As a result, the vertex form of the f(x) equation is: [tex]f(x) = -(x - 5)^2 + 2[/tex]which is equivalent to choice (b).
what is quadratic equation ?A quadratic function is a sort of second-degree polynomial equation, meaning it has at least two squared element. A quadratic equation's generic form is: [tex]ax^2 + bx + c = 0[/tex] where the variable x and the constants a, b, and c. If the coefficient a were zero, the expression would be linear rather than quadratic. Several ways to solve a quadratic equation, including factoring, squaring the square, and utilising the quadratic formula. The negative numbers or roots of the quadratic equation are the values of x which it make the equation true and are the solutions to the quadratic equation.
given
The factored form of the quadratic function f(x), which has roots of 3 and 7, is as follows:
f(x) = a(x - 3)(x - 7) (x - 7) where "a" stands for a fixed coefficient.
We can utilise the point (1, 12) through which the function passes to determine the value of "a"
12 = a(1 - 3) (1 - 3)(1 - 7)
12 = -24a
a = -1/2
Inputting the value of "a" into the factored form yields the following results:
[tex]f(x) = -1/2(x - 3)(x - 7) (x - 7)[/tex]
By extending this phrase, we get:
[tex]f(x) = -1/2(x^2 - 10x + 21)[/tex]
We need to finish the square before we can transform this into vertex form. To achieve this, add and remove the square of the coefficient of x's half:
[tex]f(x) = -1/2(x^2 - 10x + 25 - 4)[/tex]
If we condense this phrase, we get:
[tex]f(x) = -1/2[(x - 5)^2 - 4][/tex]
As a result, the vertex form of the f(x) equation is: [tex]f(x) = -(x - 5)^2 + 2[/tex]which is equivalent to choice (b).
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Which statement explains the type of function that is represented by the equation y = x^2 + 9?
The function is nonlinear because the variable x is raised to the second power. So, the correct option is D) .
Describe Linear Function?A linear function is a mathematical equation that can be represented by a straight line. It is a function in which the independent variable, say "x," is raised only to the first power, and the dependent variable, say "y," is not multiplied or divided by any variable. Linear functions have a constant rate of change, which means that the slope of the line is the same at all points.
The general form of a linear function is y = mx + b, where m is the slope of the line and b is the y-intercept, which is the point at which the line crosses the y-axis. The slope m represents the rate of change of y with respect to x, and can be calculated as the change in y divided by the change in x between any two points on the line.
A linear function is a function that has a constant rate of change, meaning that as x increases by a certain amount, y also increases by a constant amount. A linear function can be written in the form y = mx + b, where m is the slope and b is the y-intercept.
In the given equation y = x² + 9, the variable x is raised to the second power, which means that the rate of change of y with respect to x is not constant. This is the characteristic of a nonlinear function. Moreover, the graph of the function is a parabola, which is also a characteristic of a nonlinear function.
Therefore, the correct answer is D) The function is nonlinear because the variable x is raised to the second power.
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The complete question is :
Which statement explains the type of function that is represented by the equation y=x² +9?
A The function is linear because it contains more than one term.
B) The function is linear because the variable x is raised to the second power.
C) The function is nonlinear because it contains more than one term.
D) The function is nonlinear because the variable x is raised to the second power.
Need help Asap please
Answer:
Summer for 9th Graders: 0.14
Fall for 10th Graders: 0.15
Spring overall total: 0.36
Summer overall total: 0.22
Fall overall total: 0.33
Winter overall total: 0.09
Step-by-step explanation:
Relative frequencies are related to percentages so you can find the answer through that given the total from each grade.
However, adding or subtracting makes the process easier (in my opinion) to find the relative frequency
The owner of a sports complex wants to carpet a hallway connecting to buildings. The carpet costs $1.50 per square foot. How much does it cost to carpet the hallway?
Answer:
$526.75 i believe
Step-by-step explanation:
Evaluate the expression for the given value.
–a – 7 for a = –4
A11
B–11
C3
D–3
A waiter made $288 in tips after waiting on 12 tables. What was the waiter’s average tip per table?
A$24
B$13
C$15
D$16
Answer:
24
Step-by-step explanation:
Answer:
A. $24
Step-by-step explanation:
Given:
total of $288number of values is 12 tablesSolve for average tip:
Average is the same as the meanTo solve you have add up the total and divide by the total number of values288 / 12 = 24Answer:
Thus, the waiter's average tip per table is $24.
