The cost of the hotel for 1 night is $130 using the ratio concept.
What is meant by ratio and proportion?If b is not equal to 0, an ordered pair of real numbers a and b, represented as a / b, is a ratio. An equation that balances two ratios is called a proportion. For illustration, the ratio may be expressed as follows: 1: 3 in the case of 1 male and 3 girls. The formula a: b or a/b can be used to compare any two values.
However, the percentage formula is represented as a:b::c:d or a:b=cd.
There are three types of proportion. They are:
1) Direct Proportion.
2) Inverse Proportion.
3) Compound Proportion.
4) Continued Proportion
Given,
Cost for four rental nights = $520
The cost for one rental night is given by
x = 520/4
x = $130 per night
Therefore, the cost of the hotel for 1 night is $130.
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At the beginning of spring, Sophia planted a small sunflower in her backyard. When
it was first planted, the sunflower was 25 inches tall. The sunflower then began to
grow at a rate of 3 inches per week. How tall would the sunflower be after 9 weeks?
How tall would the sunflower be after w weeks?
Height after 9 weeks:
Height after w weeks:
The height of the sunflower after 9 weeks is 52 inches and the function that represent the height of the sunflower after w weeks = 25 + 3w weeks.
Sophia planted a tiny sunflower in her backyard at the start of spring.
When she planted the sunflower,
The height of the sunflower = Initial height of the sunflower = 25 inches.
Now, The sunflower then began to grow at a rate of 3 inches per week.
Thus, the growth rate of the sunflower = 3 inches/week
The growth in 9 weeks = 3*9 = 27 inches,
The height of the sunflower after 9 weeks = initial height + growth = 25 +27 = 52 inches.
The growth in w week = 3w inches,
The height of the sunflower after w weeks = initial height + growth = 25 + 3w inches.
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describe and correct the error in graphing the function y = x - 1 with the domain 1 , 2 , 3 ,4 ,and 5
The graph of the function is y - 1 = x, not y = x - 1.
What is a graph?The set of ordered pairings (x, y) where f(x) = y makes up the graph of a function.
These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the general case when f(x) are real values.
Given, y = (x - 1).
When x = 1, y = 0 ⇒ (1, 0).
When x = 2, y = 1 ⇒ (2, 1).
When x = 3, y = 2 ⇒ (3, 2).
When x = 4, y = 3 ⇒ (4, 3).
When x = 5, y = 4 ⇒ (5, 4)
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Can you help me PLEASE,
The answers are:
Q1 = x < -1
Q2 = x ≤ 2
Q3 = x > -2
Q4 = x > 0
Code = 4776
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
We have,
Solve for x.
3 < -5x + 2x
3 < -3x
Divide both sides by 3.
1 < -x
Change sign.
x < -1
18 ≥ 5x + 4x
18 ≥ 9x
Divide both sides by 9.
2 ≥ x
-6x - 16 < 2x
Add 16 on both sides.
-6x < 2x + 16
Subtract 2x on both sides.
-6x - 2x < 16
-8x < 16
Divide both sides by 8.
-x < 2
Change sign.
x > -2
(1/2)x - 4 > -4
1/2x > -4 + 4
1/2x > 0
x > 0
Code = 4776
Thus,
The answers are:
Q1 = x < -1
Q2 = x ≤ 2
Q3 = x > -2
Q4 = x > 0
Code = 4776
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3-6n-4<17
What is the Answer for this??
Answer:
-6n-4+3<17
-6n-1<17
-6n<17+1
-6n<18
DIVIDE BOTH SIDE WITH THE COEFFICIENT OF n WHICH IS (-6)
-6n =18
-6 -6
n= -3
A line parallel to the line produced by 6x-2y=25 has what gradient?
the slope goes by several names
• average rate of change
• rate of change
• deltaY over deltaX
• Δy over Δx
• rise over run
• gradient
• constant of proportionality
however, is the same cat wearing different costumes.
keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above
[tex]6x-2y=25\implies -2y=-6x+25\implies y=\cfrac{-6x+25}{-2} \\\\\\ y=\cfrac{-6x}{-2}+\cfrac{25}{-2}\implies y=\stackrel{\stackrel{m}{\downarrow }}{3}x-\cfrac{25}{2}\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}[/tex]
10.) Christina cuts 4 squares with side length x inches from the corners of a 5 inch by 10 inch cardboard
rectangle. She folds the remaining cardboard to make a tray that is x inches high.
Write and simplify a polynomial function for the volume V of the tray in terms of x.
