a) The piecewise function is 80p, if p > 100 b) For p > 100, the graph will be a straight line passing through the point (100, 100 × 80) with a slope of 8
How to determine the piecewise function for the problema) We can define a piecewise function f(p) to represent the cost of catering service depending on the number of persons (pax).
f(p) =
120p, if p ≤ 30
105p, if 31 ≤ p ≤ 60
95p, if 61 ≤ p ≤ 100
80p, if p > 100
b) To graph the piecewise function, we can plot the points for each of the four parts of the function, and connect them with line segments. The graph will have four segments, each with a different slope.
For p ≤ 30, the graph will be a straight line passing through the origin with a slope of 120.
For 31 ≤ p ≤ 60, the graph will be a straight line passing through the point (31, 31 × 105) with a slope of 105.
For 61 ≤ p ≤ 100, the graph will be a straight line passing through the point (61, 61 × 95) with a slope of 95.
For p > 100, the graph will be a straight line passing through the point (100, 100 × 80) with a slope of 80.
c) To find how many persons they invite to their wedding, we can use the inverse function of f(p) and plug in the given cost of RM9025.
Let C = RM9025, then
120p, if p ≤ 30
105p, if 31 ≤ p ≤ 60
95p, if 61 ≤ p ≤ 100
80p, if p > 100
Case 1: p ≤ 30
120p = C
p = C/120 = 9025/120 = 75.2083
Since p must be an integer, we round up to the nearest integer. Therefore, if they invite 76 persons, the cost of catering service will be more than RM9025.
Case 2: 31 ≤ p ≤ 60
Let x = p - 30, then
105x + 120 × 30 = C
105x = C - 3600
x = (C - 3600)/105 = (9025 - 3600)/105 = 54.5238
Therefore, if they invite 31 + 54 = 85 persons, the cost of catering service will be RM9025.
Case 3: 61 ≤ p ≤ 100
Let x = p - 60, then
95x + 120 × 30 + 105 × 30 = C
95x = C - 9750
x = (C - 9750)/95 = (9025 - 9750)/95 = 0.7632
Therefore, if they invite 60 + 0.7632 × 100 = 137 persons, the cost of catering service will be RM9025.
Case 4: p > 100
Let x = p - 100, then
80x + 120 × 30 + 105 × 30 + 95 × 40 = C
80x = C - 17700
x = (C - 17700)/80 = (9025 - 17700)/80 = -109.375
Since p must be a positive integer, this case is not possible.
Therefore, Mohammed and Mira should invite 85 persons to their wedding to pay RM9025 for the catering service.
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what are the answers to these questions?
a) The function of h in terms of r is h=1400/(πr²).
b) The surface area of the can in terms of r is 2800/r+2πr².
c) The corresponding values of r and h that minimize the amount of required material are r≈14.04 cm and h≈2.98 cm.
a) The volume of a cylinder is given by
V = πr²h.
In this case, the volume of the can is
1400 cm³
So we have
1400 = πr²h.
Solving for h, we get
h = 1400/(πr²).
b) The surface area of a cylinder is given by
A = 2πrh+2πr².
Using the expression we obtained for h in part (a), we can substitute it in the equation and get
A = 2πr(1400/(πr²))+2πr²
= 2800/r+2πr².
c) To minimize the amount of required material, we need to find the value of r that minimizes the surface area.
To do this, we take the derivative of the surface area expression with respect to r and set it equal to zero:
dA/dr = -2800/r²+4πr = 0.
Solving for r, we get
r = √(700/π), which is approximately 14.04 cm.
Substituting this value in the expression for h that we obtained in part (a), we get
h = 1400/(π(14.04)²), which is approximately 2.98 cm.
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(x+3) (x-1)squared
????
Answer:
x^3 + x^2 - 5x + 3
Last week Kristen spent 4 hours gardening over a period of 7 days .she spent the same amount of time gardening each day.about how much time did she spend gardening each day last week
Answer:
28
Step-by-step explanation:
i did 7 times 4
in the figure below, m JKM=106 degrees, m LKM=66, and KN bisects LKM. Find m JKN
The value of angle JKN is 73°.
