The inverse of the following matrix X is X-1 = 3/416/4-1/4-3/44/30/4-2/41/41/4.
The inverse of a matrix is a matrix that, when multiplied by the original matrix, produces the identity matrix. To find the inverse of the following matrix X, we need to use the formula X-1 = 1/|X| adj(X), where |X| is the determinant of X and adj(X) is the adjoint of X.
First, let's find the determinant of X:
|X| = (1)(-12)(-3) + (2)(-1)(-2) + (2)(3)(-1) - (-2)(-1)(2) - (1)(3)(-2) - (4)(-1)(-3)
|X| = -36 + 4 + -6 + 4 - -6 - -12
|X| = -16
Since the determinant of X is not equal to 0, the inverse of X exists.
Now, let's find the adjoint of X:
adj(X) = -12-2-134-3024−11−3
Finally, let's use the formula X-1 = 1/|X| adj(X) to find the inverse of X:
X-1 = 1/(-16) -12-2-134-3024−11−3
X-1 = 3/416/4-1/4-3/44/30/4-2/41/41/4
Therefore, the inverse of the following matrix X is X-1 = 3/416/4-1/4-3/44/30/4-2/41/41/4.
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A probability distribution table is as follows Х 1 2 3 P(x) 1/6 2/3 1/6 The value of E(x^2) is____
a. 13/3
b. 4
c. 1
d. 16/3
The correct answer to this question is a. 13/3.
To find the value of E(x^2), we need to multiply each value of x by its corresponding probability and then sum the results. This can be written as E(x^2) = (1^2)(1/6) + (2^2)(2/3) + (3^2)(1/6).
Simplifying the equation gives us:
E(x^2) = (1/6) + (8/3) + (9/6) = (1/6) + (16/6) + (9/6) = (26/6) = 13/3
Therefore, the value of E(x^2) is 13/3.
In conclusion, the correct answer to this question is a. 13/3.
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Write the polynomial as the product of linear factors. 9(x) = x4 - 2x3 + 5x2 8x + 4 g(x) = _________ List all the zeros of the function. (Enter your answers as a comma-separated list.) XE =__________
The polynomial as a product of linear factor [tex]9(x) = x4 - 2x3 + 5x2 8x + 4 g(x)[/tex] are g(x) = (x-2)(x-1)(x+1)(x+4) , all the zeros of function are 2,1,-1,-4.
In order to write the polynomial as a product of linear factors, we must first find its zeros. The zeros of a polynomial are the values of x that make the polynomial equal to zero. The way to find the zeros is to set the polynomial equal to zero, and solve for x.
For this particular polynomial, the equation would be: x^4 - 2x^3 + 5x^2 + 8x + 4 = 0.
We can solve this equation by factoring. When factoring, we look for common factors among the terms and group them together. After factoring, the equation becomes: (x - 2)(x - 1)(x + 1)(x + 4) = 0.
The zeros of the equation are x = 2, 1, -1, -4. This means that the polynomial can be written as the product of linear factors, which is (x-2)(x-1)(x+1)(x+4). The zeros of this function are x = 2, 1, -1, -4.
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The polynomial as the product of linear factors. 9(x) = x4 - 2x3 + 5x2 8x + 4 g(x) is a product of (x - 2)(x - 1)(x + 1)(x + 4) . All the zeros of function are x = 2,1,-1,-4.
In order to write the polynomial as a product of linear factors, we must first find its zeros. The zeros of a polynomial are the values of x that make the polynomial equal to zero. The way to find the zeros is to set the polynomial equal to zero, and solve for x.
For this particular polynomial, the equation would be: x^4 - 2x^3 + 5x^2 + 8x + 4 = 0.
We can solve this equation by factoring. When factoring, we look for common factors among the terms and group them together. After factoring, the equation becomes: (x - 2)(x - 1)(x + 1)(x + 4) = 0.
The zeros of the equation are x = 2, 1, -1, -4. This means that the polynomial can be written as the product of linear factors, which is (x-2)(x-1)(x+1)(x+4).
