She would use 9/7 of a bottle of conditioner for a full year.
What is the proportion?A mathematical assessment of two numbers is called a proportion. If two sets of provided numbers rise or fall in the same relation, then the ratios are said to be directly proportional to each other.
We have been given that Martina used 3/4 of a bottle of conditioner in 7/12 of a year.
Let the amount of conditioner would be x she uses in a full year
As per the given condition, we can write a proportion as
3/4 of a bottle : 7/12 of a year = x : 1
⇒ (3/4) / (7/12) = x / 1
Reciprocal the terms of the denominators,
⇒ (3/4) × (12/7) = x
⇒ 36 / 28 = x
⇒ x = 9/7
Therefore, she would use 9/7 of a bottle of conditioner for a full year.
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Thirty increased by 5 times a number equals 80. Write only the equation!!!!!
Answer:
5 times x + 30 = 80 (x=10)
Step-by-step explanation:
5 times 10 is 50
50+30 is 80
A basketball coach will choose 5 players from a group of 9 players to start the next game. How many different groups of starting players are possible?
Answer:
45?
Step-by-step explanation:
A map of Nevada in the shape of a trapezoid is shown. The length of one base is 483 miles, the length of the other base is 207 miles, and the length of a side is 405 miles. The length of the altitude is 320 miles. Hien would like to estimate the area of Nevada using a trapezoid. She uses the dimensions shown as approximations. What is the approximate area of Nevada? sq. mi
Hey there! I'm happy to help!
To find the area of a trapezoid, you add the lengths of the two bases, divide by two, and then multiply by the height.
We add our two bases.
483+207=690
We divide by 2.
690/2=345
We multiply by the height.
345(320)=110,400
Therefore, Hien can estimate that the area of Nevada is 110,400 square miles.
Have a wonderful day! :D
The formula for area of a trapezoid is [tex](b_{1} + b_{2})*\frac{1}{2} h=A[/tex]
b=base
h=height AKA altitude.
A=area.
Base 1 is 483.
Base 2 is 405.
483+405=888
888×320 (h) = 284160
284160 × [tex]\frac{1}{2}[/tex] = 142080
The approximate area of Nevada is 142080 square miles.
♡ Hope this helps! ♡
❀ 0ranges ❀
Find the complex number solutions to the quadratic f(x)=2x^2-6x+17
Answer:
im pretty sure the answer is b. im not 100% though
Step-by-step explanation:
A farmer was asked how many cows and chickens she has. The farmer replied, "between the cows and the chickens, there are 162 eyes and 270 feet." How many cows does she have? How many chickens does she have? (Note: chickens have 2 feet and cows have 4 feet.)
Answer:
Step-by-step explanation:
yo
The number of cows is 54 and the number of chickens is 27 if the cows and the chickens, there are 162 eyes and 270 feet.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
We have:
A farmer was asked how many cows and chickens she has. The farmer replied, "between the cows and the chickens, there are 162 eyes and 270 feet.
Let x be the number of cows and y be the number of chickens.
2x + 2y = 162 (there are 162 eyes)
4x + 2y = 270 (there are 270 feet)
From the first equation take the value of x and plug it into the equation second.
2y = 162 - 2x
y = 81 - x
4x + 2(81 - x) = 270
4x + 162 - 2x = 270
2x = 108
x = 54
y = 27
Thus, the number of cows is 54 and the number of chickens is 27 if the cows and the chickens, there are 162 eyes and 270 feet.
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Write the equation for a line in standard form (Ax+By+C) that is perpendicular to y = 3x -
2 and passes through the point (6,4).
Answer:
x+3y-6=0
Step-by-step explanation:
given eqn is y=3x-2 which is 3x-y-2=0
the eqn of line perpendicular to given eqn is -x+3y+k=0
it passes through (6,4)
-6+3*4+k=0
or,. -6+12+k=0
or, k= -6
therefore, the eqn of line perpendicular to given eqn is x+3y-6=0
y = 3x – 5. Find the value of y when x = 1
Select the equivalent expression.