The answer is A.
Help Please...
You have 67 coins consisting of half-dollars and quarters. The number of quarters is 7 more than three times the number of half-dollars.
How many quarters do you have?
How many half -dollars do you have?
There are 52 quarters and 15 half-dollars
To solve this problem
Let's represent the number of half-dollars as "x" and the number of quarters as "y".
From the problem statement, we know that:
x + y = 67 (because there are a total of 67 coins)
y = 3x + 7 (because the number of quarters is 7 more than three times the number of half-dollars)
We can use substitution to solve for x:
x + (3x + 7) = 67
4x + 7 = 67
4x = 60
x = 15
So there are 15 half-dollars. We can use this to find the number of quarters:
y = 3x + 7
y = 3(15) + 7
y = 52
So there are 52 quarters.
Therefore, there are 52 quarters and 15 half-dollars.
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In art class students are mixing blue and red paint to make purple paint. Deondra
mixes 6 cups of blue paint and 7 cups of red paint. Arun mixes 2 cups of blue paint
and 3 cups of red paint. Use Deondra and Arun's percent of red paint to determine
whose purple paint will be redder.
Deondra percent of red paint (to nearest whole number) =
Arun percent of red paint (to nearest whole number) =
O Deondra's purple paint will be redder.
O Arun's purple paint will be redder.
o The two purple paints will be equally red.
Submit Answer
%
%
attempt 1 out of 2
Arun's purple paint will be redder.
Define percentagePercentage is a way of expressing a proportion or a fraction as a number out of 100. It is represented by the symbol "%". For example, if you say that 20% of students in a class scored an A grade in a test, it means that 20 out of every 100 students received an A grade.
Deondra mixed 6 cups of blue paint and 7 cups of red paint, so the percent of red paint in her mixture is:
7 / (6 + 7) × 100% = 53.8%, which rounds to 54%.
Arun mixed 2 cups of blue paint and 3 cups of red paint, so the percent of red paint in his mixture is:
3 / (2 + 3) × 100% = 60%.
Since Arun's mixture has a higher percentage of red paint, his purple paint will be redder than Deondra's.
Therefore, the answer is Arun's purple paint will be redder.
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1. Dorie Sparrow, assistant manager of The Clothes Horse, Inc., must mark all clearance rack dresses back
to their regular selling price. She had marked all of them down 70%. What regular selling price does Dorie
need to sell a dress for that had been marked down to $104.98?
Therefore, Dorie needs to sell the dress for $349.93 in order to mark it back to its regular selling price.
What is selling price?
Selling price refers to the price at which a product or service is sold to customers. It is the amount of money that a buyer pays to the seller in exchange for the product or service. The selling price is usually higher than the cost price, which is the amount that the seller paid to acquire or produce the product or service. The difference between the selling price and the cost price is called the profit margin, and it is the profit that the seller makes on the sale of the product or service.
If a dress had been marked down 70%, this means that it is being sold for only 30% of its original selling price.
Let P be the original selling price of the dress. Then:
0.3P = $104.98
Solving for P, we get:
P = $104.98 / 0.3
P = $349.93
Therefore, Dorie needs to sell the dress for $349.93 in order to mark it back to its regular selling price.
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An economy is operating with output $400 billion above its natural level, and fiscal policymakers want to close this expansionary gap. The central bank agrees to adjust the money supply to hold the interest rate constant, so there is no crowding out. The marginal propensity to consume is 3/4, and the price level is completely fixed in the short run.
to close the expansionary gap, the government would need to increase or decrease spending by $ billion.
Hence, to close the expansionary gap, the government would need to decrease spending by $100 billion.
To close the expansionary gap, the government would need to decrease spending by $100 billion.
The formula to calculate the change in equilibrium output due to a change in government spending is:
∆Y = (∆G / (1 - MPC))
Where:
∆Y = change in equilibrium output
∆G = change in government spending
MPC = marginal propensity to consume
Here, the output is $400 billion above its natural level, and the central bank agrees to adjust the money supply to hold the interest rate constant, so there is no crowding out. Therefore, we can assume that the change in government spending (∆G) would have a one-to-one effect on the equilibrium output (∆Y).
Given that MPC = 3/4, we can plug in the values into the formula:
400 = (∆G / (1 - 3/4))
∆G = (1 - 3/4) * 400
∆G = (1/4) * 400
∆G = 100
Hence, to close the expansionary gap, the government would need to decrease spending by $100 billion.
