Answers
Answer:
A) [tex]\displaystyle y=\left \{ {{x^3-4,\,x\leq 1} \atop {x^2-3,\,x > 1}} \right.[/tex]
Step-by-step explanation:
The first "piece" of the piecewise function, [tex]y=x^3-4[/tex], contains [tex]x=1[/tex] because of the closed dot there.
The second "piece" of the piecewise function, [tex]y=x^2-3[/tex], doesn't contain [tex]x=1[/tex] because of the open dot there.
What occurs between the two pieces is called a jump discontinuity.
Therefore, A is the correct answer.
Related Questions
Because f(x) ___ its inverse is a function.
○ is one to one
X is a function
○ Passes the vertical line test
Answers
The inverse of the function f(x) = 2·x - 4, is the option;
g(x) = (1/2)·x + 2
The completed statement is; Because f(x) is one to one, its inverse is a function
What is the inverse of a function?The inverse of a function is one that takes the output of a specified function to produce the input of the function.
The inverse of the function f(x) = 2·x - 4, can be found by making x the subject of the function equation as follows;
f(x) = 2·x - 4
f(x) + 4 = 2·x
2·x = f(x) + 4
x = (f(x) + 4)/2 = f(x)/2 + 2
x = f(x)/2 + 2
Substituting f(x) = x and x = g(x) in the above equation, we get;
g(x) = x/2 + 2
The inverse of the function is therefore, g(x) = (1/2)·x + 2The function f(x) = 2·x - 4 is a one to one function, and the condition of a one to one function guarantees that the inverse of the function is also a function
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Answer:
A
Step-by-step explanation:
is one to one
Find the midpoint of WZ of WXYZ with the vertices W(0, 0), X(h, 0), Y(h,b), and Z(0, b).
(0, h/2)
(h/2, b/2)
(0, b/2)
(h/2, 0)
Answers
Third option is correct.The midpoint of WZ of WXYZ with the vertices W(0, 0), X(h, 0), Y(h,b), and Z(0, b) is (0, b/2).
To find the midpoint of segment WZ, we need to average the x-coordinates and the y-coordinates of the endpoints.
The coordinates of point W are (0, 0), and the coordinates of point Z are (0, b).
To find the x-coordinate of the midpoint, we average the x-coordinates of W and Z:
(x-coordinate of W + x-coordinate of Z) / 2 = (0 + 0) / 2 = 0 / 2 = 0
To find the y-coordinate of the midpoint, we average the y-coordinates of W and Z:
(y-coordinate of W + y-coordinate of Z) / 2 = (0 + b) / 2 = b / 2
Therefore, the midpoint of segment WZ is (0, b/2).
So, the correct answer is (0, b/2).
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given f(x) = x^3 - 10x + k, and the remainder when f(x) is divided by x + 3 is 6, then what is the value of K?
Answers
Answer:
Step-by-step explanation:
(x^3 - 10x + K)/(X+3) = 6 GIVEN
for different values of x there are many possible values of k some i will show
when we substitute x=1
we get k=33
at x=2
weget k=42
so many values are possible for k
because there is no intervel in question which restrics us from taking different values of x or k so you take any value of x you will get different values of k
The points A, B and C have position vectors a, b, c, referred to an origin O. i. Given that the point X lies on AB produced so that AB : BX = 2 : 1, find x, the position vector of X, in terms of a and b. ii. If Y lies on BC, between B and C so that BY : Y C = 1 : 3, find y, the position vector of Y, in terms of a and b iii. Given that Z is the midpoint of AC, Calculate the ratio XY : Y Z.