(3^-8 • 7^3)^-2 =?
Answer:
C
Step-by-step explanation:
We can expand, getting 3^(-8)(-2) multiplied by 7^(3)(-2).
The exponents on the 3 is 16 and -6 on the 7.
This is the same as c.
The equivalent expression of (3⁻⁸ • 7³)⁻² will be 3¹⁶• 7⁻⁶. The correct option is C.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
The expression will be simplified as below:-
(3⁻⁸ • 7³)⁻² = ( 3⁻⁸ˣ⁻²• 7³ ˣ ⁻² )
= ( 3¹⁶• 7⁻⁶)
Therefore, the equivalent expression of (3⁻⁸ • 7³)⁻² will be 3¹⁶• 7⁻⁶. The correct option is C.
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A single carton of juice costs $4.20. A special offer pack of 3 cartons costs $9.45. Ali bought a special offer pack instead of 3 single cartons. Calculate his percentage saving
1 cartons of juice = $4.20
3 single cartons = 4.20 * 3 = $12.60
1 pack = $9.45
He saved 12.60 - 9.45 = $3.15
So, he saved $3.15, compared to the total ($12.60)
To calculate the percentage, we will do a proportion:
3.15 (money saved) : 12.60 (total of 3 single cartons) = x (how much percentage) : 100 (total)
3.15 : 12.6 = x : 100
To calculate x, we will moltiplicate the ends (where we have known numbers) than divide all per 12.6
So
x = (3.15 * 100) / 12.60 = 315 / 12.6 = 25
So the percentage saving is 25%
in a mixture of 60 litres, the ratio of milk to water is 2:1. if this ratio is to be 1:2, then find the quantity of water to be further added.
Answer: 20 liters
Step-by-step explanation:
The mixture is 60 liters. The ratio is 2 : 1 (2 parts to one part)
60 ÷ (2 + 1) = one part
60 ÷ 3 = 20
Therefore, the ratio of 2 : 1 means 2(20) liters milk to 1(20) liters water
If we change it to a ratio of 1 : 2, then we have 1(20) liters milk to 2(20) liters water.
2:1 ratio has 20 liters water
1:2 ratio has 40 liters water
The amount of water added is 40 - 20 = 20 liters
The diagram shows a solid formed by joining a hemisphere, of radius rcm, to a cylinder, of radius rcm and height hcm. The total height of the solid is 18 cm and the surface area is 205pie cm? Find the value of r and the value of h cm
Answer:
Step-by-step explanation:
The total surface area of the sphere = 2πr²
Total surface area of the cylinder = 2πr²+2πrh
Total surface area of the solid = 4πr²+2πrh
r is the radius of the sphere and the cylinder
h is the height of the cylinder
Total surface area of the solid = 2πr(r+h)
If the total height of the solid is 18 cm, then r+h = 18cm
Given the Total surface area of the solid = 205π cm
205π = 2πr(r+h)
205π = 2πr(18)
205π = 36πr
205 = 36r
Divide both sides by 36
205/36 = 36r/36
r = 5.69cm
Since r+h = 18cm
5.69+h = 18
h = 18-5.69
h = 12.31cm
A phone company offers two monthly plans. Plan A costs 8 plus an additional 0.16 for each minute of calls. Plan B costs 20 plus an additional 0.14 for each minute of calls.