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Luisa has great news, she communicates it to 3 people. Each of them tells 3 more. This is how a chain is set up, since each new person who learns the news communicates it to three others. It takes one person approximately 10 minutes to communicate the news to three others. If an hour has passed, how many people have heard the news?
Answer:
The amount of persons who have heard in 30mins would be:
45 persons
How could Marc mathematically try to prove that he hit the ball near the top of the tower?While on the golf course last weekend Marc hit into the rough, landing the ball behind a tall tree. To get out of the scenario, his best option was to hit the ball high enough so it goes over the tree and hopefully comes down in the fairway for his next shot. So with a mighty swing, he hit the ball into the air and was surprised to see it hit near the top of a 300 foot tall tower that he had not noticed. The formula for this shot is h(x) = -16xsquared + 120x , where h is the height of the ball and x is the number of seconds the ball is in the air. How could Marc mathematically try to prove that he hit the ball near the top of the tower?While on the golf course last weekend Marc hit into the rough, landing the ball behind a tall tree. To get out of the scenario, his best option was to hit the ball high enough so it goes over the tree and hopefully comes down in the fairway for his next shot. So with a mighty swing, he hit the ball into the air and was surprised to see it hit near the top of a 300 foot tall tower that he had not noticed. The formula for this shot is h(x) = -16xsquared + 120x , where h is the height of the ball and x is the number of seconds the ball is in the air. How could Marc mathematically try to prove that he hit the ball near the top of the tower?
Answer:
To mathematically prove that Marc hit the ball near the top of the tower, he could use the equation h(x) = -16x^2 + 120x, where h is the height of the ball and x is the number of seconds the ball is in the air.
First, Marc would need to determine the maximum height the ball reached during its flight. This can be found by using the vertex formula, which is x = -b/2a. In this case, a = -16 and b = 120, so x = -120/(2*-16) = 3.75 seconds.
Next, Marc can substitute this value back into the original equation to find the maximum height the ball reached. h(3.75) = -16(3.75)^2 + 120(3.75) = 135 feet.
Since the tower is 300 feet tall, Marc could conclude that if the ball hit near the top of the tower, it would have reached a height close to 300 feet. Since the ball reached a maximum height of 135 feet, it is unlikely that it hit the top of the tower.
However, this calculation assumes that the tower is directly in line with Marc's shot and that the ball did not have any horizontal movement. In reality, the tower could have been to the left or right of the shot, and the ball could have had some horizontal movement, which would affect its height at impact. Therefore, this calculation can only provide a rough estimate and cannot definitively prove whether or not the ball hit near the top of the tower.
a right triangle has a hypotenuse of length 7 inches. If one angle is 38 degrees, find the length of each leg.
Check the picture below.
[tex]\sin(38^o )=\cfrac{\stackrel{opposite}{x}}{\underset{hypotenuse}{7}}\implies 7\sin(38^o)=x\implies 4.31\approx x \\\\[-0.35em] ~\dotfill\\\\ \cos(38^o )=\cfrac{\stackrel{adjacent}{y}}{\underset{hypotenuse}{7}}\implies 7\cos(38^o)=y\implies 5.52\approx y[/tex]
Make sure your calculator is in Degree mode.
Answer:
4.31 in5.52 inStep-by-step explanation:
You want the leg measures in a right triangle with a hypotenuse of 7 inches and an angle of 38°.
Trig functionsThe mnemonic SOH CAH TOA reminds you of the relations between side lengths and trig functions:
Sin = Opposite/Hypotenuse ⇒ Opposite = Hypotenuse×Sin
Cos = Adjacent/Hypotenuse ⇒ Adjacent = Hypotenuse×Cos
ApplicationThe given triangle will have opposite and adjacent sides of ...
opposite = (7 in)sin(38°) ≈ 4.31 in
adjacent = (7 in)cos(38°) = 5.52 in
The leg lengths of the triangle are 4.31 inches and 5.52 inches.
