The value of the percent increase in the value of W is 50%.
How can I determine the ratio between two quantities?
When the ratio of each of the two quantities' values is equal, the two quantities are said to be proportionate. It comes in two varieties: direct and indirect. The ratio is more than one for direct relations whereas it is less than one for indirect relations.
The relationship provided in the issue can be expressed as,
W ∝ X
X now has a new value when it is increased by 50%:
X + 50% × X
⇒ X + 50/100 × X = 3X/2
Assume that X and W now have values of X1 and W1, respectively.
Consequently, they are related in the following ways:
W ∝ X
⇒ 3/2W ∝ 3/2X
⇒ 3/2W ∝ X₁
W's value is increased by 3/2W - W, which equals 1/2W.
The percentage growth
⇒ (1/2W)/W × 100% = 50%
Hence, the percent increase is obtained as 50%.
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a researcher wishes to test the claim that the average age of lifeguards in ocean city is greater than 24 years. she selects a sample of 36 lifeguards and finds the mean age of the sample to be 24.7 years. from past data, she knows the population standard deviation is years. is there evidence to support the claim at a 5% level of significance?
The average age of lifeguards in Ocean City is significantly greater than 24 years at a 5% level of significance.
What is Standard deviation?
Standard deviation is a measure of how spread out numbers are. It is the square root of the Variance, and the Variance is the average of the squared differences from the Mean.
To determine whether there is evidence to support the claim that the average age of lifeguards in Ocean City is greater than 24 years at a 5% level of significance, we need to perform a one-tailed t-test. A one-tailed t-test is used to test whether the mean of a sample is significantly greater than (or less than) a certain value.
To perform the t-test, we first need to calculate the t-statistic, which is defined as:
[tex]t = (mean - null value) / (standard error / \sqrt{n} )[/tex]
where mean is the mean age of the sample of lifeguards, null value is the value that the null hypothesis is testing against (in this case, 24 years), standard error is the standard error of the mean age, and n is the number of lifeguards in the sample.
Plugging in the values from the problem, we get:
[tex]t = (24.7 - 24) / (standard \ error / \sqrt{36} )\\\\= 0.7 / (standard\ error / 6)[/tex]
The standard error of the mean is a measure of the variability of the sample mean, and is calculated as:
[tex]standard \ error = population \ standard\ deviation / \sqrt{(n)}[/tex]
Plugging in the values from the problem, we get:
standard error = / sqrt(36) = / 6 =
Substituting this value back into our expression for t, we get:
t = 0.7 / ( 6)
= 1.8
For a one-tailed t-test at a 5% level of significance, the critical value is 1.645. This means that if the t-statistic is greater than 1.645, we can reject the null hypothesis and conclude that there is evidence to support the claim.
So we can reject the null hypothesis and conclude that there is evidence to support the claim that the average age of lifeguards in Ocean City is significantly greater than 24 years at a 5% level of significance.
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a 600 l tank is filled with pure water. a copper sulfate solution with a concentration of 20 g/l flows into the tank at a rate of 2 l/min. the thoroughly mixed solution is drained from the tank at a rate of 2 l/min. a. write a differential equation (initial value problem) for the mass of the copper sulfate. b. solve the differential equation.
a) Differential equation (initial value problem) for the mass of the copper sulfate would be dm/dt = 0
b) m(t)=0
What is Differential equation?
A differential equation in mathematics is an equation that connects the derivatives of one or more unknown functions. Applications typically use functions to describe physical quantities, derivatives to indicate the rates at which those quantities change, and differential equations to create a relationship between the two.
a) Solution is flowing out of the tank. This can be expressed mathematically as:
dm/dt = (flow rate of solution into tank) - (flow rate of solution out of tank)
= (2 l/min) - (2 l/min)
= 0
Therefore, the differential equation for the mass of the copper sulfate in the tank is:
dm/dt = 0
This is a simple differential equation with a constant coefficient of 0, and it can be easily solved by integrating both sides of the equation with respect to time.
b. To solve the differential equation, we can write:
m(t) = integral(0, t, dm/dt)
= integral(0, t, 0)
= 0
Since the coefficient of the derivative is 0, the solution to the differential equation is a constant function with a value of 0. This means that the mass of the copper sulfate in the tank will remain constant over time, regardless of the flow rates of the solution into and out of the tank.