The polynomial function to find the volume of the tray is [tex]4x^{3} -30x^{2} +50x[/tex] cubic inches.
According to the question,
We have the following information:
Christina cuts 4 squares with side length x inches from the corners of a 5 inch by 10 inch cardboard rectangle. She folds the remaining cardboard to make a tray that is x inches high.
Now, the length of the tray will be (10-2x) inches and the breadth of the tray will be (5-2x) inches.
Volume of tray = length*breadth*height
Volume of tray = (10-2x)(5-2x)x
Volume of tray = x(50-20x-10x+4[tex]x^{2}[/tex])
Volume of tray = x(4[tex]x^{2}[/tex]-30x+50)
Volume of tray = [tex]4x^{3} -30x^{2} +50x[/tex] cubic inches
Hence, the polynomial function to find the volume of the tray is [tex]4x^{3} -30x^{2} +50x[/tex] cubic inches.
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1
Apply the Linear Programming Theorem and interpret the results.
2) Answer the questions below for the following situation:
For a certain lawn, a landscaping contractor plans to use the least expensive combination of two brands of
fertilizer. A package of Brand X costs $16 and contains 12 oz of phosphates and 10 oz of nitrates. A package of
Brand Y costs $7 and contains 10 oz of phosphates and 5 oz of nitrates. The lawn requires at least 60 oz of
phosphates and 40 oz of nitrates. Which combination of the two brands should be used?
a. Translate the constraints into a system of inequalities.
b. Graph the system and label the vertices of the feasible set.
c. Apply the Linear Programming Theorem and interpret the results.
X
The minimum cost will be at (2.5 , 3) and the minimum cost be $25.
Given, a landscaping contractor plans to use the least expensive combination of two brands of fertilizer.
A package of Brand X costs $16 and contains 12 oz of phosphates and 10 oz of nitrates.
A package of Brand Y costs $7 and contains 10 oz of phosphates and 5 oz of nitrates.
The lawn requires at least 60 oz of phosphates and 40 oz of nitrates.
Let the number of Brand X packages be, x
the number of Brand Y packages be, y
According to the question,
12x + 10y ≥ 60 = 6x + 5y ≥ 30
10x + 5y ≥ 40 = 2x + y ≥ 8
x ≥ 0
y ≥ 0
Z = 16x + 7y
On solving the equations, we get
6x + 5y = 30
6x + 3y = 24
On subtracting, we get
2y = 6
y = 3
and x = 2.5
So, minimum cost will be at (2.5 , 3) and the minimum cost be
Z = 16(2.5) + 7(3)
Z = 4 + 21
Z = 25
Hence, the minimum cost will be at (2.5 , 3) and the minimum cost be $25.
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can someone help me really quick
Q8.
The area of this rectangle is 28 cm²
(x+2)cm
(x+2)cm
(6x-1)cm
(6x-1)cm
Work out the perimeter of the rectangle.
Hi! I can’t seem to figure out this proof can anyone help me? I tried labeling the sides and angles.
Answer:
3. line XZ is congruent to line XZ | reflexive property
4. triangle WXZ is congruent to triangle YZX | HL (i think)
5. angle WXZ is congruent to angle YXZ | CPCTC
Step-by-step explanation:
If there are fewer than 200 band members and each time they line up in rows there are always 3 members left over, how many members are there in total?
The total number of members there is 199
What is logic reasoning?Two kinds of logical reasoning are often distinguished in addition to formal deduction: induction and abduction. Given a precondition or premise, a conclusion or logical consequence and a rule or material conditional that implies the conclusion given the precondition, one can explain the following.
Since the number of members of the band is <200. the members are arranged in rows and 3 will be left out
therefore assume the members on row are 200- 3= 197, but 197 is a prime number ,therefore we choose the closet number to 197 which is 196.
therefore the total number of members = 196+3= 199.
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WILL GIVE BRAINLIEST
A farmer has 300 yards of fencing. He is trying to figure out how to build his fence so that he has a rectangle with the greatest square footage inside. What are the side lengths of the fence he can build with the greatest area inside?
60 yards and 60 yards
60 yards and 75 yards
75 yards and 75 yards
75 yards and 80 yards
The side lengths of the fence he can build with the greatest area inside are of:
75 yards and 75 yards.
What are the area and the perimeter of a rectangle?Considering a rectangle of length l and width w, we have that the area and the perimeter of the rectangle are given as follows:
The area is given by the multiplication of the dimesions, that is, A = lw.The perimeter is given by twice the sum of the dimensions, that is, P = 2(l + w).A farmer has 300 yards of fencing, hence the perimeter is:
P = 300.