I BEG U FOR HELP WILL GIVE BRAINLIEST PLLSSSS
Answer:
3,4,5 is the answer
Step-by-step explanation:
for the explanation using pythagoras theoem
[tex] {3}^{2} + {4}^{2} = {5 \\ }^{2} \\ 3 \times 3 + 4 \times 4 = 5 \times 5 \\ 9 + 16 = 25 \\ 25 = 25[/tex]
may you give me branliest as you promised
Choose scales for the coordinate plane shown so that you can graph the points J (5, 50), K(3, 50), L (4, -40), M (-2, 40), and N (-5, -10). on the x-axis use a scale of ____ units for each grid square. on the y-axis use a scale of ____ units of each grid square. complete the explanation for using these scales for each axis. the x-coordinates range from ____ to ____, and the y-coordinates range from ____ to ____.
On the x-axis use a scale of 2 units for each grid square. on the y-axis use a scale of 10 units of each grid square. The x-coordinates range from -5 to 5. y-coordinates range from -40 to 50.
What is coordinate plane?In mathematics, points and functions are represented and graphed on the coordinate plane, commonly known as the Cartesian plane. The x-axis and y-axis are two perpendicular number lines that meet at the origin to form the plane (0,0).
On the coordinate plane, points are denoted by ordered pairs (x, y), where x denotes the point's separation from the y-axis and y denotes its separation from the x-axis.
For the given coordinates the range of x and y coordinates are:
x-coordinates range from -5 to 5
y-coordinates range from -40 to 50.
Thus, we use a scale of 2 on the x-axis and 10 units on the y axis.
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A machine in a factory makes chairs at rate of two chairs every 10 minutes how much time does the machine take to make five chairs how many minutes would it take for the factory to fulfill an order for 32 chairs show your work or explain how you determine your answers
What is the range of the relation whose graph is shown?
The range of the relation whose graph is shown include the following: C. -1 ≤ y ≤ 1.
What is a domain?In Mathematics and Geometry, a domain is the set of all real numbers for which a particular function is defined.
Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:
Domain = {-4, 4} or -4 ≤ x ≤ 4.
Range = {-1, 1} or -1 ≤ y ≤ 1.
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Which of the numbers 0, 1, 2, 3 or 4 make the equation 8/y2 + 2 true?
None of the given numbers make the equation 8/y² + 2 true.
What is algebra?
Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas.
To solve this problem, we can substitute each of the given numbers (0, 1, 2, 3, 4) for y in the equation 8/y² + 2 and see if the equation is true.
Substituting y=0 would make the denominator of the fraction zero, which is undefined, so y=0 is not a valid choice.
Substituting y=1 would give us:
8/1² + 2 = 8 + 2 = 10
So, 1 is not the answer.
Substituting y=2 would give us:
8/2² + 2 = 8/4 + 2 = 2 + 2 = 4
So, 2 is not the answer.
Substituting y=3 would give us:
8/3² + 2 = 8/9 + 2 = 0.888 + 2 = 2.888
So, 3 is not the answer.
Substituting y=4 would give us:
8/4² + 2 = 8/16 + 2 = 0.5 + 2 = 2.5
So, 4 is not the answer.
Therefore, none of the given numbers make the equation 8/y² + 2 true.
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Use the slip and y-intercept to identify the equation of this line
Answer:
y=2x
Step-by-step explanation:
equation formula is y=mx+b
m is slope
b is y-intercept
you know that slope is 2
y intercept is 0
so plug it into the equation
y=2x+0 or just y=2x
Suppose that the function h is defined as follows.
if
-2
-1
h(x)= 0
1
2
Graph the function h.
-3.5
if-2.5
if-1.5
if -0.5
if 0.5 ≤x≤1.5
Suppose that the function h is defined as follows. -2 -1 h(x)= if – 2, the graph is given below: (see image)
What is a Graph?A graph is a mathematical structure used to represent relationships between objects or entities. It consists of a set of vertices (also known as nodes) and a set of edges that connect pairs of vertices.
In a graph, the vertices represent the objects or entities being studied, while the edges represent the connections or relationships between them.
For example, in a social network graph, the vertices might represent individual users, and the edges might represent their connections (e.g. friendships) with other users.
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Will mark brainliest if answer is correct
Answer:
[tex]3( {2}^{2} ) - {2}^{2} + 4 = 12[/tex]
[tex] {2}^{3} + b( {2}^{2} ) + 43(2) - 126 = 4b - 204[/tex]
[tex]4b - 32 = 12[/tex]
[tex]4b = 44[/tex]
[tex]b = 11[/tex]
For this value of b, these graphs will intersect at (2, 12). Please use your graphing calculator to confirm that this is the only point of intersection.
The width of the set of the shelves needs to be 5 times the height of the set of shelves and the set of shelves must have three shelves If there are 80 feet of wood to use to build the set of shelves what should the dimensions the set of shelves be?
