To find the general solution of the given system using substitution, we need to solve for one variable in terms of the other in one of the equations, and then substitute that expression into the other equation. In this case, we can solve the second equation for x1 in terms of x2, which gives us x1 = (3/2)x2. We can then substitute this expression for x1 into the first equation, which becomes x'2 = 9x2 - 18x2 = -9x2. Thus, we have the system x1 = (3/2)x2, x2 = Ce^(-9t), where C is a constant of integration. This is the general solution to the system.
The process of substitution involves solving for one variable in terms of the other in one of the equations, and then substituting that expression into the other equation. This allows us to reduce the system to a single equation in one variable, which we can then solve to find the general solution.
The general solution of the given system using substitution is x1 = (3/2)x2, x2 = Ce^(-9t), where C is a constant of integration. This solution shows the relationship between the two variables and how they change over time. The process of substitution is a useful tool for solving systems of linear differential equations and can be applied to more complex systems as well.
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Find the unit rate
Miles 3/5
Hours
1/3
? miles in 1 hour
When adopting the unitary technique, a mile is equivalent to 1.8 miles per hour when it takes 3/5 miles and 1/3 hour.
what is unitary method ?The unit technique is a method of problem-solving where you first calculate the value of a single unit, then multiply that value to get the answer. Simply expressed, a single unit value is extracted from a specified multiple using the unit method. For instance, 40 pens will set you back 400 rupees, or $1.01. The method used to accomplish this might be standardized. a solitary nation. anything has a distinctive component. (Mathematics, Algebra) Its adjoint and reciprocal are equivalent. (Linear Algebra, Mathematical Analysis, Mathematics of Matrix or Operators)
given
3/5 miles were traveled in one third of an hour.
The distance that can be traveled in 1 hour is equal to (3/5) (1/3)
= (3/5)×3= 1.8 mph
Here, unit rate is expressed as mph=1.8 mph.
When adopting the unitary technique, a mile is equivalent to 1.8 miles per hour when it takes 3/5 miles and 1/3 hour.
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Which equation has infinitely many solutions?
A. 6(3x - 5) = 10 - 2x
B. -3(4x - 8) = 6x + 12
C. -7(-8x + 3) = -21 + 56x
D. 9(3x - 4) = 27x + 36
The equation -3(4x - 8) = 6x + 12 has infinitely many solutions.
How to find if a equation has infinitely many solution?An equation has infinitely many solutions when the equation is true for all possible values of the variable. One way to identify that an equation has infinitely many solutions is to see if the equation is true when the variable is replaced by any value.
What is system of equation?A system of equations is a set of two or more equations that involve the same variables. The goal is to find the values of the variables that satisfy all of the equations in the system. There are different methods to solve a system of equations, depending on the type of equations and the number of variables involved.
The equation that has infinitely many solutions is:
B. -3(4x - 8) = 6x + 12
To see this, we can simplify the equation to:
-12x + 24 = 6x + 12
-12x = 12
x = -1
Now, if we put x = -1 in the equation, we see that it is true. If we put x = -2, x=0, x = 1, x = 3 and so on, we can see that the equation is true for all values of x.
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Which function could have produced the values in the table? Explain why you chose this answer. i will mark you brainliest!!
Answer:
The answer is (d) y=3x+2
Inserting the given points in the given equation yields the answer. To make the process faster, insert the zero first then you will get y=2. You have to choose whether B and D. Then insert the x values and you will obtain the correct answer which is valid for the given points x and y.
9 (3x - 5) = 9 (3x + 5)
What must be added to X² 4x+?
To make the given expression x² + 4x + ___ a perfect square ( x + 2)² we must add 4 to the given expression.
As given in the question,
Given expression is equal to :
x² + 4x + ___
Using the formula of perfect square we have :
( a + b )² = a² + 2ab + b²
Here in the given expression x² + 4x + ___
a = x
b = 2
This implies that :
x² + 4x + ___
= x² + 2 ( 2 ) ( x ) + ( 2 )²
= x² + 2 ( 2 ) ( x ) + 4
= ( x + 2 )²
We must add '4' to the given expression.
