Answer:
The height of the plant is less than 10 centimeters if less than 3 weeks have passed.
Step-by-step explanation:
If less than 3 weeks have passed, then the value of t is less than 3. We can express this as t < 3.
Using the formula h = 3t + 1, we can substitute t < 3 to get:
h = 3t + 1 < 3(3) + 1
h < 10
in which place is the first digit of the quotient: 3,587 ÷ 18
Answer: The quotient is 199.277777778, the answer is the hundreds place
Step-by-step explanation:
199.277777778, the 1 in 199 is in the hundreds place :)
How much bigger is the 5 in 35.76 than the 5 in 26.95
The five in 35.76 is 100 times bigger than the five in 26.95.
How to compare the place values?Here we want to compare the values of the 5's in two different numbers, which are 35.76 and 26.95.
To compare them we need to compare the place value in which each five is.
To compare them, just write the numbers but replacing all the other values by zeros:
35.76 = 05.00 = 5
26.95 = 00.05 = 0.05
Now take the quotient of these two, we will get:
5/0.05 = 100
Thus, the 5 in 35.76 is 100 times bigger than the 5 in 26.95.
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jay eats 2/3 of a pizza but if dan eats 4 times that amount how much did dan eat
Answer:
Dan eat 2 2/3 of a pizza
Step-by-step explanation:
the answer is above
Let
x-----> amount of pizza Jay ate
y-----> amount of pizza Dan ate
we know that
----> equation A
-----> equation B
substitute equation A in the equation B and solve for y
Convert to mixed number
A merchant mixed 12 lb of a cinnamon tea with 3 lb of spice tea. The 15-pound mixture cost $39. A second mixture included 16 lb of the cinnamon tea and 6 lb of the spice tea. The 22-pound mixture cost $58. Find the
cost per pound of the cinnamon tea and of the spice tea.
cinnamon
spice
Answer:
Step-by-step explanation:
Let x be the cost per pound of the cinnamon tea and y be the cost per pound of the spice tea.
From the first mixture, we have:
12x + 3y = 39
From the second mixture, we have:
16x + 6y = 58
We can solve this system of equations by elimination. Multiplying the first equation by 2 and subtracting it from the second equation gives:
16x + 6y = 58
(24x + 6y = 78)
-8x = -20
Dividing both sides by -8 gives:
x = 2.5
Substituting this value of x into the first equation, we get:
12(2.5) + 3y = 39
Simplifying, we get:
30 + 3y = 39
Subtracting 30 from both sides gives:
3y = 9
Dividing both sides by 3 gives:
y = 3
Therefore, the cost per pound of the cinnamon tea is $2.50 and the cost per pound of the spice tea is $3.
change 3 5 to a decimal fraction
Answer:
7/20
its the answer to your question
1pt equal how many mL
Answer:
1 American pt equals approximately 568.261 mL
OR
1 British Imperial pt is approximately 473 mL
I recommend choosing the answer that better relates to where you are from.
Step-by-step explanation:
There seem to be TWO kinds of pint sizes. A US pint is 16 ounces and an Imperial pint is 20 ounces.
The circumference of the circle is 20 pi inches. What is the arc length of the shaded sector? Express the answer in terms of Pi. A circle. The shaded sector has an angle measure of 45 degrees. Recall that StartFraction Arc length over Circumference EndFraction = StartFraction n degrees over 360 degrees EndFraction. 2.5 pi inches 5 pi inches 7.9 pi inches 10 pi inches
The provided remark indicates that option (A) is accurate for 2.5 inches.
What length of time is an example?The measurement or size of something to end to end is referred to as its length. To put it another way, it is the bigger of the upper two or three dimensions of a geometric form or object. For instance, the length and width of a parallelogram define its measurements.
Using the given equation:
Arc Length / 20π = 45/360
Cross multiply:
Arc length × 360 = 20π x 45
Arc length x 360 = 900π
Divide both sides by 360:
Arc length = 900π / 360
Arc Length = 2.5 π inches.
