For rectangle type books, the difference in the heights of their stacks of books is 15 3/4 inches.
What exactly is a rectangle?
A rectangle is a type of quadrilateral (a four-sided polygon) that has four straight sides and four right angles. It is a two-dimensional shape, meaning it lies flat in a plane, and is defined by its two sets of parallel sides, each pair of which are equal in length.
In a rectangle, opposite sides are parallel and congruent (equal in length), and adjacent sides are perpendicular (meet at a right angle). The diagonals of a rectangle bisect each other (divide each other into two equal parts) and are congruent.
The area of a rectangle is calculated by multiplying its length and width, while its perimeter is found by adding the lengths of all its sides. The formula for the area of a rectangle is A = l x w, where A is the area, l is the length, and w is the width. The formula for the perimeter of a rectangle is P = 2l + 2w, where P is the perimeter, l is the length, and w is the width.
Now,
To solve this problem, we need to first find out the height of Rick's stack of books. We know that his stack is 3 times as tall as Trevor's stack, so:
Rick's stack = 3 x Trevor's stack
Rick's stack = 3 x 7 7/8 inches
Rick's stack = 23 5/8 inches
Now that we know the height of both stacks, we can find the difference between them:
Difference = Rick's stack - Trevor's stack
Difference = 23 5/8 inches - 7 7/8 inches
Difference = 15 6/8 inches
Difference = 15 3/4 inches
Therefore, the difference in the heights of their stacks of books is 15 3/4 inches.
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The area of the shape that includes squares will be 9 m² and perimeter will be 16m.
What are squares?
A square has four equal sides and four right angles. It is a special type of rectangle, and like rectangles, it is also a two-dimensional shape with all its sides lying in a plane.
A square has several important properties. Its sides are equal in length, and its diagonals are congruent (equal in length) and bisect each other at right angles. All angles in a square are also right angles, which means that it is a special type of rectangle where all angles measure 90 degrees.
The area of a square is calculated by squaring the side. For example, if a square has a side length of s, its area would be A = s². The perimeter of a square is found by adding up the lengths of all four sides, which is P = 4s.
Now,
The sides of the squares will be 2m, 2m and 1 m.
then area of the figure will be =2²+2²+1²
=4+4+1
=9 m²
and
Perimeter = sum of all sides
then Perimeter=5+2+2+2+2+1+1+1
=16 m
Hence,
The area of the shape that includes squares will be 9 m² and perimeter will be 16m.
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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.
? 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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Solve the equation: 7x = 42
A. x = 7
B. x = 6
C. x = -7
D. x = -6
Answer:
x = 6
Step-by-step explanation:
7x = 42
To solve the equation, divide each side by 7.
7x/7 = 42/7
x = 6
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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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.
shape R is reflected in the line x = -1 to give R'
a. what is the coordinates of C?
R' is then translated by by (-1, -6) to give R''
b. what is the coordinates of C?
When the shape R is reflected R' the coordinates of C (2, 5) when translated to R" C (1, -1).
What are Transformations:
Transformations are changes made to a geometric figure in a plane or space. There are three main types of transformations: translation, rotation, and reflection.
Rotation is a transformation where a figure is turned around a fixed point, called the center of rotation. This can be a clockwise or counterclockwise turn, and the degree of rotation is determined by the angle between the original and final positions of the figure.
Here we have a shape R
From the graph,
The coordinate of C is (-4, 5)
Shape R is reflected in line x = -1 to give R'
=> (x, y ) → (-x - 2, y)
=> (-4, 5) → (4- 2, 5)
=> Coordinates of C are (2, 5)
R' is then translated by (-1, -6) to give R''
Hence, the R is moved 1 unit left words and 6 units downwards
=> (2, 5) → (-1 + 2, 5 - 6)
=> (2, 5) → (1, -1)
Therefore,
When the shape R is reflected R' the coordinates of C (2, 5) when translated to R" C (1, -1).
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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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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
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.
I need some help please
The solution of the inequality is x ≤ - 7 / 2 or x > 1
How to solve inequality?Inequalities are mathematical expressions involving the symbols >, <, ≥ and ≤.
Therefore, let's solve the inequalities. The variable in the inequality is x. A variable is a number represented with letter in an equality or inequality.
