The quantity of water in milliliters left in the water bottle after pouring 400 milliliters of water in glass is 4100 milliliters.
Milliliter is the smaller unit of quantity in the SI unit. One liter is equal to thousand times of one milliliter. It is given that the bottle contains 4.5 liters of water which means there is 4500 milliliters of water in it. Since Kevin pours 400 milliliters of water in the glass, this means 400 milliliters was emptied from the water bottle and hence the remaining amount can be calculated by subtracting the amount of water taken out from the bottle from the total amount.
Therefore the arithmetic equation will be as follows:
Amount of water left in bottle = Total quantity of water in the bottle - Water emptied out
Amount of water left in bottle = 4500 - 400 = 4100 milliliters
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someone help me simplify pls
Answer:
10^0
Step-by-step explanation:
Anything that has a exponent of 0 will always equal 1 therefore if 10^-3/10^-3 it will equal 1 so they both are 1
Answer: A 10^0
10^-3 is 0.001. 0.001 divided into 0.001 is 1.
A- 10^0 is 1 so this correct.
B- 10^-6 is 1.0e-6, so this is incorrect.
C-10^1 is 10, so this is incorrect.
D.10^6 is 1000000, so this is incorrect.
After solving our equation 10^-3/ 10^-3, we have concluded that that answer is 1, meaning that answer choice A, 10^0 is our correct answer.
Notes- ^ means to the power of, which is an exponent.
I hope this helped & Good Luck <3!!!!
two kinds of pine trees, bristlecone and aleppo, are planted in rows. in each row, the ratio of bristlecone to aleppo is 10:910:9. altogether, 600600 bristlecone pine trees are planted.how many aleppo pines are planted?
There are 288 Aleppo pines are planted in each ratio.
First, let's determine the total number of pine trees in each row. Since the ratio is 10 : 9, that means that for every 10 bristlecone pine trees planted, 9 Aleppo pine trees were planted. Therefore,
10 bristlecone pine trees + 9 Aleppo pine trees = 19 pine trees in each row.
Next, we need to determine how many rows of pine trees were planted. Since 600 bristlecone pine trees were planted, we can divide 600 by 19 to determine the number of rows.
600 ÷ 19 = 31.578947368421
Therefore, there were 32 rows of pine trees planted.
Now, we need to calculate how many Aleppo pine trees were planted. Since we know that for every 10 bristlecone pine trees planted, 9 Aleppo pine trees were planted,
So, the number of Aleppo pine trees planted.
32 x 9 = 288
Therefore, 288 Aleppo pine trees were planted.
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If f (x)=5x^3−44x^2 −13+36f(x)=5x 3 −44x 2 −13x+36 and x−9 is a factor of f (x), then find all of the zeros of f (x) algebraically.
On solving the above question, As a result, the polynomials f(x) zeros are x = 9 and x = 44/5.
what are polynomials?A polynomial is a mathematical statement composed of coefficients and variance that exclusively uses additions, subtractions, operations such as addition, and nonzero powers of variables. The form x2 4x + 7 indicates a single determinate x algebraic. A polynomial expression in mathematics is made up of determinants (also known as freshly made) and polynomials that may be multiplied, subtracted, repeated, and raised through negative integer ones of – anti. A polynomial is an algebraic statement that includes variables and coefficients. An expression can really only incorporate the operations addition, deletion, duplication, and non-negative integer factors. These expressions are referred to as polynomials.
If x - 9 is a factor of f(x), we get:
f(x) = (x - 9)g(x) (x)
g(x) denotes a polynomial.
When we plug this into the supplied f(x) equation, we get:
5x^3 - 44x^2 - 13x + 36 = (x - 9)g (x)
Using polynomial long division to expand the right side, we get:
x(g(x)) = 5x3 - 44x2 - 13x + 36 - 9g(x) (x)
When we multiply the coefficients of similar terms on both sides, we get:
5 = g(x) (x)
-44 = g'(x) (x)
-13 = g''(x) (x)
36 = -9g''(x) (x)
When we solve these equations, we get:
5 g'(x) = -44 g"(x) = -13/2 g"'(x) = -12
Hence, g(x) is a constant function, and g'(x) = -44 suggests that x = 44/5 is the sole real root of g(x).
