Answer:
9/16
Step-by-step explanation:
9/16. The ratio of areas of two similar squares is the square of the ratios of their similar side lengths. Since the ratio of the smaller side length to the larger side length is 3/4, the ratio of areas of two similar squares is: (3/4)² = 3²/4² = 9/16.
Determine which equation will solve the problem. The gratuity on a restaurant bill was $18. If a 20% tip was left, what was the original amount of the bill? to solve, use this equation:. The original amount of the bill is.
The original amount of the bill exists $ 90.
What is the Gratuity amount?
A gratuity exists as a totality of money customarily provided by a customer to specific service sector workers such as hospitality for the service they have executed, in addition to the basic expense of the service.
Gratuity on a restaurant bill = $18 and tip = 20%.
To find the original amount of the bill.
The tip exists directly proportional to the total cost = $ 90
18/(20%)
=(18/(20/100))
=$90
Therefore, the original amount of the bill exists as $ 90.
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The function f(x) is a cubic function and a limited table of values is provided below.
Write the equation of the cubic polynomial in standard form.
The cubic polynomial for the given function in question can be written as: x³ -2x² - 16x+ 32 = 0.
What is polynomial?
All the exponents of an algebraic expression called a polynomial must be whole numbers. Any polynomial must have non-negative integer variable exponents. We cannot divide a polynomial by a variable even though it contains variables and constants.
From the table given, we can see the function f(x) = 0 when, x = -4, 2, 4
It means, x+4 = 0, x-4 = 0, x-2 = 0
Multiplying these equations,
(x+4)(x-4)(x-2) = 0
(x²-4x+4x-16)(x-2) = 0
x³- 16x -2x² + 32 = 0
Therefore the cubic polynomial for the given function is:
x³ -2x² - 16x+ 32 = 0
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Find the value of x. Round to the
nearest tenth.
12
X
X=?
The value of x = 6 cm
The hypotenuse of a right triangle is its longest side. In other words, the hypotenuse is the side opposite the right angle.
Given that
Adjacent side = 12cm
Angle = 26
We must determine the value of x.
Here we have to use the tan ratio to find the value of x.
tan θ = opposite side/adjacent side
tan 26 = x / 12
Now Multiplying both sides by 12, we get
x = 12 tan 26 [tan 35 = 0.7]
x = 12 x 0.5
x = 6
Therefore, the value of x = 6 cm
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I need help with problems 19 through 21!!!
After t=1 or t=4 seconds, the ball will reach 20 meters high.
The ball will go up to 31.25 meters high.
After 4.5 seconds, the ball will be at a height of 11.25 meters.
What is a quadratic equation?
A quadratic equation is any equation in algebra that can be rearranged in standard form as ax²+bx+c=0, where x is an unknown value and a, b, and c are known numbers.
For 19)
The given equation is h = 25t - 5t²
Now the height of the ball is 20 meters, so put h = 20, so the equation will become,
20 = 25t - 5t²
⇒ 5t² -25t + 20 = 0
⇒ t² - 5t + 4 = 0
finding factors, we get
t² - 4t - t + 4 = 0
t (t - 4) - 1(t - 4) = 0
(t - 4)(t - 1) = 0
t = 4 seconds (or) t = 1 second.
For 20)
To find the maximum height, we have to differentiate the given function with respect to the 't'
so differentiating 'h' with respect to 't', we get
dh/dt = 25 - 10t
dh/dt = velocity.
v = 25 - 10t,
The maximum height will attain at v = 0,
25 - 10t = 0
⇒ t = 2.5 seconds
so at t = 2.5 seconds, the ball will achieve its maximum height.
put t = 2.5 in the given function, we get
h = 25(2.5) - 5(2.5)²
h = 62.5 - 31.25
h = 31.25 meters.
For 21)
Put t = 4.5 seconds,
h = 25(4.5) - 5(4.5)²
h = 112.5 - 101.25
h = 11.25 meters.
Hence,
After t=1 or t=4 seconds, the ball will reach 20 meters high.
The ball will go up to 31.25 meters high.
After 4.5 seconds, the ball will be at a height of 11.25 meters.
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Pls help pls pls pls pls pls
Tom is mailing packages. Each small package costs him $2.50 to send. Each large package costs him $3.10 . How much will it cost him to send 4 small packages and 1 large package?