Then:
2(l + w) = 300
l + w = 150
l = 150 - w.
Then the equation giving the area of the fence is:
A = lw
A = w(150 - w)
A = -w² + 150w.
Which is a quadratic equation with coefficients given by:
a = -1, b = 150.
The width that will give the highest possible area is the x-coordinate of the vertex, hence:
w = -150/(2(-1)) = 75 yards.
The length is of:
l = 150 - w = 150 - 75 = 75 yards.
Which means that the third option is correct.
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What is the greatest number of rectangles 6 cm x 4cm that can be cut from a piece of metal that measures 16 cm x 20 cm?
The greatest number of rectangles 6cm×4cm that can be cut from a metal that measure 16cm×20cm is 13 rectangles.
What is a rectangle?A rectangle is a plane shape that has pair of opposite sides equala and parallel.
To calculate the greatest number of rectangles, we use the formula below.
Formula:
n = LW/lw.................... Equation 1Where:
n = Number of rectangleL = Lenght of the metalW = Width of the metall = Length of the small rectanglew = Width of the small rectangleFerom the question,
Given:
L = 20 cmW = 16 cml = 6 cmw = 4 cmSubstitute these values into equation 1
n = (20×16)/(6×4)n = 13.33n ≈ 13 rectangles.Hence, the greatest number of rectangles is 13 rectangles.
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big ben, the nickname for the clock in elizabeth tower (named after the queen in 2012) in london, has an hour hand 2.70 m long with a mass of 60.0 kg and a minute hand 4.50 m long with a mass of 100 kg (figure). calculate the total rotational kinetic energy of the two hands about the axis of rotation. (you may model the hands as long, thin rods rotated about one end. assume the hour and minute hands are rotating at a constant rate of one revolution per 12 hours and 60 minutes, respectively.)
The hour hand is 2.70 m long and minute hand is 4.50m long with mass of 60 kg and 100 kg. Therefore. Total angular momentum is 1.2 kgm²/s.
Mass of Hour hand = 60 kg
length of hour hand = 2.70 m
Now,
Moment of inertia of the hour hand is given by:
I = mL²/ 3
I = 60(2.70)²/3
I = 145.8 kgm²
Now,
The angular speed of hour hand is:
ω = 2π/ T
⇒ ω = 2π / 12×3600
⇒ ω = 1.45 × 10⁻¹ rad/s
Now,
Angular momentum is given as:
L₁ = Iω = 145.8 × 1.45× 10⁻¹
= 0.021 kgm²/s
Mass of minute hand = 100 kg
length of minute hand = 4.50 m
Now,
Moment of inertia of the minute hand is given by:
I = mL²/ 3
I = 100(4.50)² /3
I = 675 kgm²
Now,
The angular speed of minute hand is
ω = 2π/ T
ω = 2π / 60× 60
ω = 1.74 × 10⁻³ rad/s
Now,
Angular momentum is given as:
L₂ = Iω = 675 × 1.74 ×10⁻³
= 1.178 kgm²/s
Total angular momentum is given as
L = L₁ + L₂
= 0.021 + 1.178
= 1.2 kgm²/s
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using a similar argument to solve teh hw problem 1, show that if a is an integer, then 7 divides a^7 -a
The expression a⁷- a is divisible by 7 if a is an integer.
Given that,
7 divides a^7−a
To find that if a is an integer, then 7 divides a^7 -a or a⁷- a is divisible by the number 7
We can write, where k is an integer
a^7−a=7k
a(a^6−1)=7k
Now if a=k then
a^6−1=7
a^6=8
and a=±1.414 so a^7−a=9.898
If a is not equal to k then
a(a^6−1)=a(a^3+1)(a^3−1)=7k
since a(a+1)(a−1) is the not product of 3 consecutive integers, the expression is divisible by 7.
Hence, The expression a⁷- a is divisible by 7 if a is an integer.
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Some students in Grade 7 and Grade 8 take a survey about whether they would prefer to join
a dance club or a hiking club. The table shows the results. The students want to make
25 POINTS
The completion for the row of the table will be:
Grade 8
Dance club: 0.25
Hiking club: 0.75
Total : 1
Grade 9:
Dance club: 0.40
Hiking club: 0.60
Total : 1
How to calculate the values?The dance club for grade 8 will be calculated as:
= Number of dancers / Total number
= 5/20
= 0.25
The hiking club will be:
= 15/20
= 0.75
The dance club for grade 9 will be calculated as:
= Number of dancers / Total number
= 20/50
= 0.4
The hiking club will be:
= 30/50
= 0.6
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Your mother made some pumpkin cookies and put half of them on a
plate for your brother and you. Your dog Gobbles ate six! Your
brother ate half of what was left, and you ate the last four.