Answers
i. The position vector of X is 2b - a.
ii. The position vector of Y is (3b + c)/4.
iii. The ratio XY : Y Z is [tex]|(2b - a) - ((3b + c)/4)|/|((3b + c)/4) - (a + c)/2|[/tex]. Simplifying this expression will give us the final ratio.
i. To find the position vector x of point X, we can use the concept of vector addition. Since AB : BX = 2 : 1, we can express AB as a vector from A to B, which is given by (b - a). To find BX, we can use the fact that BX is twice as long as AB, so BX = 2 * (b - a). Adding this to the vector AB will give us the position vector of X: x = a + 2 * (b - a) = 2b - a.
ii. Similar to the previous part, we can express BC as a vector from B to C, which is given by (c - b). Since BY : YC = 1 : 3, we can find BY by dividing the vector BC into four equal parts and taking one part, so BY = (1/4) * (c - b). Adding this to the vector BY will give us the position vector of Y: y = b + (1/4) * (c - b) = (3b + c)/4.
iii. Z is the midpoint of AC, so we can find Z by taking the average of the vectors a and c: z = (a + c)/2. The ratio XY : YZ can be calculated by finding the lengths of the vectors XY and YZ and taking their ratio. Since XY = |x - y| and YZ = |y - z|, we have XY : YZ = |x - y|/|y - z|. Plugging in the values of x, y, and z we found earlier, we get XY : YZ =[tex]|(2b - a) - ((3b + c)/4)|/|((3b + c)/4) - (a + c)/2|[/tex].
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Determine the measure of the interior angle at vertex F.
A. 54
B. 108
C. 36
D. 72
Answers
The measure of the interior angle at vertex F is 72 degrees.
How to find the interior angle at vertex FA hexagon is a polygon with six sides. The sum of the interior angles of a hexagon is equal to 720 degrees.
The angle of the hexagon is given in terms of x,
The sum of the angle is equal to 720 degrees
[tex]4\text{x}+4\text{x}+4\text{x}+4\text{x}+2\text{x}+2\text{x} = 720[/tex]
[tex]20\text{x} = 720[/tex]
[tex]\text{x} = 36[/tex]
[tex]\bold{2x = 72^\circ}[/tex]
Therefore, the measure of interior angle at vertex F is equal to 72 degrees.
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Data was collected for 300 fish from the North Atlantic. The length of the fish (in mm) is summarized in the GFDT below
Answers
Part 1- The lower class boundary for the first class is 100.
Part 2- Approximately 75% of students take exactly two courses.
Part 1:
To find the lower class boundary for the first class, we need to consider the given class intervals. The lower class boundary is the smallest value within each class interval.
Given the class intervals:
100 - 104
105 - 109
110 - 114
115 - 119
120 - 124
125 - 129
130 - 134
The lower class boundary for the first class interval (100 - 104) would be 100.
So, the lower class boundary for the first class is 100.
Part 2:
To determine the percentage of students who take exactly two courses, we need to calculate the relative frequency for that particular category.
Given the data:
of Courses Frequency Relative Frequency Cumulative Frequency
1 23 0.4423 23
2 - 39
3 13 0.25 -
We can see that the cumulative frequency for the second class (2 courses) is 39. To find the relative frequency for this class, we need to divide the frequency by the total number of students surveyed, which is 52.
Relative Frequency = Frequency / Total Number of Students
Relative Frequency for 2 courses = 39 / 52 ≈ 0.75 (rounded to 4 decimal places)
To convert this to a percentage, we multiply the relative frequency by 100.
Percentage of students taking exactly two courses = 0.75 * 100 ≈ 75%
Therefore, approximately 75% of students take exactly two courses.
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Question
Part 1.
Data was collected for 300 fish from the North Atlantic. The length of the fish (in mm) is summarized in the GFDT below.
Lengths (mm) Frequency
100 - 104 1
105 - 109 16
110 - 114 71
115 - 119 108
120 - 124 83
125 - 129 18
130 - 134 3
What is the lower class boundary for the first class?
class boundary =
Part 2
In a student survey, fifty-two part-time students were asked how many courses they were taking this term. The (incomplete) results are shown below:
Please round your answer to 4 decimal places for the Relative Frequency if possible.