Answer:
Total time when cost are equal = 600 minutes
Total cost = 104
Step-by-step explanation:
Given:
Plan A = costs 8 plus an additional 0.16 for each minute
Plan B = costs 20 plus an additional 0.14 for each minute
Find:
Total time when cost are equal
Computation:
Assume total time = x minutes
Plan A = 8 + 0.16x
Plan B = 20 + 0.14x
Plan A = Plan B
8 + 0.16x = 20 + 0.14x
0.02x = 12
x = 600 minutes
Total time when cost are equal = 600 minutes
Total cost = 8 + 0.16x
Total cost = 8 + 0.16(600)
Total cost = 104
Solve the equation
(If possible please show work)
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{n = 1}}}}}[/tex]
Step-by-step explanation:
[tex] \sf{2 - 4n = 2 - 4(3 - 2n)} [/tex]
Distribute 4 through the parentheses
⇒[tex] \sf{ 2 - 4n = 2 - 12 + 8n}[/tex]
Move 8n to left hand side and change it's sign
⇒[tex] \sf{2 - 4n - 8n = 2 - 12}[/tex]
Collect like terms
⇒[tex] \sf{2 - 12n = 2 - 12}[/tex]
Move 2 to right hand side and change it's sign
⇒[tex] \sf{ - 12n = 2 - 12 - 2}[/tex]
Calculate
⇒[tex] \sf{ - 12n = - 12}[/tex]
Divide both sides of the equation by -12
⇒[tex] \sf{ \frac{ - 12n}{ - 12} = \frac{ - 12}{ - 12} }[/tex]
Calculate
⇒[tex] \sf{n = 1}[/tex]
Hope I helped!
Best regards!!
Choose the correct expressions using the fewest number of bases possible that are equivalent to the current expression. (Select all that apply); (Hint: There are 2 correct choices) Question 2 options: 53+2 53×52 53×2 55
Answer:
[tex]\huge \boxed{\mathrm{5^{3+2} \ \ \ \ 5^5 }}[/tex]
Step-by-step explanation:
5³ × 25
25 can be written as a base of 5.
5³ × 5²
We need expressions with fewest number of bases possible.
Apply exponent rule : [tex]a^b \times a^c = a^{b+c}[/tex]
[tex]5^{3+2}[/tex]
Add exponents.
[tex]5^5[/tex]
Answer:
The answer is easy its 53 times 2 and 52 times 2
Step-by-step explanation:
change .
0.9kg into grams
Answer:
900 grams.
Step-by-step explanation:
1 kg = 1000 grams.
0.9 kg = 1000 * 0.9
= 900 grams.
Answer:
900 grams is the answer
is 3/8 a natural whole integer or rational number
3/8 is classified as a rational number.
All fractions, positive or negative, are rational numbers.
Natural numbers, whole numbers, and integers don't include fractions.
Answer:
Rational
Step-by-step explanation:
A natural number is a whole number, so that eliminates natural and whole. An integer is a whole number that includes negative numbers. Since 3/8 is not a whole number, we can eliminate that too. Rational numbers are fractions that don't go on forever. 3/8 is a rational number.
Given the function f(x)=3x-6 select all true statements that apply
Answer:
f(-4) = -18 and if f(x) = -9, then x = -1
Step-by-step explanation:
To find f(-4), we plug x = -4 into f(x) so f(-4) = 3 * (-4) - 6 = -12 - 6 = -18. To find x when f(x) = -9, we can write:
-9 = 3x - 6
-3 = 3x
x = -1
Given f (x) = x2 + 7, evaluate f (4).
Answer:
f(4) = 23
Step-by-step explanation:
[tex] f(x) = x^2 + 7[/tex]
Plug x = 4
[tex] f(4) = 4^2 + 7[/tex]
[tex] f(4) = 16 + 7[/tex]
[tex] f(4) = 23[/tex]
Answer: f(4) = 23
Step-by-step explanation: Notice that f is a function of x.
So we want to find f(4).
We find f(4) by plugging 4 in for x, everywhere that x appears in the function.
So we have f(4) = (4)² + 7.
(4)² is 16 so we have 16 + 7 which is 23.
So f(4) is 23.
Match the property name with the appropriate equation. Use each once.