How many cookies did your mother bake altogether?
The total cookies she baked altogether is 28 cookies
What are word problems?A word problem is a math problem written out as a short story or scenario. Basically, it describes a realistic problem and asks you to imagine how you would solve it using math.
Half of the cookies is placed on the table, 6 is eaten by my dog, half is eaten by my brother and I ate the last 4, the means my brother ate 4 cookies too.
Therefore the total cookies put on the plate is 6+4+4= 14cookies
half of all the cookies were put in the plate,
therefore the total cookies made is 14×2= 28cookies.
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I need help please!!!!!!
Answer: -1
Step-by-step e
What number (let's call it x ) must be added to the numerator and denominator of the fraction 6/29 so that the new fraction is equal to 2/3 ?
Answer:
add 54 to the numerator and 61 to the denominator because after you add it the fraction, it should be 60/90: simplified to 2/3 if you divide the numerator and denominator by 30.
The number that must be added to the numerator and denominator is 40.
What is a fraction?A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.
Example: 1/2, 1/3 is a fraction.
We have,
Fraction = 6/29
The new fraction = 2/3
Now,
(6 + x)/(29 + x) = 2/3
3(6 + x) = 2(29 + x)
18 + 3x = 58 + 2x
3x - 2x = 58 - 18
x = 40
Thus,
The number x is 40.
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Select the correct answer.
What is the inverse of function f?
f(x)=10 9x+11
A.f−1(x)=9x+11 /10
B. f−1(x)=9 10x+11
C. f−1(x)=9x−99 /10
D. f−1(x)=10x−110/ 9
Edmuntem btw
PLEASEEE ANSWERRRRR ASAP!!!!
The inverse function of the given function will be f(x)⁻¹ = ( 10 ) / ( 9x - 99).
From the question, we have
f(x) = ( 10/9x) + 11
x = ( 10 / 9y ) + 11
x - 11 = ( 10 / 9y )
9y / 10 = ( 1 / ( x - 11 )
9y = 10 / ( x - 11 )
y = ( 10 ) / ( 9x - 99 )
Inverse function :
The expression that established the relationship between the dependent variable and the independent variable is referred to as a function. An inverse function is a function that is applied to the value of y after switching the values of two variables, x and y.
Complete question:
What is the inverse of function f?
f(x) = 10/9x+11
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Name the postulate or theorem that proves the pair of triangles is congruent. List the vertices of the congruent tri-
A
B
с
D
E
F
Y
AABC Ayxz by the AAS Postulate/Theorem.
X
i
Z
G
H
Answer:1712
Step-by-step explanation: is 1712
An arithmetic sequence has this recursive formula: What is the
explicit formula?
Answer:
the correct answer is -32+43
Step-by-step explanation:
I just know
What is the slope NEED HELP PLEASEEEEEEEE
The slope of the graph above is [tex]-\frac{4}{3}[/tex]
How to find the slope of a line?The slope of a line is the change in the dependent variable with respect to the change in the independent variable. The slope of a line is rise over run.
Therefore,
slope = m = y₂ - y₁ / x₂ - x₁
Hence, using the coordinates on the graph let's find the slope of the graph.
(-2, 1)(1, -3)
Therefore,
x₁ = - 2
x₂ = 1
y₁ = 1
y₂ = - 3
Hence,
[tex]slope = \frac{-3-1}{1-(-2)}[/tex]
[tex]slope = \frac{-4}{1+2}[/tex]
[tex]slope = \frac{-4}{3}[/tex]
Therefore, the slope of the line is [tex]-\frac{4}{3}[/tex]
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Help again anyone ?.
The values of x, y and z in the given Rhombus are
x = -98, y = 36 and z = -97/4.
Given, the figure shown is a rhombus
as, the opposite angles of the rhombus are equal
So, 3y - 1 = 107
3y = 107 + 1
3y = 108
y = 36
and (-x - 8) = (-4z - 7)
x + 8 = 4z + 7
x - 4z = -1
also, the sum of the opposite angles of the rhombus is 180°.
So, (-x - 8) + (-4z - 7) = 180
-x - 4z = 180 + 15
x + 4z = -195
On adding the equations, we get
2x = -196
x = -98
and z = -97/4
Hence, the values of x, y and z are
x = -98, y = 36 and z = -97/4.