As a result, the f(x) zeros are x = 9 and x = 44/5.
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Find the measure of each angle a positive angle measure, a negative angle measure, and an angle measure that is greater 360 degrees.
Help with the 3 problems attached, please. :)
This is an Angles and Coordinate Systems problem.
6)
7)
Positive angle measure: 410°Negative angle measure: -310°Angle measure greater than 360°: 770°.8)
Positive angle measure: 660°Negative angle measure: -660°Angle measure greater than 360 degrees: 1020°.What is Positive Angle Measure and Negative angle measure?Positive angle measure is measured counterclockwise and negative angle measure is measured clockwise. These concepts are used in navigation, engineering, and physics.
6)
An angle of 40 degrees measured out in the upper left quadrant will have its initial side along the positive x-axis and its terminal side in the upper left quadrant, making it a counter-clockwise angle.
-(360° - 40°) = -320°
So the angle of 40 degrees is equivalent to a negative angle measure of -320 degrees.
320° + 360° = 680°
So the angle of 40 degrees is equivalent to an angle measure of 680 degrees.
7)
To convert the angle measure of 50 degrees in the lower right quadrant to a positive angle measure, we add 360 degrees to it since one full revolution around the coordinate system is equal to 360 degrees.
To convert the angle measure to a negative angle measure, we subtract it from 360 degrees, since a negative angle is measured in the clockwise direction.
Negative angle measure: 360 degrees - 50 degrees = -310 degreesTo find an angle measure that is greater than 360 degrees, we simply add 360 degrees to the positive angle measure.
Angle measure greater than 360 degrees: 410 degrees + 360 degrees = 770 degrees.8)
The angle 60 degrees measured in the lower right quadrant in a counter-clockwise direction is equivalent to the angle 360 degrees - 60 degrees = 300 degrees measured in the upper right quadrant in a counter-clockwise direction.
To convert the angle measure of 300 degrees to a positive angle measure, we add 360 degrees to it since one full revolution around the coordinate system is equal to 360 degrees.
Positive angle measure: 300 degrees + 360 degrees = 660 degreesTo convert the angle measure to a negative angle measure, we simply add a negative sign to the positive angle measure.
Negative angle measure: -660 degreesTo find an angle measure that is greater than 360 degrees, we simply add 360 degrees to the positive angle measure.
Angle measure greater than 360 degrees: 660 degrees + 360 degrees = 1020 degrees.Learn more about Angles and Coordinate Systems:
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I really need some help please
The solution of the absolute inequality is as follows:
x < 22 / 5 or x > 6 / 5
How to solve absolute inequalities?The absolute inequalities can be solved as follows:
An absolute value inequality is an inequality that has an absolute value sign with a variable inside, modulus of a complex number.
Therefore,
|14 - 5x| > 8
let's find x as follows:
|14 - 5x| > 8
14 - 5x > 8 or 14 - 5x < - 8
-5x > 8 - 14 or - 5x < - 8 - 14
-5x > -6 or - 5x < - 22
Therefore,
x > 6 / 5 or x < 22 / 5
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NEED HELP WITH ALL QUESTIONS! Find x for all of them.
The value of x for all the figures are given below respectively.
What is trigonometry?The branch of mathematics that studies the relationships between the sides and angles of triangles is known as Trigonometry.
1. In given figure base = 5 and hypotenuse = 10 .
to find x i.e height we will use trigonometry-
tan 60° = x/5
√3 = x/5
5√3=x
Therefore, the value of x is 5√3.
2. In given figure base = 1 and height = √3 and angle given is 60°.
to find x i.e hypotenuse we will use trigonometry-
sin 60° = √3/x
√3/2 = √3/x
x = √3×2/ √3
x = 2
Therefore ,value of x is 2.
