As per given by the question,
There are given that, 4 green marbles and 1 blue marble contains in a box and pick a marble at randomly.
Now,
Here pick a marble out at random, so first pick a marble for blue;
Then,
Total number of green marbles is 4, and the total number of blue marble is 1, and;
The total numbers of marbles in a bag is, 4+1=5.
So,
For pick the blue marble from 5 marble,
Now,
[tex]\begin{gathered} 5_{C_1}=\frac{5!}{1!\times(5-1)!} \\ =\frac{5!}{1!\times4!} \\ =\frac{5\times4!}{1!\times4!} \\ =5 \end{gathered}[/tex]Now, for pick the green marble from 5 marbles.
Here, total green marble is 4.
So,
[tex]\begin{gathered} 5_{C_4}=\frac{5!}{4!\times(5-4)!} \\ =\frac{5\times4!}{4!\times1!} \\ =5 \end{gathered}[/tex]Now,
From the question, there are clearly mention that if pick a blue, then stop because you won 20 points.
So,
Probability of the blue marble that won the 20 points.
then,
[tex]\begin{gathered} P(x=20)=\frac{total\text{ number of blue marble}}{\text{total number of marble}} \\ P(x=20)=\frac{1}{5} \end{gathered}[/tex]Now,
There are also mention that, pick a green marbles without replacing and if its blue then win the 10 points,
So,
probability of the blue marbles that won 10 pointss is,
[tex]P(x=10)=\frac{1}{4}[/tex]Now,
Here, find the probability that no points for the first green ball is,
[tex]P(x=0)=\frac{4}{5}[/tex]Now,
If you played this game 100 time, then the probability is,
[tex]\begin{gathered} P(x=0)+_{}P(x=10)+P(x=20)=\frac{4}{5}+\frac{1}{4}+\frac{1}{5} \\ =1.25 \end{gathered}[/tex]now,
For 100 times,
[tex]1.25\times100=125\text{ points.}[/tex]Hence, 125 points can you expect to win.
Suppose you want to have $400,000 for retirement in 25 years. Your account earns 4% interest.
a) How much would you need to deposit in the account each month?
$
b) How much interest will you earn?
$
[tex]~~~~~~~~~~~~\stackrel{\textit{payments at the beginning of the period}}{\textit{Future Value of an annuity due}} \\\\ A=pmt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right]\left(1+\frac{r}{n}\right)[/tex]
[tex]\qquad \begin{cases} A=\textit{accumulated amount}\dotfill&\$400000 \\ pmt=\textit{periodic payments}\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &25 \end{cases}[/tex]
[tex]400000=pmt\left[ \cfrac{\left( 1+\frac{0.04}{12} \right)^{12 \cdot 25}-1}{\frac{0.04}{12}} \right]\left(1+\frac{0.04}{12}\right)[/tex]
[tex]\cfrac{400000}{\left[ \frac{\left( 1+\frac{0.04}{12} \right)^{12 \cdot 25}-1}{\frac{0.04}{12}} \right]\left(1+\frac{0.04}{12}\right)}=pmt\implies \cfrac{400000}{\left[ \frac{\left( \frac{301}{300} \right)^{300}-1}{\frac{1}{300}} \right]\left(\frac{301}{300}\right)}=pmt \\\\\\ \cfrac{400000}{515.84}\approx pmt\implies {\Large \begin{array}{llll} 775.43\approx pmt \end{array}}[/tex]
how much will it be in interest alone?
well, for 25 years every month you'd have been putting down that much, so we can just subtract what you put it from the 400,000 and what's left is the interest earned
[tex]400000~~ - ~~(25)(12)(775.43) ~~ \approx ~~ \text{\LARGE 167317}[/tex]
I need help with my pre-calculus homework, please show me how to solve them step by step if possible. The image of the problem is attached. These are 2 parts of the same question.