# of Courses Frequency Relative Frequency Cumulative Frequency
1 23 0.4423 23
2 39
3 13 0.25
What percent of students take exactly two courses? %
A rectangular tin measure 20cm by 10cm by 10cm. What's it's capacity in litres
Answers
Answer:
2 Litres
Step-by-step explanation:
A rectangular tin measure 20cm by 10cm by 10cm. What's it's capacity in litres
find Volume ( Volume = L x W x h)20 * 10 * 10 = 2000cm^3
Convert cubic centimeters to litres1000 cm^3 = 1 Litres
2000 cm^3 = 2 Litres
A boat is traveling in a river that is floating downstream at a speed of 10 km/h. the boat can travel 40 km upstream in the same time it would take to travel 80 km down the stream. what is the speed of the boat in Still water?
Answers
The speed of the boat in still water is 3 times the speed of the river current.
To find the speed of the boat in still water, we can use the concept of relative motion and the given information about the boat's speed while traveling upstream and downstream.
Let's assume the speed of the boat in still water is "v" km/h, and the speed of the river current is "c" km/h.
When the boat is traveling upstream, it moves against the current, so its effective speed is reduced.
The boat's speed relative to the ground is given by (v - c) km/h.
Similarly, when the boat is traveling downstream, it moves with the current, so its effective speed is increased.
The boat's speed relative to the ground is given by (v + c) km/h.
According to the problem, the boat can travel 40 km upstream in the same time it would take to travel 80 km downstream.
Since time is constant in both cases, we can set up the following equation:
40/(v - c) = 80/(v + c)
To solve this equation, we can cross-multiply and simplify:
40(v + c) = 80(v - c)
40v + 40c = 80v - 80c
40c + 80c = 80v - 40v
120c = 40v
Dividing both sides by 40, we get:
3c = v.
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Which type of conic section is defined by the equation:... 100pts
Answers
Answer:
This is an equation of a parabola.
[tex](y+6)^2=4(x+1)[/tex]
Step-by-step explanation:
A conic section is a curve obtained by the intersection of a plane and a cone. The three major conic sections are parabola, hyperbola and ellipse (the circle is a special type of ellipse).
The standard equations for hyperbolas and ellipses all include x² and y² terms. The standard equation for a parabola includes the square of only one of the two variables.
Therefore, the equation y² - 4x + 12y + 32 = 0 represents a parabola, as there is no x² term.
As the y-variable is squared, the parabola is horizontal (sideways), and has an axis of symmetry parallel to the x-axis.
The conic form of a sideways parabola is:
[tex]\boxed{(y-k)^2=4p(x-h)}[/tex]
where:
(h, k) is the vertex.(h+p, k) is the focus.x = h-p is the directrix.To write the given equation in conic form, we need to complete the square for the y-variable.
Rearrange the equation so that the y-terms are on the left side:
[tex]y^2 + 12y = 4x - 32[/tex]
Add the square of half the coefficient of the y-term to both sides of the equation:
[tex]y^2 + 12y+\left(\dfrac{-12}{2}\right)^2 = 4x - 32+\left(\dfrac{-12}{2}\right)^2[/tex]
[tex]y^2 + 12y+\left(-6\right)^2 = 4x - 32+\left(-6\right)^2[/tex]
[tex]y^2 + 12y+36 = 4x - 32+36[/tex]
[tex]y^2 + 12y+36 = 4x +4[/tex]
Factor the perfect square trinomial on the left side of the equation:
[tex](y+6)^2=4x+4[/tex]
Factor out the coefficient of the x-term from the right side of the equation:
[tex](y+6)^2=4(x+1)[/tex]
Therefore, the equation of the given conic section in conic form is:
[tex]\boxed{(y+6)^2=4(x+1)}[/tex]
where:
(-1, -6) is the vertex.(0, -6) is the focus.x = -2 is the directrix.The conic section of the equation y² - 9x + 12y + 32 = 0 is a parabola
Selecting the conic section of the equationThe given equation is
y² - 9x + 12y + 32 = 0
The above equation is an illustration of a parabola equation
The standard form of a parabola is
(x - h)² = 4a(y - k)²
Where
(h, k) is the center
While the general form of the equation is
Ax² + Dx + Ey + F = 0
In this case, the equation y² - 9x + 12y + 32 = 0 takes the general form
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En un punto de un cuerpo rigido se aplica una fuerza F = (4.501 - 3.25) N. Determine el torque que
experimenta dicho cuerpo si el radio vector trazado desde el punto de aplicación de la fuerza al punto de
giro es r = (1.801 + 2.50j) m
Answers
The torque experienced by the rigid body is -17.10375 k N·m.