3. In given figure base = 3 and hypotenuse = 6 .
to find x i.e height we will use trigonometry-
tan 60° = x/3
√3 = x/3
3√3 = x
Therefore,value of x is 3√3.
4. In given figure base = 1 and height = 1 and angle given is 45°.
to find x i.e hypotenuse we will use trigonometry-
sin 45° = 1/x
1/√2 = 1/x
x = √2
Therefore ,value of x is √2.
5. In given figure height = 4√2 and angle given is 45°.
to find x i.e hypotenuse we will use trigonometry-
sin 45° = 4√2/x
1/√2 = 4√2/x
x = 4√2 × √2
x = 8
Therefore,value of x is 6.
6. In given figure hypotenuse = 10 and angle given is 45°.
to find x i.e base we will use trigonometry-
cos 45° = x/10
1/√2 = x/10
10/√2 = x
Therefore,value of x is 10/√2.
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Make a table of ordered pairs for the equation
Y= - 1/3x + 1
In this equation, the ordered pairings are (0, 1), (3, 0), (6, -1), and (9, -2).
What are equations used for?A mathematical equation is a statement that two amounts and values are equal, such as 6 x 4 = 12 x 2. 2. A noun that counts. When two or more components must be taken into account simultaneously in order to comprehend or describe the overall situation, this is known as an equation.
We may select several values of x and enter them into the equation to get the associated values of y to create a table of tuple for the solution y = (-1/3)x + 1:
x y = (-1/3)x + 1
0 1
3 0
6 -1
9 -2
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In this equatiοn, the οrdered pairings are (0, 1), (3, 0), (6, -1), and (9, -2).
What are equatiοns used fοr?A mathematical equatiοn, like 6 + 4 = 12, states that twο amοunts and values are equal. An equatiοn is when twο οr mοre cοmpοnents must be cοnsidered simultaneοusly in οrder tο cοmprehend οr describe the οverall situatiοn.
We may select several values οf x and enter them intο the equatiοn tο get the assοciated values οf y tο create a table οf tuple fοr the sοlutiοn y = (-1/3)x + 1:
x y = (-1/3)x + 1
0 1
3 0
6 -1
9 -2
Therefοre, In this equatiοn, the οrdered pairings are (0, 1), (3, 0), (6, -1), and (9, -2).
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Solve the following inequality. Please put it in sl 4y>12x-48
The inequality expression 4y > 12x - 48 when evaluated is y > 3x - 12
How to evaluate the inequalityFrom the question, we have the following parameters that can be used in our computation:
4y>12x-48
Express properly
4y > 12x - 48
Multiply 1/4 to both sides of the inequality
So, we have the following representation
1/4 * 4y > 12x * 1/4 - 48 * 1/4
Evaluate the products
y > 3x - 12
Hence, the solution is y > 3x - 12
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An instructor has given a short quiz consisting of two parts. For a randomly selected student, let X = the number of points earned on the first part and Y = the number of points earned on the second part. Suppose that the joint pmf of X and Y is given in the accompanying table.
y
p(x, y)
0 5 10 15
x 0 0. 03 0. 06 0. 02 0. 10
5 0. 04 0. 15 0. 20 0. 10
10 0. 01 0. 15 0. 13 0. 01
(a) Compute the covariance for X and Y. (Round your answer to two decimal places. )
Cov(X, Y) =
(b) Compute rho for X and Y. (Round your answer to two decimal places. )
rho =
(a) The covariance for X and Y Cov(X, Y) = -1.05
(b) The correlation number (rho) is rho = Cov(X, Y)/(X, Y) = -1.05/(5).
The expected values of X and Y must first be determined in order to find the covariance and correlation coefficient for X and Y.