We are given the following triangle:
We need to determine the area of the triangle. To do that we need to determine sides "a" and "b". We will use the sine law to determine the side "b":
[tex]\frac{b}{sin107}=\frac{98}{sin48}[/tex]Now, we multiply both sides by "sin107":
[tex]b=sin(107)\frac{98ft}{sin(48)}[/tex]Solving the operations:
[tex]b=126.11ft[/tex]Now, before determining side "a" we will determine the angle "x" that is opposed to "a". To do that we will use the fact that the sum of the interior angles of a triangle is 180, therefore:
[tex]107+48+x=180[/tex]Adding the values:
[tex]155+x=180[/tex]Now, we subtract 155 from both sides:
[tex]\begin{gathered} x=180-155 \\ x=25 \end{gathered}[/tex]Therefore, the angle opposite to "a" is 25 degrees. Now, we apply the sine law:
[tex]\frac{a}{sin(25)}=\frac{98}{sin(48)}[/tex]Now, we multiply both sides by "sin(25)":
[tex]a=sin(25)\frac{98}{sin(48)}[/tex]Solving the operations:
[tex]a=55.73ft[/tex]Now, we determine the area using the following formula:
[tex]A=\sqrt{s(s-a)(s-b)(s-c)}[/tex]Where:
[tex]s=\frac{a+b+c}{2}[/tex]Now, we determine the value of "s":
[tex]s=\frac{55.73ft+126.11ft+98ft}{2}[/tex]Solving the operation:
[tex]s=139.92ft[/tex]Now, we substitute the value in the formula for the area:
[tex]A=\sqrt{(139.92ft)(139.92ft-55.73ft)(139.92ft-126.11ft)(139.92ft-98ft)}[/tex]Solving the operations:
[tex]A=2611.43ft^2[/tex]Now, since the search party can cover 300 ft^2/h we can use a rule of 3 to determine the number of hours it takes them to cover 2611.43 ft^2:
[tex]\begin{gathered} 300ft^2\rightarrow1h \\ 2611.43ft^2\rightarrow x \end{gathered}[/tex]Now, we cross multiply:
[tex](300ft^2)(x)=(1h)(2611.43ft^2)[/tex]Now, we divide both sides by 300ft^2:
[tex]x=\frac{(1h)(2611.43ft^2)}{(300ft^2)}[/tex]Solving the operations:
[tex]x=8.7h[/tex]Therefore, it takes 8.7 hours to cover the area. Therefore, the search party won't be able to conclude before the sun goes down.
A square pyramid has a volume of 108 cubic feet and a height of 4 feet.What is the length of each side of the base of the pyramid?A 4 ftOLOB. 9 ftC. 18 ftD. 27 ftO E. 81 ftHelp please very hard
okay so the answer is 9ft so option B
now we can take a look at how we arrived to that answer
do you know the formula for the volume?
which statement is true and why? & why not the others?
For this problem, we have three circles with different radii. We need to determine which circles are similar and point out the reason for our statement.
Every circle has the same shape, the only thing that sets them apart is the radii. Since we can represent the relationship between the radii as fractions, then all circles are similar. Due to this, the only correct option is the second one. "Circle 1 is similar to both circle 2 and circle 3".
Using everyday knowledge, indicate whether the if-then statements are correct forward-only or both forward and reverse.
Statement 1: If Bob is Sally’s spouse, then Sally is Bob’s spouse.
Statement 2: If the light is red Northbound, then the traffic is stopped.
Rewrite the function by completing the square. f (x)= x^2 - 9x + 14
f (x) = _ ( x + _ )^2 + _
Answer:
f(x) = 1(x - 4.5)² - 6.25
Step-by-step explanation:
Hello!
Let's find the Vertex Form of the quadratic by Completing the Square.
f(x) = x² - 9x + 14x² - 9x + 14 = 0x² - 9x = -14The formula for a Perfect Square Trinomial is (a+b)² = a² + 2ab + b².
To find b², we need to divide -9 by 2 and square it.
-9-4.520.25Add this number to both sides and factor. Remember, the b term here is simply half of the b term in the equation (-4.5).
x² - 9x + 20.25 = -14 + 20.25(x - 4.5)² = 6.25(x - 4.5)²- 6.25 = 0Convert this back to function form:
f(x) = 1(x - 4.5)² - 6.25The equation is f(x) = 1(x - 4.5)² - 6.25.
2. (5 × 2 + 20/2) + (10 x 2/2 + 5) =
a. 35
b. 42
c. 103
Answer:
a.35
Step-by-step explanation:
10 + 20/2 equals 20
20/2+5 equals 15
20+15 equals 35
please let me know of question 4 is correct which is not true30 > 1030 < 1010 > 3010 < 30
Number 4
The meaning of the symbols are
> means greater than
< means less than
For the first statement, 30 is greater than 10. It is true
For the second statement, 30 is less than 10. It is not true
For the third statement, 10 is greater than 30. It is not true
For the fourth statement, 10 is less than 30. It is true
Maria is planting a row of flowers in a bed 77 feet long. The instructions say to space the plants 1 foot apart, allowing room for 77 flowers. The flowers come in flats containing 6 plants per flat.