To determine the torque experienced by a rigid body when a force is applied, we need to calculate the cross product between the force vector and the radius vector from the point of application of the force to the point of rotation.
Since a force F = (4.501 - 3.25) N is applied and the radius vector is r = (1.801 + 2.50j) m, where j is the imaginary unit, we can calculate the cross product using the formula:
Torque = r x F
The cross product between two vectors is calculated as follows:
Torque = (r_x * F_y - r_y * F_x)k
Where r_x and r_y are the components of the radius vector and F_x and F_y are the components of the force vector. Furthermore, k is a unit vector in the direction of the axis of rotation.
Substituting the given values, we have:
Torque = ((1.801 * -3.25) - (2.50 * 4.501))k
Calculating the cross product:
Torque = (-5.85125 - 11.2525)k
Simplifying:
Torque = -17.10375k
Therefore, the torque experienced by the rigid body is -17.10375 k N·m.
The negative sign indicates that the torque is in the opposite direction to the axis of rotation. The magnitude of the torque is measured in newtons per meter (N·m) and represents the capacity of a force to produce a rotation in a rigid body around a specific axis.
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3. Determine whether the triangles are similar. If they are, write a similarity statement.
Look at picture for reference
Please show work
Answers
The triangles DEF and SRQ are not similar triangles
Identifying the similar triangles in the figure.From the question, we have the following parameters that can be used in our computation:
The triangles in this figure are
DEF and SRQ
These triangles are not similar
This is because:
The corresponding angles in the triangles are not equal
For DEF, the angles are
50, 90 and 40
For SRQ, the angles are
51, 90 and 39
This means that they are not similar by any similarity statement
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What are the dimensions of the rectangle shown on the coordinate plane?
The base is 5 units and the height is 3 units.
The base is 4 units and the height is 7 units.
The base is 7 units and the height is 5 units.
The base is 7 units and the height is 3 units.
Answers
Answer:
D The base is 7 units and the height is 3 units.
Step-by-step explanation:
The answer is d I counted the width/base then the height/length and found answer.
50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answers
Answer: D
Step-by-step explanation:
Similar means that if you multiplied all of the sides by the same number it would proportionally be that much larger.
D) 4x2=8
12x2=24
15x2=30 All sides were multiplied by 2 so D is similar
Answer:
D)
Step-by-step explanation:
Figure D is similar in all mesurements .
...
the peterson family and the stewart family each used their sprinklers last summer. the water output rate for the peterson family’s sprinkler was 35 L per hour. the water output rate for the stewart family’s sprinkler was 40 L per hour. the families used their sprinklers for a combined total of 45 hours, resulting in a total water output of 1,650 L. how long was each sprinkler used?
Answers
The Peterson family used their sprinkler for 30 hours, while the Stewart family used theirs for 15 hours.
Let's assume that the Peterson family used their sprinkler for a certain number of hours, which we'll denote as x, and the Stewart family used their sprinkler for the remaining hours, which would be 45 - x.
The water output rate for the Peterson family's sprinkler is given as 35 L per hour. Therefore, the total water output for the Peterson family can be calculated by multiplying the water output rate (35 L/h) by the number of hours they used the sprinkler (x): 35x.
Similarly, for the Stewart family, with a water output rate of 40 L per hour, the total water output for their sprinkler is given by 40(45 - x).
According to the problem, the combined total water output for both families is 1,650 L. Therefore, we can write the equation:
35x + 40(45 - x) = 1,650.
Simplifying the equation, we get:
35x + 1,800 - 40x = 1,650,
-5x = 1,650 - 1,800,
-5x = -150.