The zeros of this function are x = 2, 1, -1, -4.
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You and your pen pal record the weather in your respective countries on weekend days over the summer. Complete parts a through b.
We have the following response after answering the given question: As a equation result, Country A saw more erratic weather throughout the summer, with a 6°C difference in temperatures.
What is equation?In a mathematical equation, the equals sign (=), which connects two claims and denotes equality, is utilised. In algebra, an equation is a mathematical statement that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a space. Mathematical expressions can be used to describe the relationship between the two sentences on either side of a letter. The logo and the particular piece of software frequently correspond. like, for instance, 2x - 4 = 2.
Which nation experienced the hottest summer?
We may examine the average temperature for each nation throughout the observed weekends to determine which nation experienced the hottest summer.
Country A: (21.4°C) (18+20+22+23+24)/5
(24+26+28+29+27)/5 = 26.8°C for Country B.
The summer was therefore hotter in Country B, with an average temperature of 26.8°C.
b) Over the summer, which nation saw more erratic weather?
We may examine the temperature ranges recorded for each nation to determine which experienced more erratic weather during the summer.
24°C - 18°C equals 6°C in Country A.
29°C - 24°C equals 5°C in country B.
As a result, Country A saw more erratic weather throughout the summer, with a 6°C difference in temperatures.
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Help please ill give everything and a good amount of points please. See image . Solve for the missing angle, round to the nearest degree
Answer: x = 47.2°
Step-by-step explanation:
We can use a trigonometry function to solve this question since it's a right triangle.
Equation:
tanx = [tex]\frac{27}{25}[/tex]
The tangent inverse of both sides of the equation:
[tex]\displaystyle tan^{-1} (\text{tan}x)=(\frac{27}{25} )tan^{-1}[/tex]
x = 47.2°
Complete the slope-intercept form of the linear equation that represents the relationship in the table.3 −5 −2 5
In response to supplied query, we may state that The connection shown in the table is represented by a linear equation in the slope-intercept form.
what is slope intercept?In mathematics, the intersection point is where the line's slope intersects the y-axis. a point on a line or curve where the y-axis crosses. The equation for the straight line is given as Y = mx+c, where m denotes the slope and c the y-intercept. In the intercept form of the equation, the line's slope (m) and y-intercept (b) are highlighted. The slope and y-intercept of an equation with the intercept form (y=mx+b) are m and b, respectively. There are several equations that may be rewritten to seem to be slope intercepts. The slope and y-intercept are both modified to 1 if y=x is rewritten as y=1x+0, for example.
We must know the slope and the y-intercept of the line in order to find the slope-intercept form of a linear equation.
The first and last points in the table should be chosen:
slope = [tex](5 - (-5)) / (3 - (-2)) = 10/5 = 2[/tex]
Now that we have the slope, we can write the equation of the line using the point-slope form of a linear equation:
y - y1 = m(x - x1) (x - x1)
Each position along the line may be chosen as (x1, y1). Let's pick point number one (3, -5):
[tex]y - (-5) = 2(x - 3) (x - 3)\\y + 5 = 2x - 6\\y = 2x - 11[/tex]
The connection shown in the table is represented by a linear equation in the slope-intercept form.
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Daniel built a wooden, cubic toy box for his daughter. Each edgeof the box measures 2 feet. How many square feet of wood did he use to build the house? A.
There are 6 faces in a cube, the total surface area of the toy box is 6 x 4 = 24 square feet. So correct option is B.
Describe Cube?In geometry, a cube is a three-dimensional shape that is bounded by six square faces, with each face meeting at right angles. A cube is a regular polyhedron, which means that all of its faces are congruent and all of its edges have the same length.
The cube has a total of eight vertices (corners) and twelve edges, with each vertex connecting three edges and each edge connecting two vertices. The volume of a cube can be calculated using the formula V = s^3, where s is the length of one edge.