The amount of X is anticipated to be:
(a) E(X) = xP(X=x) = (0.03) + (5) (0.04 + 0.15 + 0.01) + (10) (0.06 + 0.20 + 0.15 + 0.13) + (15) (0.02 + 0.10 + 0.01) = 8.4
E(Y) = yP(Y=y) = (0.05) + (5) (0.04 + 0.01) + (10) (0.06 + 0.15 + 0.15) + (15) (0.02 + 0.20 + 0.13 + 0.01) = 10.5
X and Y's correlation is:
Cov(X, Y) = XY - XE (Y)
Each number of X and Y must be multiplied by their combined probability before the products are added to determine E(XY):
(0)(0)(0.05) + (0)(5)(0.03) + (0)(10)(0.06 + 0.01) + (0)(15)(0.02) + (5)(0)(0.04) + (5)(5)(0.15) + (5)(10)(0.20) + (5)(15)(0.10) + (10)(0)(0.01) + (10)(5)(0.15) + (10)(10)(0.13) + (10)(15)(0.01) + (15)(0)(0.02) + (15)(5)(0.10)
Therefore: Cov(X, Y)=E(XY)-E(X)E(Y) =119.25-(8.4)(10.5) = -1.05
As a result, X and Y have a correlation of -1.05.
(b) The standard errors of X and Y must also be computed in order to determine the correlation coefficient:
sqrt(Var(X)) = sqrt(E(X) - [E(X)]) = sqrt((0^2)(0.03) + (5^2)(0.04 + 0.15 + 0.01) + (10^2)(0.06 + 0.20 + 0.15 + 0.13) + (15^2)(0.02 + 0.10 + 0.01) - (8.4)^2) ≈ 5.23
The expression "_Y = sqrt(Var(Y)) = sqrt(E(Y)2 - [E(Y)]2)" = sqrt((0^2)(0.05) + (5^2)(0.04 + 0.01) + (10^2)(0.06 + 0.15 + 0.15) + (15^2)(0.02 + 0.20 + 0.13 + 0.01) - (10.5)^2) ≈ 5.07
The correlation number (rho) is rho = Cov(X, Y)/(X, Y) = -1.05/(5).
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A workman has two pieces of wire, each of length 26 m. One is a piece to be bent into a square. The other piece is to be bent into a rectangle whose width is 3 m shorter than its length
a)Hence the side of the square = 15.5 m
b)Hence the length of the rectangle is 8m and the width is 5m.
c)Hence the rectangle is greater than the square.
a)
The length of each wire =26m
To bend it into a square it has to be bent into four parts = [tex]\frac{26}{4}[/tex] = 5.15m
Hence the side of the square = 15.5 m
b)
A rectangle whose width is 3 m shorter than its length,
let the length of the rectangle = l
And the width of the rectangle h= l-3,
now,
2(l+l-3)=26
4l-6=26
4l=32
l=8m
h=8-3=5
Hence the length of the rectangle is 8m and the width is 5m.
c)
The area of the square= 5.15²=26.52 sq cm
The area of the rectangle = 8*5=40 sq cm
Hence the rectangle is greater than the square.
The complete question is-
A workman has two pieces of wire, each of
length 26 m. One piece is to be bent into a
square. The other piece is to be bent into a
rectangle whose width is 3 m shorter than its
length.
(a) What is the length of a side of the square?
(b) What are the dimensions of the rectangle?
(c) Which shape has the greater area?