Given that the m ∠JKM = 106 degrees, m ∠LKM = 66, and KN bisects LKM.
So we need to find the value of ∠JKN,
So, using the angles addition postulate,
∠LKM = ∠LKN + ∠MKN
Therefore,
∠LKN = 66/2 [definition of bisector]
∠LKN = 33°
Again, using the angles addition postulate,
∠JKM = ∠JKL + ∠LKM
∠JKL = 106 - 66
∠JKL = 40°
Therefore,
∠JKN = ∠JKL + ∠LKN
∠JKN = 40 + 33
∠JKN = 73°
Hence, the value of angle JKN is 73°.
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The figure below is a net for a triangular prism. What is the surface area of the triangular prism, in square meters?
The surface area of the triangular prism is given as follows:
S = 549.15 m².
How to calculate the surface area?The surface area of a prism is given by the sum of the areas of all the parts that compose the prism.
The prism for this problem is composed as follows:
Rectangle of dimensions 15 m and 13 m.Rectangle of dimensions 15 m and 15.81 m.Two right triangles of sides 9 m and 13 m.Hence the surface area is obtained as follows:
S = 15 x 13 + 15 x 15.81 + 2 x 0.5 x 9 x 13
S = 549.15 m².
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The triangular prism's surface area is given as follows:
S = 549.15 m².
The total area of all the prism's component components determines the prism's surface area.
The following is the structure of the prism for this issue:
rectangle with 15 and 13 meter sides.
rectangle with measurements of 15 and 15.81 meters.
two right triangles with 9 and 13 meter sides. So, the following is how the surface area is determined:
S is equal to 15 x 13 plus 15 x 15.81 and 2 x 0.5 x 9 x 13
S = 549.15 m².
In AABC, AB=32, AC= 22, and BC= 20. What is mZA?
m
(Do not round until the final answer. Then round to the nearest tenth as needed.)
The value of measure of ∠A would be,
⇒ ∠ A = 38.68 degree
We have to given that;
In triangle ABC,
AB=32, AC= 22, and BC= 20
Hence, We can formulate;
⇒ sin A = BC / AB
⇒ sin A = 20 / 32
⇒ sin A = 0.625
⇒ A = 38.68 degree
Thus, The value of measure of ∠A would be,
⇒ ∠ A = 38.68 degree
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if a spinner has 2 blue, 2 green and 2 red what is the probability of landing on red when it is spinned
The probability of landing on red is given by the number of red sections divided by the total number of sections. In this case, there are 2 red sections out of a total of 6 sections. Therefore, the probability of landing on red is:
P(red) = 2/6 = 1/3
So the probability of landing on red is 1/3.
Jordan is tracking a recent online purchase. The shipping costs state that the item will be shipped in a 24-inch long box with a volume of 2,880 cubic inches. The width of the box is seven inches less than the height.
The volume of a rectangular prism is found using the formula V = lwh, where l is the length, w is the width, and h is the height.
Complete the equation that models the volume of the box in terms of its height, x, in inches.
Is it possible for the height of the box to be 15 inches?
also the question has 3 boxes
Answer:
Sure, I can help you with that.
Given:
* The box is 24 inches long.
* The width of the box is seven inches less than the height.
* The volume of the box is 2,880 cubic inches.
To solve:
* Complete the equation that models the box's volume in terms of its height, x, in inches.
* Determine if the height of the box can be 15 inches.
Solution:
Let's define the following variables:
* $h$ = the height of the box (in inches)
* $w$ = the width of the box (in inches)
* $l$ = the length of the box (in inches)
We are given that l=24 and w=h−7. We can use these values to find the volume of the box:
[tex]V = lwh = 24(h - 7)h[/tex]
We can simplify this expression to get the following equation:
[tex]V = 24h^2 - 168h[/tex]
To determine if the height of the box can be 15 inches, we can substitute 15 for $h$ in the equation and see if we get a positive value for the volume.