Answer: $13.10
Step-by-step explanation: 4 small packages, 4*2.50 is $10. Add one large package which is $3.10 and you'll have your answer, it costs $13.10.
Answer:
It will cost him $13.10 to send 4 small packages and 1 large package.
Step-by-step explanation:
1. Cost of sending 4 small packages = 4 * $2.5 = 4 * $2.50 = $10
2. Cost of sending 1 large package = 1 * 3.1 = $3.1
Total cost of sending 4 small and 1 large packages = $10 + $3.10 = $13.10
. A rectangular field is 80 meters long and 40 meters wide. Calculate the area of the field.
Answer:3200 m²
Step-by-step explanation: length times width so 80*40
Answer: 3,200 meters
Step-by-step explanation:
Area of a rectangle = length times width
A=lw
A=80(40)
A=3,200 meters
what proportion of these tv sets are good? b. how many total samples (without replacement) of size five can be selected from this population?
The combination of 6 are total samples (without replacement) of size five can be selected from this population
What is permutation and combination?
Combination and permutation are two alternative strategies to divide up a collection of elements into subsets in mathematics. The components of the subset may be arranged in any order when combined. The subset's components are listed in a permutation in a certain order.ⁿCr = n!/( n-r)! r!
r = 5
total samples
⁶C₅ = 6!/(6-5)!5!
= 6!/1!5!
= 6 * 5!/1*5!
= 6
Hence, there are 6 ways
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Two teenagers are standing on a 28-meter-high walking bridge and see a boat coming down the river toward the bridge. The angle of depression formed by the
teenagers' horizontal line of sight and their line of sight to the front of the boat is 21°. If the teenagers' horizontal line of sight is 1.8 meters above the bridge, how far away from the bridge is the front of the boat? Round your answer to the nearest tenth.
Answer:
77.6 m
Step-by-step explanation:
Angle of Depression
If a person stands at a point and looks down at an object, the angle between their horizontal line of sight and the object is called the angle of depression.
To find how far the bridge is from the front of the boat, model as a right triangle and solve using the tan trigonometric ratio.
Tan trigonometric ratio
[tex]\sf \tan(\theta)=\dfrac{O}{A}[/tex]
where:
θ is the angle.O is the side opposite the angle.A is the side adjacent the angle.Given information:
Height of bridge = 28 mPerson height = 1.8 mAngle of depression = 21°As the teenagers' line of sight is 1.8 m above the bridge, the side of the right triangle opposite the angle of depression is:
28 + 1.8 = 29.8 mTherefore:
[tex]\implies \sf \tan21^{\circ}=\dfrac{29.8}{A}[/tex]
[tex]\implies \sf A=\dfrac{29.8}{\tan21^{\circ}}[/tex]
[tex]\implies \sf A=77.6\;m\;\;(nearest\;tenth)[/tex]
BY SELLING AN ARTICLE FOR $10.80, A SHOPKEEPER MAKES A PROFIT OF 8%. WHAT SHOULD BE THE SELLING PRICE FOR A PROFIT OF 20%?
To make a profit of 20% the article should be sold for $12.1
How to calculate the new selling priceThe new selling price will be solved by comparing the percentage increment with the old selling price
The selling price is $10.8 and the profit is 8%
The cost of the item is gotten from the profit percent as below
10.8 * 0.08 = 0.864 (profit)
cost price + profit = selling price
cost price = selling price - profit
cost price = 10.8 - 0.864
cost price = 9.936
comparing the percentages
8% profit is 0.864, 20% profit will be
8 = 0.864
20 = ?
cross multiplying
8 * ? = 20 * 0.864
? = 2.16
The new selling price
= cost price + profit
= 9.936 + 2.16
= 12.096 approximately $12.1
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The diagram shows a triangle.
Answer:
38
Step-by-step explanation:
the sum of the interior angles of a triangle is 180
2c + 3c -48 +2c -38 = 180 Combine like terms
7c + -86 = 180 Add 86 to both sides
7x = 266 Divide both sides by 7
x = 38
Answer: c = 38
Step-by-step explanation:
We know that a triangle's angles add up to 180 degrees. We will write an equation and solve it by combining like terms and then using inverse operations.