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What is the positive solution to 2x^2−9x−5
2x²-9x-5
2x²-x-10x-5
(x-5)(2x+1)
What is the equation of the line that passes through the point (-6, -4) and has a slope of 1/3
Answer:
y = 1/3x - 2
Step-by-step explanation:
The equation is y = mx + b
m = the slope
b = y-intercept
We know
m = 1/3
Y-intercept is located at (0, -2)
So, the equation is y = 1/3x - 2
The six balls can also fit exactly into a closed cylindrical container, as shown in the diagram. Find (i) the volume of the cylindrical container, Answer(c)(i) (ii) the volume of the cylindrical container not occupied by the balls, Answer(c)(ii) ‒‒‒‒‒‒‒‒‒‒‒‒‒‒ (iii) the surface area of the cylindrical container. 3 cm [3] cm³ [1]
The volume of the container is 127.23 cubic cm
The volume not occupied is 42.41 cubic cmThe surface area is 183.78 square cmThe volume of the containerThe given parameters are
Number of balls = 6
Height of ball = 3 cm
This means that
Height of cylinder, h = 6 * 3 cm = 18 cm
Radius of cylinder, r = 3/2 cm = 1.5 cm
So, we have
Volume = πr²h
Volume = π * 1.5² * 18
Volume = 127.23
The volume not occupied by ballsThe volume of a ball is
Ball = 4/3πr³
For 6 balls, we have
Balls = 6 * 4/3πr³
Balls = 8πr³
So, we have
Balls = 8π * 1.5³
Balls = 84.82
So, the unoccupied space is
Space = 127.23 - 84.82
Space = 42.41
The surface area of the cylindrical containerThis is calculated as
Area = 2πrh + 2πr²
So, we have
Area = 2π * 1.5 * 18 + 2π * 1.5²
Area = 183.78
Hence, the surface area is 183.78 square cm
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There are three colors of marbles in the
bag: red, green, and purple. There are
4 green marbles in the bag. What is the
probability of Carol picking a purple
marble and, without replacing this marble,
then picking a green marble?
The expression for the probability of picking a purple marble and then a green marble without replacement is: P(P and G') = (p / (4 + p + r)) * (3 / (3 + r))
Let's denote the event of picking a purple marble by P and the event of picking a green marble after a purple marble has been picked by G'. Since we do not replace the marble after the first pick, the probability of picking a purple marble is the proportion of purple marbles in the bag. Let's assume that there are r red marbles, g green marbles (including the 4 already picked), and p purple marbles. Then the total number of marbles in the bag is r + g + p.
Since we know that there are 4 green marbles already in the bag, the total number of marbles in the bag is g + p + r = 4 + p + r. We can use this equation to eliminate g from the probability calculation.
The probability of picking a purple marble is:
P(P) = p / (4 + p + r)
After a purple marble is picked, the total number of marbles in the bag is 4 + r. The probability of picking a green marble from this reduced bag is:
P(G' | P) = (4 - 1) / (4 + r - 1) = 3 / (3 + r)
The probability of both events occurring is the product of their probabilities:
P(P and G') = P(P) * P(G' | P) = (p / (4 + p + r)) * (3 / (3 + r))
We don't have enough information to determine the values of p and r, so we cannot calculate the exact probability. However, we can give an expression for the probability in terms of p and r.
As a final step, we can check that our expression for the probability satisfies some common-sense constraints. The probability should be between 0 and 1, and it should increase as the number of purple marbles increases (since this makes it more likely to pick a purple marble) and decrease as the number of red marbles increases (since this makes it less likely to pick a green marble after a purple one has been picked).
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4.
Use Synthetic Division To Solve.
(x3-3x2-7x+6) / (x-2)
A. x2+x+9+ 12 /x-2
B. x2+5x+3+ 12 / x-2
C. x2-5x+3
D. x2-x-9-12/x-2
Answer:
D. x^2-x-9-12/x-2
Step-by-step explanation:
We can use synthetic division to divide (x^3 - 3x^2 - 7x + 6) by (x - 2). First, we set up the division as follows:
2 | 1 -3 -7 6
|______2___-2__-18
| 1 -1 -9 -12
The numbers on the bottom row of the synthetic division table represent the coefficients of the quotient polynomial. Therefore, the quotient is x^2 - x - 9, and the remainder is -12.
So, we have:
(x^3 - 3x^2 - 7x + 6) / (x - 2) = x^2 - x - 9 + (-12 / x - 2)
Therefore, the correct option is D: x^2 - x - 9 - 12/(x - 2).
A random sample of students was surveyed and asked to list their grade level and what movie genre they prefer. Results are shown in the table below.
Movie Genre
Superhero Comedy Drama
6th grade 17 11 10
7th Grade 16 17 13
8th Grade 15 15 13
What percent of the 6th graders prefer superhero movies? Round your answer to the nearest whole number percent.