Therefore, '4' must be added to the given expression x² + 4x + ___ to make it perfect square ( x + 2 )².
The above question is incomplete , the complete question is :
What must be added to the given expression x² + 4x + ___ to make it perfect square ?
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Classify the polynomial 2q⁹.
Trinomial
Monomial
Binomial
None of these
The polynomial 2q⁹ is monomial.A polynomial can have one or more terms, whereas a monomial, binomial, trinomial, and a trinomial all have one term each.
What category does a polynomial fall under?By the degree of the polynomial, polynomials can be categorized. A polynomial's degree is equal to the highest degree term in the polynomial. Consequently, the result of 2x3+3x2+8x+5 is 3, or 3. When terms are organized in a polynomial from greatest to lowest degree, it is said to be expressed in standard form.A polynomial can have one or more terms, whereas a monomial, binomial, trinomial, and a trinomial all have one term each.The polynomial 2q⁹ is monomial.A polynomial can have one or more terms, whereas a monomial, binomial, trinomial, and a trinomial all have one term each.To learn more about polynomial refer to:
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blank minutes= 7/10 hour
Answer: 42 minutes
Step-by-step explanation:
To find 7/10 of an hour, you can multiply 7/10 by 60 (the number of minutes in an hour) to get 420/10 minutes which simplifies to 42.
When solving a system of equations, which of the following is a possible outcome? select all that apply. explain why you chose this answer! please help I will mark you brainliest.
Answer: When solving a system of equations, the following are possible outcomes:
Consistent and dependent: The system has infinitely many solutions, and the equations are dependent. This occurs when the equations represent the same line.
Consistent and independent: The system has a unique solution, and the equations are independent. This occurs when the equations represent two distinct lines that intersect at one point.
Inconsistent: The system has no solutions, and the equations do not have a point of intersection. This occurs when the equations represent parallel lines or lines that do not intersect.
Option A,B,C are possible outcomes.
A: Consistent and dependent: The system has infinitely many solutions, and the equations are dependent. This occurs when the equations represent the same line.
B: Consistent and independent: The system has a unique solution, and the equations are independent. This occurs when the equations represent two distinct lines that intersect at one point.
C: Inconsistent: The system has no solutions, and the equations do not have a point of intersection. This occurs when the equations represent parallel lines or lines that do not intersect.
Step-by-step explanation:
Which description best matches the graph below? please explain why you chose this answer. I will mark you brainliest
When the value of r is 0.8 the two variables have high correlation?
There is a significant association if is between 0.85 and 1. There is a moderate connection if lies between 0.5 and 0.85. If, then there is a weak association between the two variables.
What is Correlation Coefficient?The strength of the linear link between two separate variables, x and y, is shown by correlation coefficients.
A positive relationship is shown by a linear correlation coefficient greater than zero.
Indicating a negative association is a value less than zero. The two variables x and y do not have any relationship when their values are 0, to sum up.
The correlation coefficient (r2) is a statistic that expresses how closely two variables' movements are related to one another.
To determine the linear relationship between two variables, the Pearson product-moment correlation, the most popular correlation coefficient, is used.
However, this correlation value might not necessarily be a reliable indicator of reliance in a non-linear connection.
Hence, There is a significant association if is between 0.85 and 1. There is a moderate connection if lies between 0.5 and 0.85. If, then there is a weak association between the two variables.
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A 148kg object is going a constant -3.5m/s. Then it experiences an impulse of -80kg*m/s, what is its new velocity?
The new velocity of the object is -4.04 m/s
How to determine the new velocity of the object?
Impulse is the change in momentum of an object which a force causes. It is equal to the magnitude of the force multiplied by the length of time the force is applied.