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The perimeter of an isoceles triangle is 392cm and its unequal sides are 195 cm.Find the area
9,603.75 cm² is the area of the given triangle.
What are triangles?A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. △ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane. Equilateral, isosceles, scalene and right-angled triangles are the four different forms of triangles.So, the perimeter of the triangle is 392 cm.
The unequal side is 195.Then, let the rest 2 sides be x, where x = x.
x + x + 195 = 3922x + 195 = 3922x = 392 - 1952x = 197x = 197/2x = 98.5Now, we know that the rest 2 equal sides are of length 98.5 cm.
Area of triangle: 1/2 × base × heightNow, calculate the area as follows:
1/2 × base × height1/2 × 98.5 × 1951/2 × 19,207.59,603.75Therefore, 9,603.75 cm² is the area of the given triangle.
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Does each pair of expressions form an equation when joined with an equals sign?
Solving each pair of expression shows that
(1/5)^2 + 1 ≠ 2 * 12 / 25
( 1 + 1/4 )^2 = 2 - 7/16
Analysis of the expressionPutting equals sign implies that the the expression in left hand side of the equation is equal to the expression on the right hand side
If they are not equal the sigh to be used is not not equal to
(1/5)^2 + 1 & 2 * 12 / 25
1/25 + 1 & 24/25
26/25 ≠ 24/25
( 1 + 1/4 )^2 & 2 - 7/16
(5/4)^2 & 25/16
25/16 = 25/16
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what does the solution of equality look like?
Answer:no image I can’t see on mobile
Step-by-step explanation:
h
eight points are in/on the circle of radius 1cm. show that distance between some two points is less than 1cm.
According to the circle, if 8 points in a plane are chosen to lie on or inside a circle of diameter 2cm then show that the distance between some two points will be less than 1cm.
Circle:
Circle refers the round shape that has no corners or line segments. And it is a closed curve shape in geometry.
Given,
Eight points are in/on the circle of radius 1cm.
Here we need to show that distance between some two points is less than 1cm.
Let us consider the points be p1,p2,…,p8
Noe, we have to place the point p8 at the center of the circle and placing other seven points on the periphery of the circle, at equal distances
Here we have to remember that we are required to prove that there are at least a pair of points whose distance from each-other is less than 1cm.
So, now we have one point at the center and seven at the periphery of the circle.
Based on this the heptagon which will be formed by joining the seven points on the circle will have all its side equal in length.
Then the length of the side of the heptagon is less than 2π/7 cm which is less than 1cm.
Therefore, if we replace the position of any point then too we get a pair of points whose distance from each-other is less than 1cm.
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Which expression gives the volume of a sphere with radius /?
O A. (7³)
OB. 4(7²)
O C.
(7²)
O D. 4 (7³)
The expression that gives the volume of the Sphere with radius 7 is (4/3)π(7³) , the correct option is (a) .
In the question ,
it is given that
the radius of the sphere is 7 .
we need to find the expression that represents the Volume of the Sphere when radius is 7 .
the formula for the Volume of the Sphere is (4/3)π(r³) .
Substituting the value of radius = 7 , in the formula ,
we get ,
Volume = (4/3)π(7³)
Therefore , The expression that gives the volume of the Sphere with radius 7 is (4/3)π(7³) .
The given question is incomplete , the complete question is
Which expression gives the volume of a sphere with radius 7 ?
(a) (4/3)π(7³)
(b) (4/3)π(7²)
(c) 4π(7²)
(d) 4π(7³)
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4. because we are using a coin flip app, this experiment really tests only that app inventor's random integer block generates 1 around half the time. is this a sufficient test for app inventor's prng? what other experiments might you do to increase your confidence in app inventor's prng?
App inventor's random integer block test is sufficient for app inventor's prng . but to increase our confidence in app inventor's prng we can do other tests like random fraction test and random set speed test.
The Coin Flip Experiment app allows you to run experiments aimed at determining how "good" the App Inventor PRNGs are. The app allows the user to "flip a coin" her N times and the results are displayed. They should record and count the results and calculate the average head percentage. The expectation of should reach 50% on average as N increases.
To properly test an App Inventor PRNG, you must test both the Random Integer and Random Fraction blocks along with the Random Fraction and Random set speed to blocks. Create dice simulations to get better than 50/50 predictions and reuse dice simulators for all combinations of different App Inventor random blocks. If such a combination yields the same results, then you can be confident that her PRNG in App Inventor provides a good model of randomness from all angles.
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