The dimensions of the set of shelves should be approximately 4.21 feet in height and 21.05 feet in width.
What is a linear equation?When plotted on a coordinate plane, an algebraic equation known as a linear equation looks like a straight line. The variable (or variables) in this equation always have a greatest power of 1, making it a constant. In other words, a linear equation simply makes use of the fundamental operations of addition, subtraction, and multiplication of variables to the first power, as well as constants.
Given:
Width of the set of shelves = 5 times the height of the set of shelves
Number of shelves = 3
Total amount of wood available = 80 feet
Let's denote the height of the set of shelves as "h" and the width of the set of shelves as "w".
Using the first given information, we can write the equation:
Width (w) = 5 times the height (h) ==> w = 5h
Next, we know that the set of shelves has 3 shelves, so the number of shelves is fixed at 3.
Finally, we are given that we have 80 feet of wood available to build the shelves.
Using these equations, we can substitute w = 5h into the equation for the total amount of wood:
3w + 4h = 80
Substituting w = 5h, we get:
3(5h) + 4h = 80
15h + 4h = 80
19h = 80
h = 80/19
So, the height of the set of shelves is approximately 4.21 feet.
Now, substituting this value of h back into w = 5h, we get:
w = 5(4.21)
w = 21.05
So, the width of the set of shelves is approximately 21.05 feet.
Therefore, the dimensions of the set of shelves should be approximately 4.21 feet in height and 21.05 feet in width.
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-4(2-x) less than or equal to 8
Answer: less than
Step-by-step explanation:
Help pleasee
The half-life of Palladium-100 is 4 days. After 16 days a sample of Palladium-100 has been reduced to a mass of 2 mg.
What was the initial mass (in mg) of the sample? --------------
What is the mass 7 weeks after the start?-------------
The initial mass (in mg) of the sample is 32 mg
The mass 7 weeks after the start is 0.198 mg
What is exponential decay:Exponential decay is a process in which a quantity decreases at a rate proportional to its value. This means that the larger the quantity, the faster it will decrease.
Exponential decay is modeled by the following formula:
[tex]A = A_{0} \times (1/2)^{\frac{t}{T} }[/tex]
where A is the amount after time t, A₀ is the initial amount,
T is the half-life, and t is the time elapsed
Here we have
The half-life of Palladium-100 is 4 days. After 16 days a sample of Palladium-100 has been reduced to a mass of 2 mg.
For the first question, we know that after 16 days, the amount is 2 mg, and the half-life is 4 days. We can plug these values into the formula:
[tex]2 = A_{0} \times (1/2)^{\frac{16}{4}}[/tex]
Simplifying, we get:
2 = A₀ × (1/2)⁴
2 = A₀ × (1/16)
A₀ = 2 × 16
A₀ = 32 mg
So the initial mass of the sample was 32 mg.
For the second question, we need to find the mass after 7 weeks, or 49 days. We can use the same formula, but with t = 49:
[tex]A = 32 \times (1/2)^{\frac{49}{4} }[/tex]
A ≈ 0.198 mg
Therefore,
The initial mass (in mg) of the sample is 32 mg
The mass 7 weeks after the start is 0.198 mg
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Solve the equations using suntraction. Show all your work.
X-6y=11 and 2x-5y=1
7. Can the following be the lengths of the sides of a triangle?
a. 20 cm, 40 cm, 50 cm
b. 20 cm, 40 cm, 60 cm
c. 41 cm, 250 mm, 12 cm
Answer:
B
Step-by-step explanation:
THE TWO SMALLER SIDES = THE LARGER SIDE HENCE ITS A TRIANGLE
Elliot read a report from a previous year saying that 6 % 6%6, percent of adults in his city biked to work. He wanted to test whether this had changed, so he took a random sample of 240 240240 adults in his city to test H 0 : p = 0.06 H 0 :p=0.06H, start subscript, 0, end subscript, colon, p, equals, 0, point, 06 versus H a : p ≠ 0.06 H a :p =0.06H, start subscript, start text, a, end text, end subscript, colon, p, does not equal, 0, point, 06, where p pp is the proportion of adults in Elliot's city that bike to work. The sample results showed 21 2121 adults who biked to work, and the corresponding test statistic was z ≈ 1.79 z≈1.79z, approximately equals, 1, point, 79. Assuming that the necessary conditions are met, what is the approximate P-value for Elliot's significance test?