Cubes are commonly used in mathematics, physics, and engineering to represent three-dimensional objects and to model various phenomena. For example, cubes can be used to represent the atoms in a crystal lattice, the cells in a grid, or the pixels in a digital image
The toy box is a cube, and each edge measures 2 feet. So, the surface area of one face of the cube is 2 x 2 = 4 square feet. Since there are 6 faces in a cube, the total surface area of the toy box is 6 x 4 = 24 square feet.
Therefore, the answer is (B) 24 feet squared.
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The complete question is:
equipment tells her that the angle of depression from the plane to the beginning of the runway is 11 degrees. to the nearest tenth of a kilometer, what is the horizontal distance between the airplane and runway?
The horizontal distance between the airplane and runway is, 2607.6 meters or 2.6 kilometers
How to relate angle and height to get distance?To solve the problem, we can use the tangent function, which relates the opposite side of a right triangle to its adjacent side:
tanα = opposite/adjacent
where theta is the angle of depression, opposite is the height of the airplane above the ground, and adjacent is the horizontal distance between the airplane and the beginning of the runway.
We can rearrange this formula to solve for adjacent:
adjacent = opposite/tanα
Plugging in the values, we get:
adjacent = 500/tan(11°)
adjacent ≈ 2607.6
Therefore, the horizontal distance between the airplane and the beginning of the runway is approximately 2607.6 meters or 2.6 kilometers when rounded to the nearest tenth of a kilometer.
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Solve (2)/(3)m=(5)/(8). Check your solution. (2)/(3)m=(5)/(8) ((2)/(3)m)/((2)/(3))=(5)/(8) (2)/(3) Write the equation. Division Property of Equality (2)/(3)((3)/(2))m=(5)/(8)((3)/(2)) Multiply by the reciprocal.
The solution to the equation (2)/(3)m=(5)/(8) is m = (15)/(16)
To solve the equation (2)/(3)m=(5)/(8), we can use the Division Property of Equality and the Multiplication Property of Equality.
Here are the steps:
1. Start with the original equation: (2)/(3)m=(5)/(8)
2. Multiply both sides of the equation by the reciprocal of (2)/(3), which is (3)/(2): (2)/(3)m * (3)/(2) = (5)/(8) * (3)/(2)
3. Simplify the left side of the equation: m = (5)/(8) * (3)/(2)
4. Simplify the right side of the equation: m = (15)/(16)
5. Check your solution by plugging it back into the original equation: (2)/(3) * (15)/(16) = (5)/(8)
6. Simplify the left side of the equation: (30)/(48) = (5)/(8)
7. Simplify the right side of the equation: (5)/(8) = (5)/(8)
8. Since both sides of the equation are equal, the solution is correct.
So the solution to the equation (2)/(3)m=(5)/(8) is m = (15)/(16).
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√(6-(-1)² + (-2-(-1)²
Answer:
To simplify this expression, we need to first evaluate the terms inside the square root:
(-1)² = 1
(-2 - (-1))² = (-2 + 1)² = (-1)² = 1
Now we can substitute these values and simplify the expression:
√(6 - (-1)² + (-2 - (-1))²)
= √(6 - 1 + 1)
= √6
Therefore, the simplified form of the expression is √6.
Answer:
To evaluate the expression √(6-(-1)² + (-2-(-1)²), we need to follow the order of operations, which is Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
1. First, we need to evaluate the expressions inside the parentheses:
-1² = (-1) × (-1) = 1
-2-(-1)² = -2-1 = -3
2. Next, we substitute these values into the expression:
√(6-(-1)² + (-2-(-1)²)
= √(6-1 + (-2-1))
= √(5 - 3)
= √2
Therefore, the value of the expression √(6-(-1)² + (-2-(-1)²) is √2.
Step-by-step explanation:
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a square and a rectangle have the same perimeter. calculate the area of a rectangle if the side of a square is 60cmand the length of a rectangle is 80cm
Answer:
3,200 Square centimeters
Step-by-step explanation:
In order to solve for the perimeter of a square with side lengths of 60, we can use this expression:
60 × 4 = 240(We multiply by 4 because a square has four equal side lengths, and the perimeter is all of the side lengths added up)
Therefore, the perimeter of the square is 240cm.
