The solution is Option B.
The recursive formula to calculate Marta's salary is given by the equation
f ( n ) = f ( n - 1 ) + 2700
The salary of Marta after 4 years will be $ 33,000
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the initial salary of Marta be f ( 0 ) = $ 24,900
The increment in Marta's salary every year = $ 2700
So , the equation will be
f ( n ) = f ( n - 1 ) + 2700
when n = 1
Substitute the value of n = 1 in the equation , we get
f ( 1 ) = f ( 1 - 1 ) + 2700
f ( 1 ) = f ( 0 ) + 2700
f ( 1 ) = 24,900 + 2700
f ( 1 ) = $ 27,600
when n = 2
Substitute the value of n = 2 in the equation , we get
f ( 2 ) = f ( 2 - 1 ) + 2700
f ( 2 ) = f ( 1 ) + 2700
f ( 2 ) = 27,600 + 2700
f ( 2 ) = $ 30,300
when n = 3
Substitute the value of n = 3 in the equation , we get
f ( 3 ) = f ( 3 - 1 ) + 2700
f ( 3 ) = f ( 2 ) + 2700
f ( 3 ) = 30,300 + 2700
f ( 3 ) = $ 33,000
Hence , after 4 years the salary of Marta will be $ 33,000
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Marta's annual salary increases by $2700 each year. Applying the recursive formula: f(n) = f(n-1) + 2700; f(4)=f(3)+2700=f(2)+2700+2700=f(1)+2700+2700+2700=f(0)+2700+2700+2700+2700=24900+4*2700=35500, we determine that Marta's salary in 4 years would be $35,500.
Explanation:The subject of the question involves recursion, or constructing a sequence of numbers in a specific way. In Marta's case, her salary can be calculated using a recursive formula that builds upon her previous salary. This formula relies on the concept of numerical patterns and can be represented as follows: f(n) = f(n-1) + 2700; where f(n) is Marta's salary after n years and f(n-1) is her salary the previous year.
At the start, Marta's salary is 24,900, which serves as the base case for our recursive function. Therefore, her income increases by $2700 each year. To get Marta's salary in 4 years, we would use the recursive formula: f(4) = f(3) + 2700 = f(2) + 2700 + 2700 = f(1) + 2700 + 2700 + 2700 = f(0) + 2700 + 2700 + 2700 + 2700 = 24,900 + 4*2700 = 35,500. So, Marta's salary is $35,500 after 4 years.
Therefore, the correct option among choices provided is none from the given options.
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Thomas earns 15 per hour if he recurved a 10% per hour pay increase how much does Thomas now make per hour
Answer:
He now makes 16.50 per hour
Step-by-step explanation:
15.00 x .10 = 1.50
15.00 + 1.50 = 16.50
Please answer this question correctly!!
f(x) + n - translate the graph n units up
f(x) - n - translate the graph n units down
f(x + n) - translate the graph n units left
f(x - n) - translate the graph n units right
|f(x)| - reflect over x-axis for x < 0.
[tex]f(x)=|x+2|-5[/tex]
Graph g(x) = x
g(x + 2) = x + 2 → translate 2 units left
|g(x + 2)| = |x + 2| → reflect over x-axis for x < 0
|g(x + 2)| - 5 = |x + 2| - 5 → translate 5 units down
A delivery company purchased a new delivery truck for $43,200. The depreciated value of the truck can be estimated by the number of t years in service. If the the truck depreciates at a rate of $7,200 per year, which of the functions ƒ(t) could be used to estimate the truck's depreciated value after t years?
Answer:
[tex]f(t)=43,200-7200t[/tex]
Step-by-step explanation:
We have been given that a delivery company purchased a new delivery truck for $43,200. The depreciated value of the truck can be estimated by the number of t years in service. The truck depreciates at a rate of $7,200 per year.
This means that after t years truck will depreciate 7200t. To find the truck's depreciated value after t years we will subtract 7200t from the cost of new delivery truck (43,200).
[tex]f(t)=43,200-7200t[/tex]
Therefore, the function [tex]f(t)=43,200-7200t[/tex] could be used to estimate the truck's depreciated value after t years.
The depreciated value of the truck after t years can be estimated by the linear function ƒ(t) = 43200 - 7200t, reflecting a straight-line depreciation method at a rate of $7,200 per year.