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Theories have been developed about the heights of winning candidates for the US presidency and the heights of candidates who were runners-up. Listed in the table are heights from recent presidential elections. Find the correlation coefficient and the corresponding critical values assuming a 0.05 level of significance. Is there a linear correlation between the heights of candidates who won and the heights of candidates who were runners-up?
There is a significant linear correlation (r=0.80) between the heights of winning candidates and runners-up in recent US presidential elections.
Using the data from the table, here are the steps to determine the correlation coefficient and test for a linear correlation:
Calculate the correlation coefficient (r) using the formula: r = (nΣXY - ΣXΣY) / sqrt[(nΣX² - (ΣX)²)(nΣY² - (ΣY)²)], where n is the sample size, X and Y are the two variables (heights of candidates who won and runners-up), Σ denotes the sum of the values, and sqrt is the square root function.
Using a spreadsheet, we get r = 0.80.
Using the formula: df = n - 2.
The sample size (n) is 10, so df = 10 - 2 = 8.
Find the critical values of r using a table or calculator based on the degrees of freedom and the desired level of significance (0.05).
For a two-tailed test with df = 8 and α = 0.05, the critical values are ±0.632.
Since |0.80| > 0.632, we can conclude that there is a significant linear correlation between the heights of winning candidates and runners-up.
Therefore, the correlation coefficient is 0.80, and the critical values are ±0.632. There is a significant linear correlation between the heights of winning candidates and runners-up in recent presidential elections.
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How will the product change if one number is decreased by a factor of 2 and the other is decreased by a factor of 8 ?
The product is decreased by a factor of 16.
What is a factor?
In mathematics, a factor is a number or quantity that, when multiplied with another number or quantity, produces a given result. For example, in the expression 3 x 4 = 12, 3 and 4 are factors of 12. Factors can also refer to algebraic expressions, where they are the expressions that are multiplied together to obtain a larger expression.
Let's say we have two numbers, A and B, and we want to find the product of A and B.
The product of A and B is AB.
If we decrease A by a factor of 2, the new value of A becomes A/2. If we decrease B by a factor of 8, the new value of B becomes B/8.
So the new product of A/2 and B/8 is:
(A/2)(B/8) = AB/16
Therefore, the product is decreased by a factor of 16.
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help I don't understand
With the help of proportions in the given similar triangles we know that the value of x is 3.5 units.
What is triangle similarity?Euclidean geometry states that two objects are comparable if they have the same shape or the same shape as each other's mirror image.
One can be created from the other more precisely by evenly scaling, possibly with the inclusion of further translation, rotation, and reflection.
These three theorems—Angle-Angle (AA), Side-Angle-Side (SAS), and Side-Side-Side (SSS)—are reliable techniques for figuring out how similar triangles are to one another.
So, in the given situation:
TR and WY are as follows:
TR/WU
24/2
2/1
Similarly,
TS/WV
2/1
7/x
7/3.5
Therefore, with the help of proportions in the given similar triangles we know that the value of x is 3.5 units.
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FACTOR BY GROUPING
SEE ATTACHED IMAGE
SOLVE 4-6 BY STEPS 1-4
Answer:
see explanation
Step-by-step explanation:
(4)
5x³ - 10x² - 3x + 6
factor out 5x² from first 2 terms and - 3 from last 2 terms
= 5x²(x - 2) - 3(x - 2) ← factor out (x - 2) from each term
= (x - 2)(5x² - 3)
----------------------------------------------------
(5)
9a³ - 45a² - 7a + 35
factor out 9a² from first 2 terms and - 7 from last 2 terms
= 9a²(a - 5) - 7(a - 5) ← factor out (a - 5) from each term
= (a - 5)(9a² - 7)
-----------------------------------------------------
(6)
5x²y - 15y - 2x² + 6
factor out 5y from the first 2 terms and - 2 from the last 2 terms
= 5y(x² - 3) - 2(x² - 3) ← factor out (x² - 3) from each term
= (x² - 3)(5y - 2)
Oliver spots an airplane on radar that is currently approaching in a straight line, and
that will fly directly overhead. The plane maintains a constant altitude of 6900 feet.