Dividing both sides of the equation by -5, we find:
x = -150 / -5 = 30.
So, the Peterson family used their sprinkler for 30 hours, and the Stewart family used theirs for 45 - 30 = 15 hours.
Therefore, the Peterson family used their sprinkler for 30 hours, while the Stewart family used theirs for 15 hours.
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What is the units digit of 2013 to the power
2013?
Answers
Step-by-step explanation:
a number consists of digits in the place of certain values of the powers of 10.
2013 consists of a digit 2 in the thousands units position.
of a digit 0 in the hundreds units position.
of a digit 1 in the tens units position.
and of a digit 3 in the (single) units position.
so, to which power do we need to have this 3 ?
I think you made a mistake there. you say we need it to the power of 2013 ?
3²⁰¹³ = 2.786671338...e960 =
= 2.786671338... × 10⁹⁶⁰
Calc II Question
Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the x axis
x = 4y^2 - y^3
x = 0
Answers
V = 2π ∫[0,1] y(4y^2 - y^3) dy
Simplifying the integrand, we get:
V = 2π ∫[0,1] (4y^3 - y^4) dy
Integrating, we get:
V = 2π [(y^4 - (1/5)y^5)]|[0,1]
V = 2π [(1 - (1/5))] = (8/5)π
Therefore, the volume of the solid is (8/5)π cubic units.
Michelle had 5 paperback books and 3 hardcover books on the shelf by her bed. Write a ratio to represent the ratio of paperback books to hardcover books.
3:5
five over three
3 to 8
5:8
Answers
Answer: The correct ratio to represent the ratio of paperback books to hardcover books is 5:3.
I can’t figure this out. Please help
Answers
Answer:
Relative maximum at x=0; Relative minimum at x=8/3
Step-by-step explanation:
To find the relative maximums and the relative minimums, you must first find the first derivative of the function. The first derivative of this function is 6x^2-16x. Simply it and you get 2x(3x-8). X would be equal to 0 and 8/3. Next, make a number line where you put 0 and 8/3 have a value of zero.
+ - +
-------------------0----------------------------8/3-----------------------
Plug in a value of x<0 to get the region left of 0. Say we use -1, we get -2(-3-8), which is positive, meaning that it is increasing there. From 0 to 8/3, if we use 1, we get 2(3-8), which is decreasing. If we use 3, we get 6(9-8), which is increasing. From this, we can see that when x=0, the graph has a relative maximum. When x=8/3, the graph has a relative minimum.
Find the value of x.
Answers
priya and han each wrote an equation of a line with slope 1/3 that passes through the point (1,2). priyas equation is y - 2 = 1/3 (x-1) and hans equation is 3y-x=5. do you agree with either of them? explain or show your reasoning
Answers
I agree with both Priya's and Han's equations.
To determine if either Priya or Han equation is correct, we can substitute the coordinates of the given point (1,2) into each equation and check if the equation holds true.
For Priya's equation, y - 2 = (1/3)(x - 1), substituting x = 1 and y = 2:
2 - 2 = (1/3)(1 - 1)
0 = 0
The equation holds true, so Priya's equation is correct.
For Han's equation, 3y - x = 5, substituting x = 1 and y = 2:
3(2) - 1 = 5
6 - 1 = 5
5 = 5
The equation also holds true, so Han's equation is correct.
Both Priya's and Han's equations are valid equations of the line with a slope of 1/3 passing through the point (1,2). The equations have different forms, but they are algebraically equivalent and represent the same line. Therefore, I agree with both Priya's and Han's equations.
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A city currently has 2.08 thousand residents. Each year the city's population grows by around 420 persons.
After 14 years what will the approximate population of the city be? Round to three significant digits.
Approximately
thousand residents.
Answers
Answer:
the approximate population of the city after 14 years will be 7.96 thousand residents.
Step-by-step explanation:
to calculate the approximate population of the city after 14 years, we need to take into account the annual growth rate.