Mathematically:
Impulse (I) = change in momentum = force(F) × time (t)
Also,
Ft = m(v-u)
I = m(v-u)
where m is the mass of the object, v is the new velocity and u is the initial velocity
From the given information; m = 148kg, u = -3.5m/s, I = -80 kg m/s:
I = m(v-u)
-80 = 148(v - (-3.5))
-80 = 148(v +3.5)
-80 = 148v + 518
148v = -80-518
148v = -598
v = -598/148
v = -4.04 m/s
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There are five brothers in a family. The oldest brother is 11 3/4 years old. Each of the four younger brothers is 2 7/12 years than the brother right before him. In how many years and months will another brother be born
In linear equation , The fifth son is younger than first son will be 31/3. And The age of the fifth son will be 1 and 5/12.
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.
In a family, there are five sons. The oldest son is 11 and 3/4 years old, and every next younger brother is younger than the next by 2 and 7/12 years.
Then the fifth son is younger than first son will be
⇒ 4(2 + 7/12)
⇒ 4(31/12)
⇒ (31/3)
The age of the fifth son will be
⇒ (11 + 3/4) – 4(2 + 7/12)
⇒ (47/4) – 4(31/12)
⇒ (47/4) – (31/3)
⇒ 17/12
⇒ 1 + 5/12
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I don't undertand thi:
There are 22 event at an indoor track and field meet. The ratio of track event to field event i 8:3. How many of the event are track event?
Can I jut have the ratio without the tory problem? Thank
There are 22 event at an indoor track and field meet. The ratio of track event to field event is 8:3. Therefore, there are 16 track events.
Ratio:
In mathematics, ratios indicate the number of times one number contains another number. For example, if you have 8 oranges and 6 lemons in your fruit bowl, the ratio of oranges to lemons is 8 to 6 (that is, a ratio of 8:6, or 4:3). Similarly, the ratio of lemons to oranges is 6:8 (or 3:4) and the ratio of oranges to whole fruit is 8:14 (or 4:7).
Now,
If you want to know the number of events in track events, we can calculate it in two steps:
Divide 22 in the ratio 8:3.
First,
add the numbers = 8 + 3 =11
Second,
For 08, We Multiple and divide = 8/11 × 22
= 16
Again,
For 03, We again multiple and Divide = 3/11 × 22
= 06.
Therefore, there are 16 track events.
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could someone pls help me with thissssss
The slope of the line through the points is -5/7.
What is slope ?
A number that describes a line's direction and steepness is known as the slope or gradient of a line in mathematics.
A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).
The slope is calculated as the ratio of the rise, which is the vertical change between two points, to the run, which is the horizontal change between those same two sites.
Typically, a line's slope provides information about the steepness and direction of the line. Finding the difference between the coordinates of the locations will allow you to quickly compute the slope of a straight line connecting two points, (x1,y1) and (x2,y2).
m=Δy/Δx
m=(y2−y1)/(x2−x1)
m=(4−−1)/(−3−4)
m=5/−7
m=−5/7
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The temperature is recorded in 65 cities on a given day in California. The
average temperature is 74 degrees Fahrenheit with a standard deviation of 4
degrees. What is the z-score for a temperature of 71 degrees?
The z-score for a temperature of 71 degrees is -0.75.
What is the z-score?
When assessed in terms of standard deviation units, a raw score's location in relation to its distance from the mean is indicated by a z-score. If a value is above the mean, the z-score is positive; if it is below the mean, it is negative.
The raw score less the population mean, divided by the population standard deviation, is the z-score.
Here, the mean average temperature is 74°, standard deviation is 4, and the raw score is 71°.
The formula for calculating z-score is -
Z = (x-μ)/σ
Where x is raw score, μ is mean and σ is standard deviation.
Plugging in the values -
Z = (71-74)/4
Z = -3/4
Z = -0.75
Therefore, the z-score is obtained as -0.75.