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6 1/2+2/3+3/4 calcution with distribution
By the distribution property 6(1/2 + 2/3+3/4) = 23/2
Distribution Property:According to the distributive property, multiplying the difference or aum of numbers will be equivalent to multiplying the individual parts of the difference or sum.
The expression that can explain the above rule is A ( B+ C) = AB + AC
Here we have
6(1/2 + 2/3+3/4)
By distribution property
=> 6(1/2 + 2/3+3/4)
= 6(1/2) + 6(2/3)+ 6(3/4)
= 3 + 2(2) + 3(3/2)
= 3 + 4 + 9/2
= 7 + 9/2
= (14+9)/2 [ add 7 and 9/2 by taking 2 as LCM ]
= 23/2
Therefore,
By the distribution property 6(1/2 + 2/3+3/4) = 23/2
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Complete Question:
1. Find the value of this fraction computation: 6(1/2 + 2/3+3/4)
Can someone please help me
Answer:
20+7k=8k+16
Step-by-step explanation:
8(k+2)
8 x k = 8k
8 x 2 = 16
Therefore, its 20+7k=8k+16
Answer:
8k+16
Step-by-step explanation:
20 + 7k = 8(k + 2)
20 + 7k = (8)(k) + (8)(2)
20 + 7k = 8k + 16
How do you graph a slope inequality?
The level of a line's slope indicates its steepness.
How do one find the slope of a graph?The slope is computed mathematically as "rise over run" (change in y divided by change in x).
In accordance with the slope equation, the slope of such a line may be determined by dividing the rise of the line between two positions by the run of the same line between the same two sites.
The above equation is a standard straight-line equation, and we are asked to change it to slope-intercept form, which is given as y = mx + c. "m" denotes the slope of the line and "c" denotes its intercept.
Now, let's take an example ,
2x - 3y ≤ 12
or, - 3y ≤ 12 - 2x
or, 3y ≤ 2x - 12
or y ≤ (2/3)x - 4
So, here slope (m) = 2/3, graph is shown below:
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Solve z (z-1) + 16 = 0 by using the Quadratic Formula.
(Do not round, enter an exact answer, and use a comma to separate mult
Provide your answer below:
Z=
Answer:
Z = -15
Step-by-step explanation:
z - 1 +16 = 0
z + 15 = 0
subtract 15 from both side to get z by itself
z+15-15 = -15
so the answer will be z=-15
what is the distance from the focus to the vertex of a parabola with the equation
x = 1/12 (y-1)²
help please!
Answer:
3 units.
Step-by-step explanation:
In the equation x = 1/12 (y-1)², the vertex of the parabola is at the point (1,1). The focus of the parabola is located a distance called the "focal length" from the vertex.
The focal length is given by the formula f = 1/(4*p), where p is the coefficient of the x term in the standard form of the equation of the parabola.
In this case, the coefficient of the x term is 1/12, so the focal length is f = 1/(4*(1/12)) = 3. This means that the distance from the focus to the vertex is 3 units.
What is the 70% out of 20?
Answer:
Step-by-step explanation:
14
Answer: 70% of 20 is 14.
The bunny had 1/2 to eat in the morning and 1/5 left over how much did the bunny eat at night
By applying the fraction concept, we can conclude that the bunny ate 3/10 food at night.
Application of the concept of fractions in real life
In real life, the concept of a fraction is often used when we want to talk about a part of a whole, a part of something, a part of a group of people, etc.
In the problem above it is stated that initially the bunny has food, which will be eaten in the morning and at night, and some food was left over.
If x is the total food for the bunny, then the given problem can be written mathematically as follows:
breakfast (a) : a = 1/2x
dinner (b)
food left (c) : c = 1/5x
Then the mathematical expression that describes the above situation is as follows:
x = a + b + c
= 1/2x + b + 1/5x --> then we make the denominators the same, so it becomes:
x = 5/10x + b + 2/10x
= 7/10x + b
x - 7/10x = b
3/10x = b
So, the food that the bunny eats at night was 3/10.