[tex]V = 24(15)^2 - 168(15) = 2160 - 2490 = -330[/tex]
Since the volume is negative, the height of the box can't be 15 inches.
Therefore, the equation that models the box's volume in terms of its height, x, in inches is [tex]$V = 24x^2 - 168x$[/tex]. Consequently, the size of the box can't be 15 inches.
Answer:
Yes
Step-by-step explanation:
The only answer is height = 15 because the -8 will be rejected
Find the equation of the line that passes through the point (3,−5) and is perpendicular to the line y=1/5x-2
8) If Bonnie can waterproof 450 square foot of decking with 2 gallons of sealant, she will need 6 gallons (10pts)
of sealant for 1200 square foot of decking.
True
O False
Answer:
FALSSOO
Step-by-step explanation:
lol srry I pretty sure its false I did teh math
Hope its right and it helps! c:
Jazmine has 3 dogs She wants to give each dog 2 treats. How many treats does she need to have total?
Answer: 6
Step-by-step explanation:
you just get those numbers and times them 3 times 2 is 6
What’s the answer? Will give brainliest if correct
Explain reasoning
The statement that is not true is: C. The translation of a line is a pair of parallel lines.
What is transformation?In geometry, a transformation is a procedure that modifies a figure's position, size, or shape. Translation, rotation, reflection, and dilation are the four main categories of transformations.
Every point in a figure is translated by the same amount and in the same direction. A rotation revolves a figure around the centre of rotation, a fixed point. A figure is reversed over a line known as the line of reflection in a reflection.
In relation to a fixed point known as the centre of dilation, a dilation expands or contracts a figure by a specific scale factor.
The statement that is not true is: C. The translation of a line is a pair of parallel lines as translation is a transformation that moves every point of a figure the same distance in the same direction.
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HELP ITS AN EMERGENCY
Given the expression: 4x2 + 18x − 10
Part A: What is the greatest common factor? Explain how to find it. (3 points)
Part B: Factor the expression completely. Show all necessary steps. (5 points)
Part C: Check your factoring from Part B by multiplying. Show all necessary steps. (2 points)
Answer:
Part A ----> 2
Part B ----> 2 (2x - 1) (x + 5)
Part C -----> See explanation below
Step-by-step explanation:
Given expression is
4x² + 18x - 10
Part A
The greatest common factor (GCF) of the terms 4x², 18x and 10 is the largest number that divides into all three numbers without a remainder
To find this
Find the prime factors of each of the terms
4x² = 2 · 2 · x · x
18x = 2 · 3 · 3 · x
10 = 2 · 5
The prime factor common to all 3 is 2
Therefore the GCF of the expression is 2
Part B
The factored expression can be obtained by factoring out the GCF
4x² + 18x - 10 = 2(2x² + 9x - 5)
We can further factor the term in parentheses:
2x² + 9x - 5
To do this,
Break the expression into groups:
= (2x² - x) + (10x - 5)
Factor x from 2x² - x: x(2x - 1)
Factor 5 from 10x - 5: 5(2x - 1)
Therefore
(2x² - x) + (10x - 5) = x(2x - 1) + 5(2x - 1)
Factor out the common term 2x -1 to get
(2x - 1)(x + 5)
Therefore
4x² + 18x + 10 = 2 (2x - 1) (x + 5)
Part C
Checking if factorization is correct
Multiply (2x - 1)(x + 5) using the FOIL method
= 2x ·x + 2x · 5 + (-1) · x + (-1) · 5
= 2x² + 10x -1x -5
= 2x² + 9x - 5
Multiply the whole expression by 2
2 · 2x² + ² · 9x - 2 · 5
= 4x² + 18x + 10
which is the original expression
So the factorization is correct
Find the horizontal asymptotes and vertical asymptotes of the function [tex]k(x)= \frac{3x^{2} }{(x+1)(x-4)}[/tex]
the vertical asymptotes are x = -1 and x = 4, and there is no horizontal asymptote.
what is vertical asymptotes ?