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Exercie 4 An IQ tet wa adminitered to a random ample of 101 ixth grader. The ample mean wa 104. 2 with a tandard deviation of 12. Find a 99% confidence interval
A 99% confidence interval for an IQ test conducted for a sample of 101 sixth graders, where the sample mean was 104.2, with a standard deviation of 12 is 104.2 ± 3.076.
A 99% confidence interval can be calculated using the formula:
sample mean ± (critical value) x (standard deviation of the mean/ √(sample size))
[tex]sample\ mean\± (critical\ value) ( \frac{standard\ deviation\ of\ the\ mean}{\sqrt{sample\ size} } )[/tex]
To find the critical value, we can use the standard normal distribution table. For a 99% confidence interval, the critical value for a two-tailed test is approximately 2.576.
So, for this problem where sample mean = 104.2 and standard deviation of mean = 12, the 99% confidence interval would be:
104.2 ± 2.576 x (12 / √101)
≈ 104.2 ± 3.076
The standard deviation of the mean is the standard deviation of the sample divided by the square root of the sample size.
This gives us a range of approximately (101.124, 107.276). So we can say that there is a 99% probability that the true population mean IQ score of sixth graders is between 101.122 and 107.276.
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What is second set of coordinate called?
The second set of coordinates is known as the Polar Coordinates.
Polar coordinates are a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point (the pole) and an angle from a reference direction (the polar axis). The reference point is usually the origin (0,0) of a Cartesian coordinate system, and the reference direction is usually the positive x-axis of the Cartesian coordinate system. Polar coordinates are useful when dealing with circular shapes and symmetric patterns because all points on a circle can be represented by a single polar coordinate. For example, if you want to draw a circle, you only need to specify the center point, the radius, and the number of degrees you want to cover. Polar coordinates also allow for an easy conversion to Cartesian coordinates, which can be used for plotting points and finding distances. Additionally, polar coordinates can be used to determine angles and distances between two points in a two-dimensional plane. Polar coordinates are a powerful tool in mathematics and engineering, allowing for more efficient analysis of shapes and patterns.
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would appreciate help
Answer:
59040
Step-by-step explanation:
Answer:
Step-by-step explanation:
ygyggygy
what is 6root 2 - 5 root2
As the value of 2 is 1.414, 6root 2 is 8.484, and 5 root2 is 7.071, the value of 6root 2 - 5 root2 is 1.413.
what is square root ?The square root or nth root is represented by the radical sign. Square roots are a component of root expressions. There is a radical's radicand—a number or word that appears. Radicals like 7 and 2y+1 serve as examples. Additional terms that describe radicals include: Radical equations are those equations that include radicals. A "root expression" is the phrase used to describe the expression contained within the square root. To demonstrate radical representations, consider the numbers 2, 372, 2x+7, and 41p. The phrase "root expression" refers to the expression contained within the square root. Examples of radical representations are the numbers 2, 372, 2x+7, and 41p.
given
6root 2 - 5 root2
√2 value is 1.414. therefore 6×1.414
= 8.484
5 root2
√2 value is 1.414. therefore 5 * 1.414
= 7.071
so 6root 2 - 5 root2 = 8.484 - 7.071
= 1.413
As the value of 2 is 1.414, 6root 2 is 8.484, and 5 root2 is 7.071, the value of 6root 2 - 5 root2 is 1.413.
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PLEASE HELP
The fuel for a chain saw is a mix of oil and gas. The ratio of ounces of oil to gallons of gas is 9:19 . There are 152 gallons of gas. How many ounces of oil are there?
please help me w this
Answer:
Opposite Sides are perpendicular (only correct answer)
Step-by-step explanation:
Not every parallelogram has diagonals that are perp to each other (form right angles.
Exercises 9 and 10, write a function that represents the balance after t years.
9. $3000 deposit that earns 6% annual interest compounded quarterly.
10. $5000 deposit that earns 7.2% annual interest compounded monthly.