Now that we know this, we can now take that perimeter, and subtract 160 from it.
(We subtract 160 from it because the length of the rectangle is 80cm, and because a rectangle has two sides that represent the length, we multiply the 80 by 2.)
240 - 160 = 80Now, we can divide the 80 by 2 to get the length of the other 2 sides.
80 ÷ 2 = 40Therefore, the rectangles dimensions are 80cm by 40cm.
What is the area?The area is the total space taken up by a flat (2-D) surface or shape. The area is always measured in square units.
To solve for the area of a rectangle, we use the expression:
length × width = heightInserting the numbers into the equation:
80 × 40 = 3200Therefore, the area of the rectangle is 3,200 square centimeters.
Exact surface area. Radius is 1 3/4 and height is 3 1/4
The surface area of the cylinder with a radius of 1 ³/₄ and height of 3 ¹/₄ units will be 35.72 square units.
What is the surface area of a right circular cylinder?Let r be the radius and h be the height of the cylinder. Then the surface area of the cylinder will be given as,
SA = 2πrh square units
The radius is 1 ³/₄ units and the height is 3 ¹/₄ units.
First, convert the mixed fraction number into a fraction number. Then we have
1 ³/₄ = 7/4 units
3 ¹/₄ = 13/4 units
The surface area of the cylinder is calculated as,
SA = 2 x 3.14 x (7/4) x (13/4)
SA = 35.72 square units
The surface area of the cylinder with a radius of 1 ³/₄ and height of 3 ¹/₄ units will be 35.72 square units.
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The complete question is given below.
Exact surface area. The radius is 1 3/4 and the height is 3 1/4 of the cylinder.
60 percent off 44. What is the answer to this Question?
Answer: 24
Step-by-step explanation:
Answer:
60% of 44 is 26.4
Step-by-step explanation:
Solve the following inequality involving absolute value. Enter the answer in interval notation.
∣x+4∣>−9
Interval notation is (−∞, −4) U (−4, ∞)
The given inequality is ∣x + 4∣ > − 9. Step-by-step explanation: Absolute value inequalities: Inequalities that contain absolute values are known as absolute value inequalities. The absolute value inequality ∣x + 4∣ > − 9 is given.Inequality means that x can take any value except the value that makes the inequality false. If x satisfies the inequality, we write x ∈ (A, B) or x ∈ [A, B), where A and B are any two values that satisfy the inequality.The inequality ∣x + 4∣ > − 9 implies that the absolute value of x + 4 is greater than −9. The absolute value of x + 4 is always greater than or equal to zero.Therefore, the inequality can be written as∣x + 4∣ > 0This inequality implies that x is not equal to −4.The interval of x satisfying the given inequality is x ∈ (−∞, −4) U (−4, ∞), where U represents the union of two intervals. Therefore, the answer in interval notation is (−∞, −4) U (−4, ∞).Thus, the solution to the inequality |x + 4| > -9 in interval notation is (−∞, −4) U (−4, ∞).
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Find the five-number summary of the data set:
135, 149, 156, 112, 134, 141, 154, 116, 134, 156
Question 12 options:
Minimum: 112
Minimum: 135
Minimum: 116
First Quartile (Q1): 138
First Quartile (Q1): 134
First Quartile (Q1): 116
Second Quartile (Q2): 135
Second Quartile (Q2): 141
Second Quartile (Q2): 138
Third Quartile (Q3): 151.5
Third Quartile (Q3): 155
Third Quartile (Q3): 154
Maximum: 156
Maximum: 154
Maximum: 149
The median is 138.
What is the median?
The median is the value that divides a data sample, a population, or a probability distribution's upper and lower halves in statistics and probability theory. It could be referred to as "the middle" value for a data set.
Here, we have
Given: data set:
135, 149, 156, 112, 134, 141, 154, 116, 134, 156.