Given:
(2c)° + (2c - 38)° + (3c - 48)° = 180°
Distribute it out:
2c° + 2c° - 38° + 3c° - 48° = 180°
Combine like terms:
7c° - 86° = 180°
Add 86 to both sides:
7c° = 266°
Divide both sides by 7:
c = 38
there are 14 3-digit numbers in a list. can you conclude that there are two distinct subsets of the 14 numbers that have the same sum? justify your answer.
The answer to the given question is Yes, we can. We can conclude that there are two distinct subsets of the 14 3-digit numbers in the list which have the same sum.
There are [tex]2^{14}[/tex] = 16384 subsets. Since each number goes in the range from 0 through 999 and there are at most 14 3-digit numbers in a subset, the sum of any subset of the numbers will be in the range from 0 through 14 x 1000.
So, there are at most 14001 possible values for the sum of a subset of the 3-digit numbers. Since 16384 > 14001, if each subset is plotted to the value of its sum, then there need to be at least two different subsets which are plotted on to the same value.
For that reason, there are at least two different subsets whose numbers sum to the same value.
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In the word hawks, how many ways is it possible to rearrange the letters if none repeat and the letter w must go last? responses 5 5 15 15 24 24 120 120 650
In the word hawks, it is possible to rearrange the letters if none repeat and the letter w must go last as follows,
In the word “HAWKS” there are 24 possible ways to rearrange the letters so that no letter can be repeated and letter ‘w’ must go last.
It can be solved using Factorial concept.
Given word = “HAWKS”
Number of letters in Hawks = 5
There is a condition that W must be the last letter. So according to that we are now left with the 4 letters that we have to place so that no letter should be repeated.
By using the Factorial concept, (solve the numbers of letters left)! which is 4!
4! = 4x3x2x1
= 24
By this way we can say that there are 24 possible ways to rearrange the letters of “Hawks” by fulfilling all the conditions.
Hence there are 24 possible ways to rearrange the letters of Hawks.
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How do u find area of triangle?.
Answer:
Area of triangle = ½ × b × h
Step-by-step explanation:
Now we have to,
→ write formula of area of triangle.
Formula we use,
→ A = ½ × b × h
Hence, this is the formula.
Answer: Use the formula
Step-by-step explanation:
Jack's family spends $250 per month on rent. How much will they pay for the whole year?
Answer:
3000 dollars per year
Step-by-step explanation:
hope this helped :)
To win at LOTTO in one state, one must correctly select 6 numbers from a collection of 54 numbers (1 through 54). The order in which the selection is made
does not matter. How many different selections are possible?
There are different LOTTO selections.
The number of different possible selections for the lottery is of:
25,872,165.
How to obtain the number of possible selections?First we decide which formula is used, as follows:
Permutation formula -> order is not important.Combination formula -> order in important.It is stated in this problem that the order of the numbers is not important, hence the combination formula is used.
The number of different combinations of x objects from a set of n elements is obtained with the formula presented as follows, using factorials.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem, 6 numbers are selected from a set of 54, hence the number of different combinations is of:
[tex]C_{54,6} = \frac{54!}{6!48!} = 25,872,165[/tex]
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The team's engagement score was 4.89 this month. The score has been improving at a rate of 12% per month. What was the score 4 months ago?
1.09
2.54
3.11
4.30
4.77​​​​​​​
The engagement score in 4 months ago would be 7.69.
Future worth is the value of an asset in the future. It estimates the nominal amount of money that a certain quantity of money will be "worth" at a specified moment in the future under the assumption of a particular interest rate and is calculated by multiplying the present value by the accumulation function.
In four months, we must determine the future value of the engagement score.
The formula for calculating future value:
FV = P (1 + r)^n
FV = Future value
P = Present value = 4.89
R = rate of increase = 12%
N = number of months = 4
4.89 ( 1.12)^4 = 7.69
Therefore the engagement score in 4 months ago would be 7.69.
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help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
There would be 150 students enrolled in the school, according to estimates, in 2001.