Oliver initially measures an angle of elevation of 16° to the plane at point A. At some
later time, he measures an angle of elevation of 27° to the plane at point B. Find the
distance the plane traveled from point A to point B. Round your answer to the
nearest tenth of a foot if necessary.
The distance the plane traveled from point A to point B is approximately 8.15 miles or 43056 feet (rounded to the nearest tenth of a foot).
What are angles?An angle is a geometric figure formed by two rays, called the sides of the angle, that share a common endpoint, called the vertex of the angle. Angles are typically measured in degrees or radians, and they are used to describe the amount of rotation or turning between two lines or planes. In a two-dimensional plane, angles are usually measured as the amount of rotation required to move one line or plane to coincide with the other line or plane.
Let's first draw a diagram to visualize the problem:
/ |
/ |
/ |P (plane)
/ |
/ |
/ | h = 6900 ft
/
/ θ2. |
/ |
/ |
B ___/θ1__ _|___ A
d
We need to find the distance the plane traveled from point A to point B, which we'll call d. We can use trigonometry to solve for d.
From point A, we have an angle of elevation of 16° to the plane. This means that the angle between the horizontal and the line from point A to the plane is 90° - 16° = 74°. Similarly, from point B, we have an angle of elevation of 27° to the plane, so the angle between the horizontal and the line from point B to the plane is 90° - 27° = 63°.
Let's use the tangent function to solve for d:
x = h / tan(74°) = 19906.5 ft
d - x = h / tan(63°) = 23205.2 ft
So,
d = x + h / tan(63°) ≈ 43111.7 ft ≈ 8.15 miles.
Therefore, the distance the plane travelled from point A to point B is approximately 8.15 miles or 43056 feet (rounded to the nearest tenth of a foot).
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If triangle ABC has points A(2, -4) B(-3, 1) C(-2, -6) and you perform the following transformations, where will B' be?
Reflection over the y-axis, rotation 90° clockwise, and translation (x + 2, y - 1)
The coordinates of B' after the sequence of transformations are given as follows:
B'(3,-4).
How to obtain the coordinates of B'?The coordinates of B are given as follows:
B(-3,1).
After a reflection over the y-axis, the x-coordinate of B is exchanged, hence:
B'(3, 1).
The rule for a 90º clockwise rotation is that (x,y) becomes (y,-x), hence the coordinates of B' after the 90º clockwise rotation are given as follows:
B'(1, -3).
The translation (x + 2, y - 1) means that 2 is added to the x-coordinate while 1 is subtracted from the y-coordinate, hence the final coordinates of B' are given as follows:
B'(3,-4).
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If triangle ABC has points A(2, -4), B(-3, 1), and C(-2, -6) and you perform the following transformations, B' would be at B' (3, -4).
What is a rotation?In Geometry, the rotation of a point 90° about the center (origin) in a clockwise direction would produce a point that has these coordinates (y, -x).
By applying a reflection over the y-axis to the coordinate of the given point B (-3, 1), we have the following coordinates:
Coordinate B = (-3, 1) → Coordinate B' = (-(-3), 1) = (-3, 1).
Next, we would apply a rotation of 90° clockwise as follows;
(x, y) → (y, -x)
Coordinate B' = (-3, 1) → Coordinate B' = (1, (-3)) = (1, 3)
Finally, we would apply a translation (x + 2, y - 1) as follows:
Coordinate B' = (1, 3) → (1 + 2, 3 - 1) = B' (3, 2).
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If Planet I is 31.1 million miles farther from the sun than Planet II, then Planet III is 24.6 million miles farther from the sun than Planet I. When the total of the distances for these three planets from the sun is 197.8
million miles, how far away from the sun is Planet II?
After solving the equations e know that Planet II is 35 million miles away from the sun.
What are equations?The equals sign is a symbol used in mathematical formulas to denote the equality of two expressions.
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, let x be the separation between planet I and the sun.
Planet II's distance from the sun is x-30.2.
Planet iii's distance from the sun is equal to x+24.8.
x + x-30.2 + x+24.8 = 190.2
Mix related phrases to find x.
3x - 5.4 = 190.2
3x = 195.6
x = 65.2
65.2 million miles separate planet I from the sun.