Vertical asymptotes are vertical lines on a graph where a function approaches infinity or negative infinity as the input (x) approaches a certain value. In other words, vertical asymptotes occur when the denominator of a function becomes zero and the function is undefined at that point
In the given question,
To find the horizontal and vertical asymptotes of the function f(x) = 3x²/[(x+1)(x-4)], we need to analyze the behavior of the function as x approaches infinity or negative infinity and as x approaches the vertical asymptotes (if any).
Vertical asymptotes occur at the values of x that make the denominator of the fraction equal to zero. In this case, we have vertical asymptotes at x = -1 and x = 4.
To find the horizontal asymptote, we need to divide the leading term of the numerator by the leading term of the denominator when x approaches infinity or negative infinity. Since the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote. However, we can use long division or synthetic division to write the function in the form of a polynomial plus a proper fraction:
f(x) = 3x²/[(x+1)(x-4)] = (3x + 15)/(x² - 3x - 4)
As x approaches infinity or negative infinity, the fraction approaches the value of 3/1 (the ratio of the leading terms of the numerator and denominator), but there is no horizontal asymptote.
Therefore, the vertical asymptotes are x = -1 and x = 4, and there is no horizontal asymptote.
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please help with these questions it's due tommore
7:
To find 6% of 45.50=
0.06x45.50= 2.73
and than 17% of 45.50
0.17x45.50= 7.735
so add 2.73 and 7.735= 10.465
than add 10.465 to $45.50 = $55.965 So the answer is $55.965.
8:
again the same thing but with the different numbers.
0.06x105.75= 6.345
0.20x105.75= 21.15
21.15+6.345= 27.495
so than 105.75-27.495= $78.255
9:
same thing again
146.75x0.25= 36.6875
0.09x146.75= 13.2075
But this time add the tax (13.2075)= 146.75+13.2075= 159.9575
but than you subtract the discount which is 25% so 159.9575-36.6875=123.7
So that is the price! $123.7
I hope that helps!
thickness of piece of metal in m. 0.00053
The thickness of the said metal piece is 560 micrometers
How to solveSolving this question would require us to switch the thickness of the metal from meters to micrometers.
So, 1 meter is equivalent to 1,000,000 micrometers; and when 0.00053 meters is multiplied by 1,000,000, we get:
0.00053 m * 1,000,000 = 560 µm
Consequently, the thickness of the said metal piece is 560 micrometers.
A metal piece's thickness is defined as the distance, measured perpendicular to its opposing surfaces, between those surfaces. It is a crucial aspect in determining the strength and longevity of the metal object and is often stated in length measures like millimeters, inches, or micrometers.
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What is the thickness of the metal piece in micrometers, given that it is 0.00053 meters thick?
the coordinate (-1,0) (1,0) and (0,1) form the vertices of a square true or false
Since the line splits the square into two regions with equal area, it goes through center of square.
Equation of line through point (12,12)
with slope 5
y−12=5(x−12)
y=5x−2
y-intercept=(0,−2)
Since line passes through points (0.4,0)
and (0.6,1)
it divides both the bottom and top of squares in the same ratio, to that the line divides the square into 2
trapezoids with height =1
and bases =0.4
and 0.6
. Therefore, they have the same area.
On Saturday, the temperature was 75.5°F. The temperature rose by 6°F on Sunday, then dropped by 3.5°F on Monday. What was the temperature, in degrees Fahrenheit, on Monday?
Answer:
78°F
Step-by-step explanation:
If the temperature was 75.5°F, and it rose by 6°F on Sunday, then the temperature on Sunday was:
75.5°F + 6°F = 81.5°F
If the temperature on Sunday was 81.5°F, and it dropped by 3.5°F on Monday, then the temperature on Monday was:
81.5°F - 3.5°F = 78°F
Therefore, the temperature on Monday was 78°F.