To estimate the depreciated value of the delivery truck after t years, we can use a linear equation which reflects a straight-line depreciation method. Since the truck cost $43,200 and depreciates at a rate of $7,200 per year, the equation representing the depreciated value of the truck after t years would be ƒ(t) = 43200 - 7200t. This equation starts with the initial value of the truck and subtracts the depreciation cost multiplied by the number of years the truck has been in service.
Depreciation is a way businesses can allocate the cost of a physical asset over its useful life. In this case, each year the truck is in service, it loses $7,200 in value. After one year, the value of the truck would be $43,200 - $7,200, which equals $36,000, and you would continue to subtract $7,200 for each additional year to determine the truck's value at any given time.
Please help!!
Divide. 2 5/8 ÷ 2 1/2 Enter your answer, as a mixed number in simplest form, in the box.
The simplest form of [tex]2\frac{5}{8}[/tex] ÷ [tex]2 \frac{1}{2}[/tex] is [tex]1\frac{1}{20}[/tex] .
Simplification: Consider,[tex]2\frac{5}{8}[/tex] ÷ [tex]2\frac{1}{2}[/tex]
write the mixed fraction to improper fraction
= [tex]\frac{21}{8}[/tex] ÷ [tex]\frac{5}{2}[/tex]
Now change the division sign to the multiplication sign by writing the second number as [tex]\frac{2}{5}[/tex] .
= [tex]\frac{21}{8}[/tex] × [tex]\frac{2}{5}[/tex]
= [tex]\frac{21}{20}[/tex]
Write the above improper fraction into a mixed fraction.
= [tex]1\frac{1}{20}[/tex]
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y = 2x + 3
2y = 4x + 6
The system of equations has _____ solution(s).
A.no
B.one
C.infinite
Trevor and Marissa together have 26 t-shirts to sell. If marissa has 6 fewer t shirts than trever, how many t shirts does Trevor have
A restaurant automatically charges a 20% gratuity if a party has 6 or more people. How much gratuity is added to a party of 6 on and $141 bill?
Answer:
The gratuity added is $28.2 .
Step-by-step explanation:
As given
A restaurant automatically charges a 20% gratuity if a party has 6 or more people.
The bill of the party is $141.
20% is written in the decimal form.
[tex]= \frac{20}{100}[/tex]
= 0.20
Gratuity is added to a party = 0.20 × 141
= $28.2
Therefore the gratuity added is $28.2 .
Answer: The gratuity added is $28.2.
In a cube, all the dimensions have the same measure. True or False
Answer:true
Step-by-step explanation:
Answer:
true
Step-by-step explanation:
The centre of each semicircle is on DC.
Work out the area of the shaded region.
Give your answer correct to 3 significant figures.
The shaded region, which is approximately 251.74 cm².
For the area of the shaded region, we need to calculate the area of a trapezium and the area of two semicircles.
Given data: AB = 28 cm , DC = 12cm and h = 14 cm
The formula for the Area of Trapezium:
Area of trapezium = 1/2 × (AB + DC) × h
Substituting the given values:
Area of trapezium = 1/2 × (28 + 12) × 14 = 280 cm²
The formula for the Area of a Semicircle:
Area of semicircle = πr²/2
Given that the radius r is 3 cm:
Area of two semicircles = 2 × π × 3²/2 = 28.26 cm²
Area of the Shaded Region:
Area of shaded region = Area of trapezium - Area of two semicircles
Area of shaded region = 280 - 28.26 ≈ 251.74 cm²
Therefore, the area of the shaded region is approximately 251.74 cm².
Three different golfers played a different number of holes today. Rory played 9 holes and had a total of 42 strokes. Jordan played 18 holes and had a total of 79 strokes. Rickie played 27 holes and had a total of 123 strokes. Which golfer had the lowest number of strokes per hole? Choose 1 answer:
Answer:
See below
Step-by-step explanation:
The units are stokes per hole or strokes / hole
Rory: 42/9 = 4.66667Jordan: 79/18 = 4.38889 <<< AnswerRickie: 123/27 = 4.5555Jordan had the lowest number of strokes / hole followed by Rickie and finally Rory.
