x = -10
Therefore, the value of x and y is -10 and 5 respectively.
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Find the minimum value of fsx, y, zd − x2 1 2y2 1 3z2 subject to the constraint x 1 2y 1 3z − 10. Show that f has no maximum value with this constraint
50/3 is the minimum function value.
∇f(x,y,z)=(2x,4y,6z)
∇g(x,y.z)=(1,2,3)
set up the system of equations:
2x=λ
4y=2λ
6z=3λ
x+2y+3z=10-----(1)
solve the first three equations for λ.
2x=λ
2y=λ
2z=λ
From these three equations, we conclude that
x=y=z.
Plug this into the constant equation.
x+2y+3z=10
x+2x+3x=10
6x=10
x=3/5
Therefore, there is one point of interest and it occurs at (5/3,5/3,5/3).
f (5/3,5/3,5/3)=50/3
This is the minimum function value. Notice that the function is unbounded above and therefore has no maximum.
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13y+7-11-4y as a sum
Answer: 9y-4
Step-by-step explanation:
13y-4y=9y
7-11=-4
Answer:
13y+7-11-4y
13y-4y+7-11
9y-4 ans
Step-by-step explanation:
first combine the like terms along with their front sign
then sbtract 13y by 4y ,after subtract 7 from 11
[ here 7 have (+) and 11 have (-) before itself
according to the rule,(+) + (-) = (-)
hence we have to subtract 7 from 11 and put the (-) before answer]
but put sign (-) before the answer because we should always put that sign before answer which have more value
1) The end behavior of a rational function is equal to
A) Holes
B) Horizontal Asymptote
C) Vertical Asymptote
D) Domain
Answer:
B) Horizontal Asymptote
A horizontal asymptote is a horizontal line that the graph of a function approaches as the input values get larger or smaller. The end behavior of a rational function is determined by the degree of the numerator and denominator. If the degree of the numerator is less than the degree of the denominator, the function will approach a horizontal asymptote as the x-values get larger or smaller. If the degree of the numerator is greater than the degree of the denominator, the function will not have a horizontal asymptote.
The table shows conversions of common units of length.
Unit of Length
Customary System Units
Metric System Units
1 inch
2.54 centimeters
1 foot
0.3048 meters
1 mile
1.61 kilometers
1 yard = 3 feet
1 yard = 36 inches
Which shows the best path to find the number of centimeters in 1 yard?
The number of centimetres in the 1 yard will be 9.144 cm.
What is unit conversion?Multiplication or division by a numerical factor, selection of the correct number of significant figures, and unit conversion are all steps in a multi-step procedure.
Given that:-
Metric System Units
1 inch = 2.54 centimetres
1 foot = 0.3048 meters
1 mile = 1.61 kilometres
1 yard = 3 feet
1 yard = 36 inches
First, we will calculate 1 yard to feet.
1 yard = 3 feet
1 feet = 0.3048 meters
1 feet = 3.048 centimeters
1 yard = 3 x 3.048 centimeters
1 yard = 9.144 centimeters
Hence, the length of 1 yard in cm is 9.144 cm.
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The team won the game 114-113. The teams scored only 2s and 3s. The winning team scored 50 baskets and the losing team scored 48 baskets. How many more 3s did the winning team than the losing team?
By using linear equations, The winning team scored 3 less 3s than the losing team.
What are linear equations?
A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant.
Now,
For winning team
let x=no. of 2s and y=no. of 3s
Therefore, these linear equations will be formed
x+y=50
2x+3y=114
After solving these we get x=36 and y=14
For losing team
let a=no. of 2s and b=no. of 3s
Therefore, these linear equations will be formed
a+b= 48
2a+3b=113
After solving these we get a=31 and b=17
Difference between 3s scored=17-14
Difference between 3s scored=3
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Help me please help thank you and have a great day
Hey Mate,
Answer is (4,3),
Thank you .
Hi, I am trying to solve a the sin graph y=1-3sin(3/2)Theta. can someone explain to me how to get the y-values for each x value?
The graph of the function is added as an attachment and the function values are y = 4 for all x values
How to detemrine the function valuesFrom the question, we have the following parameters that can be used in our computation:
y=1-3sin(3/2)Theta
Express properly
So, we have the following representation
y = 1 - 3sin(3/2π)
Next, we create a plot of the graph (see attachment)
From the graph, we can see that the function is a horizontal line at y = 4
This means that for all x values, the y value is constant at 4
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Convert each equation from slope-form to standard form
The conversion of the equation from slope-form to standard form is 3x + y = 2.