She will need 12 flats and there will be 5 leftovers
The number of flats she will needFrom the question, we have
Length = 77 feetDistance apart = 1 footNumber of flowers = 77Rate = 6 plants per flatThe number of flats is calculated as
So, we have the following equation
Number of flats = (Length)/Rate
So, we have
Number of flats = (77)/6
Evaluate
Number of flats = 12
The number of plants leftoverThis is calculated as
Leftover = Length - Number of flats * Rate
So, we have
Leftover = 77 - 12 * 6
Evaluate
Leftover = 5
Hence, the left over is 5
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Missing information in the question
How many flats will she need?How many plants will she have left over?Elena is traveling to visit her grandparents who live 125 miles away.
a. Elena stops for lunch 2/3 of the way. How far has Elena traveled?
b. Elena enters the city where her grandmother lives after 110 miles. Is she more or less than 9/10 of the way there?
PLS PLS PLS HELPP
Answer:
A. 83 1/3 miles
B. Less than 9/10 of the way there
Step-by-step explanation:
A.
2/3 of the way. "of" means to multiply, so multiply 2/3 and 125.
[tex]\frac{2}{3}[/tex] × [tex]\frac{125}{1}[/tex] = [tex]\frac{250}{3}[/tex]
Simplify by dividing 250 and 3.
250 ÷ 3
[tex]83 \frac{1}{3}[/tex] miles
B.
Multiply 125 by 9/10 then compare the answer to 110 to see if she is more or less than 110 miles.
[tex]\frac{125}{1}[/tex] × [tex]\frac{9}{10}[/tex] [tex]= \frac{1125}{10}[/tex]
Divide 1125 by 10
1125 ÷ 10 = 112.5
Since 9/10 of the distance is 112.5 miles, 110 miles is less than 9/10 of the way there.
The number of books he collects, n, is defined by n = 140 + 21 where d is the number of days he spends collectingRobert is collecting books to donate to the library.books.What does 14 represent in the context of Robert's book collecting?A represents the number of books per day that are collected,® represents the number of books per week that are collected.represents the number of books per month that are collected.o represents the number of books per year that are collected.
The equation for number of books collected by Robert is given as;
n= 14 d + 21
where d is the number of days he spent collecting .
Answer A. represents the number of books per day that are collected
The Muffin Shop makes no-fat blueberry muffins that cost $.70 each. The Muffin Shop knows that 15% of the muffins will spoil. If The Muffin Shop wants 40% markup on cost and produces 800 muffins, what should The Muffin Shop price each muffin?
If The Muffin Shop wants a 40% markup on cost and produces 800 muffins, The Muffin Shop should price each muffin at $1.15.
How is the price determined?The total expected revenue is divided by the total unspoiled units sold to determine the selling price.
This is illustrated below.
Cost per unit of muffins = $0.70
The spoilage rate = 15%
Expected markup on cost = 40%
The total production units = 800 muffins
The total good units sold = 680 (800 x 1 - 15%)
Total cost for 800 units = $560 (0.70 x 800)
The markup on cost = $224 ($560 x 40%)
The total expected sales revenue = $784 ($560 + $224)
Seling price per unit = $1.15 ($784/680)
Thus, The Muffin Shop should price each muffin at $1.15 to meet its goals.
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Yon buys tickets to a concert for himself and a friend. There is a tax of 6% on the price of the tickets andan additional booking fee of $20 for the transaction. Enter an algebraic expression to represent the priceper person. Simplify the expression if possible. Use variablet for the price of the 2 tickets in dollars.The algebraic expression is
Let the price of each ticket be represented by
[tex]=x[/tex]The price of two tickets will be
[tex]t=2x[/tex]The tax on the price of the tickets is 6% which be represented as
[tex]\begin{gathered} =\frac{6}{100}\times t \\ =\frac{6t}{100}=0.06t \end{gathered}[/tex]The price of the two tickets after tax will be
[tex]\begin{gathered} the\text{price of the two tickets+the tax on the two tickets} \\ =t+0.06t \\ =1.06t \end{gathered}[/tex]Therefore,
The price of the tickets after adding an additional booking fee of $20 will be given below as
[tex]=1.06t+20[/tex]Since,
We were asked to get the algebraic expression person, we would therefore divide the above expression by 2
[tex]\begin{gathered} =\frac{1.06t+20}{2}=\frac{1.06t}{2}+\frac{20}{2} \\ =0.53t+10 \end{gathered}[/tex]Hence,
The algebraic expression to represent the price per person using variable t is
=0.53t + 10
Between what two consecutive integers must solution 2^x=7 lie?