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Answer:
So, the food that the bunny eats at night was 3/10.
:D im jus smart.
Elsie's aunt borrows $400 with an interest rate of 1.5%. How much interest will she pay after 4 years?
Answer: $24 after 4 years
Step-by-step explanation:
1.5% = 0.015
Take 400 times 0.015 = $6 per year
6 times 4 = $24 after 4 years
ITS DUE TODAY HELP At a football stadium, 2% of the fans in attendance were teenagers. If there were 290 teenagers at the football stadium, what was the total number of people at the stadium?
The required total number of people in the stadium are 14500.
Explain percentage.In math, a percentage is a number or proportion that can be communicated as a small part of 100. On the off chance that we need to compute percent of a number, partition the number by the entire and increase by 100. Thus, the rate implies, a section for each hundred
According to question:2% of the fans in attendance were teenagers, and there are 290 teenagers in number.
Let x be the total number of people in stadium.
So, 2% of x = 290
2x/100 = 290
x = 29000/2 = 14500 people
Thus, there are 14500 people in the stadium.
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Resa wanted to find out what percentage of her daily Vitamin C she gets from one carrot.
Answer:
See the picture.
Step-by-step explanation:
What is the mean and standard deviation of 1 2 3 4 and 5 respectively?
The mean of 1, 2, 3, 4, and 5 is 3, and the standard deviation is 1.58.
To find the mean, you add up all the numbers and divide by the number of numbers you have.
To find the standard deviation, you first find the difference between each number and the mean, square each of these differences, add them up, and divide by the number of numbers you have. Then, you take the square root of this result.
Mean = (1 + 2 + 3 + 4 + 5) / 5 = 15 / 5 = 3
Standard deviation = sqrt(((1 - 3)^2 + (2 - 3)^2 + (3 - 3)^2 + (4 - 3)^2 + (5 - 3)^2) / 5) = sqrt((4 + 1 + 0 + 1 + 4) / 5) = sqrt(10 / 5) = sqrt(2) = 1.58
How to interpret a standard deviation?The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
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What is the factor of 12x² 11x 2?
Therefore , the solution to the given problem of the equation whose factors are (4x+1)(3x+2) .
How to analyze the equation?
An equation is a mathematical statement made up of two expressions connected together by the equal sign. For instance, 2x – 5 = 15 is an equation. By resolving this equation, we can establish that the variable x has a value of 5.
According to the given question:
Given expression: 12x² +11x+2
=> 12x² +11x+2
Break the expression into groups
=> (12+3x) + (8x+2)
Subtract 3x from 12x+3x to get 3x(4x+1).
Add 2 to 8x+2 to get 2(4x+1)
= 3x(4x+1)+2(4x+1)
Factor out common term 4x+10
= (4x+1)(3x+2)
Therefore , the solution to the given problem of the equation whose factors are (4x+1)(3x+2) .
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What is the coefficient of 3x²?
The coefficient of the expression 3x² is the number 3
What are the coefficients?The coefficients are the numbers on the left side or before each variable.
What is an algebraic expression?Is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.
If the expression of a single term is:. 3x²
Then the only coefficient will be the number that is placed before it and it is:
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What math do 11th graders take?
Answer:
Depends on your school. I took Pre-calculus my 11th grade year. Sometimes it is Algebra 2.
What would be the price for an 11-mile ride with taxi company B?
please, help!!!!!!!