Therefore,
x + 1 / 2 ≤ - 3 or x - 3 > - 2
Let's solve them individually,
x + 1 / 2 ≤ - 3
subtract 1 / 2 from both sides of the inequality
x ≤ - 3 - 1 / 2
x ≤ - 7 / 2
Hence,
x - 3 > - 2
add 3 to both sides of the inequality
x - 3 + 3 > - 2 + 3
x > 1
Hence,
x ≤ - 7 / 2 or x > 1
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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!!!!
Drag the tiles to the correct boxes to complete the pairs.
angles congruent to 21
angles congruent to 26
DOOD
23,27,26
In the figure, line a and line b are parallel. Based on the figure, match each given angle with its congruent angles.
23,27,22
1/2
angles congruent to 22
24,28,25
3/4
23,26,22
5/6
7/8
-a
-b
angles congruent to 27
Angles congruent to ∠1= ∠4,∠8,∠5
Angles congruent to ∠2= ∠3,∠7,∠6
Angles congruent to ∠6= ∠3,∠7,∠2
Angles congruent to ∠7= ∠3,∠6,∠2
Define vertically opposite anglesThe opposing angles created by the connection of two straight lines are known as vertical angles or vertically opposed angles.
Part1)(Vertically opposite angle ∠1=∠4
Vertically opposite angle ∠8=∠5
consecutive exterior angle ∠4=∠8)
Angles congruent to ∠2= ∠3,∠7,∠6
Hence, Angles congruent to ∠1= ∠4,∠8,∠5
Part2)(Vertically opposite angle ∠2=∠3
Vertically opposite angle ∠7=∠6
consecutive exterior angle ∠3=∠7)
Angles congruent to ∠7= ∠3,∠6,∠2
part3)(Vertically opposite angle ∠7=∠6
Vertically opposite angle ∠2=∠3
consecutive exterior angle ∠6=∠2)
Hence, Angles congruent to ∠6= ∠3,∠7,∠2
Part4)(Vertically opposite angle ∠6=∠7
Vertically opposite angle ∠3=∠2
consecutive exterior angle ∠7=∠3)
Hence, Angles congruent to ∠2= ∠3,∠7,∠6
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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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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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What is the positive solution to 2x^2−9x−5
2x²-9x-5
2x²-x-10x-5
(x-5)(2x+1)
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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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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Please answer with formula and how to find it
The radius of a circle is half of the diameter. Therefore, the radius of the circle is 7 yards and the diameter of the circle is 14 yards.
How to find the radius and diameter of a square?The above shape is a circle. The area of the circle is given as 49πyards square. The radius of a circle is the distance of the circumference to the centre of a square. The diameter of a circle is twice the radius of the circle.
Therefore, let's find the radius and diameter of a circle as follows:
area of a circle = πr²
where
r = radiusArea of the circle = πr²
49π = πr²
divide both sides of the equation by π
r² = 49
square root both sides of the equation
r = √49
r = 7 yards
Therefore,
diameter = 7 × 2
diameter = 14 yards
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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).
WILL GIVE BRAINLEST
(dont worry about the name just put joe for the name)
1. Answer the following questions.
Questions
What is an amount between $2 and $10? (A) __________
What is an amount between $10 and $20? (B) __________
What is an amount greater than $50? (C) __________
What is your name? (D) ____________________
What is the name of an item that you will buy only once? (E) ____________________
What is the name of an item that you will buy more than once? (F) ____________________
2. Create a word problem that leads to an inequality by filling in the blanks with your corresponding answers.
Word Problem
(D) ____________________ is going shopping for (E) ____________________ and (F) ____________________. The cost of (E) ____________________ is (B) __________ and the cost of each (F) ____________________ is (A) __________.
If (D) ____________________ can spend at most (C) __________, how many (F) ____________________ can be purchased?
3. Write an inequality of the form Ax + B ≤ C to represent the word problem using your answers for A, B, and C. Solve the inequality and show your work.
4. Graph the solution to your inequality on a number line or describe, in words, how to graph the inequality on a number line.
5. Explain what the solution means in the context of the word problem.
The questiοn is an illustratiοn οf inequalities and mathematical οperatiοns the amοunt between $2 and $10 is $8.