Answer:
28%
Step-by-step explanation:
Answer: 45% of the 6th graders surveyed prefer superhero movies.
Step-by-step explanation:
To find the percentage of 6th graders who prefer superhero movies, we need to divide the number of 6th graders who prefer superhero movies by the total number of 6th graders, and then multiply by 100 to get a percentage.
According to the table, there are 17 6th graders who prefer superhero movies. The total number of 6th graders is:
10 + 11 + 17 = 38
Therefore, the percentage of 6th graders who prefer superhero movies is:
(17 / 38) x 100% = 44.74%
Rounded to the nearest whole number percent, the answer is:
45%
So approximately 45% of the 6th graders surveyed prefer superhero movies.
what is 30.7% of 520
Answer:
159.64
Step-by-step explanation:
30.7% / 100 = 0.307 then you would do
0.307 x 520 = 159.64
An arc subtends an angle of 86 at the cir- cumference of a circle whose radius is 8 cm. Find the length of the are to the near- est whole number. (Take = 3.14) (Hint: an angle at the centre = 2x the angle at the circumference).
Answer:
We can use the formula for the length of an arc of a circle, which is:
length of arc = (angle/360) × 2πr
where angle is the angle subtended by the arc at the center of the circle, r is the radius of the circle, and π is approximately 3.14.
In this problem, the angle subtended by the arc at the circumference of the circle is 86 degrees. Since the radius of the circle is 8 cm, the diameter is 2 × 8 = 16 cm, and the circumference is 2πr = 2π(8) = 16π cm.
Using the hint given in the problem, we can find the angle subtended by the arc at the center of the circle:
angle at center = 2 × angle at circumference
= 2 × 86
= 172 degrees
Substituting into the formula, we have:
length of arc = (172/360) × 2π(8)
≈ 7.5 cm
Rounding to the nearest whole number, the length of the arc is 8 cm.
The graph below represents the solution set of which inequality?
+
-5-4-3-2-1 0 1 2 3 4 5 x
Ox²-2x-8 <0
Ox²+2x-8 <0
Ox²-2x-8>0
Ox²+2x-8>0
Answer:
x^2-2x-8<0
Step-by-step explanation:
It is difficult visualizing the expressions, so lets change them to equations by substituting a "y" in place of the 0 of the inequality. This will allow us to graph the expressions. Then if we focus on only the y=0 line in the graph, we can find the correct inequality.
All four expressions are graphed with this substitution and included on the attached worksheet. Note the marked their marked differences. The two points on the given number line (-4,0) and (2,0) are marked on each graph.
What we should focus on first is which graphs actually intersect the two end values of x given on the number line: -4 and 2. Since we used y instead of "0" in the expressions, we are seeing everything, for all values of x. But what we really want are -4 and 2, which we can mark with (-4,0) and (2,0).
Only two graphs intersect (-4,0) and (2,0): the first and third (lower left). The first (x^2-2x-8<y) has the interior of the parabola colored blue - these are the valid points for the inequality. The number line between (-4,0) and (2,0) in included. The third (x^2-2x-8>y) is colored everywhere outside the parabola, and thus exclues the number line in the region we are interested. So the equation for this graph is not a valid possibility.
We may conclude that graph 1 is correct. The important section of the graph is expanded at the bottom. Since the graph line is dotted, the two points (-4,0) and (2,0) are not actually included on the line - they are simply a boundary, due to the < function. They would be included if the expression had said ≤ or ≥ (with the = sign).
The expression that represents the solution set is x^2-2x-8<0
If it take me 5 hours to drive to grandmas house and I drive at a constant speed of 65 mph.
How far away is her house to mine?
Answer:
325 miles
Step-by-step explanation:
speed = distance/time
=> distance = speed x time = 65 x 5 = 325 miles
Step-by-step explanation:
If you drive at a constant speed of 65 miles per hour for 5 hours, you would cover a distance of:
Distance = Speed x Time
Distance = 65 mph x 5 hours
Distance = 325 miles
Therefore, your grandmother's house is 325 miles away from yours.