468 students are projected to be enrolled in the school in the academic year 2018
How to solve for the number of personsWe have the equation as
[tex]y = 123.1(1.069)^x[/tex]
where we have x to be the difference in the number of years
2001 - 1998 = 3
y = 123.1(1.069)³
y = 123.1 * 1.2216115
y = 150.4
The estimated number of persons that would be studying in the school in the year 2001 would be 150.
b. 2018
We have to take the difference
x = 2018 - 1998 = 20
y = 123.1(1.069)²⁰
y = 123.1 * 3.798
y = 467.5
y ~ 468
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emily wants to buy shoes 68$ and 5 1/2 tax
Answer:
Total cost for her new boots is $71.74!
Step-by-step explanation:
Find the range of possible values for x
The range of possible values of X are X>12.5
What is meant by range?In mathematics, the range of a function can refer to one of two closely related concepts:
1. The function's codomain
2. The function's image
In mathematics, a function is an expression, rule, or law that explains a relationship between one variable (the independent variable) and another variable (the dependent variable).
A function is a sort of rule that generates a single output for a single input. In mathematics, a function is an expression, rule, or law that explains a relationship between one variable and another variable. A good example is Y=X². You will only get one output for y if you enter anything for x. We can say that y is a function of X because X represents the input value.
By using Hin-ges theorem,
(4X-10) > 40
4X > 50
X > 12.5
The range of possible values of X are X>12.5
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A basketball player can make 25 free throws in 8 minutes. How
many free throws can he make in 12 minutes?
Answer:
37.5
Step-by-step explanation:
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Florence and Anna are preparing meals to serve at a local homeless shelter. The number of people they will be able to serve depends on the number of meals they prepare. p = the number of people Florence and Anna will be able to serve m = the number of meals Florence and Anna prepare Which of the variables is independent and which is dependent?
A)p is the independent variable and m is the dependent variable
B) m is the independent variable and p is the dependent variable
B) m is the independent variable and p is the dependent variable.
Its given in question,
The number of people they will be able to serve depends on the number of meals they prepare. p = the number of people Florence and Anna will be able to serve m = the number of meals Florence and Anna prepare.
Which means people served depends on the meals prepared.
Therefore, p depends on m.
Hence, m is the independent variable and p is the dependent variable.
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question no 5 first question
Answer:
∆APQ is isosceles, so sides AP, AQ are congruent
Step-by-step explanation:
You want to show that AP≅AQ in the given figure.
Angles of Intersecting Chords TheoremThe Angles of Intersecting Chords Theorem tells you that the angle where chords cross is half the sum of the intercepted arcs. Here, that means ...
∠APY = (arc BX +arc AY)/2
∠AQX = (arc AX +arc CY)/2
Substituting equalsGiven that arc AX ≅ arc BX, and arc AY ≅ arc CY, we can substitute for BX and CY to get ...
∠APY = (arc AX +arc AY)/2
∠AQX = (arc AX +arc AY)/2
Two angles equal to the same thing are equal (substitution property), so ...
∠APY ≅ ∠AQX
These are base angles in the isosceles triangle APQ, so their opposite sides, AQ and AP, respectively, are congruent.
AP ≅ AQ
how do you write the equation of the line passing through (-2,-1) and y=-1/3x-5
The equation of the line passes through (-2, -1) and parallel to y = -1/3x - 5 is y = - 1 / 3 x - 5 / 3
How to find the equation of a line?The equation of a line can be represented in slope intercept form as follows:
y = mx + b
where
m = slopeb = y-interceptThe equation of the line passes through (-2, -1) and parallel to y = -1/3x - 5
Therefore, the slope of the line is - 1 / 3.
Parallel lines have the same slopes.
Therefore, let's find the y-intercept using (-2, -1)
y = - 1 / 3 x + b
-1 = - 1 / 3 (-2) + b
b = -1 - 2 / 3
b = -3 - 2/ 3
b = - 5 / 3
Therefore, the equation is y = - 1 / 3 x - 5 / 3
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Add
2x+1/x + -3/x^2+3x
Answer:
it hi
Step-by-step explanation:
During the month of march, hazure services made purchases on account totaling $43,500. Also during the month of march, hazure was paid $8,000 by a customer for services to be provided in the future and paid $36,900 of cash on its accounts payable balance. If the balance in the accounts payable account at the beginning of march was $77,300, what is the balance in accounts payable at the end of march?.
The balance of Accounts Payable at the end of March is $83,900.