The price for an 11-mile ride with taxi company is $12
How to determine the price for an 11-mile ride with taxi company B?From the question, we have the following parameters that can be used in our computation:
Taxi cab: Company B:
6.50 per ride0.50 per mileGiven that the number of rides is 1, we have the following equation that represents the total price
Total price = 6.50 * 1 ride + 0.50 * Number of miles
So, we have
Total price = 6.50+ 0.50 * Number of miles
For an 11-mile ride with taxi company B, we have
Total price = 6.50+ 0.50 * 11
Evaluate
Total price = 12
Hence, the price is $12
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(3x-2)-3(2x+1)=4(4x-3)
Answer:
x = 7/19
Step-by-step explanation:
(3x-2)-3(2x+1)=4(4x-3)
3x - 2 - 6x - 3 = 16x - 12
-19x = -7
x = 7/19
Answer:
x = 7/19
Step-by-step explanation:
(3x-2)-3(2x+1)=4(4x-3)
3x - 2 -6x -3 = 16x -12
-3x -5 = 16x -12
-5 = 19x -12
7 = 19x
x = 7/19
What is an expression in math examples?
Expression is a constant, variable or constant multiplied by a variable separated by operator.
What is algebraic expression and identity?Identity, as we all know, is equality, which holds true regardless of the variable's value. These identities are algebraic formulas that show that for all possible values of the variable, the Left-Hand Side (LHS) and the Right-Hand Side (RHS) of the equation are equal. A phrase that can have any value is called a variable.
What are the types of algebraic expressions?Monomial, polynomial and binomial are the three types of algebraic expression.
An expression with variables, constants, and algebraic operations is known as an algebraic expression (like subtraction, addition, multiplication, etc.). Terms comprise expressions. For instance: 5x+20y, 6-8x.
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x+5y[tex]\leq[/tex]-15
Answer:
y<= -1/5x-3
Step-by-step explanation:
x+5y<=-15
5y<=-x-15
y<=-1/5x-3
Is equidistant same as mid point?
Yes, since the midpoint of a line segment is at an equal distance from the two endpoints, it is said to be equidistant from them.
A point is said to be equally far from a group of objects if there is an equal distance between it and each member of the group.
The perpendicular bisector of two specified (different) points is their location in two-dimensional Euclidean geometry. The locus of points equidistant from two provided points in three dimensions is a plane, and generalizing further, the locus of points equidistant from two given locations in n-dimensional space is a (n1)-space.
The circumcenter of a triangle is a location that is equally spaced from each of the three vertices. This point exists in every non-degenerate triangle. The circumcentre of cyclic polygons is equally far from all of the vertices, and this conclusion may be generalized to them.
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Urgent!! Help plsssss
Answer:
Step-by-step explanation:B
deli owner sold 90 sandwiches in one day. Of those sandwiches, 36 were pastrami. What percent of sandwiches sold were NOT pastrami
Answer:60%
Step-by-step explanation:
90-36=54 54/90 = 60
60%
A 20-foot ladder is leaning against the side of a house so that the bottom of the ladder is 12 feet from the base of the house. Will the ladder reach a window that is 14.5 feet above the ground?
Yes, because the 16 feet ladder will reach to the window that is 14.5 feet above the ground.
What is Pythagoras theorem?Pythagoras' Theorem states that the square of the hypotenuse side of a right-angled triangle equals the sum of the squares of the other two sides.
The hypotenuse of a triangle, which has a straight angle of 90 degrees, has a square that, according to the Pythagoras theorem, equals the sum of the squares of the other two sides.
According to the question;
A 20-foot ladder is leaning against the side of a house.
Hypotenuse H= 20 feet
The bottom of the ladder is 12 feet from the base of the house.
Base B = 12 feet
And let P be the perpendicular.
Using Pythagoras theorem
H²= P² + B²
20² =12² +P²
P²= 400-144
P²= 256
Taking the square root.
P= 16 feet.
Since the height of the ladder is 16 feet, and we have to reach 14.5 feet above the ground.
16 > 14.5
That means, the ladder will reach to the window.
Hence, Yes, the 16 feet ladder will reach to the window.
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The density of copper is 9.86 g/cm".
Work out the mass of the solid copper cuboid in kg.
10 cm
3 cm
5 cm
Answer:
volume of copper cuboid(V) =10cm×3cm×5cm=150cm³=150/10⁶ m³=1.5×10-⁴ m³
density of copper(d)=9.86×10-³+²=0.986 kg/m
we know,
mass=V/d=1.5×10-⁴/0.986=1.47×10-⁴ kg
Tyrese bought 35 tickets to use at a carnival. He used some of the tickets to ride the bumper cars and play some games. Now he has 28 tickets left. What is the percent of decrease in the number of tickets that he has?
