The Royal Fruit Company produces two types of fruit drinks. The first type is 65% pure fruit juice, and the second type is 90% pure fruit juice. The company is attempting to produce a fruit drink that contains 80% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 120 pints of a mixture that is 80% pure fruit juice?
If f(x) = 2/x and g(x) = x^2 what is f of g
Answer: The required value is [tex]f(g(x))=\dfrac{2}{x^2}.[/tex]
Step-by-step explanation: We are given two functions as follows :
[tex]f(x)=\dfrac{2}{x},~~~~~~~g(x)=x^2.[/tex]
We are to find f of g, i.e., f(g(x)).
To find the required value, first we have to find the f value of the function g(x).
We have
[tex]f(g(x))=f(x^2)=\dfrac{2}{x^2}.[/tex]
Thus, the required value is [tex]f(g(x))=\dfrac{2}{x^2}.[/tex]
The amount that results when $4,000 is compounded at 6% annually over seven years.
The polynomial equation x^3-4x^2+2x+10=x^2-5x-3 has complex roots 3+2i What is the other root? Use a graphing calculator and a system of equations.
a –3
b –1
c 3
d 10
Answer:
The correct option is b.
Step-by-step explanation:
The given expression is
[tex]x^3-4x^2+2x+10=x^2-5x-3[/tex]
Simplify the equation.
[tex]x^3-4x^2+2x+10-x^2+5x+3=0[/tex]
[tex]x^3-5x^2+7x+13=0[/tex]
It is given that 3+2i is a root of the equation and (x-3-2i) is a factor.
By complex conjugate root theorem if a+ib is a root of an equation then a-ib must be the root of the equation.
It means 3-2i is a root of the equation and (x-3+2i) is a factor.
[tex](x-3-2i)(x-3+2i)=(x-3)^2-(2i)^2=x^2-6x+9+4=x^2-6x+13[/tex]
Divide [tex]x^3-5x^2+7x+13=0[/tex] by [tex]x^2-6x+13[/tex], to find the remaining factor.
By the long division method, the quotient is (x+1) and remainder is 0. It means (x+1) is a remaining factor of the given equation. Equate each factor equal to 0, to find the remaining roots.
[tex]x+1=0[/tex]
[tex]x=-1[/tex]
Therefore the correct option is b.
Deniz had a full gallon of milk. She poured out 4 cups of milk. There are 16 cups in 1 gallon. About what percent of the original volume is left?
Answer:
75% of the original volume is left.
Step-by-step explanation:
Deniz had a full gallon of milk, or 16 cups of milk, and then she poured out 4 cups of milk. That is:
[tex]\\ A_{full-gallon} = \frac{16}{16}[/tex] cups of milk, since [tex]\\ \frac{16}{16} = 1[/tex] or [tex]\\ 1 * 100\% = 100\%[/tex] of the original volume.Deniz poured out 4 cups of milk from the 16 available (or [tex]\\ \frac{4}{16}[/tex]).Then,
The total left is:
[tex]\\ Total_{left} = \frac{16}{16} - \frac{4}{16} = \frac{12}{16} = \frac{3}{4}[/tex], since we are dealing here with fractions with the same denominator.
In other words, [tex]\\ \frac{3}{4} = 0.75[/tex] is the amount of milk left in the container.
In terms of percentage, [tex]\\ \frac{3}{4} = 0.75[/tex] is equivalent to [tex]\\ 0.75*100\% = 75\%[/tex] of the original volume, because Deniz poured out [tex]\\ \frac{4}{16} = \frac{1}{4} = 0.25[/tex] or [tex]\\ 0.25*100\% = 25\%[/tex] from the original volume.
So, Deniz left 75% of the original volume of milk after pouring out 25% of it.
This can be represented in the graph below.
Answer:
75%
Step-by-step explanation:
The figure shows △ABC . BD is the angle bisector of ∠ABC .
What is AD ?
Enter your answer in the box as a fraction.
____ units
The length of AD is [tex]\dfrac{8}{3}[/tex].
Given:
BD is the angle bisector of the triangle ABC.
The figure of the triangle ABC.
To find:
The length of AD.
Explanation:
According to the Angle Bisector Theorem, the angle bisector of a triangle divides the opposite side in the same proportion of the other two sides.
Let [tex]x[/tex] be the length of AD. Then, the length of DC is [tex]6-x[/tex].
Using the Angle Bisector Theorem, we get
[tex]\dfrac{8}{10}=\dfrac{x}{6-x}[/tex]
[tex]\dfrac{4}{5}=\dfrac{x}{6-x}[/tex]
[tex]4(6-x)=5(x)[/tex]
[tex]24-4x=5x[/tex]
[tex]24=5x+4x[/tex]
[tex]24=9x[/tex]
[tex]\dfrac{24}{9}=x[/tex]
[tex]\dfrac{8}{3}=x[/tex]
Therefore, the length of AD is [tex]\dfrac{8}{3}[/tex].
Learn more:
https://brainly.com/question/10130247
Evaluate. 12+4⋅3−15 Enter your answer in the box.