Answer:
Jordan had the lowest number of strokes per hole
Step-by-step explanation:
1) Total holes played by Rory = 9
Total strokes of Rory = 42
Number of stroke per hole: Rory
[tex]\frac{42 strokes}{9 hole}=4.667 strokes/hole[/tex]
2)Total holes played by Jordan = 18
Total strokes of Jordan = 79
Number of stroke per hole: Jordan
[tex]\frac{79 strokes}{18 hole}=4.389 strokes/hole[/tex]
3) Total holes played by Rickie = 27
Total strokes of Rickie = 123
Number of stroke per hole: Rickie
[tex]\frac{123 strokes}{27 hole}=4.556 strokes/hole[/tex]
4.667 strokes/hole > 4.556 strokes/hole > 4.389 strokes/hole
Rory > Rickie > Jordan
Jordan had the lowest number of strokes per hole
If x varies inversely as y, and x = 11 when y = 15, find x when y = 3.
a:11/5
b:33/15
c:55
Answer:
55
Step-by-step explanation:
The equation of inverse variation is
y = k/x,
where k is a constant.
We can use the given x- and y-coordinates to find k.
y = k/x
15 = k/11
k = 165
The inverse variation equation for this problem is
y = 165/x
For y = 3,
3 = 165/x
3x = 165
x = 55
Answer:
C
Step-by-step explanation:
given x varies inversely as y then the equation relating them is
x = [tex]\frac{k}{y}[/tex] ← k is the constant of variation
To find k use the given condition x = 11 when y = 15
k = xy = 11 × 15 = 165 , hence
x = [tex]\frac{165}{y}[/tex] ← inverse variation equation
when y = 3, then
x = [tex]\frac{165}{3}[/tex] - 55 → C
A city has 3 new houses for every 7 old houses. If there are 15 new houses in the city, how many old houses are there? A. 37 B. 35 C. 33 D. 38
The solution is Option B.
The number of old houses in the city are 35 houses
What is Proportion?
The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
The proportional equation is given as y ∝ x
And , y = kx where k is the proportionality constant
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Given data ,
Let the proportion be represented as A
Now , the value of A is
The number of new houses = 3
The number of old houses = 7
So , the ratio of old houses to new houses = number of old houses : number of new houses
Substituting the values in the equation , we get
Ratio of old houses to new houses = 7 : 3
Now , the number of new houses = 15
So , the number of old houses A is given by the proportion equation ,
7 : 3 : : A : 15
On simplifying the equation , we get
7/3 = A / 15
Multiply by 15 on both sides of the equation , we get
A = ( 7 x 15 ) / 3
A = 7 x 5
A = 35 houses
Therefore , the value of A is 35 houses
Hence , the number of old houses is 35
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Final answer:
The correct number of old houses is found by determining how many times the 3:7 ratio of new to old houses fits into the 15 new houses and then applying that to the 7 old houses in the ratio, which results in 35 old houses.
Explanation:
The question asks to find the number of old houses in a city given the ratio of new to old houses and the number of new houses. There is a ratio of 3 new houses for every 7 old houses. If there are 15 new houses, we need to find how many times the ratio fits into the number of new houses and then apply that same multiplier to the number of old houses.
To find this, we divide the number of new houses by the number of new houses in the ratio:
Number of times the ratio fits = 15 new houses ÷ 3 new houses per ratio = 5 times
Now, we multiply the number of old houses in the ratio by 5:
Number of old houses = 7 old houses per ratio × 5 times = 35 old houses
Therefore, the correct answer is B. 35.
Consider the function f(x)=−23x+1.
What is f(3)?
Please help! Urgent!
What is the measure of angle B?
-78°
-92°
-102°
-282°
Determine the standard form of the equation of the line that passes through (-6,6) and (3,-2)
Considering the expression of a line, the equation of the line that passes through the pair of points (-66) and (3,-2) is 8/9x +y= 2/3.
Linear equation
A linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope m of said line can be calculated using:
m= (y₂ - y₁)÷ (x₂ - x₁)
Substituting the value of the slope m and the value of one of the points in the expression y = mx + b, the value of the ordinate to the origin b can be obtained.
The standard form of the line is Ax +By= C
Equation in this case
In this case, being (x₁, y₁)= (-6, 6) and (x₂, y₂)= (3, -2), the slope can be calculated as:
m= (-2 - 6)÷ (3 - (-6))
m= (-2 - 6)÷ (3 + 6)
m= (-8)÷ 9
m= -8/9
Considering point 2 and the slope, you obtain:
-2= (-8/9)×3 + b
-2= -8/3 + b
-2 +8/3= b
2/3= b
The equation of the line is y= -8/9x +2/3.
Finally, the standard form of the line is 8/9x +y= 2/3
The latest online craze is a new game, Khan on Seven. You get 100 points for playing the game. In addition, you get 50 points for each seven-letter word you are able to make with the ten letters you are given. The game leader currently has 17,950 points. Sal wants to break the record, and needs 18,000 points or more to do so. Write an inequality to determine how many seven-letter words, ww, Sal will need to make to break the record.