The percent of decrease, in the number of tickets that he has, is 20%.
What is a percentage?The term "percentage" refers to any ratio or number that may be expressed as a fraction of 100. And the sign "%" is used to denote it.
Given, Tyrese bought 35 tickets to use at a carnival.
He used some of the tickets to ride the bumper cars and play some games. Now he has 28 tickets left.
That means,
he used 35 - 28 = 7 tickets.
To find the percentage of decrease:
Let m be the percentage of decrease.
Then,
7 = m x 35 / 100
m = 700 / 35
m = 20
Therefore, the percentage of decrease is 20%
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Is real the maximum value of 3x² 9x 17 3x² 9x 7?
Therefore, the answer of the given question of the equation maximum value is 41 .
What is equation?
The equal sign is used between numerical or changeable expressions to create an equation, such as 3x+5=11.
A number that can be entered as the variable's replacement in an equation serves as the solution.
According to the given question:
Correct option is D)
f(x)= 3+9x+17 / 3+9x+7
=> 3+9x+7+10 / 3+9x+7
=> 1 + 10 / 3+9x+7
f(x) = 0 for maximum value
f(x)= 10 (6x+9) / (3x2+9x+7)2
6x+9=0
X=-3/2
Given that x is real, the highest value of f(x) is => 1 +
=> 1 +
=> 1 + 40/1 = 41
Therefore, the answer of the given question of the equation is 41 .
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How many rows and columns are there in Excel 2013?
From Excel 2007 onwards (2010, 2016, etc.) we have exactly 10,48,576 rows and 16,384 columns.
Now, According to the question:
How many rows and columns does Excel 2013 have?
From Excel 2007 onwards (2010, 2016, etc.) we have exactly 10,48,576 rows and 16,384 columns.
Excel sheet:-
In Microsoft Excel, a sheet is often called a worksheet. A sheet is a single page that contains its own collection of cells to help you organize your data. There can be many sheets in your Excel document and you can see the sheets listed as tabs along the bottom of your document.
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What is the relationship between the volumes of a rectangular prism and a rectangular pyramid whose length width and height are all equal?
The volume of the rectangular prism is 3 times the volume of the rectangular pyramid.
Consider a rectangular prism with length l, width w and height h.
The volume of the rectangular prism is:
volume of a rectangular prism = length * width * height
V1 = l * w * h
Consider a rectangular pyramid with rectangular base of length l1, width w1 and the height of pyramid is h1.
The volume of the rectangular pyramid is:
volume of a rectangular pyramid = 1/3 * base area * height
Here, base area = length * width
= l1 * w1
So, volume of a rectangular pyramid = 1/3 * base area * height
V2 = 1/3 * l1 * w1 * h1
We have been given a rectangular prism and a rectangular pyramid have equal length, width and height .
l1 = l, w1 = w and h1 = h
so, V2 = 1/3 * l * w * h
V2 = 1/3 * V1
V1 = 3 * V2
volume of a rectangular prism = 3 * volume of a rectangular pyramid
Therefore, the relationship between the volumes of a rectangular prism and a rectangular pyramid whose length width and height are all equal:
volume of rectangular prism = 3 * volume of a rectangular pyramid
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What law do you use for SSS?
All the three sides of one triangle are equivalent to the corresponding three sides of the second triangle, then the two triangles are said to be congruent by SSS rule.
SSS Theorem: The Side Side Side (SSS) Theorem states that all three sides of a triangle are congruent (identical) to the corresponding sides of another triangle, then the triangles themselves are also congruent.
Example of SSS Triangles:
From the figure:
These are SSS triangles. Given that they have the exact same measurements, we can deduce the following:
AB = XY
BC = YZ
AC = XZ
If we know that AB = 5 units, then XY also equals 5 units.
And if BC = 4 units, then YZ also equals 4 units.
Further, if AC = 7 units, then XZ also equals 7 units.
Then the two triangles are said to be congruent by SSS rule.
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