To get the box plot we begin by arranging the data in ascending order:
135, 149, 156, 112, 134, 141, 154, 116, 134, 156
rearranging the data set we get:
112,116, 134, 134, 135, 141, 149, 154, 156, 156
then:
Lower value = 112
Q1 = 134
Median = (135+141)/2 = 138
Q3 = 154
Largest value =156
Hence, the median is 138.
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Krystal throws a rappelling rope at a speed of 10 m/s down a 50 m cliff. When will the rope hit the ground? Use the drop-down to put the correct order to solve for when the rope will hit the ground.
Answer: It will take the rope 5 seconds to reach the ground if it continues travelling at a speed of 10 m/s
Step-by-step explanation:If the rope is going 10 m/s down a 50 m cliff,
50/10=5 It will take it 5 seconds becuase it is going at a speed of 10 meters a second
I figured out the 1st part, now what’s this next one has to be 22 cm [?]
[tex]Area = \dfrac{6(7)}{2} = \dfrac{42}{2} = 21 \ cm^{2}[/tex]
A quadrilateral is called cyclic if its vertices lie on a circle. Show that opposite interior angles of a quadrilateral are supplementary if and only if the quadrilateral is cyclic. [Hint: Use the preceding problem and facts about circumcircles of triangles]
Opposite interior bof a quadrilateral are supplementary if and only if the quadrilateral is cyclic.
A quadrilateral is called cyclic if its vertices lie on a circle. This means that there is a circumcircle that passes through all four vertices of the quadrilateral. If opposite interior angles of a quadrilateral are supplementary, then the sum of these angles is 180 degrees. This means that the opposite angles of a cyclic quadrilateral are supplementary.
To prove this, let us consider a quadrilateral ABCD that is cyclic. Let O be the center of the circumcircle that passes through all four vertices of the quadrilateral.
Since the quadrilateral is cyclic, angle AOB and angle COD are both subtended by the same arc, and therefore they are equal. Similarly, angle BOC and angle DOA are both subtended by the same arc, and therefore they are equal.
Now, let us consider the sum of the opposite interior angles of the quadrilateral.
Angle A + angle C = angle AOB + angle BOC + angle COD + angle DOA = 2(angle AOB) + 2(angle BOC) = 2(180) = 360
Since the sum of the opposite interior angles of the quadrilateral is 360 degrees, this means that the opposite interior angles of the quadrilateral are supplementary.
Therefore, opposite interior angles of a quadrilateral are supplementary if and only if the quadrilateral is cyclic.
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helpppp asap please explain what i did wrong
The statistical measures or five-number summary for the given data set are as follows:
Minimum (Min) = 4.First quartile (Q₁) = 6.Median (Med) = 9.5.Third quartile (Q₃) = 12.5.Maximum (Max) = 17.What is a box-and-whisker plot?In Mathematics, a box plot is sometimes referred to as box-and-whisker plot and it can be defined as a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.
In order to determine the five-number summary, we would arrange the data set in an ascending order:
4,6,6,8,11,12,13,17
Next, we would use an online graphing calculator to create the box plot as shown in the image attached below.
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3 to the second is the prime factorization of what number?
Answer:
3^2 = 9
So 9 is the number.
Georgia made a scale drawing of her apartment. Her bathroom is 3 inches in the drawing and 8 feet in real life. What scale factor did she use?
The scale factor that Georgia used her scale drawing is 3/8.
What scale factor did Georgia used in her drawing?A scale factor is simply a ratio between two corresponding lengths, areas, or volumes of two similar geometric figures.
Given that, Georgia made a scale drawing of her apartment. Her bathroom is 3 inches in the drawing and 8 feet in real life.
To find the scale factor, we need to determine how many inches in the drawing represent 1 foot in real life. We can set up a proportion:
3 inches : 8 feet = x inches : 1 foot
Cross-multiplying, we get:
3 inches × 1 foot = 8 feet × x inches
Simplifying, we get:
3 = 8x
Dividing both sides by 8, we get:
x = 3/8
Therefore, the scale factor is 3/8, which means that for every 3 inches in the drawing, there is 8 feet in real life.