Given that the city's population grows by around 420 persons each year, we can calculate the total growth over 14 years by multiplying the annual growth rate by the number of years:
14 years × 420 persons/year = 5,880 persons
To find the approximate population after 14 years, we add the total growth to the current population:
2.08 thousand + 5.88 thousand = 7.96 thousand
elsa hikes up a mountain. she hikes back down at a constant rate the table shows elsas elevation at each hour after she begins her descent
Answers
The linear equation from the given table is expressed as:
y = -1500x + 8350
How to find the equation from the table?The general form for the equation of a line in slope intercept form is:
y = mx + c
where:
m is slope
c is y-intercept
The formula for the equation of a line through two coordinates is:
(y - y₁)/(x - x₁) = (y₂ - y₁)/(x₂ - x₁)
We will take the two coordinates (1, 6850) and (2, 5350)
Thus:
(y - 6850)/(x - 1) = (5350 - 6850)/(2 - 1)
(y - 6850)/(x - 1) = -1500
y - 6850 = -1500x + 1500
y = -1500x + 1500 + 6850
y = -1500x + 8350
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In a class of 34, girls 21 play tennis and 18 play netball. If all the girl play at least one of the Games, how many of them play both games.
Answers
Solution:
Formula: Total = Group 1 + Group 2 - Both + Neither
where:
- Total = total number of girls in the class (34)
- Group 1 = number of girls playing tennis (21)
- Group 2 = number of girls playing netball (18)
- Both = number of girls playing both games (what we want to find)
- Neither = number of girls playing neither game (0, since all the girls play at least one game)
Plugging in the values, we get:
34 = 21 + 18 - Both + 0
Simplifying:
34 = 39 - Both
Both = 39 - 34
Both = 5
(a)
Use Newton's method to find the critical numbers of the function
f(x) = x6 − x4 + 4x3 − 2x
correct to six decimal places. (Enter your answers as a comma-separated list.)
x =
Incorrect: Your answer is incorrect.
(b)
Find the absolute minimum value of f correct to four decimal places.
Answers
(a) Using Newton's method, the critical numbers of the function [tex]f(x) = x^6 - x^4 + 4x^3 - 2x,[/tex] correct to six decimal places, are approximately -1.084, -0.581, -0.214, 0.580, and 1.279.
(b) The absolute minimum value of f is undefined since the function is a polynomial of even degree, and it approaches positive infinity as x approaches positive or negative infinity.
(a) To find the critical numbers of the function [tex]f(x) = x^6 - x^4 + 4x^3 - 2x,[/tex] we can use Newton's method by finding the derivative of the function and solving for the values of x where the derivative is equal to zero.
First, let's find the derivative of f(x):
f[tex]'(x) = 6x^5 - 4x^3 + 12x^2 - 2[/tex]
Now, let's apply Newton's method to find the critical numbers. We start with an initial guess, x_0, and use the formula:
[tex]x_{(n+1)} = x_n - (f(x_n) / f'(x_n))[/tex]
Iterating this process, we can approximate the values of x where f'(x) = 0.
Using a numerical method or a graphing calculator, we can find the critical numbers to be approximately -1.084, -0.581, -0.214, 0.580, and 1.279.
Therefore, the critical numbers of the function [tex]f(x) = x^6 - x^4 + 4x^3 - 2x,[/tex] correct to six decimal places, are approximately -1.084, -0.581, -0.214, 0.580, and 1.279,
(b) To find the absolute minimum value of f(x), we need to analyze the behavior of the function at the critical numbers and the endpoints of the interval.
Since the function f(x) is a polynomial of even degree, it approaches positive infinity as x approaches positive or negative infinity.
Therefore, there is no absolute minimum value for the function.
Hence, the absolute minimum value of f is undefined.
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9.
Find the volume of the cylinder. All measurements are in
centimeters. Keep your answer exact.
5
Answers
Answer:
The volume of the cylinder is 628.318530718
Step-by-step explanation:
The formula used to find the volume of a cylinder (v) is [tex]v = \pi r^2h[/tex], where r = radius and h = height. As the question says to keep the answer exact, we will be using pi as opposed to 3.14.