Answer:
2 and 3
Explanation:
Given the equation:
[tex]2^x=7[/tex]Now, observe the following:
[tex]\begin{gathered} 2^2=4 \\ 2^3=8 \\ 4<7<8 \\ \implies2^2<2^x<2^3 \end{gathered}[/tex]Taking the indices:
[tex]2Therefore, the solution of 2^x=7 lies between the consecutive integers 2 and 3.please help me with this question
The amount should be charged to each attendee to cover the cost of the event is (300 + 45x) / x
Given,
The cost of a convention center to host an event = $300 + $45 per person attending
Number of attendees = x
We have to find a rational expression that represents how much you would need to charge each attendee in order to cover the cost of hosting the event.
Here,
Total cost for the event = Fixed cost + cost per person attending x number of person
Total cost = 300 + 45 × x
Total cost = 300 + 45x
Now,
The amount should be charged to each attendee to cover the cost of the event = (300 + 45x) / x
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= The number of counties in state A and the number of counties in state B are consecutive even integers whose sum is 82. If state A has more counties than state B, how many counties does each state have? State A has counties.
State A have 42 counties and State B have 40 counties.
Define Linear equation
An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is 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
Let,
x = The number of counties of state B
x + 2 = The number of counties of State A
It's given, The sum of counties of state A and state B is 82
so, the equation become is linear.
The linear equation will be,
x + (x + 2) = 82
solve for x,
2x + 2 = 82
2x = 82 - 2
2x = 80
x = 80/2
x = 40 (counties of State B)
put the value in x in x + 2,
40 + 2 = 42 (counties of State A)
Therefore, State A have 42 counties and State B have 40 counties.
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Find extreme values of function f(x) = x³ - (3/2)x² on interval [- 1,2]
we have the function
[tex]f(x)=x^3-\frac{3}{2}x^2[/tex]Find out the first derivative of the given function
[tex]f^{\prime}(x)=3x^2-3x[/tex]Equate to zero the first derivative
[tex]\begin{gathered} 3x^2-3x=0 \\ 3x(x-1)=0 \end{gathered}[/tex]The values of x are
x=0 and x=1
we have the intervals
(-infinite,0) (0,1) (1,infinite)
Interval (-infinite,0) -----> f'(x) is positive
interval (0,1) ---------> f'(x) is negative
interval (1,infinite) -----> f'(x) is positive
that means
x=0 is a local maximum
x=1 is a local minimum
Find out the y-coordinates of the extreme values
For x=0 -----> substitute in the function f(x) ---------> f(x)=0
For x=1 ------> substitute in the function f(x) ------> f(x)=-0.5
therefore
The extreme values are
local maximum at (0,0)local minimum at (1,-0.5)-2 decimal 3/% because if you divide the principal in half its 1% of 3
b. Find a pair of numbers that have a sum of 50 and will produce the largest possible product. Example: +_ = 50 (sum) so _* _ = _ (maximum area) and (enter answers from the sum)
A pair of numbers that have a sum of 50
Let the number is x, so the other number is 50 - x
Let f(x) be the largest product so:
[tex]f(x)=\text{ x(50-x)}[/tex]Simplify the expression :
[tex]\begin{gathered} f(x)=\text{ x(50-x)} \\ f(x)=50x-x^2 \end{gathered}[/tex]Diffrentiate with respect to x
[tex]\begin{gathered} f(x)=\text{ x(50-x)} \\ f(x)=50x-x^2 \\ \text{ Diffrentiate with respect to x} \\ f^{\prime}(x)=50-2x \\ \text{Apply derivative equal to zero:} \\ 50-2x=0 \\ 50=2x \\ x=25 \end{gathered}[/tex]Now for to check for the f(x) is maximum for x = 25
Calculate the second derivative and put x = 25 is the f(x) is negative then the multiplication f(x) is maximum
[tex]\begin{gathered} f^{\prime}(x)=50-2x \\ \text{ Differentiate with respect to x} \\ f^{\prime}^{\prime}(x)=0-2 \\ \text{ Substitute x = 25} \\ f^{\doubleprime}(25)=-2 \\ f^{\doubleprime}(25)<0 \\ \text{Thus the function f(x) is maximum for x = 25} \end{gathered}[/tex]Thus, the first number is 25
Second number is : 50 -x = 50-25 = 25
Numbers are 25, 25
Answer : 25 + 25 =50 (sum)
25 * 25 = 625 (maximum possible product)
Factor the polynomial completely if possible. If the expression cannot be factored, enter the expression as is
Given the polynomial:
[tex]w^2+7w-18[/tex]Let's factor the polynomial.