What coefficient of term xy² in expression 2xy² + x³ – x⁵ + xy² is?
Answer:
The coefficient is 3.
Answer:
3
Step-by-step explanation:
Here 2xy² + x³ – x⁵ + xy², there are two like terms
2xy² and xy², so the coefficient of xy² = 2 + 1
Coefficient of xy² in the given expression is 3.
You roll a number cube. Find the probability
you roll a number that is greater than 2 and
less than 5. Write your answer as a fraction
in simplest form.
Please helpp
Answer:
1/3
Step-by-step explanation:
There are only two ways to roll a die and get a number bigger than 2 (not1 or not 2) and smaller than 5 (not 5 and not 6) You can roll a 3 (bigger than 2, smaller than 5) OR you can roll a 4 (also bigger than 2 a, smaller than 5)
There are only 6 different results when you roll a die (1-6).
To write a probability you put the total number of ways on the bottom. Put 2 on top because there's two ways to roll the desired result.
P = 2/6 and simplify
P = 1/3
The first three questions refer to the following information:The random variable X, representing the number of accidents in a certain intersection in a week, has the following probability distribution:x 0 1 2 3 4 5P(X=x) 0.20 0.30 0.20 0.15 0.10 0.05Question 1Select one answer.10 pointsWhat is the probability that in a given week there will be at most 3 accidents?0.700.850.350.151.00
The probability that in a given week there will be at most 3 accidents is 0.85. These event would be mutually exclusive as they do not influence the other results, Therefore the correct answer is 0.850.
The probability that in a given week there will be at most 3 accidents can be found by adding the probabilities of having 0, 1, 2, or 3 accidents. This is because the events are mutually exclusive, meaning that they cannot occur at the same time.
[tex]P(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]
From the given probability distribution, we can find the probabilities of each of these events:
[tex]P(X = 0) = 0.20P(X = 1) = 0.30P(X = 2) = 0.20P(X = 3) = 0.15[/tex]
Plugging these values into the equation, we get:
[tex]P(X ≤ 3) = 0.20 + 0.30 + 0.20 + 0.15P(X ≤ 3) = 0.85[/tex]
Therefore, the probability that in a given week there will be at most 3 accidents is 0.85. The correct answer is 0.850.
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Given cot � = − 4 5 and that angle � A is in Quadrant II, find the exact value of sec � secA in simplest radical form using a rational denominator.
Therefore, the exact value of sec(θ) sec(A) in simplest radical form using a rational denominator is 41/16.
What is trigonometry?Trigonometry is based on the ratios of the sides of a right triangle, which are defined in terms of the angles of the triangle. The three main trigonometric functions are sine, cosine, and tangent, which are abbreviated as sin, cos, and tan, respectively. These functions are used to relate the angles of a triangle to the lengths of its sides, and can be calculated using a scientific calculator or a table of values.
Here,
We can start by using the definition of cotangent:
cot(θ) = adjacent / opposite
From the given information, we have cot(θ) = -4/5. Since θ is in Quadrant II, we know that the adjacent side is negative and the opposite side is positive. We can use the Pythagorean theorem to find the hypotenuse:
a² + b² = c²
(-4)² + 5² = c²
16 + 25 = c²
c² = 41
c = √(41)
Now we can use the fact that secant is the reciprocal of cosine:
sec(θ) = 1 / cos(θ)
cos(θ) = adjacent / hypotenuse
cos(θ) = -4 / √(41)
cos(A) = adjacent / hypotenuse
cos(A) = 4 / √(41)
sec(θ) sec(A) = (1/cos(θ))(1/cos(A))
sec(θ) sec(A) = (√(41) / -4)(√(41) / 4)
sec(θ) sec(A) = (41 / 16)
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Becky wants to buy some fish for her aquarium. she has $20 to spend and the fish cost $2.50 each. write an inequality that can be used to determine how many fish, x, becky can afford to buy.