The amοunt between $10 and $20 is $10
$100 is greater than $50
What is inequality?In mathematics, an inequality is a cοnnectiοn that is nοt equal between twο expressiοns οr values. Cοnsequently, imbalance leads tο inequity. In mathematics, an inequality cοnnects twο unrelated values. Inequality is distinct frοm equality. When twο values are nοt equal, the nοt equal sign is mοst usually used ().
Variοus inequalities are emplοyed tο cοntrast values, nο matter hοw small οr huge. Many basic inequalities can be sοlved by altering the twο sides until the variables are all that remain. Yet, a variety οf factοrs cοntribute tο inequality: Negative values οn bοth sides are split οr added. Trade οff the left and right.
(a) Amοunt between $2 and $10.
The amοunt is calculated as:
Hence, the amοunt between $2 and $10 is $8
(b) Amοunt between $10 and $20.
The amοunt is calculated as:
Hence, the amοunt between $10 and $20 is $10
(c) Amοunt greater than $50.
An amοunt greater than $50 is an amοunt that have an higher value.
Take fοr instance: $100
$100 is greater than $50, because it has a higher value.
There is nο enοugh infοrmatiοn tο sοlve the οther questiοns
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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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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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you have some standard six-sided dice. what is the probability of rolling a total of ten when you roll three dice
You have some standard six-sided dice. So, the probability of rolling a total of ten when you roll three dice is 5/216.
To find the probability of rolling a total of ten when rolling three dice, we can use the formula:
P(event) = desired outcomes / total outcomes
Given that we have six-sided dice, we know that the total outcomes for rolling one die is six.
Therefore, the total outcomes for rolling three dice would be[tex]6^3[/tex]= 216.
To find the desired outcomes, we can use combinations.
There are three ways we can roll a total of ten with three dice:
1-3-62-4-43-5-24-3-34-2-45-1-5
Therefore, there are five combinations that result in a total of ten.
Therefore, the probability of rolling a total of ten when rolling three dice is:
P(event) = 5/216
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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.
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
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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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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Una congeladora industrial se mantiene a -8°C. Si de pronto aumenta su
temperatura en 5°C, ¿cuál es su nueva temperatura?
La nueva temperatura de la congeladora industrial es de -3°C.
Si una congeladora industrial se mantiene a -8°C y aumenta su temperatura en 5°C, podemos encontrar su nueva temperatura sumando -8°C y 5°C:
-8°C + 5°C = -3°C
Por lo tanto, la nueva temperatura de la congeladora industrial es de -3°C.
La temperatura es una magnitud física que mide el grado de calor o frío de un objeto, sustancia o ambiente. Esta magnitud está relacionada con la energía cinética promedio de las moléculas que componen el objeto o sustancia, y se expresa en unidades de medida como grados Celsius (°C), grados Fahrenheit (°F) o kelvin (K).
Es importante tener en cuenta que una temperatura de -3°C sigue siendo fría, pero es importante asegurarse de que la congeladora se mantenga a la temperatura adecuada para preservar los alimentos y evitar su descomposición.
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Kayla and Maria are selling cookie dough for a school fundraiser. Customers can buy packages of sugar cookie dough and packages of double chocolate cookie dough. Kayla sold 7 packages f sugar cookie dough and 1 package of double chocolate cookie dough for a total of $53. Maria old 1 package of sugar cookie dough and 1 package of double chocolate cookie dough for a total f $17. Find the cost each of one package of sugar cookie dough and one package of double hocolate cookie dough.
One package of sugar cookie dough costs $6 and one package of double chocolate cookie dough costs $11.
How to solve the variables?
Let's use the following variables:
Let x be the cost of one package of sugar cookie dough.
Let y be the cost of one package of double chocolate cookie dough.
We can create a system of two equations to represent the information given in the problem:
Equation 1: 7x + y = 53 (from Kayla's sales)
Equation 2: x + y = 17 (from Maria's sales)
We can solve for x and y by using the substitution method, which involves solving one equation for one variable and substituting the result into the other equation. Here's how we can do it:
Solve Equation 2 for y:
y = 17 - x
Substitute y = 17 - x into Equation 1 and solve for x:
7x + (17 - x) = 53
6x + 17 = 53
6x = 36
x = 6
Substitute x = 6 into Equation 2 and solve for y:
y = 17 - x
y = 17 - 6
y = 11
Therefore, one package of sugar cookie dough costs $6 and one package of double chocolate cookie dough costs $11.
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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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