The function for the given compound interest will be A = 3000(1+6/4) and A = 5000(1+7.2) .
What is compound interest?
The interest on savings that is computed on both the initial principal and the interest accrued over time is known as compound interest. Compound interest is computed by multiplying the starting principal amount by one and the annual interest rate is raised to the number of compound periods minus one. The final step is to deduct the initial loan principal from the calculated value.
When the amount compounds quarterly, it means that the amount compounds 4 times in a year. i.e., n = 4. We use this fact to derive the quarterly compound interest formula. Thus, the quarterly compound interest formula is:
$3000 deposit that earns 6% annual interest compounded quarterly.
A = P (1 + r/4)4
A = 3000(1+6/4)
$5000 deposit that earns 7.2% annual interest compounded monthly.
A = P (1 + r)
A = 5000(1+7.2)
Hence the function for the given compound interest will be A = 3000(1+6/4) and A = 5000(1+7.2) .
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help please im timed
So, on solving the question the inequality equation, that will be formed here is 3x3+2y>1 and 4xx-y< -3
What do you call the solution to the system of linear inequalities?If not, shade the other side of the plane. Graph each of the system's inequalities similarly. The place where all of the system's solutions intersect is where the system of inequalities' solution is located.
One solution pair exists for each independent system (x,y). There is just one possible location: the intersection of the two lines. There is no way to fix an inconsistent system. The two lines are parallel and will never cross one another, as you can see. There are countless ways to solve a dependent system.
If the inequality is true when the values of x and y are substituted, then an ordered pair (x,y) is the solution to the linear inequality. As a result, if the absolute value expression is set to a negative number, there is no solution.
the inequality equation, that will be formed here is
3x3+2y>1
and 4xx-y< -3
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17 ≥ 6x is the inequality which can be represented for the given variable x.
What do you call the solution to the system of linear inequalities?If not, shade the other side of the plane. Graph each of the system's inequalities similarly. The place where all of the system's solutions intersect is where the system of inequalities' solution is located.
One solution pair exists for each independent system (x, y). There is just one possible location: the intersection of the two lines. There is no way to fix an inconsistent system. The two lines are parallel and will never cross one another, as you can see. There are countless ways to solve a dependent system.
If the inequality is true when the values of x and y are substituted, then an ordered pair (x,y) is the solution to the linear inequality. As a result, if the absolute value expression is set to a negative number, there is no solution.
You must pay $8.50 or less for the copies and each copy is $0.30
Let the number of copies be x and we have the inequality,
8.50 ≥ 0.30x
Divide 5 and multiply 10 from both sides
17 ≥ 6x
Thus, 17 ≥ 6x is the inequality which can be represented for the given variable x.
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What is the sum?
X
3
2
+
X+3 x+3 x+3
O
+
colch
53
X+5
X+3
X+5
3x+27
6x
X+3
The outcome or result of adding two or more integers is known as the SUM.
What is a sum?The outcome of adding numbers or quantities mathematically is a summation, often known as a sum. A summation always has an even number of terms in it. There may be just two terms, or there may be 100, 1000, or even a million. Some summations include an infinite number of terms.
the sum of two or more numbers, magnitudes, quantities, or specifics as determined by or as though decided by the addition process in mathematics.
The outcome of adding two or more numbers, objects, or things is referred to in mathematics as the sum.
The result or solution we obtain from adding two or more integers is known as the SUM. Addends are the figures that are combined.
[tex]Simplify $\frac{x}{x+3}+\frac{3}{x+3}+\frac{2}{x+3}: \frac{x+5}{x+3}$Steps$$\frac{x}{x+3}+\frac{3}{x+3}+\frac{2}{x+3}$$Apply the fraction rule: $\frac{a}{c}+\frac{b}{c}=\frac{a+b}{c}$$$=\frac{x+3+2}{x+3}$$Add the numbers: $3+2=5$$$=\frac{x+5}{x+3}$$[/tex]
Therefore, the correct answer is option b) [tex]$=\frac{x+5}{x+3}$[/tex]
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what is the answer for this question? Answer ASAP
The value of the expression as a fraction in its simplest form is 2/7.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
1 ÷ ( 5/2 x (2 x (1(3/5) - 2/5) - 1) )
Step 1:
Removing the parenthesis.