19. Opposite of a Difference
A. -[(-r) + 2p] =-(-r) - 2p
20. Opposite of a Sum
B. 160 - (3d + 2)(0) = 160 - 0
21. Opposite of an Opposite
C. 5(2 - x) = 10 - 5x
22. Multiplication by 0
D. -(4r + 3s) + t = (-1)(4r + 3s) + t
23. Multiplication by -1
E. -(8 - 3m) = 3m - 8
24. Distributive Property
F. [-19 - 2w)] = 9 - 2w
Answer:
19. Opposite of a Difference ↔ E. -(8 - 3·m) = 3·m - 8
20. Opposite of a sum ↔ A. -[(-r) + 2p] = -(-r) - 2p
21. Opposite of an Opposite ↔ F. -1[ -1(9 - 2w)] = 9 - 2w
22. Multiplication by 0 ↔ B. 160 - (3d + 2)(0) = 160 - 0
23. Multiplication by ↔ D. -1 -(4r + 3s) + t = (-1)(4r + 3s) + t
21. Distributive property ↔ C. 5(2 - x) = 10 - 5x
Step-by-step explanation:
19. Opposite of a difference is the difference of the opposites
20. Opposite of a sum is the sum if the opposites
21. Opposite of an opposite is the original number
22. Multiplication by 0- The result of multiplication by 0 is 0
23. Multiplication by -1 results in the change in sign of a number
24. Distributive property - Multiplying the sum or difference of two numbers by a number, will have the same result as multiplying each each of the addends by the number individually and adding the product together.
Domain And Range. Need Help
Answer:
The first option.
Step-by-step explanation:
Domain is anything less than or equal to 2, but anything greater than or equal to -4
Range is anything greater than or equal to -4, but also less than or equal to 4
Worksheet 1.3
Part 1: Write a math expression for each problem (model the problem).
1)
Lumpy drove for h hours at 50 mph. How far did he drive?
Answer:
50h milesStep-by-step explanation:
For us to write a math expression for the problem, we will use the formula for calculating speed.
Speed is the change of distance of a body with respect to time.
Mathematically, Speed = Distance/Time
Distance = Speed * Time
If Lumpy drove for h hours at 50 mph, then Lumpy speed = 50mph and time = h hours.
Substituting the given parameters into the formula to get the distance;
Distance = 50mph * h hours
Distance = 50h miles
Hence the math expression that modeled how far Lumpy drive is 50h miles
Given x=-3, y=6, and z=-4
-15+(-x)+y=
Answer:
-6
Step-by-step explanation:
We are given x=- 3 , y= 6 and z= -4.
We are also given the expression:
-15 + (-x) +y
Substitute -3 in for x and 6 in for y.
-15 + (- -3) + 6
2 negative signs creates a positive sign
-15 + (+3) +6
-15 + 3+ 6
Add -15 and 3.
(-15+3) +6
-12 +6
Add -12 and 6.
-6
-15+(-x)+y evaluated at x= -3 and y=6 is equal to -6.
Gasoline at a particular gas station cost $2.78 per gallon if Cory buys $18 of gas how many gallons did he buy?
Answer:
6.47 gal
Step-by-step explanation:
cost of gas per gallon = $2.78
rate of change is cost of gas per gallon as cost to buy gas changes with the change in quantity of gallon.
Total cost for x gallons = cost of gas per gallon*x = 2.78x
Given that total money paid by him is $18
2.78x = 18
x = 18/2.78 = 6.47
Answer:
6.47 gallons
Step-by-step explanation:
18 divided by 2.78 = 6.47
Which of the following statements is not true concerning the equation x2−c=0 for c>0? A. The left-hand side of this equation is called a difference of two squares. B. This equation is not considered to be a quadratic equation because it is not of the form ax2+bx+c=0. C. A quadratic equation in this form can always be solved by factoring. D. A quadratic equation in this form can always be solved using the square root property.
Answer:
The correct option is;
B. This equation is not considered to be a quadratic equation because it is not in the form a·x² + b·x + c = 0
Step-by-step explanation:
A. The given equation, x² - c = 0, can be presented in the form of the difference of two squares as follows;
(x + √c)·(x - √c) = 0
B. The equation x² - c = 0, is a quadratic equation because it is a polynomial equation of degree 2
C. The equation x² - c = 0 can always be factored as (x + √c)·(x - √c) = 0
D. Where c > 0, the equation x² - c = 0 can by the square root property as follows;
x² - c = 0
x² = c
x = √c
Solve the following simultaneous equations :
1. x + 2y = 1, 3x - y = 17
Answer: x= 5 and y= -2
Step-by-step explanation:
evaluate g(x)=3x when x= -2,0, and 5
Answer:
-6, 0, 15
Step-by-step explanation:
You just replace x with the given number.
g(-2)= 3(-2)
=-6
g(0)=3(0)
=0
g(5)=3(5)
=15
The required evaluated values of g(x) = 3x would be -6, 0, 15 respectevily when substitute the values x = -2, 0, and 5.
What is the algebraic expression?Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.
We have been the given expression:
g(x) = 3x
To determine the evaluated values of g(x) = 3x when x= -2, 0, and 5
We have to substitute x with the given number.
⇒ g(x) = 3x
Substitute the value of x = -2 in the g(x) = 3x
⇒ g(-2) = 3(-2)
⇒ g(-2) = -6
Substitute the value of x = 0 in the g(x) = 3x
⇒ g(0) = 3(0)
⇒ g(0) = 0
Substitute the value of x = 5 in the g(x) = 3x
⇒ g(5) = 3(5)
⇒ g(5) = 15
Hence, the required evaluated values of g(x) = 3x would be -6, 0, 15 respectevily when substitute the values x = -2, 0, and 5.
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what is the expression of 4 +34times7
Answer:
242
Step-by-step explanation:
Instead of times you should use * to represent multiplication.
So, the expression is 4 + 34*7
We follow PEMDAS,
So first we multiply,
4 + 238
Now we add.
242
The Patterson family has 3 kids, 1 boy and 2 girls. Suppose that for each birth, the probability of a boy birth is 1/2, and the probability of a girl birth is also 1/2. What is the fractional probability of having 1 boy and 2 girls, in any order, in a family's first 3 births?
Answer:
[tex]Probability = \frac{1}{8}[/tex]
Step-by-step explanation:
Given
Represent Boys with B and Girls with G
[tex]P(B) = \frac{1}{2}[/tex]
[tex]P(G) = \frac{1}{2}[/tex]
Required
Find the probability or having 1 boy 2 girls
Since the order is not important, the probability is calculated as follows;
[tex]Probability = P(B) * P(G) * P(G)[/tex]
Substitute [tex]\frac{1}{2}[/tex] for P(B) and P(G)
[tex]Probability = \frac{1}{2} * \frac{1}{2} * \frac{1}{2}[/tex]
[tex]Probability = \frac{1 * 1 * 1}{2 * 2 *2}[/tex]
[tex]Probability = \frac{1}{8}[/tex]
Hence, the fractional probability is [tex]\frac{1}{8}[/tex]
please help me on this
Answer: The coordinate of L is 4.
Step-by-step explanation:
Let's say you were to plot the point on a number line and find the distance between P and G.
P is -6 on the number and G is 18 on the number so to find the distance between them we will need to find the different between the number and find its absolute value.
-6- 18 = -24 and the absolute value of -24 is 24.
In other words to get from -6 to 18 on the number line you need to move 24 units to the right.
Now to answer the question, we know that the distance between the two numbers is 24 and and it says that L is 1/6 of the distance.
We can represent that by the equation,
L = [tex]\frac{1}{6} * 24[/tex]
L = 4
Can you please help me 4(x+4)=4x+16 justify solutions of an equation one variable
Answer:
any x value would work
Step-by-step explanation:
4(x+4)
4*x=4x
4*4=16
4x+16=4(x+4)