Please help!!!!!!!!!!!
Solve for X
Find the measure of each angle using the solution to part C
Is c = 3 a solution to the inequality below?
122 c
yes
no
The value c = 3 is not a solution to the inequality
Checking if c = 3 is a solution to the inequalityFrom the question, we have the following parameters that can be used in our computation:
122 c
Express properly
So, we have
1 ≥ c
When this inequality is rewriiten. we have
c ≤ 1
This means that the values of c do not exceed 1
The number 3 exceeds 1
So, it means that c = 3 is not a solution to the inequality
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Which expression is not equivalent to 2/3×4
The only expression that is not equivalent to the given fraction expression is: D (2 x 1/3) + (4 x 1/3)
How to multiply fractions?The correct procedure that we will use to multiply fractions is:
- find a common denominator
- multiply the numerators
- multiply the denominators
- Simplify if necessary.
- Add the numerators and add the denominators
Looking at the options and comparing with the given fraction multiplication problem 2/3 * 4, we see that only option D is not equivalent to it because:
(2 x 1/3) + (4 x 1/3) = 6/3 = 2
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Complete question is:
Which expression is NOT equivalent to 2/3 x 4
A (2x4) /3
B 1/3 x (2x4)
C (4 x 1/3) x 2
D (2 x 1/3) + (4 x 1/3)
Find the length of the missing side
Answer:
x = 45°
Because there are 180° in a triangle
25 Points! Multiple choice algebra question. Photo attached. Thank you!
14 A national standardized test is given in May that generates a mean score of 350 with a standard
deviation of 18. What is the probability that a randomly selected test score will fall in the
interval 360 to 380?
(1) 0.56
(2) 0.013
(3) 0.24
(4) 0.76
The probability that a randomly selected test score will fall in the interval 360 to 380 is the option (3), 0.24.
How to solveTo calculate the probability that a test score falls between 360 and 380, we need to standardize these values by subtracting the mean and dividing by the standard deviation.
This gives us:
z(360) = (360-350)/18 = 0.56
z(380) = (380-350)/18 = 1.67
We can then use a standard normal distribution table or a calculator to find the area under the curve between these two z-scores.
The probability is approximately 0.24.
Therefore, the answer is option (3), 0.24.
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Two coins are tossed. Assume that each event is equally likely to occur.
a) Use the counting principle to determine the number of sample points in the sample space.
b) Construct a tree diagram and list the sample space.
c) Determine the probability that no tails are tossed.
d) Determine the probability that exactly one tail is tossed.
e) Determine the probability that two tails are tossed.
f) Determine the probability that at least one tail is tossed.
Question content area bottom
Part 1
a) There is/are --------- sample point(s) in the sample space.
a. There are 4 sample points in the sample space.
What are the probability values for the toss?a) There are 4 sample points in the sample space.
b) The tree diagram and sample space are:
HH (two heads)
HT (one head, one tail)
TH (one head, one tail)
TT (two tails)
c) The probability that no tails are tossed (two heads) is 1/4 or 0.25.
d) The probability that exactly one tail is tossed (HT or TH) is 1/2 or 0.5.
e) The probability that two tails are tossed is 1/4 or 0.25.
f) The probability that at least one tail is tossed (HT, TH, or TT) is 3/4 or 0.75.
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College Level Trig Question
Note tha given the above trigonometric expression, the solution is
x = 2π/3 or 4π/3
How did we arrive at that ?We will start by simplifing the equation by moving all the terms involving sin (x/2) to one side..
2sin (x /2) = √(3)
Then, we can solve for sin(x/2) by dividing both sides by two
sin (x /2) = √(3)/2
This is true when x/2 is π /3 or 2π/3, since these are the values where
sin ( π/3) = √(3)/2 and
sin (2π/3) = √(3)/2.