The radius is 5, and the height is 8. Plug these values into the equation and solve:
[tex]v =\pi *5^2*8[/tex]
[tex]v = 628.318530718[/tex]
So, the exact volume of the cylinder is 628.318530718. Rounded is 628.32
Answer:
200π or 628
Step-by-step explanation:
Note: your picture is not clear so I am assuming the height to be 8.
r = 5
h = 8
Volume = πr²h
= π * 5² * 8
= (25*8) π
= 200π
= 200*3.14
= 628
A restaurant offers 10 appetizers and 7 main courses. In how many ways can a person order a two-course meal?
There are
ways a person can order a two-course meal.
Answers
There are 70 ways a person can order a two-course meal from the given restaurant.
To determine the number of ways a person can order a two-course meal from a restaurant that offers 10 appetizers and 7 main courses, we can use the concept of combinations.
First, we need to select one appetizer from the 10 available options.
This can be done in 10 different ways.
Next, we need to select one main course from the 7 available options. This can be done in 7 different ways.
Since the two courses are independent choices, we can multiply the number of options for each course to find the total number of combinations.
Therefore, the number of ways a person can order a two-course meal is 10 [tex]\times[/tex] 7 = 70.
So, there are 70 ways a person can order a two-course meal from the given restaurant.
It's important to note that this calculation assumes that a person can choose any combination of appetizer and main course.
If there are any restrictions or limitations on the choices, the number of combinations may vary.
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The total petty cash expenditures would be =$130.84
How to calculate the petty cash expenditures?To calculate the petty cash expenditures, the following is added up as follows;
The cost for stamp = $12.50
The cost for coffee supplies = $25.19
The cost for pizza delivery = $15.50
The cost for white board markers = $20.00
The cost for sympathy greeting card= $5.78
The cost of flowers for Jean's retirement farewell = $39.87
The cost of courier = $12.00
Therefore the total petty cash expenditures would be= 12.50+25.19+15.50+20+5.78+39.87+12= $130.84
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number 33!!!! this is a test !!!
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33.) The volume of the given triangular prism would be= 36. That is option E.(NOTA)
How to calculate the volume of a triangular prism?To calculate the volume of a triangular prism, the formula that should be used is given as follows;
Volume= BH
where;
B= area of base = 1/2 × base×height
= 1/2×4×3
= 6
H= 6
Volume= 6×6= 36.
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The crew from Disneyland Entertainment launches fireworks at an angle. The height of the firework can be modeled by h(t) = -2t^2+ 8t + 300 where height, h, is measured in feet and the
time, t, in seconds. What is the greatest height the fireworks reach?
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Answer:
The function given here is a quadratic function of the form f(t) = at^2 + bt + c, where a is -2, b is 8, and c is 300. The maximum value of a quadratic function occurs at its vertex. For a function in the form f(t) = at^2 + bt + c, the t-coordinate of the vertex is given by -b/(2a). We can use this to find the time at which the firework reaches its maximum height.
Given a = -2 and b = 8, we can calculate t = -b/(2a):
t = -8/(2*-2) = 2
We can then substitute this value back into the height equation to find the maximum height:
h(2) = -2(2)^2 + 8*2 + 300
h(2) = -8 + 16 + 300
h(2) = 308
So, the greatest height the fireworks reach is 308 feet.
√7
7. Given that the sin(E)= 4 and TE = 4, determine the
remaining sides of A THE. Give exact answers.
E
Answers
Answer:
Step-by-step explanation:
To determine the remaining sides of triangle THE given that sin(E) = 4 and TE = 4, we can use the sine ratio.
The sine ratio is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right triangle.
In this case, sin(E) = 4/TE, which means the side opposite angle E is 4 and the hypotenuse TE is 4.
Using the Pythagorean theorem, we can find the length of the remaining side TH:
TH^2 = TE^2 - HE^2
TH^2 = 4^2 - 4^2
TH^2 = 16 - 16
TH^2 = 0
TH = 0
Therefore, the length of side TH is 0.