According to question;
Balance in the beginning Accounts payable account =$77,300
Add: Purchases made during the month on account = $43,500
Less: Cash already paid on account payable balance =$36,900
Balance at the end of march in Accounts payable = $83,900
Therefore, balance left at the end of march is $83900.
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PLEASE HELP ASAP! NEED REAL ANSWERS!
The vertex of y=|2x+4|+5 is (-2, 5) and Range of the y=|2x+4|+5 is 5≤y<∞
What is a function?A relation is a function if it has only one y-value for each x-value.
We need to find the vertex and range of y=|2x+4|+5
f(x)=2x+4
f of x is equal to zero
2x+4=0
Subtract 4 from both sides
2x=-4
Divide both sides by 2
x=-2
y=|2x+4|+5
=|2(-2)+4|+5=|-4+4|+5=5
Hence vertex is (-2, 5)
The range of the y=|2x+4|+5 is 5≤y<∞
Hence vertex is (-2, 5) and Range of the y=|2x+4|+5 is 5≤y<∞
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Erica is cutting a 7/1/2 foot wooden board into pieces that are 5/8 of a foot long. How many pieces Will she be able to cut
Answer: 12
Step-by-step explanation: 7 1/2 divided by 5/8 equals 12.
Answer:
12
Step-by-step explanation:
7 1/2 = 15/2
15/2 divided by 5/8 = 12
Hope this helps
The population P of a small town, measured in hundreds, is modeled by the inverse of the function P−1(t) = 20ln(40t − 1200), where t is measured in years. Find the equation to model the population.
P = 2t + 60
P equals 1 over 40 times e to the power of the quantity five hundredths times t end quantity plus 30 where P 0 equals 30
P equals 1 over 40 times ln of the quantity five hundredths times t end quantity plus 30 where P 0 equals 30
P equals 1 over 800 times e to the power of t plus 30 where P 0 equals 30
The equation to model the population is P = [tex]\frac{1}{40}[/tex] [tex]e^{0.05t}[/tex] + 30
What is equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.An equation is a formula that expresses the equality of two expressions.Here the population P of a small town, measured in hundreds, is modeled by the inverse of the function,P−1(t) = 20ln(40t − 1200)
where t is measured in years.
We need to find an equation to model the population.
let y = [tex]p^{-1}[/tex](t)
where t is measured in years.
We need to find an equation to model the population.
20[tex]ln[/tex](40y - 1200) = t
[tex]ln[/tex](40y - 1200) = t/20
[tex]e^{ln(40y - 1200)}[/tex] = [tex]e^{0.05t}[/tex]
(40y - 1200) = [tex]e^{0.05t}[/tex]
40y = [tex]e^{0.05t}[/tex] + 1200
y = [tex]\frac{1}{40}[/tex] [tex]e^{0.05t}[/tex] + 30
Now, we determine the initial value.
P(0) = [tex]\frac{1}{40}[/tex] + 30
P(0) = 30
The equation to model the population is P = [tex]\frac{1}{40}[/tex] [tex]e^{0.05t}[/tex] + 30
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a linear function f models a relationship in which the dependant variable decreases 6 units for every 3 units the independant variable decreases. the value of the function at 0 is 4.graph the function.identify the slope, y intercept, and x intercept of the graph
The slope, y-intercept, and x-intercept of the graph of the linear function are 2, 4 and -2 respectively
How to graph the function and identify the slope, y-intercept, and x-intercept?The general equation of a straight line is:
y = mx + c,
where m is the slope of the line and c is the y-intercept
Given that: the linear function f models a relationship in which the dependent variable decreases 6 units for every 3 units the independent variable decreases. This implies:
slope (m) = (-6)/(-3) = 2
And that the value of the function at 0 is 4. This implies:
y-intercept (c) = 4
Substitute m = 2 and c = 4 into the general equation:
y = mx + c
y = 2x + 4 (This is the linear function)
To plot the graph:
Using y = 2x + 4
find y when x = 0:
y = 2(0) + 4
y = 4
=> x = 0, y = 4
Also, find x when y = 0:
0 = 2x + 4
2x = -4
x = -4/2 = -2
=> x = -2, y = 0
Thus, graph x = 0, y = 4 and x = -2, y = 0 as shown in the image attached
Therefore, the slope, y-intercept, and x-intercept of the graph are 2, 4 and -2 respectively
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