Planet II is 35 million miles from the sun or 65.2-30.2.
Planet iii is 90 million miles from the sun (65.2 + 24.8 = miles).
Therefore, after solving the equations e know that Planet II is 35 million miles away from the sun.
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A plane rises from take-off and flies at an angle of 15° with the horizontal runway. Find the
distance that the plane has flown when it has reached an altitude of 300 feet. Round your answer
the nearest whole number.
As we are looking for the distance to the nearest whole number, we can round this answer to 517 feet. This means that when the plane has reached an altitude of 300 feet, it has flown a distance of 517 feet.
To find the distance that the plane has flown when it has reached an altitude of 300 feet, we can use the formula d = x * tan(a) where d is the distance, x is the altitude, and a is the angle. We are given the altitude of 300 feet and the angle of 15°. Plugging those values into the formula, we get d = 300 * tan(15°) = 517.4 feet. Rounding this to the nearest whole number, we get 517 feet.
To find the distance that the plane has flown when it has reached an altitude of 300 feet, we can use the formula d = x * tan(a). This equation is derived from the Pythagorean Theorem, where d is the distance, x is the altitude, and a is the angle. We are given the altitude of 300 feet and the angle of 15°, so we can plug these values into the equation. When we do this, we get d = 300 * tan(15°) = 517.4 feet. As we are looking for the distance to the nearest whole number, we can round this answer to 517 feet. This means that when the plane has reached an altitude of 300 feet, it has flown a distance of 517 feet.
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Write the letter of the definition next to the matching word as you work through the lesson.
The matching word are as follows:- center of dilation - C,corresponding angles - D,dilation - E,scale factor (of a dilation) - A,similar polygons - B respectively.
What are corresponding angles?Corresponding angles are a pair of angles that have the same relative position at the intersection of two lines when one line is crossed by a transversal.
They are located in corresponding (matching) positions in congruent or similar figures, and are congruent if the figures are similar.
center of dilation: C.The fixed point that is parallel to each point on the pre-image and the corresponding point on the picture during a dilatation
corresponding angles: D.a pair of angles in two congruent or similar figures that are in the same relative position
dilation: E. The transformation in which each point on the image lies on the same line as the corresponding point on pre-image and a fixed point called the center of dilation.
scale factor (of a dilation): in a dilation, the constant rate between the distance from the center of dilation and a point on the image and the distance from the center of dilation and the matching point on thepre-image
similar polygons: B.two or further polygons in which corresponding angles are harmonious and the lengths of corresponding sides are in proportion.
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4) It has been known that 18% of victims of financial fraud know the perpetrator of the fraud
personally. If a sample of 156 people were victims of fraud, what is the mean number of those
victims that know the perpetrator of the fraud personally?
Answer:
If 18% of victims of financial fraud know the perpetrator of the fraud personally, and a sample of 156 people were victims of fraud, we can find the mean number of those victims that know the perpetrator by multiplying the sample size by the percentage. Therefore, the mean number of victims that know the perpetrator is 156 x 0.18 = 28.08. However, since we cannot have a fraction of a person, we can round the answer to the nearest whole number. Therefore, the mean number of victims that know the perpetrator is 28.
If I get paid $12.50 an hour and I worked a total of 15 hours and 35 minutes how much did I make?
Answer: $194.79
Step-by-step explanation:
It is easiest to approach this question in two parts.
First part is simple - multiply the wage per hour times the number of whole number you have worked. ($12.50)(15) = $187.50
Next you need to find how much you make in 35 minutes at a wage rate of 12.50 an hour. You can set up a ratio to find this out -
($12.50) | (60 min) - (x dollars) | (35 min)
then cross multiply and divide - (12.5 * 35) / 60 = 7.291
This means you make $7.29 for 35 minutes of work.
$187.50 + $7.29 = $194.79 for 15 hours 35 minutes of work.
(this is based on a per minute/hour scale)
The radius of a circle is 11 meters. What is the circle's circumference?
Use 3.14 for л.
r=11 m
Answer:
The formula for the circumference of a circle is C = 2πr, where r is the radius of the circle and π (pi) is a mathematical constant approximately equal to 3.14.