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area of prism
thank you
Check the picture below.
so the base of the pyramid is a triangle whose base is 12 and altitude is "x", and the pyramid has a height/altitude of 15, so
[tex]\textit{volume of a pyramid}\\\\ V=\cfrac{1}{3}Bh ~~ \begin{cases} B=\stackrel{base's}{area}\\ h=height\\[-0.5em] \hrulefill\\ B=\frac{1}{2}(12)(x)\\[1em] h=15\\ V=240 \end{cases}\implies 240=\cfrac{1}{3}\left[\cfrac{1}{2}(12)(x) \right](15) \\\\\\ 240=30x\implies \cfrac{240}{30}=x\implies 8=x[/tex]
If three pens are randomly selected from the following basket of pens, without replacement, find the probability that (a) all three pens are blue (b) none of the pens are blue (c) at least one of the pens is black
If three pens are randomly selected from the following basket of pens, without replacement, the probability that all three pens are blue is 0.027, none of the pens are blue is 0.343, and at least one of the pens is black is 0.657.
The probability of selecting three blue pens without replacement from the basket of pens is:
P(all 3 blue) = (Number of blue pens / Total number of pens)³
= (3 / 10)³
= 0.027
The probability of selecting three pens that are not blue without replacement from the basket of pens is:
P(none blue) = (Number of pens that are not blue / Total number of pens)3
= (7 / 10)³
= 0.343
The probability of selecting at least one black pen without replacement from the basket of pens is:
P(at least one black) = 1 - (Number of pens that are not black / Total number of pens)3
= 1 - (7 / 10)³
= 0.657
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The mean of a set of five score is 27. What must the sixth score be to increase the mean to 28?? Help please
If the mean of five scores is 27, then the number 33 must be added to the previous five scores to make the mean of six scores as 28.
It is given that mean of five scores is 27. If the unknown number x is added to the five scores, the new mean becomes 28. To calculate the value of x, the following equations are considered.
Let us say that the five scores are A, B, C, D and E.
∴ Mean of five scores = (A+B+C+D+E)/ 5 = 27
⇒ (A+B+C+D+E) = 27 × 5 = 135
Now, if sixth score x is added, then mean score becomes 28.
⇒ (A+B+C+D+E+x)/ 6 = 28
⇒ (A+B+C+D+E+x) = 28×6 = 168
Putting the value of (A+B+C+D+E) in above equation, we get:
135 + x = 168
x = 168 - 135 = 33
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A new movie is coming out that you and your family really want to see. You are going to buy tickets for
opening day as soon as they go on sale and want to get extra tickets so friends could come too. You
have $224.50 and wants to get as many tickets as possible. You want to get at least 5 adult tickets and
4 kids tickets.
Use the ticket prices from your local movie theater or look up the average prices of child and adult
tickets for the movie theater.
In your discussion post, share the equations that you used to model this situation and answer the
following questions:
1. Can you get at least 5 adult tickets and 4 kids tickets?
2. What is the most tickets you could have bought and met the given conditions? What number of
each type of ticket is that?
3. After doing more research, you find out that you can rent out a whole theater for $190. If you rent
the theater out, you can have up to 24 people, regardless of whether they are children or adults. In
what situations would it be a better deal to rent out the theater?
1. The equation for the cost of adult tickets is:
$8.97 x number of adult tickets
The equation for the cost of child tickets is:
$6.79 x number of child tickets
The equation for the cost of renting out the theater is:
$190
2. Yes, you can get at least 5 adult tickets and 4 kids tickets.
3. The most tickets you could have bought and met the given conditions is 9 adult tickets and 8 kids tickets.
4. It would be a better deal to rent out the theater if you had more than 24 people.
You must be aware of the costs of adult and child tickets in order to determine if you can purchase at least 5 adult tickets and 4 child tickets. A cinema ticket for an adult costs $8.97 on average, while a ticket for a child costs $6.79 on average. 4 children's tickets would cost $27.16 and 5 adult tickets would cost $44.85 as a result. You would then have $202.49 remaining, which would be enough to pay for 7 additional child tickets. Thus, you can purchase at least 5 adult and 4 child tickets.