To find the values of x, we multiply these solutions by two
x = 2pi/3 or 4pi/3
Since we need to make sure that these solutions are in the given interval (0, 2π)
both solutions are in the interval, so our final answer is
x = 2π/3 or 4 π/3
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What is deviance? Identify the term and provide an overview. Think of a time when you or a
friend used informal negative sanctions. To what act of deviance were you or your friend
responding? Did this reaction help maintain social control? Is it possible to function as a society
without the threat of physical violence to keep people under control? Why or why not?
Deviance is a term used in sociology to describe behavior that violates social norms or expectations. It refers to any behavior that is considered outside of the established rules and expectations of a society or culture.
What are informal negative sanctions?Informal negative sanctions are the social disapproval or punishment that people receive for violating social norms. An example of informal negative sanctions could be a group of friends ostracizing another friend for breaking a social rule, such as not showing up to a planned event.
In terms of the act of deviance, it could be anything from breaking a minor social norm to committing a serious crime. The reaction of informal negative sanctions is often an attempt to maintain social control by encouraging conformity to the established norms of the group or society.
While physical violence is not necessary to maintain social control, the threat of punishment is an important part of any functioning society. People follow the rules and norms of society because they know that if they do not, there will be consequences. However, it is important to note that violence and punishment should not be the only means of social control. Positive reinforcement, such as rewards for good behavior, can also be an effective way of encouraging conformity to social norms.
In summary, deviance refers to behavior that violates social norms, and informal negative sanctions are a way of enforcing social norms. The threat of physical violence is not necessary to maintain social control, but consequences for deviant behavior are essential for any functioning society.
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PLEASE HURRY
Let u = - 4i + 2j , v = 3i - j and w = - 6j
Find the specified scalar or vector
5u(3v - 4w)
The specified scalar or vector 5u(3v - 4w) is equal to -420i + 250j.
We can begin by distributing the scalar 5 to the vector 3v - 4w:
5u(3v - 4w) = 5u(3v) - 5u(4w)
Next, we can find the scalar multiples:
5u(3v) = 5(-4i + 2j)(3(3i - j)) = 5(-36i + 10j)
5u(4w) = 5(-4i + 2j)(4(-6j)) = 5(48i - 40j)
Now we can substitute these values back into the original expression:
5u(3v - 4w) = 5(-36i + 10j) - 5(48i - 40j)
Simplifying:
5u(3v - 4w) = -420i + 250j
Therefore, 5u(3v - 4w) = -420i + 250j.
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Stan lawn mower had 1/8 of a gallon of gasoline in the tank he added 6/10 to the tank after he only had 1/4 of a gallon what was the total used
Stan used 19/40 of a gallon of gasoline.
Given that;
At first, Stan's lawn mower had 1/8 of a gallon of gasoline in the tank. When it got finished, he put 6/10 of a gallon of gasoline in the tank.
Hence, It means that the number of gallons of gasoline that he has already put in the tank is
1/8 + 6/10 = 29/40 of a gallon.
Now, After he mowed, 1/4 of a gallon was left in the tank.
Therefore, the total amount of gasoline Stan used is
29/40 - 1/4 = 19/40 of a gallon
Thus, the total amount of gasoline Stan used is, 19/40 of a gallon
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you are melting a rectangular block of wax to make candles. how many candles of the given shape can be made using a block that measures 10 cm by 9cm by 20 cm
The rectangular block of wax can make approximately 2 candles.
How do we determine the number of candles that could be made by that block of wax?To calculate the number of candles, we use the formula
V of wax = l x w x h = 10 cm x 9 cm x 20 cm = 1800 cubic cm
V of candle = l x w x h = 9 cm x 9 cm x 12 cm = 972 cubic cm
1800 / 972 = 1.85
The above answer is based on the full question below;
you are melting a rectangular block of wax to make candles. how many candles of the given shape can be made using a block that measures 10 cm by 9cm by 20 cm.
The height of the candle is 12cm and the base width is 9cm
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