Answer:
I think it is 9 because I know u multiply at the start plus I used a calculator and got 9 so if it is not my calculator it broke
What number needs to be added to both sides of the equation in order to complete the square? x2+14x=−32
49 is the number to be added to both the sides of the equation to complete the square.
The equation given in the question is
[tex]x^{2} +14x=-32[/tex]Which can be written as [tex]x^{2} +2\times (7x)=-32[/tex]
We have to convert it into square form.
Since the standard form of the equation in square form is
(a + b)² = a² + 2ab + b²
By comparing this standard equation with the given equation,
a = x
&
b = 7
By substituting the values of 'a' and 'x' in the standard square form,
x² + 14x + 7² = -(32) + 7²
x² + 14x + 49 = -32 + 49
(x + 7)² = 17
Therefore, 49 should be added in both the sides of the equation in order to complete the square.
Learn more,
https://brainly.com/question/11242754
Find the area of a circle with a diameter of 10 units. Round answer to the nearest hundredth of a square unit.
Answer:
Step-by-step explanation:
The area of a circle is given by A = π*r²
If diameter is 10 units, the radius is 5, so:
A = π * 5² = 78,54units²
A wallet contains 23 bills. All the bills are $1 bills and $5 bills. There are 7 more $1 bills than 5 bills. How much money does the wallet contain
Final answer:
The wallet contains a total of $55, given that there are 8 $5 bills and 15 $1 bills.
Explanation:
The student's question involves determining the total amount of money in a wallet given a specific mix of $1 bills and $5 bills. According to the information provided, there are 23 bills in total, with 7 more $1 bills than $5 bills.
Let's denote the number of $5 bills as x. Therefore, there are x + 7 $1 bills. The total number of bills is the sum of the number of $1 bills and the number of $5 bills, which gives us the equation:
x + (x + 7) = 23
Solving the equation for x will give us the number of $5 bills:
2x + 7 = 23
2x = 23 - 7
2x = 16
x = 8
Now, since there are 8 $5 bills, and 7 more $1 bills than $5 bills, we have:
Number of $1 bills = 8 + 7 = 15
Thus, the total amount of money in the wallet is:
($5 × 8) + ($1 × 15) = $40 + $15 = $55
Therefore, the wallet contains $55.
62394 rounded to the nearest tenth
david kalb started a pet-walking business , he charges $20 to walk one dog, twice a day. He walks six dogs five days a week for four customers. He walks three dogs seven days a week for three other customers. How much money does David get from his customers each week? If his weekly expenses are $350, what is the profit?
Answer:
David earns $1,020 a week, and his weekly profit is $670.
Step-by-step explanation:
Since David walks six dogs per day, and each dog is $20, he earns a total of $120 per day from those six dogs. Also, knowing that he walks the six dogs five days a week, he earns $600 from walking the six dogs for five days per week alone. Using this same logic for the three dogs he walks seven days a week, we can conclude that he gets $60 from walking those three dogs. Knowing he walks those three dogs seven days a week, he gets $420 from walking those three dogs. Combining the totals gives us $1,020, the amount of money he earns per week. Since his weekly expenses are $350, we subtract that from $1,020 to get his weekly profit: $670.
What is f(6) ? Thanks
The point-slope form of the equation of the line with slope 7 passing through the point (4, 6) is
A tour group with 22 people in it is getting rooms in a motel to stay in for the night. no more than 3 people can stay in each room. how many rooms will they need
8 rooms will be needed for a tour group of 22 people and the last room will have only one member of the group.
What is unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying it with the value of a single unit.
Given is a tour group of 22 people. The group is looking for rooms in a motel to stay in for the night and no more than 3 people can stay in each room.
The number of people who can live in 1 room = 3
This means, we have 3 people for 1 room.
For 1 people, we will have - (1/3) room
For 22 people, we will need -
(22/3)
7.3 rooms
Approximately, 8 rooms will be needed and the last room will have only one member of the group.
Therefore, 8 rooms will be needed for a tour group of 22 people and the last room will have only one member of the group.
To solve more questions on unitary method, visit the link below-
brainly.com/question/18174151
#SPJ5
Solve be graphing , elimination , or substitution
Find the original price of a pair of shoes if the sale price is $44 after a 60% discount.
Final answer:
To find the original price of a pair of shoes after a 60% discount, divide the sale price by (1 minus the discount percentage). The original price of the pair of shoes is $110.
Explanation:
To find the original price of a pair of shoes after a 60% discount, we can use the formula:
Original price = Sale price / (1 - Discount percentage)
Substituting the given values:
Original price = $44 / (1 - 0.60)
Original price = $44 / 0.40
Original price = $110
Therefore, the original price of the pair of shoes was $110.
Final answer:
To determine the original price before a discount, subtract the discount percentage from 1, convert it to a decimal, and divide the sale price by this number. In this case, the original price for the shoes before a 60% discount, resulting in a $44 sale price, is $110.