What is the slope-intercept form?In Mathematics, the slope-intercept form of a line is generally modeled by using this linear equation:
y = mx + b
Where:
m represents the slope.b represents the y-intercept.x and y are the data points.In Mathematics, the standard form of a linear function is is generally modeled by this mathematical expression:
Ax + By = C
Where:
A, B, and C represents a number, numeral or numerical value.
Next, we would convert the given linear function in slope-intercept form to standard form as follows:
3x + y = 2.
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Dupe's age
and Olu's
age
add
up to 25 years.
Eight years ago, Dupe was twice as old as
Olu. How old are they now?
Dupes's age is 14 year and Olu's age is 11 year now.
What is linear algebraic equations?
Unknown quantities can often be determined using linear algebra. Among linear algebra's practical uses are the following: to calculate time, distance, or speed. used by linear maps to translate a three-dimensional image into a two-dimensional plane.
Mathematical structures that can be closed under addition and scalar multiplication are the focus of this area of study, which also encompasses the theory of linear equation systems, matrices, determinants, vector spaces, and linear transformations.
Assume that Dupe is x years old and Olu is y. We may create two linear algebraic equations using the given data:
x + y = 25
(x - 8) = 2(y - 8)
This system of linear equations can be transformed into the following by using a little algebraic trickery:
x + y = 25
x - 2y = -8
To obtain x = 14 and y = 11, construct an augmented matrix and use either Gaussian elimination or Gauss-Jordan elimination.
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Hotel P offer two type of room for it cutomer: a Deluxe room and a Suite room. The price per night for the uite room for check-in on Sunday until Thurday i 70% higher than the price per night for a Deluxe room for the exact check-in period. The price per night for the Deluxe room for check-in on Friday and Saturday i 25% higher than for price per night for the Deluxe room for check-in on Sunday until Thurday. If the hotel management want to maintain the price difference between the two type of pace, and the price per night for a Suite room for check-in on Sunday until Thurday i $223, what hould be the price per night for a Suite room for check-in on Friday and Saturday?
The price per night for a Suite room for check-in on Friday and Saturday would be amount $278.50 .
The price per night for a Suite room for check-in on Friday and Saturday would be amount $278.50.
1. Calculate the price of a Deluxe room for check-in on Sunday until Thursday:
$223 / 1.70 = $131.18
2. Calculate the price of a Deluxe room for check-in on Friday and Saturday:
$131.18 x 1.25 = $163.98
3. Calculate the price of a Suite room for check-in on Friday and Saturday:
$163.98 x 1.70 = $278.50
The price per night for a Suite room for check-in on Friday and Saturday would be $278.50.
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Dana sees a street sign and a pine tree. The street sign is 8 feet tall and casts a shadow that is 15 feet long. What is the height of the pine tree if the pine tree's shadow is 30 feet long?
For this polynomial function, state the coordinate points of the zeros
The zeros of this polynomial are (1, 0), (2, 0), and (0, 4).
How determine the zeros of the polynomial?The zeros of the polynomial can be determined by setting the equation equal to zero and solving for the roots.
For example, if the polynomial is given as [tex]ax^{2}[/tex] + bx + c, then the zeros can be determined by solving the equation [tex]ax^{2}[/tex] + bx + c=0.
Step 1: To determine the zeros of the polynomial, set the polynomial equal to 0 and solve for x.
f(x) = [tex]x^{3}[/tex] - [tex]3x^{2}[/tex] + 4 = 0
Step 2: Factor the polynomial to solve for x.
[tex]x^{3}[/tex] - [tex]3x^{2}[/tex] + 4 = 0
x([tex]x^{2}[/tex] - 3x + 4) = 0
Step 3: Factor the quadratic equation.
x(x - 1)(x - 2) = 0
Step 4: Set each factor equal to 0 and solve for x.
x = 0, x = 1, x = 2
Step 5: Plug each x-value into the original equation to determine the corresponding y-value for each zero.
When x = 0, y = 4
When x = 1, y = 0
When x = 2, y = 0
Step 6: The coordinate points of the zeros are (1, 0), (2, 0), and (0, 4).
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