Answer:
x is greater than or equal to 358
Step-by-step explanation:
1. Subtract 100 from 18,000
2. Divide by 50 to get your number of seven letter words
PLEASE HELP PLEASE PLEASE
Answer:
2.5 rad ( to the nearest tenth )
Step-by-step explanation:
the time difference between the given times is 24 minutes
In 1 hour the hand moves 2π radians, hence in 1 minute moves
[tex]\frac{2\pi }{60}[/tex], thus in 24 minutes moves
[tex]\frac{2\pi }{60}[/tex] × 24 ≈ 2.5 radians
Bob has a standard deck of playing cards. If he randomly draws a J, K, 2, and 2, what is the probability that the next card he draws to add to his hand is a K? Please answer in fraction form.
Answer:
The correct answer has already been given (twice). I'd like to present two solutions that expand on (and explain more completely) the reasoning of the ones already given.
One is using the hypergeometric distribution, which is meant exactly for the type of problem you describe (sampling without replacement):
P(X=k)=(Kk)(N−Kn−k)(Nn)
where N is the total number of cards in the deck, K is the total number of ace cards in the deck, k is the number of ace cards you intend to select, and n is the number of cards overall that you intend to select.
P(X=2)=(42)(480)(522)
P(X=2)=61326=1221
In essence, this would give you the number of possible combinations of drawing two of the four ace cards in the deck (6, already enumerated by Ravish) over the number of possible combinations of drawing any two cards out of the 52 in the deck (1326). This is the way Ravish chose to solve the problem.
Another way is using simple probabilities and combinations:
P(X=2)=(4C1∗152)∗(3C1∗151)
P(X=2)=452∗351=1221
The chance of picking an ace for the first time (same as the chance of picking any card for the first time) is 1/52, multiplied by the number of ways you can pick one of the four aces in the deck, 4C1. This probability is multiplied by the probability of picking a card for the second time (1/51) times the number of ways to get one of the three remaining aces (3C1). This is the way Larry chose to solve the this.
Step-by-step explanation:
Hi There!
Answer:
4/52 (With cards picked before put back.)
3/48 (With cards picked before not put back.)
Step-by-step explanation:
A standard deck of cards is made up of 52 cards.
There are 4 kings in a deck.
4/52
Bob has a 4/52 chance of picking a king.
I don't know if the cards he picked prior to this he put back or not. If he didn't then it's 3/48.
Hope This Helps :)
HELP ASAP!! ∵ Question in Pictures... ∵ 65 POINTS!
1. The graph of y=2/3x-2 is the top right corner, the -2 in the equation makes the line cross the y axis at -2
2. The slope is always with x and the y intercept is the second part of the equation.
The equation would be y = 5/6x -3
3. The slope is the change in Y over the change in X
slope = 10-7 / 2 - -1 = 3/3 = 1
Using the line formula y = mx+b, solve for b using the first point and the slope:
7 = 1 (-1)x +b
b = 7+1
b =8
The equation is -x +y =8
4. the jar starts with 6 , then they add 2 each day, multiply 2 by the number of days (x) and add it to 6:
The equation would be y = 2x + 6
5. point (5,9) slope = 2
Point-slope formula is written as y - y1 = m(x-x1)
y1 = 9, x1 = 5, m = 2
equation becomes y-9 =2(x-5)
Answer:
The answer is the first graph
The equation is y = 5/6x -3
The next equation is -x +y =8
The equation after would be y = 2x + 6
And, the final answer is y-9 =2(x-5)
Hope this helps!
Carlos swam to the bottom of a pool that is 12 ft deep. What is the opposite of Carlos's elevation relative to the surface
Answer:
The opposite of Carlos's elevation would be +12ft.
Step-by-step explanation:
This question is using positive and negative integers to represent elevation and descending. The surface of the pool would represent an elevation of 0, where we are level. However, when Carlos descends (swims to the bottom) of the pool, he is at an elevation of -12 because he is below the surface. The opposite of -12 would be +12. So the opposite of where Carlos is -12ft below the surface of the water would be +12 foot above the surface of the water.
Please help on this one ?
Answer:
A
Step-by-step explanation:
The expansion of (x +y)⁴ is ...
... x⁴ +4x³y +6x²y² +4xy³ +y⁴
The expansion coefficients are 1, 4, 6, 4, 1; the sum of exponents is always 4, and there are 5 terms.