The most tickets you could have purchased while still fulfilling the requirements is nine adult and eight child tickets. The total price would be $135.05. The adult tickets would cost $80.73 and the child tickets would cost $54.32. You would now have $89.45, which is insufficient to purchase any additional tickets.
Renting out the theater might be a great option if you have more than 24 individuals. This is due to the fact that hiring out the theater costs $190 and allows for a maximum of 24 guests, both adults and children. Consequently, renting the theater would be less expensive than purchasing individual tickets if you had more than 24 individuals.
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A catapult launches a boulder with an upward velocity of 132 ft/s. The height of the boulder, h, in feet after t seconds is given by the function h= -16t^2+132t+30 How long does it take the boulder to reach its maximum height? What is the boulder’s maximum height? Round to the nearest hundredth, if necessary.
Boulder takes 4.13 seconds to reach its maximum height.
The boulder's maximum height is 282.38 feet.
What is a velocity?Velocity is a physical quantity that describes the rate of change of an object's position over time. Velocity has both magnitude as well as direction that's why it is a vector quantity.
Given that:
Upward velocity of the boulder = 132 ft/s
Function for the height of the boulder as a function of time, t:
h(t) = -16[tex]t^{2}[/tex] + 132t + 30
We can find the maximum height of the boulder and the time it takes to reach that height by finding the vertex of the parabolic function h(t) using the formula:
t = -b/2a
where a = -16 and b = 132.
First, we need to find the time it takes the boulder to reach its maximum height, t:
t = -b/2a = -132/(2*(-16)) = 4.125 seconds
So, it takes the boulder 4.125 seconds to reach its maximum height.
Next, we need to find the maximum height of the boulder, h:
h = h(t) = -16t^2 + 132t + 30 = -16(4.125)^2 + 132(4.125) + 30 = 282.375 feet
So, the boulder's maximum height is 282.375 feet.
Rounding to the nearest hundredth, the time it takes the boulder to reach its maximum height is 4.13 seconds and the boulder's maximum height is 282.38 feet.
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At an animal shelter, a guinea pig eats cabbage at the constant rate. The table shows the
proportional relationship between minutes and pieces of cabbage eaten. 4
3
5
7
9
11
X
11
+6
.6
9
+6
-6
+6
6
18
30
42
54
66
y
The situation can be clearly represented by the equation y = 6x.
What is an equation?Equation: A declaration that two expressions with variables or integers are equal. In essence, equations are questions, and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics. Simple algebraic equations with merely addition or multiplication to differential equations, exponential equations with exponential expressions, and integral equations are examples of different types of equations. They are employed to represent a number of physics laws.
As per the given data:
Relation between different cabbage eaten and minutes is given.
To find the proportional relation:
Let's consider y as pieces of cabbage eaten.
and x as the time in minutes
If the relation is y = ax
From the table
18 = a × 3 ; a = 6
30 = a × 5 ; a = 6
42 = a × 7 ; a = 6
∴ y = 6x
Hence, the situation can be clearly represented by the equation y = 6x
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50 points and mark brainly
Answer:
Step-by-step explanation:
Well first we know that there are 25 squares. If we use some quick arithmetic, we can find how much each square represents out of 100%:
100/25 = 4
100% divided by 25 squares represents 4% for each square in the diagram. If we want to cover 48%, we can use some algebra:
4s = 48
s = 12
We need to shade in 12 squares to cover 48% of the diagram.
Hopefully this explanation was thorough enough!