We will solve (1(3/5) - 2/5) first.
8/5 - 2/5 = 6/5
1 ÷ ( 5/2 x (2 x 6/5 - 1) )
Step 2:
Solve this (2 x 6/5 - 1)
12/5 - 1 = 7/5
1 ÷ ( 5/2 x 7/5)
Step 3:
Solve (5/2 x 7/5)
5/2 x 7/5 = 7/2
1 ÷ 7/2
Step 4:
1 ÷ 7/2
= 1 x 2/7
= 2/7
Thus,
The value of the expression is 2/7.
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Simplify:
√-25-4
A. 1
B. -9
C. 5i-4
D. -5i-4
The simplified form of the expression √-25 - 4 is 5i - 4.
What is the simplified form of the expression?Given the expression in the question.
√-25 - 4
To simplify, rewrite -25 as -1(25)
√-1(25) - 4
Rewrite √-1(25) as √-1 × √25
√-1 × √25 - 4
Rewrite √-1 as i
i × √25 - 4
Rewrite 25 as 5²
i × √5² - 4
Now, pull terms out from under the radical, assuming positive real numbers.
i × 5 - 4
Multiply i and 5
5i - 4
Therefore, the simplified form is 5i - 4.
Option C) 5i - 4 is the correct answer.
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What is the correlation coefficient for the data shown in
the table?
О о
0 1
04
05
Answer:
i think the answer is one
Step-by-step explanation:
The solution is : The correlation coefficient is -1
What is correlation coefficient?A correlation coefficient is a numerical measure of some type of correlation, meaning a statistical relationship between two variables. The variables may be two columns of a given data set of observations, often called a sample, or two components of a multivariate random variable with a known distribution.
Here, we have,
we want to get the correlation coefficient for the given dataset
from the table, what do we observe?
As x is increasing by 5 units;
y is decreasing by 5 units
What this mean is that there is a negative correlation between both
This means the linear regression will go through every point, and will be a perfect fit. The correlation coefficient, r, of a data set is 1 if it is a perfect positive fit and -1 if it is a perfect negative fit; since the slope is decreasing, this is a negative correlation, and since it fits perfectly, it is -1.
Thus, what we have here is that, since the rate of increase/decrease on both ends is of equal magnitude but opposite signs, we can conclude that the correlation coefficient is -1
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Estimate the instantaneous rate of change of 2/(t-3) at the point -1
The instantaneous rate of change of 2/(t-3) when the variable is equal to -1, is:
f'(-1) = -1/8
How to find the instantaneous rate of change at the point t = -1?Here we have the function:
f(t) = 2/(t - 3)
To find the instantaneous rate of change at t = -1, we need to differentiate the function with respect to t, and then evaluate it at t = -1
First, the derivate of the function is:
f'(t) = df(t)/dt = (-1)*2/(t - 3)²
f'(t) = -2/(t - 3)²
Now to get the instantaneous rate of change, we evaluate the above function in t = -1 we will get:
f'(-1) = -2/(-1 - 3)² = -2/16 = -1/8
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Estimate: 18.6 X 6.5
Answer:
114
Explanation:
18.6 rounds up to 19
6.5 rounds down to 6
19 x 6 = 114
Caleb has 12 grams of tea. He bought 5/4 of
that amount for his mom. How many grams
did Cameron get his mom?
Answer: If Caleb bought 5/4 of the 12 grams of tea for his mom, we can use the following equation to find out how many grams he got his mom:
5/4 * 12 grams = (5/4) * 12 = 15 grams
So Caleb bought 15 grams of tea for his mom
Step-by-step explanation: