Proportionality constant of p is = 14 t
WHAT IS PROPORTIONALITY CONSTANT ?The constant proportional relationship between two variables. The proportionality constant, k, is defined as k = y/x. This is equivalent to the equation for the slope of a line through the origin, m = y/x. The value of m, which will be the same as the value of k, or the constant or proportionality, can be discovered using the equation for the slope of the line.
CALCULATIONy = kx
The rate k = 210 ÷ 15 = 14 gel pens per minute
"p" is number of pens, "t" is number of minutes
p = 14t
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Four friends went out to lunch and the bill came to $54.55 They decided to add enough tip to make a total of
$67.51, so that they could easily split the bill evenly among themselves. What percent tip did they leave?
Round your answer to two decimal places.
The percent tip is
%?
Answer: four friends went out for dinner. the bill , including tax , totaled $64.00 if they want to leave a 15% tip and want to share the bill and tip equally
Step-by-step explanation:
Find the perimeter and area of the figure if each unit on the graph measures 1 centimeter. Round answers to the nearest tenth, if necessary.
The Perimeter of polygon ABCD = 21.6 units.
What is the Perimeter of a Figure?The perimeter of figure ABCD = sum of all its sides = AB + BC + CD + AD.
To find each of the sides, apply the distance formula, d = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex].
A(-5, 5)
B(0, 3)
C(-2, -2)
D(-7, 0)
AB = √[(0−(−5))² + (3−5)²]
AB = √29
AB ≈ 5.4 units
BC = √[(0−(−2))² + (3−(−2))²]
BC = √29
BC ≈ 5.4 units
CD = √[(−7−(−2))² + (0−(−2))²]
CD = √29
CD ≈ 5.4 units
AD = √[(−7−(−5))² + (0−5)²]
AD = √29
AD ≈ 5.4 units
The Perimeter of polygon ABCD = 5.4 + 5.4 + 5.4 + 5.4 = 21.6 units.
Therefore, the Perimeter of polygon ABCD = 21.6 units.
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Calculate the volume of this regular solid. a cylinder labeled b at the top, 13 centimeters high with a radius of 4 centimeters. what is the volume of the cylinder? use the button on your calculator to complete this problem. round at the end to the nearest hundredth.
Answer:
[tex]volume = 653.71 {cm}^{3} [/tex]
Step-by-step explanation:
Volume = πr^2h
=
[tex] \frac{22}{7} \times {4}^{2} \times 13 \: c {m}^{3} [/tex]
= 22*16*13/7 cm^3
= 653.714cm^3
Rounding off = 653.71 cm^3
Answer:
653.45
Step-by-step explanation:
it told me the answer
Two hikers are 11 miles apart and walking toward eachother. they meet in 2 hours. find the rate if one hiker walkers 0.3 mph faster than the other.
If two hikers are 11 miles apart and walking towards each other and they meet in 2 hours, then if one hiker walks 0.3mph faster than the other, then the rate at which the slow hiker and fast hiker walk towards each other is equal to 2.6 and 2.9 mph respectively.
Consider, the speed of the slow hiker = s
Then, the speed of the fast hiker = s + 0.3
The distance covered by both the hikers in 1 hour = 2s + 0.3 miles
The distance covered by both the hikers in 2 hours = 2(2s + 0.3) = 4s + 0.6 miles
We can find the value of s by forming an algebraic expression as follows,
4s + 0.6 = 11
4s = 11 - 0.6
4s = 10.4
s = 10.4 / 4
s = 2.6
Speed of the slow hiker = s = 2.6 mph
Speed of the fast hiker = s + 0.3 = 2.6 + 0.3 = 2.9 mph
Hence, the rate at which the slow hiker and the fast hiker walk toward each other is equal to 2.6 and 2.9 mph respectively.
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PLEASE HELP
SHARKS Deep Blue, one of the largest great white sharks ever recorded, measures about 6.1 meters in length. If 1 meter = 3.28 feet, how long is Deep Blue in inches? Round to the nearest tenth.
6) Jessica’s cat is stuck in a tree. The fire department comes to help rescue the cat. Using a 25 foot ladder that is 10 feet away from the base of the tree, how high will the firefighter climb to reach the cat?
The firefighter needs to climb a height of 22.91 foot to reach the cat.
What is the Pythagorean Theorem ?
Pythagorean Theorem states that the square of the hypotenuse of a right triangle equals the sum of squares of the lengths of the other two sides.
It is given that the hypotenuse of the ladder is 25 foot and it's base is 10 feet away from base of tree.
Using the Pythagorean theorem which states that :
H² = P² + B²
where ;
H = Hypotenuse , P = Perpendicular and B = base
We can find out the height up to which the firefighter needs to climb to reach the cat. And it is given by :
25² - 10² = P²
625 - 100 = P²
or
P = √525
P = 22.91 foot
Therefore , the firefighter needs to climb a height of 22.91 foot to reach the cat.
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-2 1/2 divided 2 6/7
Answer:
Exact Form -- -7/8 Decimal Form -- -0.875
Step-by-step explanation:
I Didn't Now If U Wanted It Explained So...
Answer: -7/8
Step-by-step explanation:
convert from mixed number to fraction:
-5/2 ÷ 20/7
use the fraction rule
[tex]\frac{a}{b}[/tex]÷[tex]\frac{c}{d} = \frac{a}{b}[/tex]×[tex]\frac{d}{c}[/tex]
-5/2 x 7/20
cross cancel
- 1/2 x 7/4
from there multiply numerators together and denominators together
(-1*7) / (2*4)
-7/8
Question: Can it be simplified? If NO, explain why. If YES, simplify completely or rewrite as a simplified radical expression. SHOW ALL WORK.
Expression: (x^4y)^2/3
Please help me with this!
Answer:
Step-by-step explanation:
1) Use multiplication distributive property [tex](xy)^a=x^ay^a[/tex]
= [tex]\frac{(x^4)^2y^2}{3}[/tex]
2) Use Power rule [tex](x^a)^b = x^{ab}[/tex]
= [tex]\frac{x^8y^2}{3}[/tex]
What are the coordinates of the point on the directed line segment from (-1, -8) to (5, -2)(that partitions the segment into a ratio of 1 to 2?
The coordinates of the point on the directed line segment will be (1, -6).
What is the section of the line?Let A (x₁, y₁) and B (x₂, y₂) be a line segment. Then the point P (x, y) divides the line segment in the ratio of m:n. Then we have
x = (mx₂ + nx₁) / (m + n)
y = (my₂ + ny₁) / (m + n)
The coordinates of the point on the directed line segment from (-1, -8) to (5, -2). The ratio is 1: 2.
Then the coordinates of the point will be
x = (1(5) + 2(-1)) / (1 + 2)
x = (3 / 3)
x = 1
y = (1(-2) + 2(-8)) / (3)
y = - 18 / 3
y = - 6
The coordinates of the point on the directed line segment will be (1, -6).
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10. The sum of the angle measures in a triangle is 180. In triangle ABC,
the measure of angle A=4x+34, the measure of angle B=7x-10, and the
measure of angle C-5x+12. Find the measure of angle A.
Answer:
Step-by-step explanation:
Angles in a triangle add up to 180 degrees.
Therefore A+B+C = 180
This means 4x+34+7x-10+5x+12 = 180
Simplies down to 16x+36 = 180
Rearrange to have 16x = 144
Divide by 16 on both side to get x = 9
Substitue the value of x back into the equation of A
A = 4(9)+34 = 70 degrees
Find the values of a and b
Answer:
a=15, b=14
Step-by-step explanation:
We know all angles must add up to 360, so lets add all angles and set them equal to 360.
[tex]7a+33+3b+10a-12+6b-42=360\\17a+9b-21=360[/tex]
We also know that any angle opposite another is equal. Lets take 6b-42 and 3b and set them equal.
[tex]3b=6b-42[/tex]
Now solve for b in both equations
[tex]3b=6b-42\\-3b=-42\\b=14[/tex]
[tex]17a+9b-21=360\\9b-21=360-17a\\9b=381-17a\\b=\frac{381-17a}{9}[/tex]
Now we set the two equations equal to each other to solve for a:
[tex]14=\frac{381-17a}{9} \\126=381-17a\\-255=-17a\\15=a[/tex]
This gives a=15, b=14.
Find the approximate side length of a square game board with an area of 105 in2.
Answer:
Rounded to the nearest inch: 10
Rounded to the nearest tenth: 10.2
Rounded to the nearest hundredth: 10.25
Step-by-step explanation:
To find the area of a square, we multiply the side length by itself, or in other words, SQUARE the side length!
[tex]A=s^2[/tex]
We are given the area, so plugging that into our equation looks like this:
[tex]105=s^2[/tex]
To eliminate the exponent, take the square root of both sides of the equation!
[tex]\sqrt{105}=s[/tex]
From here, there are a few paths to take, depending on what your teacher is looking for. I will evaluate the approximate of the square root by finding the nearest perfect squares.
The nearest perfect square less than √105 is √100, and the nearest perfect square greater than √105 is √121.
105 is closer to 100 than to 121, so √105 is closer to √100.
√100 is equal to 10, so the √105 is approximately 10 inches!
Using a calculator to check:
[tex]\sqrt{105}=10.247[/tex] inches
Find the highest common factor (HCF) of 32, 48 and 72
highest common factor (HCF) of 32, 48 and 72= 8
HCF - Highest Common Factor
The Highest Common Factor (HCF) of two numbers is the highest possible number that divides both the numbers completely. The Highest Common Factor (HCF) is also called the Greatest Common Divisor (GCD).
There are many ways to find the HCF of two numbers. One of the quickest ways to find the HCF of two or more numbers is by using the prime factorization method. Explore the world of HCF by going through its various aspects and properties. Find answers to questions like what is the highest common factor for a group of numbers, easy ways to calculate HCF, HCF by division method, its relation with LCM, and discover more interesting facts around them.
HCF by Prime Factorization
In order to find the HCF of numbers by the prime factorization method, we use the following steps. Let us understand this method using the example given below.
Step 1: Find the common prime factors of the given numbers.
Step 2: Then, multiply these common prime factors to obtain the HCF of those numbers.
highest common factor (HCF) of 32, 48 and 72
32 = 2x2x2x2x2
48= 2x2x2x2x3
72= 2x2x2x3x3
highest common factor (HCF) of 32, 48 and 72 = 2x2x2= 8
highest common factor (HCF) of 32, 48 and 72= 8
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statistical considerations for use of composite health-related quality-of-life scores in randomized trials
Statistical considerations for the use of composite health-related quality-of-life scores in randomised trials
This is a research paper whose author is Andrew J. Vickers.
Abstract:
background: In randomised studies, first-rate of life measures are mechanically utilised as outcomes. contraptions with several subscales provide researchers the choice of combining a few or all scales right into a unmarried composite score. There is probably diverse clinically and scientifically sound alternative subscale combinations for the predominant outcome degree.foremost findings: The statistical effectiveness of diverse subscale combinations is decided with the aid of the relative effect size of the intervention on every subscale as well as the correlation between the subscales. easy formulae may be installed to determine the relative statistical efficiency of each clinically appropriate subscale aggregate. Hypothetical situations imply that the variety of participants required in a scientific trial is probably twice as huge for a few subscale combinations as for others.Conclusions:
Ina randomised examine, there are often robust scientific or scientific reasons to pick a positive subscale or composite.whilst there are several viable picks, statistical performance can help in guiding the choice of endpoint.To learn more about statistics, visit :
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estimation 31.5 and (-1.5)
Answer:
(30.00)
Step-by-step explanation:
(30.00) is the correct answer for your question/ statement you have asked. the answer is (30.00) again.
40 POINTS! Classify the function as even, odd or neither. Be sure to include your work to justify your classification.
Answer:
this is the answer of about the image is even
How are rays and angles related?
ieiejeieieiweisns xx xnsiwiwksniz
x
-3
-2
-1
0
Intro
2
f(x)
-16
-1
2
-1
-1
Analyze the table of values for the continuous function,
f(x), to complete the statements.
A local maximum occurs over the interval
A local minimum occurs over the interval
4 of 10
Done
A local maximum occurs over the interval (-2,0).
A local minimum occurs over the interval (0,2).
If the graph of the function increases first and decreases after a particular point, then the function acquires a local maximum at that point.
Similarly, if the graph of the function decreases first and then increases after a point, then the function acquires a local minimum at that point.
Here the given x and f(x) values for the continuous function f(x) are:
x f(x)
-3 -16
-2 -1
-1 2
0 -1
1 -4
2 -1
As we can see by examining the table values, the function is increasing in the intervals (-3,2) and (-2,-1).The function acquires value f(x) = 2 at x = -1 and then it starts to decrease. So this value f(x) = 2 is the local maximum and is acquired on the interval (-2,0).
The graph is then decreasing from x = -1 to x = 1. The function has the value f(x) = -4 at x = 1. Then the function starts to increase from x = 1 to x = 2. So f(x) = -4 is the local minimum of the function and is acquired on the interval (0,2).
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Hi could someone help my sister is asking me this question but I never learned this
Answer:
12 cm
Step-by-step explanation:
Volume of total shape = Volume of big rectangle - Volume of small rectangle
Volume of big rectangle = L×B×H
Volume of big rectangle = 10 cm×3 cm×2 cm
Volume of big rectangle = 60 cm
Volume of small rectangle = l×b×h
l = 10 cm - 6 cm = 4cm
Volume of small rectangle = 4 cm×3 cm×4 cm
Volume of small rectangle = 48cm³
Volume of total shape = 60cm³ - 48cm³
Volume of total shape = 12cm³
Write a program that promptsthe user for their quarterly water bill for the last four quarters. the program should find and output their average monthly water bill. if the average bill exceeds $75, the output should include a message indicating that too much water is being used. if the average bill is at least $25 but no more than $75, the output should indicate that a typical amount of water is being used. finally, if the average bill is less than $25, the output should contain a message praising the user for conserving water. also show input validation for the first entry. you may have to apply all the programming constructs that you have learned so far, as needed, to complete this exercise. (decisions, loops, input validation). sample run 1: please input your water bill for quarter 1: 300 please input your water bill for quarter 2: 200 please input your water bill for quarter 3: 225 please input your water bill for quarter 4: 275 your average monthly bill is $83.33. you are using excessive amounts of water
calculate the total of the bills= 300+200+225+275 =1000
the average monthly bill= 1000/12 = 83.333
Total =0
for i in range(4):
bill = float(input("Enter bill for quarter " + str (i+1) + ": "))
total += bill
average = total / (4 * 3)
if average > 75:
print("Average monthly bill is $" + str(average) + ". Too much water is being used")
if 25 <= average < 75:
print("Average monthly bill is $" + str(average) + ". A typical amount of water is being used")
if average < 25:
print("Average monthly bill is $" + str(average) + ". Thank you for conserving water")
calculate the total of the bills= 300+200+225+275 =1000
the average monthly bill= 1000/12 = 83.333
Total =0
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Solve the simultaneous equations:
x+y=9
x²-3xy + 2y² = 0
The solutions are (4.5, 4.5) and (6, 3).
Here,
The equations are;
x + y = 9
x²- 3xy + 2y² = 0
We have to solve the equations.
What is Expression?
Expression in math is defined as the collection of the numbers, variables and functions by using signs like addition, subtraction, multiplication, and division
Now,
The equations are;
x + y = 9
x²- 3xy + 2y² = 0
Since, x + y = 9 ⇒ y = 9 - x
And, solve the equation as;
x²- 3xy + 2y² = 0
x²- 2xy - xy + 2y² = 0
x (x - 2y) - y (x - 2y) = 0
(x - y) (x - 2y) = 0
(x - y) = 0 or (x - 2y) = 0
For, (x - y) = 0
Given, x + y = 0
Hence, Solve equation (x - y) = 0 and (x + y) = 9 we get;
2x = 9
x = 4.5
And, y = 4.5
For (x - 2y) = 0
x = 2y put in equation (x + y) = 9 we get;
(x + y) = 9
2y + y = 9
3y = 9
y = 3
And, x = 6
Therefore, The solutions are (4.5, 4.5) and (6, 3).
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Solutions are (4.5,4.5) and (6,3)
What are Quadratic equations ?
Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax2 + bx + c = 0 where a, b, c, ∈ R and a ≠ 0. It is the general form of a quadratic equation where 'a' is called the leading coefficient and 'c' is called the absolute term of f (x).
Given,
x + y = 9 => y = 9-x equation 1
x^2 - 3xy + 2y^2 = 0 equation 2
(x - y)(x - 2y)=0
x - y = 0 or x - 2y = 0
1. Equating x-y=0 and x + y = 9,
x + y = 9
x - y = 0
2x = 9
x = 4.5
y = 4.5
because y = x
2. Equating x - 2y = 0 and x + y = 9,
2x + 2y = 18
x - 2y = 0
3x = 18
x = 6
y = 9 - x = 3
therefore, possible solutions are (4.5,4.5) and (6,3)
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Find the focus and the directrix of the parabola with the equation y = -¹/2 (x-8)² -
6.
A) Focus = (-8,-5¹/2), directrix is y=-6¹/2
B) Focus = (8,-6¹/2), directrix is y= -5¹/2
○ C) Focus = (-8,-6¹⁄2), directrix is y= −5¹/2
D) Focus = (8,-5¹/2), directrix is y=-6¹/2
Answer:
focus
Step-by-step explanation:
Answer:
Step-by-step explanation:
Focus = (8,-6¹/2), directrix is y= -5¹/2
3. A local charity wants to purchase a classic 1975 Chevy Monte Carlo for use as a prize in a fundraiser.
They find the following eight prices in the paper
$18,000
$16,000
3090
$18,888
b. What is the range?
a. What is the best measure of central tendency to use to get a reasonable estimate for
the cost of the car? Explain.
Triangle EFG is similar to triangle HIJ. Find the measure of side HI.
Round your answer to the nearest tenth if necessary. Figures are not
drawn to scale.
The measure of side HI is 10.74 for the triangle EFG which is similar to HIJ.
Similar triangles are those triangles which have corresponding sides in proportion to each other and the corresponding angles of two triangles are equal to each other. Similar triangles look the same but they differ in terms of the sizes of the two triangles.
In short, If two triangles are similar that means,
All corresponding angle pairs of triangles will be equal.
All corresponding sides of triangles will be proportional.
Now, it is given in the question that ΔEFG is similar to ΔHIJ then, their corresponding sides will be in proportion.
⇒ GE/EF = HJ/HI
⇒ 19/34 = 6/HI
⇒ HI = 6 x 34/19
⇒ HI = 10.74
Therefore, the measure of side HI is 10.74.
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a house at the bottom of a hill is fed by a full tank of water 5.pm deep and connected to the house by a pipe that is 110m long at an angle of 58 degrees from the horizontal
The water gauge pressure at the house will be 9.63×10⁵ N/m².
Firstly we will be calculating the total height which will comprise of height from tank to house and elevated height. The formula for total height will be -
Total height = 5 + 110 sin 58°
Keep the value of sin 58° in formula and performing multiplication followed by addition
Total height = 5 + 110×0.848
Total height = 5 + 93.28
Total height = 98.28 meters
Now, calculating the water gauge pressure at house. The formula to be used is -
P = ρ×g×h, where P is pressure, ρ is density of water, g refers to acceleration due to gravity and h represents total height. We are aware that density of water is 1000 kg/m³ and accelerate due to gravity is 9.8 m/s².
Keep the values in formula to find the gauge pressure.
P = 1000 × 9.8 × 98.28
Performing multiplication
P = 963,144 N/m² or 9.63×10⁵ N/m²
Hence, the water gauge pressure at the house will be 9.63×10⁵ N/m².
The complete question is -
A house at the bottom of a hill is fed by a full tank of water 5m deep and connected to the house by a pipe that is 110m long at an angle of 58 degrees from the horizontal. Determine the water gauge pressure at the house.
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find the coordinates of the midpoint segment with the given endpoints: (12,-7) and (-6,15) midpoint (blank
A.Are the expressions 3(m2) + 2(m2) and 5(m2) equivalent expressions?B.in two or more complete sentences justify ur answer to A
Yes, the given expressions i.e., 3m^2+2m^2 and 5m^2 are equivalent expression.
An expression is defined as a combination of various terms or numbers that are combined by using mathematical operations in addition, subtraction, multiplication, and division.
Equivalent expressions are expressions that have similar value or worth but do not look the same. When considering if the expressions given are equivalent, at least two expressions are must.
A) Yes, by considering the above definitions we can conclude that 3m^2+2m^2 and 5m^2 are equivalent expressions.
B) Given, 3m^2+2m^2 and 5m^2
Now, solve 3m^2+2m^2 we simply get the value which is similar to other expression given to us in the question i.e., 5m^2.
Hence, 3m^2+2m^2 and 5m^2 are similar or equivalent expression.
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Use the graphs of F and G to evaluate the functions.
Someone please explain how you would solve this. This was all the info given with the problem.
The value of the functions are:
(a) ( f - g )( 1 ) = - 1
(b) ( f · g )( 4 ) = 0
Before performing operations on functions, we must first comprehend the various function rules and how to get the function value at a given x-value. By applying this concept, we can determine the function value.
From the graphs, we have the functions,
f(x) = 2( | x - 2 | )
g(x) = - x + 4
Now,
(a) ( f - g )( 1 )
( f - g )( 1 ) = f( 1 ) - g( 1 )
( f - g )( 1 ) = 2 ( | 1 - 2 | ) - ( - 1 + 4 )
( f - g )( 1 ) = 2 ( | - 1 | ) - ( 3)
( f - g )( 1 ) = 2 - 3
( f - g )( 1 ) = - 1
(b) ( f · g )( 4 )
( f · g )( 4 ) = f( 4 ) · g( 4 )
( f · g )( 4 ) = 2( | 4 - 2| ) · ( - 4 + 4 )
( f · g )( 4 ) = 0
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Lamar spent $34 on fruit at the grocery store. He spent a total of $40 at the store. What percentage of the total did he spend on fruit?
Answer:
85%
Step-by-step explanation:
Answer:
85%
Step-by-step explanation:
85% because, $40 X .85 = $34 which means, $34 is 85% of $40
4x+3y ≥9
-3x+7y< 14
point in the solution set (x,y)