Answer: To find the P-value, we first need to determine the direction of the alternative hypothesis. Since the alternative hypothesis is two-tailed, we need to divide the significance level (α) by 2 before finding the critical values and the rejection region. Therefore, we have:
H0: p = 0.06
Ha: p ≠ 0.06
α = 0.05/2 = 0.025
The test statistic is z = 1.79, which represents the number of standard errors that the sample proportion is from the hypothesized population proportion under the null hypothesis. We can find the P-value by looking up the area in the standard normal distribution table beyond the test statistic in both tails:
P-value = P(Z ≤ -1.79 or Z ≥ 1.79)
= P(Z ≤ -1.79) + P(Z ≥ 1.79)
= 0.0364 + 0.0364
= 0.0728
Therefore, the approximate P-value for Elliot's significance test is 0.0728. Since the P-value is greater than the significance level of 0.05, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that the proportion of adults who bike to work in Elliot's city has changed significantly from the previous year.
Step-by-step explanation:
if you dilate triangle ABC by a scale factor of 3 and (0,0) is the center, what will be the length of AB?
the new length of AB after a dilation by a scale factor of 3 with (0,0) as the center would be 3 times the original length of AB.
How to solve the question?
To find the new length of AB after a dilation by a scale factor of 3 with (0,0) as the center, we can use the following formula:
AB' = AB x 3
where AB' is the length of AB after the dilation, and AB is the original length of AB.
However, we need to first determine the length of AB in the original right triangle ABC. To do this, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
Let's assume that AB is the hypotenuse of the right triangle ABC, and that AC and BC are the other two sides. Then we have:
AB²= AC²+ BC²
Without more information about the lengths of AC and BC, we cannot determine the value of AB. However, once we have determined the length of AB, we can use the formula above to find the new length of AB after dilation.
Assuming we know the length of AB in the original right triangle ABC, we can now use the formula for dilation to find the new length of AB:
AB' = AB x 3
For example, if AB is 5 units long in the original triangle, then after dilation, AB' would be:
AB' = 5 x 3 = 15 units
Therefore, the new length of AB after a dilation by a scale factor of 3 with (0,0) as the center would be 3 times the original length of AB.
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The table contains some points on the graph
of an exponential function. Based on the
table, which function represents the same
relationship?
Answer: 1st one
Step-by-step explanation:
On a given planet, the weight of an object varies directly with the mass of the object. Suppose that an object whose mass is 2 kg weighs 4 N. Calculate the mass of another object that weights 18 N.
Answer:
Let m be the mass of the object and w be the weight of the object. According to the problem, weight varies directly with mass, so we can write:
w = k * m
where k is the constant of proportionality.
To find k, we can use the information given in the problem. We know that when m = 2 kg, w = 4 N. Substituting these values into the equation above, we get:
4 N = k * 2 kg
Solving for k, we get:
k = 4 N / 2 kg = 2 N/kg
Now we can use this value of k to find the mass of an object that weighs 18 N. We can rearrange the equation above to solve for m:
m = w / k
Substituting w = 18 N and k = 2 N/kg, we get:
m = 18 N / 2 N/kg = 9 kg
Therefore, the mass of the object that weighs 18 N is 9 kg.
Alberto gets a fish tank
Jackson is on point. Of all fish, catfish make up one-third of the total.
How much gravel does Alberto add to the tank in pounds?The United States of America, Great Britain, and other English-speaking countries predominately utilise the pound as a unit of weight.
Any quantity associated with something is assumed to contain one pound if it does. The pound is the most widely used weight unit in the English-speaking world, including Britain, America, and other nations.
Zebra danios make up half of all the fish.
More fancy guppies than catfish, by a factor of two.
x = guppies
2x = catfish
x + 2x = 1/2 of the fish population
3x = 1/2 of the fish population
3x * 2 = 6x
x = 1/6 number of fancy guppies
catfish:
2x = 2(1/6) = 2/6 = 1/3 catfish.
Jackson is on point. Of all fish, catfish make up one-third of the total.
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The complete question is,
Alberto puts 3 kinds of fish in his fish tank: zebra danios, fancy guppies, and cat fish. Half of Alberto's fish are zebra danios. He has 2 times as many catfish as he has fancy guppies. Alberto's friend Jackson says 1/3 of Alberto's fish are catfish. Is Jackson correct?