Rick carries a balance on his credit card each month. Today is the first day of the new, 28-day billing cycle. The current balance is $2,360 and the APR is 21%. Rick is buying a friend an expensive gift that costs $1,500 that he plans to put on his credit card. This will be his only purchase this month. How much in finance charges can he save by making the purchase on the last day of the billing cycle versus the first day of the billing cycle?
Answer:
$ 25.31 finance charges he can save by making the purchase on the last day of the billing cycle versus the first day of the billing cycle
Step-by-step explanation:
In the beginning of Month , ADB will be on the total amount of balance and the purchase that means ADB = 0.21 (2360 + 1500)/12
= $ 67.55
ADB at the end of the month
Part of 2360 for 27 days = (2360 x 27)/28 = $ 2275.71
Part of 3860 for 1 day = (3860 x 1)/28 = $ 137.85
So the total becomes $ 2275.71 + $ 137.85 = $ 2413.56
So , ADB will be $ 2413.56 x (0.21)/12
= $ 42.23
Difference in the finance charges at the beginning and at the end of the month is
$ 67.55 - $ 42.23
= $ 25.31
Which points are on the graph of f(x)=(1/3)x ?
Select each correct answer.
(0, 1)
(3, 27)
(−2, 9)
(−1, −1/3)
Answer:
the only point is (0,1) if u would look at the graph i post
Step-by-step explanation:
The point which lies on the graph of f(x) = (1/3)x will satisfy the function thus point (-1, -1/3) will lie on the graph thus option (D) is correct.
How to plot a graph?A graph is a diagram that shows the fluctuation of one variable in relation to one or more other variables.
In order to plot the graph, we need to find out y's values corresponding to x's value
As per the given function,
f(x) = (1/3)x
Substitute, x = 0,
y = f(0) = (1/3)0 = 0
So,(0,1) will not lie on the graph.
Similarly, (3, 27) and (−2, 9) also do not lie on the graph.
Substitute (-1,-1/3)
-1/3 = (1/3)(-1) = -1/3
Thus, it will be the point of the function.
Hence "The point which lies on the graph of f(x) = (1/3)x will satisfy the function thus point (-1, -1/3) will lie on the graph".
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divide. simplify your answer (2x^4-6x^3+4x^2-3x)*(2x)
Answer:
[tex]x^3-3x^2+2x-\frac{3}{2}[/tex]
Step-by-step explanation:
We can divide polynomials by other polynomials by dividing each term by the denominator. Remember, when we divide a variable by itself, we must change the exponent in our answer according to exponent rules.
[tex]\frac{ (2x^4-6x^3+4x^2-3x)}{2x}=\frac{2x^4}{2x} -\frac{6x^3}{2x} +\frac{4x^2}{2x} -\frac{3x}{2x} =x^3-3x^2+2x-\frac{3}{2}[/tex]
Answer:
3/2
Step-by-step explanation:
It takes 12 hours for a single hose to fill a large vat. When a second hose is added, the vat can be filled in 4 hours. How many hours are required for the second hose working alone to fill the vat?
6 hours
Step-by-step explanation:The two hoses together take 1/3 the time (4/12 = 1/3), so the two hoses together are equivalent to 3 of the first hose.
That is, the second hose is equivalent to 2 of the first hose. Two of the first hose could fill the vat in half the time one of them can, so 6 hours.
The second hose alone can fill the vat in 6 hours.
_____
The first hose's rate of doing work is ...
... (1 vat)/(12 hours) = (1/12) vat/hour
If h is the second hose's rate of doing work, then working together their rate is ...
... (1/12 vat/hour) + h = (1/4 vat/hour)
... h = (1/4 - 1/12) vat/hour = (3/12 -1/12) vat/hour = 2/12 vat/hour
... h = 1/6 vat/hour
so will take 6 hours to fill 1 vat.
The second hose can fill the vat alone in 6 hours, calculated by subtracting the work rate of the first hose from their combined work rate.
Explanation:The question is about the time it would take for the second hose to fill the large vat alone, given that the first hose takes 12 hours alone, but together they take 4 hours. We are not given any info about the hose size or flow rate, so those don't need to be involved here.
We can analyze this problem in terms of work done. We know that one hose can fill the vat in 12 hours, so its work rate is 1/12 of the vat per hour. When we add the second hose, the vat is filled in 4 hours. The combined work rate of both hoses is 1/4 of the vat per hour.