To solve this inequality, the left side can be divided by $2.50 and the value of x can be determined. The solution to this inequality is that Becky can afford to buy a maximum of 8 fish.$2.50x ≤ $20
$2.50x ≤ $20
The given situation is that Becky wants to buy some fish for her aquarium and she has $20 to spend and the cost of the fish is $2.50 each. To determine how many fish, x, Becky can afford to buy, an inequality can be written. Since the cost of each fish is $2.50, the total cost for buying x number of fish is $2.50x. To find out how many fish Becky can afford to buy, the inequality $2.50x ≤ $20 can be written. To solve this inequality, the left side can be divided by $2.50 and the value of x can be determined. The solution to this inequality is that Becky can afford to buy a maximum of 8 fish.
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Find the area of the triangle whose vertices are (−2,3),(3,2) and (−1,−8) by using determinant method.
11 square units
Given the vertices of a triangle in coordinate geometry, find its area by using the determinant method. The given vertices of the triangle are (-2, 3), (3, 2), and (-1, -8).Step-by-step explanation: The formula for calculating the area of the triangle with given vertices using determinant method is given as, \[\frac{1}{2}\begin{vmatrix}x_1 & y_1 & 1 \\x_2 & y_2 & 1 \\x_3 & y_3 & 1 \\\end{vmatrix}\]Here, x1, y1, x2, y2, x3, y3 are the coordinates of the given vertices. Now, substitute the given values and evaluate the determinant as shown below. \[\frac{1}{2}\begin{vmatrix}-2 & 3 & 1 \\3 & 2 & 1 \\-1 & -8 & 1 \\\end{vmatrix}=\frac{1}{2}((-2)(2(-8)-(-1)(3))+3(1(-8)-(-1)(-1))+1(3(2)-(-1)(3)))\]After multiplying, we get, \[\frac{1}{2}(-16+29+9)=\frac{1}{2}(22)=11\] Therefore, the area of the triangle whose vertices are (-2, 3), (3, 2), and (-1, -8) is 11 square units.
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Lara deposits $49,000 to be compounded monthly at 15.3% for 2 years.
Which equation will she use to determine how much money she'll have after 2 years? i
After 2 years she'll have ___
The equation she will use to determine how much money she'll have after 2 years is: A = 49,000*(1+0.153/12)^(2*12).
After 2 years she'll have $70,960.36.
How do we calculate the future value?The formula for compound interest is: A = P * (1 + r/n)^(n*t). In the formula, we convert the annual interest rate to a monthly rate by dividing it by 12 (the number of months in a year), and we multiply the number of years by 12 to get the number of months.
Using this formula, we can calculate how much money Lara will have after 2 years:
A = 49000 * (1 + 0.153/12)^(12*2)
A = $70,960.36
Therefore, Lara will have $70,960.36 after 2 years of compounding her investment monthly at 15.3%.
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? QUESTION Divide. Write your answer in simplest form. 3-:(7)/(3) OO EXPLANATION
2/3 in its simplest form.
3-(7)/(3) can be simplified to 2/3 by performing the following steps:
1. First, divide 7 by 3 to get 7/3.
2. Then, subtract 7/3 from 3 to get 3-(7/3), which equals 2/3.
Therefore, the answer is 2/3 in its simplest form.
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I dont know how to do this
the answer isnt 4
pls answer if u know with simple working
Answer:25 sticks
Step-by-step explanation:
each time you will add 4 sticks
Answer: 37
Step-by-step explanation:
Add 4
Translate this sentence into a inequality. The product of x and 4 is greater than or equal to 18
The inequality for the given sentence would be:
4x ≥ 18. This means that the product of x and 4 is greater than or equal to 18.
The inequality "4x ≥ 18" is read as "four times x is greater than or equal to 18". This means that the value of x must be equal to or greater than 4.5 for the inequality to hold true.
To solve the inequality, we can divide both sides by 4, which gives us:
x ≥ 4.5
This means that any value of x that is equal to or greater than 4.5 will satisfy the original inequality.
For example, x = 5 would satisfy the inequality because: 4(5) = 20, which is greater than or equal to 18.p
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