Find the domain and the range of the following functions 1. \( f(x)=3 x^{2}+2 \) 2. \( f(x)=\frac{1}{1-x} \) 3. \( f(x)=\sqrt{x+2} \)
The domain and range of the functions are:
1. \( f(x)=3 x^{2}+2 \) : Domain: all real numbers, Range: all real numbers
2. \( f(x)=\frac{1}{1-x} \) : Domain: all real numbers except x=1, Range: all real numbers except y=0
3. \( f(x)=\sqrt{x+2} \) : Domain: all real numbers greater than or equal to -2, Range: all real numbers greater than or equal to 0
The domain and range of a function are the set of possible inputs and outputs, respectively.
1. For the function \( f(x)=3 x^{2}+2 \), the domain is all real numbers because there are no restrictions on the input. The range is also all real numbers because the output can be any value.
2. For the function \( f(x)=\frac{1}{1-x} \), the domain is all real numbers except x=1, because when x=1, the denominator becomes 0 and the function is undefined. The range is also all real numbers except y=0, because the output can never equal 0.
3. For the function \( f(x)=\sqrt{x+2} \), the domain is all real numbers greater than or equal to -2, because the square root of a negative number is not a real number. The range is all real numbers greater than or equal to 0, because the square root of a number is always positive or 0.
In conclusion, the domain and range of the functions are:
1. \( f(x)=3 x^{2}+2 \) : Domain: all real numbers, Range: all real numbers
2. \( f(x)=\frac{1}{1-x} \) : Domain: all real numbers except x=1, Range: all real numbers except y=0
3. \( f(x)=\sqrt{x+2} \) : Domain: all real numbers greater than or equal to -2, Range: all real numbers greater than or equal to 0
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The continuous random variable X has probability density function given by f(x) = 0.1 + kx where 0 ≤ x ≤ 5 0 otherwise (a) Find the value of the constant, k, which ensures that this is a proper density function. (b) Evaluate E[X], and var[X]. (c) If G = 5X − 6, obtain the mean and standard deviation of G. (d) If H = 5 − 6X, obtain the mean and standard deviation of H.
a) The value of k is 0.04.
b) The value of E[X] is 3.3333 and the value of var[X] is 1.3889.
c) The standard deviation of G is 5.8916.
d) The standard deviation of H is 7.0711.
(a) To find the value of k that ensures that f(x) is a proper density function, we need to ensure that the integral of f(x) over its domain is equal to 1:
∫05 (0.1 + kx) dx = 1
0.5 + 12.5k = 1
12.5k = 0.5
k = 0.04
Therefore, the value of k is 0.04.
(b) To find E[X], we need to evaluate the integral of x*f(x) over its domain:
E[X] = ∫05 x(0.1 + 0.04x) dx
E[X] = 0.5 + 0.02(125/3) = 3.3333
To find var[X], we need to evaluate the integral of (x - E[X])2*f(x) over its domain:
var[X] = ∫05 (x - 3.3333)2(0.1 + 0.04x) dx = 1.3889
(c) If G = 5X - 6, then E[G] = 5E[X] - 6 = 11.6667 and var[G] = 52var[X] = 34.7225. The standard deviation of G is the square root of var[G], which is 5.8916.
(d) If H = 5 - 6X, then E[H] = 5 - 6E[X] = -14.9998 and var[H] = 62var[X] = 49.9994. The standard deviation of H is the square root of var[H], which is 7.0711.
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Identify the quadratic function(s). (Select all that apply). y(y + 4) - y = 6 (3x + 2) + (6x - 1) = 0 4b(b) = 0 3a - 7 = 2(7a - 3)
Given that it includes a quadratic term ([tex]b^{2}[/tex]), this formula reduces to 4b(b) = 0, which is a complex quantity.
What does the function's quadratic term mean?A function with the formula a=0, b=1, and c=2 is known as a quadratic function. The function is known as the quadratic term (abbreviated as ax2), the linear term (abbreviated as bx), and the constant term (abbreviated as c).
What can you infer from a quadratic equation?The quadratic formula may be used to determine a parabola's axis of symmetry, the amount of real zeros in the quadratic equation, and the noughts of any parabola. It also produces the zeros of the any parabola.
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