To find the work rate for the second hose, we subtract the work rate of the first hose from the combined work rate: 1/4 - 1/12 = 1/6. This means the second hose can fill the vat in 6 hours alone.
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If you need 3 hot dogs for every 5 people and 1,200 people show up how many hot dogs would you need
Answer:
I'd say about 720 hotdogs.
Step-by-step explanation:
Please answer both questions and show all your work. I am in a hurry... please...
1) To finish an order in time the company had to produce 40 items daily, but it produced 20 items more daily and finished the order 3 days ahead of time. In how many days was the company supposed to finish the order?
2) If eight people share equally in an inheritance, what percent of the inheritance belongs to three people? What percent belongs to them if two of the people are disinherited? By what percent does each person’s share of the inheritance increase?
Answer: 1) 9 days
2) a)37.5%
b)50%
c) 33.33%
Step-by-step explanation:
1) - Let's call:
x: number of days the company supposed to finish the order.
- You know that the company had to produce 40 items daily, but it produced 20 items more daily and finished the order 3 days ahead of time. Therefore, you can express this as following:
[tex]40x=(40+20)(x-3)\\40x=60(x-3)[/tex]
- Solve for [tex]x[/tex]:
[tex]40x=60x-180\\-20x=-180\\x=9[/tex]
(The answer is 9 days)
2) a) The percent that belongs to three people if eight eight people share equally in an inheritance, can be calculated as following:
[tex]\frac{3}{8}*100=37.5[/tex]%
b) The percent that belongs to three people if six people share equally in an inheritance (because two of the people are disinherited) can be calculated as following:
[tex]\frac{3}{6}*100=50[/tex]%
c) - The increase goes from 1/8 to 1/6, therefore, you must subtract them:
[tex]\frac{1}{6}-\frac{1}{8}=\frac{1}{24}=0.04167[/tex]
- Divide the result by 1/8 and multiply by 100 to obtain the percent:
[tex]\frac{0.04167}{\frac{1}{8}}*100=33.33[/tex]%
Need help with both 18 and 19.
18. Answer: D
Step-by-step explanation:
First, find the measure of the missing angle.
65° + 57° + x = 180°
122° + x = 180°
x = 58°
Next, match up the angles with the opposite sides:
65° ⇄ Swim
58° ⇄ Bike
57° ⇄ Run
Lastly, put them in order from least to greatest:
57° < 58° < 65°
⇒ Run < Bike < Swim
The only multiple choice option that is correct is Bike > Run.
*****************************************************************************
19. Answer: 22.3°
Step-by-step explanation:
[tex]sin\theta = \dfrac{opposite}{hypotenuse}[/tex]
[tex]sinD= \dfrac{EF}{DE}[/tex]
[tex]sinD= \dfrac{19}{50}[/tex]
[tex]D= sin^{-1}\bigg(\dfrac{19}{50}\bigg)[/tex]
D = 22.3°
Roberto'S puppy weighed 4.5 pounds at the end of May during June and July the puppy gained 18.63 pounds how much did Roberto's puppy weight at the at the end of July
Answer: 23.13 lbs
Step-by-step explanation:
Weight in May + Weight gained = Weight in July
4.5 + 18.63 =
23.13 =
NOTE: Make sure to line up the decimal point when adding decimals:
4.50
+ 18.63
23.13
NEED HELP ASAP!!!
WILL CHOOSE THE BRAINLIEST!!!!
You need a 70% alcohol solution. On hand, you have a 200 mL of a 35% alcohol mixture. You also have 90% alcohol mixture. How much of the 90% mixture will you need to add to obtain the desired solution?
Add 350 mL of the 90% alcohol mixture to obtain a 70% alcohol solution.
Let V be the volume of the 90% alcohol solution needed
Set up the equation
The final mixture volume will be 200 + V mL.
- The total amount of alcohol in the final mixture should be 70% of the total volume.
Calculate the total amount of alcohol
- Amount of alcohol from 200 mL of 35% solution: 0.35 * 200 = 70 mL.
- Amount of alcohol from V mL of 90% solution: 0.90 * V mL.
Total amount of alcohol in the final solution
- Total alcohol = 70 + 0.90V mL.
Set up the equation for the final concentration
- Final concentration: 70%
0.70 *(200 + V) = 70 + 0.90V
Solve the equation
0.70 * (200 + V) = 70 + 0.90V
140 + 0.70V = 70 + 0.90V
140 - 70 = 0.90V - 0.70V
70 = 0.20V
V = 70 / 0.20 = 350 mL.