Substituting the given value of r=11 m and using π = 3.14, we get:
C = 2πr
C = 2 x 3.14 x 11 m
C = 69.08 m
Therefore, the circumference of the circle is 69.08 meters
Christy is training for a race in the summer. Every day she jogs the same number of miles. She also rides her bicycle 7.5 miles each day. During a 5-day training period, she jogs and rides a total of 53 miles. How many miles does Christy jog each day during training? Explain how you solved the problem.
5 miles each day so 5×7=35 miles a week
Let a and b be real numbers, where Which of the following functions could represent the graph on the right? f(x) = x (x – a)(x – b)2 f(x) = (x – a)(x – b)2 f(x) = x(x – a)³(x – b) f(x) = x2(x – a) 2(x – b)2
Answer:
Without a graph provided, it's difficult to determine which of the given functions represents the graph on the right. However, we can analyze each function to see if it has any characteristics that match the shape of the graph.
f(x) = x(x – a)(x – b)2
This function has one x-intercept at x = 0 and a double root at x = b. If b > a, then the function will have a local maximum at x = a and a local minimum at x = b. This function may represent a graph with a single x-intercept, a double root, and a local maximum and minimum.
f(x) = (x – a)(x – b)2
This function has one x-intercept at x = a and a triple root at x = b. If b > a, then the function will have a local minimum at x = a and a local maximum at x = b. This function may represent a graph with a single x-intercept, a triple root, and a local minimum and maximum.
f(x) = x(x – a)³(x – b)
This function has one x-intercept at x = 0 and a triple root at x = a. If a < b, then the function will have a local minimum at x = b. This function may represent a graph with a single x-intercept, a triple root, and a local minimum.
f(x) = x²(x – a)²(x – b)²
This function has two x-intercepts at x = 0 and x = a and a double root at x = b. If b > a, then the function will have a local maximum at x = a and a local minimum at x = b. This function may represent a graph with two x-intercepts, a double root, and a local minimum and maximum.
Based on these analyses, it's unclear which function represents the graph on the right, as all four functions have characteristics that could match the shape of the graph.
Answer:
It's A
Step-by-step explanation:
2023 edge
yw
which expression is equivalent to the following 3( 8x - 2y + 7 )
Answer:
24x - 6y + 21
Step-by-step explanation:
3( 8x - 2y + 7 )
Multiply each term in the bracket by 3
= (3 x 8x) - ( 3 x 2y) + (3 x 7)
= 24x - 6y + 21
Please help, I got this and I don’t know it
By rewritting the exponential equation, we can see that the correct options are B and C.
Which equations show Nelson's balance after t years?We know that the balance is modeled by the exponential equation below:
[tex]A = 328.23\times e^{0.045*(t - 2)}[/tex]
Now we want to see which of the other equations are equivalent to this one, so we need to rewrite this equation, so let's do that.
First we can rewrite the second part to get:
[tex]A = 328.23\times e^{0.045\times(t - 2)}\\\\A = 328.23\times(e^{-2*0.045*}\times e^{0.045\times t})\\\\A = 300\times e^{0.045\times t}[/tex]
So that is an equivalent equation.
We also can keep rewritting this to get:
[tex]A = 300\times e^{0.045\times t}\\\\A = 300\times(e^{0.045})^t\\\\A = 300\times(1.046)^t[/tex]
The correct options are B and C.
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Angles M, N, and P are supplementary.
What is the measure of angle P?
60°
34°
45°
36°
Step-by-step explanation:
The measure of angle p is 60°
help! find the area of the trapezoid using 30-60-90 special right triangles theorem
AFE triangle,
FE= 6cos60
= 3
dc= 3
ae= 6sin60
= 3*squareroot3
Area= 1/2(10+4)*3*squareroot3
= 7*3*squareroot3
= 21*squareroot3
= 21*1.73
= 36.33square units
Help with number 4!!!
Answer:forgot the explanation
Step-by-step explanation: give me a equation to solve
What is the value of the angle?
The angle indicated by a green arc is 54 degrees.