Explanation:
To find the original price of an item before a discount, you can use the following steps:
First, understand that the sale price is the price after the discount has been applied to the original price.Express the discount as a decimal. A 60% discount is 0.60 when expressed as a decimal.Since the sale price reflects the remaining percentage after the discount, you subtract the discount decimal from 1 to find the multiplier for the original price. That is, 1 - 0.60 = 0.40.Divide the sale price by this multiplier to get the original price. So, $44 divided by 0.40 equals $110.Therefore, the original price of the shoes was $110 before the 60% discount was applied.
Write an equation of the line passing through the point A(−6, 5)that is parallel to the line
y = 1/2 x−7.
There were 91 books on a shelf. Twenty-eight of the books were nonfiction, 13 of the books were poetry books, and the rest were fiction books. How many books were fiction?
Which explains why the graphs of geometric sequences are a series of unconnected points rather than a smooth curve?
The range contains only natural numbers.
The domain contains only natural numbers.
Exponential bases must be whole numbers.
Initial values must be whole numbers.
The correct answer is:
The domain contains only natural numbers.
Step-by-step explanation:The graphs of geometric sequences are a series of unconnected points rather than a smooth curve because:
The domain contains only natural numbers.
As the geometric sequence us given as:
[tex]a_1=a,a_2=ar,a_3=ar^2,....[/tex]
where a is the first term of the sequence and r is the common ratio of the geometric sequence.
Also [tex]a_n[/tex] denotes the nth term of the sequence where n belongs to natural numbers that is the domain of the function is natural numbers.
The reason why the graphs of geometric sequences are a series of unconnected points rather than a smooth curve is because: B. The domain contains only natural numbers.
What is a geometric sequence?A geometric sequence is typically a series of real and natural numbers that are calculated by multiplying the next number by the same number each time.
Mathematically, a geometric sequence is given by the expression:
[tex]a, \;ar, \; ar^{2} ....a_n[/tex]
Where:
r is the common ratio.a is the first term of a geometric sequence.In a geometric sequence, the graphs of geometric sequences comprises a series of unconnected points rather than a smooth curve is because the domain is made up of only natural numbers.
Read more on geometric sequence here: https://brainly.com/question/12630565
In Saudi Arabia it takes 20 kursh to equal 1 riyal.
a. Write the two unit multipliers implied by this relationship.
b. Use one of the unit multipliers to convert 16,000 kursh to riyals.
help
The problem is about converting between two units of currency from kursh to riyals. The two unit multipliers from this scenario are: 1 riyal equals 20 kursh and 1 kursh equals 1/20 riyal. The conversion from 16,000 kursh to riyals would be 800 riyals.
Explanation:The question is about converting between two units of currency, specifically from kursh to riyals based on the exchange rate provided. It's a classic problem in unit conversion.
a. The two unit multipliers implied by this relationship are:
1 riyal = 20 kursh 1/20 riyal = 1 kursh
b. To convert 16,000 kursh to riyals, you would use the first unit multiplier. Given that 1 riyal equals 20 kursh, you simply divide the amount in kursh by 20 to get the equivalent amount in riyals. So, 16000 kursh ÷ 20 = 800 riyals.
Learn more about Currency Conversion here:https://brainly.com/question/11171380
#SPJ2
Jessica increases the temperature of a block of ice by 20º. Which integer represents the amount by which Jessica must change the temperature for the block of ice to return to its starting temperature? A. –40 B. –20 C. 20 D. 40
Answer:
B. -20
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
How to simplify rational expressions
Tina is the top seller of the store. She earns a salary plus 2%. Tina's salary is $30,000 a year. This month her sales were $48,500. How much was Tina paid this month?
Write an algebraic expression to answer the question below. if 10 calculators cost d dollars, how much, in dollars, does each calculator cost?
How many feet are in 2000 meters?
At a high school with 1100 students, Jake is in the 70th percentile for height. How
many students at the school are either the same height or shorter than Jake?
∠A
and
∠B
are vertical angles with
m∠A=x
and
m∠B=4x−30
.
What is
m∠A
?
Use the numbers 8, 6, and 2 and one operation to write and expression that includes an exponent and has a value of 8. Use each number only once
The suitable way to use the numbers 8, 6, and 2 to create an expression with an exponent that results in the value of 8 is by utilizing the equation 2^3. This equation means 'two raised to the power of three', meaning 2 multiplied by itself thrice, giving us the desired result, 8.
Explanation:To solve this question, we need to consider the mathematical operation of exponentiation, which involves a base number and an exponent. The exponent represents the number of times the base number is to be multiplied by itself.
Given the numbers 8, 6, and 2, we aim to use each number only once to create an expression that includes an exponent and yields a value of 8. The suitable way to do this is by following the equation 2^3 (where 2 is the base number and 3 is the exponent).
To explain further, an exponent is the number of times a number, known as the base, is multiplied by itself. For instance, 2^3 should be read as 'two raised to the power of three', essentially depicting 2 * 2 * 2, resulting in 8. This follows the standard rules of Exponential Arithmetic.
Learn more about Exponents here:https://brainly.com/question/5497425
#SPJ12
For exercises 14-19, find an equation for the line that satisfies the conditions