To factor, let's use the AC method.
Find a pair of numbers whose product is -18 and whose sum is 7.
We have the pair:
9 and -2
We have the factors:
(w + 9)(w - 2)
Therefore, the factored form of the polynomial is:
[tex](w+9)(w-2)[/tex]ANSWER:
[tex](w+9)(w-2)[/tex]Write a quadratic equation in standard form with the given roots. a. Write a quadratic equation with a double root of -5.
a quadratic function has any root when replacing that number the equation is equal to zero
so
[tex](x+5)(x+5)[/tex]now solve the multiplication
[tex]\begin{gathered} (x\times x)+(x\times5)+(5\times x)+(5\times5) \\ x^2+5x+5x+25 \\ x^2+10x+25 \end{gathered}[/tex]Rachel is driving to Denver. Let y represent her distance from Denver (in miles). Let x represent the time she has been driving (in hours). Suppose that x and yare related by the equation y = 475 - 60x.Answer the questions below.Note that a change can be an increase or a decrease.For an increase, use a positive number. For a decrease, use a negative number.-Picture includes the questions-
Given the equation:
[tex]y=475-60x[/tex]Let y = distance
Let x = time
- The distance from Denver when she began is given by x = 0, therefore:
[tex]y=475-60(0)=475-0=475[/tex]Answer 1. 475 miles
- The change for each four hours, this is x = 4, so:
[tex]y=475-60(4)=475-240=235[/tex]Answer 2. 235 miles
Alision has an interest in entomology, the study of insects. Her collection of insects from around the world includes the four specimens shown in the table below.
we know that
the mass of Alison's Emperor Scorpio is
[tex]2^{-5}=(\frac{1}{2})^5=\frac{1}{2^5}=\frac{1}{32}\text{ kg}[/tex]The answer is the second optionanswer this, please?
Sidney made root beer floats for her friends when they came over. The table shows the ratio of cups of ice cream to cups of soda used to make the floats.
Ice Cream (cups) Soda (cups)
3.5 10.5
8 24
12.5 37.5
19 ?
At this rate, how much soda will Sidney use for 19 cups of ice cream?
30 cups
38 cups
57 cups
72 cups
Sidney will use 57 cups of soda for 19 cups of ice cream.
What is a ratio?The ratio shows how many times one value is contained in another value.
Example:
There are 3 apples and 2 oranges in a basket.
The ratio of apples to oranges is 3:2 or 3/2.
We have,
From the table,
The ratio of cups of ice cream to cups of soda.
3.5 cups ice cream = 10.5 cups of soda
Divide both sides by 3.5.
1 cup of ice cream = 3 cups of soda
Multiply 19 on both sides.
19 cup of ice cream = 57 cups of soda
Thus,
57 cups of soda.
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Find the measure of the indicated angle to the nearest degree.A. 63B. 25C. 31D. 27
The point of the problem is to remember the cosine relation. It says, in this case, that
[tex]\cos (?)=\frac{\text{adjacent side}}{Hypotenuse}\Rightarrow\begin{cases}\text{adjacent side}=6 \\ \text{Hypotenuse}=13\end{cases}\Rightarrow\cos (?)=\frac{6}{13}[/tex]Converting the last equation by the inverse function, we get
[tex]?=\cos ^{-1}(\frac{6}{13})\approx62.5[/tex]For the first decimal place (5) equals 5, and by the rounding rule to the nearest degree, we get 63. The answer is A.
y varies directly as x, y = 7 when x = 21. Determine x when y = 5.
y varies directly as x, y = 7 when x = 21. Determine x when y = 5.