What is the definition of a simple angle?A straight line's angle size is 180°; the sum of the angles in a triangle's size is 180°; and a triangle can also have acute as well as obtuse angles.
The fact that the sum of the angles in a triangle equals 180 degrees can be used to determine the value of the angle in the given figure.
To begin, note that the angle denoted by a blue arc is the exterior angle of triangle ACD. According to the Exterior Angle Theorem, this angle is equal to the sum of the two remote interior angles, denoted by red and green arcs.
So we have:
The blue arc angle is equal to the sum of the red and green arc angles.
We get the following equation when we plug in the given angle measurements:
98° = 44° + Green arc angle
We can simplify this equation as follows:
Green arc angle = 98° - 44° = 54°
The green arc represents an interior angle of triangle ABD. As a result, we can use the fact that the sum of a triangle's angles equals 180 degrees to calculate the value of this angle.
We currently have:
Green arc angle + 70° + 56° = 180°
We get the following by substituting the value we found for the green arc angle:
54° + 70° + 56° = 180°
We can simplify this equation as follows:
180° - 70° - 56° = 54°
As a result, the angle indicated by a green arc has the value:
It is 54 degrees outside.
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when interest is compounded n times a year, the accumalated amount(A) after t years.approximately how long will take $2000.00 to double at an annual rate of 5.25% compounded monyhly?
Therefore, it will take approximately 13.47 years for $2000.00 to double at an annual rate of 5.25% compounded monthly.
What is percent?Percent is a way of expressing a number as a fraction of 100. The symbol for percent is "%". Percentages are used in many different contexts, such as finance, economics, statistics, and everyday life. Percentages can also be used to express change or growth, such as an increase or decrease in the value of something over time.
Here,
The formula for the accumulated amount (A) when interest is compounded n times per year at an annual interest rate of r, for t years, is:
[tex]A = P(1 +\frac{r}{n})^{nt}[/tex]
where P is the principal amount (initial investment).
To find approximately how long it will take $2000.00 to double at an annual rate of 5.25% compounded monthly, we need to solve for t in the above formula.
Let P = $2000.00, r = 0.0525 (5.25% expressed as a decimal), and n = 12 (monthly compounding).
Then, we have:
[tex]2P = P(1 +\frac{r}{n})^{nt}[/tex]
Dividing both sides by P, we get:
[tex]2= (1 +\frac{r}{n})^{nt}[/tex]
Taking the natural logarithm of both sides, we get:
[tex]ln(2) =ln(1 +\frac{r}{n})^{nt}[/tex]
Using the properties of logarithms, we can simplify this expression as:
[tex]ln(2) = n*t * ln(1 + r/n)[/tex]
Dividing both sides by n*ln(1 + r/n), we get:
[tex]t = ln(2) / (n * ln(1 + r/n))[/tex]
Plugging in the values for r and n, we get:
[tex]t = ln(2) / (12 * ln(1 + 0.0525/12))[/tex]
Solving this expression on a calculator, we get:
t ≈ 13.47 years
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The diagram below represents how rock is affected when water enters cracks in rock, freezes, and becomes ice.
Which geologic process is represented in the diagram?
Answer: Physical weathering, more specifically, ice wedging
Step-by-step explanation:
:D
A standard die is rolled. Find the probability that the number rolled is greater than 3
. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
Rolling a number higher than 3 has a 2/6 or 1/3 chance of happening. Another way to say this is to round a decimal to the closest millionth, which is [tex]0.333333[/tex] .
What is the fraction in the lowest terms?A standard die has 6 sides, labelled with the numbers 1 through 6. When the die is rolled, each side has an equal probability of landing face up.
Since we want to find the probability of rolling a number greater than 3, we need to determine the number of outcomes that satisfy this condition and divide it by the total number of possible outcomes.
When you roll a standard die, there are six equally likely outcomes: 1, 2, 3, 4, 5, and 6. Since we want to find the probability of rolling a number greater than 3, we need to count how many of these outcomes satisfy that condition.
Therefore, the probability of rolling a number greater than 3 is 2/6 or 1/3. Alternatively, we could express this as a decimal rounded to the nearest millionth, which would be [tex]0.333333[/tex] .
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