Step 1
Let
y varies directly as x, it is y depends on x, in math terms
f(x)=y
y = 7 when x = 21
f(21)=7
Determine x when y = 5. f(?)=5
Step 2
there is a proportion, this must be equal, make a rule of three to find the value
so
x y
[tex]\begin{gathered} 21\leftrightarrow7 \\ x\text{ }\leftrightarrow5 \\ \text{the relation is} \\ \frac{21}{7}=\frac{x}{5} \\ \text{solve for x} \\ x=\frac{21\cdot5}{7} \\ x=\frac{105}{7} \\ x=15 \end{gathered}[/tex]so , when y=5, x=15
A class has 21 children, 10 are girls and 11 are boys. what fraction of the class is made up of boys?
A class has 21 children, 10 are girls and 11 are boys. what fraction of the class is made up of boys?
Let
x -----> number of boys
y -----> total number of children
we have that
x=11 -----> given
y=21 ----> given
therefore
The fraction of the class that is made up of boys is equal to
x/y
substitute
11/21Find f(x) • g(x) if f(x) = x2 – 7 and g(x) = x2 + 3x + 7
Given the functions:
[tex]\begin{gathered} f(x)=x^2-7 \\ g(x)=x^2+3x+7 \end{gathered}[/tex]We will find: f(x) • g(x)
So, we will find the product of the functions
We will use the distributive property to get the result of the multiplications
So,
[tex]\begin{gathered} f\mleft(x\mright)•g\mleft(x\mright)=(x^2-7)\cdot(x^2+3x+7) \\ f\mleft(x\mright)•g\mleft(x\mright)=x^2\cdot(x^2+3x+7)-7\cdot(x^2+3x+7) \\ f\mleft(x\mright)•g\mleft(x\mright)=x^4+3x^3+7x^2-7x^2-21x-49 \\ f\mleft(x\mright)•g\mleft(x\mright)=x^4+3x^3-21x-49 \end{gathered}[/tex]so, the answer will be:
[tex]f\mleft(x\mright)•g\mleft(x\mright)=x^4+3x^3-21x-49[/tex]Using f(x) = 2x - 3 and g(x) = 5, find f(g(3)).7530None of the choices are correct.I don’t think my answer is right please help me thank you
As per given by the question,
There are given that function,
[tex]\begin{gathered} f(x)=2x-3,\text{ } \\ g(x)=5 \end{gathered}[/tex]Now,
Find the value of f(g(3)).
Then,
There are given that,
[tex]g(x)=5[/tex]And,
According to question, value of x is 3, that means g(3).
So,
Put the value of x in g(x).
Then,
[tex]\begin{gathered} g(x)=5 \\ g(3)=5 \end{gathered}[/tex]Now,
For find the value f(g(3));
Put the value of g(3) in the above condition,
f(g(3)).
So,
[tex]f(x)=2x-3[/tex]Instead of x in f(x), put the g(3).
Then,
[tex]\begin{gathered} f(g(3))=2x-3 \\ f(5)=2\times5-3 \\ f(5)=10-3 \\ f(5)=7 \end{gathered}[/tex]So, the value of f(g(x)) is 7.
Hence, the option first is correct.
The sum of two numbers is ten. One number is
twenty less than four times the other. Find the
numbers.
Note: List numbers with a comma separating
them, e.g. 5, 12.
By solving the equations, we can conclude that the two numbers are 4 and 6.
What are equations?An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values. As in 3x + 5 = 15, for example. There are many different types of equations, including linear, quadratic, cubic, and others. The three primary forms of linear equations are point-slope, standard, and slope-intercept.So, the two numbers are:
Let the 2nd number be 'x'.Then, the 1st number will be '4x - 20'.The equation will be:
4x - 20 + x = 10Now, solve this equation for 'x' as follows:
4x - 20 + x = 105x = 10 + 205x = 30x = 6Now, 4x - 20:
4(6) - 2024 - 204Therefore, by solving the equations, we can conclude that the two numbers are 4 and 6.
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An initial amount of $3500 is invested in an account at an interest rate of 6% per year, compounded continuously. Assuming that no withdrawals aremade, find the amount in the account after two years.Do not round any intermediate computations, and round your answer to the nearest cent.
For this problem we use the continuously compounded interest formula:
[tex]M=M_0e^{rt}[/tex]where M_0 is the initial amount, r is the interest rate per year and t is the number of years.
Substituting M_0=$3500, r=0.06, and t=2 we get:
[tex]\begin{gathered} M=3500e^{0.06\cdot2}=3500e^{0.12} \\ M=3946.24 \end{gathered}[/tex]