Find the standard parametrization for the line segment joining the points below. Draw coordinate axes and sketch the segment, indicating the direction of increasing t for the
parametrization.
(5.0,5) and (0,4,0)
Find a parametrization for the line segment joining the two points so that the parametrization moves from (5,0.5) to (0,4,0) as t increases from 0 to 1.
You need to know the direction of the line and at least one point on it in order to parametrize a line. x is 5 + 4.0t ,y is 0 + 4.0t
How is a line segment with two points parametrized?You need to know the direction of the line and at least one point on it in order to parametrize a line. You can determine the direction of the line if you know two of its points. Point-slope form → y - y₁ = m (x - x₁)Slope-intercept form → y = mx+bStandard form → ax + by = cWe must locate two vectors parallel to the plane, as well as a point on the plane, in order to discover a parametrization. Finding a location aboard the aircraft is simple. Any number for x and y may be used to compute z using the plane equation. If x and y are set (5,0.5) to (0,4.0) equation (1)means that .x = 5 + 4.0t
y = 0 + 4.0t
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The distribution of the amount of money spent by students on textbooks in a semester is
approximately normal in shape with a mean of: = 428 and a standard deviation of: σ= 24.
According to the standard deviation rule, almost 16% of the students spent more than what amount of money on
textbooks in a semester?
A normal distribution with a mean of 0 and a standard deviation of 1 is called a standard normal distribution.
What is the standard deviation of o=24?Tables of the standard normal distribution are frequently used to show different regions of the normal distribution. A standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1.
Tables of the standard normal distribution are frequently used to show different regions of the normal distribution.The standard deviation reveals the degree of data skewedness. It gauges how far away from the mean each observed value is. Approximately 95% of values in any distribution will be within two standard deviations of the mean.
A sigma value, typically represented by the Greek letter or lower case s, is a measure of how far a sample or point of data is from its mean. It is given in standard deviations.
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Matt bought 4 packages of cookies. Each package had 24 cookies. He ate 9 cookies. Write an expression to show how many cookies are left.
Answer:
4 * 24 - 9 = 87 cookies left.
Step-by-step explanation:
Repairs on victors car what hourly pay did the repair charge for labor
The hourly pay that was charged for the repairs to Victor's car was $ 57.14
How to find the hourly wage ?To find the hourly wage, find the total labor wages that were charged as a cost to Victor's repairs. This cost would be:
= 272 - 6 - 28. 50 - 20 .00 - 15. 00 - 2. 50
= $ 200
The total hourly wage charged was $ 200 for 3 . 5 hours of work.
This means that the hourly pay charged was :
= Total labor wages / Number of hours
= 200 / 3 . 5
= $ 57.14
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Let f be a function defined on all of that satisfies the additive condition f(x+y)=f(x)+f(y) for all a.) Show that f(0)=0 and that f(-x)=-f(x) for all x in .
b.) Show that is f is continuous at x=0, then f is continuous at every point in c.) Let k=f(1). Show that f(n)=kn for all n in the natural numbers, and then prove that f(z)=kz for all z in . Now, prove that f(r)=kr for any rational number r.
d.) Use (b) and (c) to conclude that f(x)=kx for all x in . Thus, any additive function that is continuous at x=0 must necessarily be a linear function through the origin.
Let f be a function defined on all of that satisfies the additive condition is,
f(x) = [tex]kx[/tex] for every x∈ R.
It is given that:
f: R → R is a continuous function such that:
[tex]f(x+y)[/tex] = [tex]f(x) + f(y)[/tex] ∀ x , y ∈ R (Equation-1)
Now, let us assume f(1)=k
Also,
f(0) = 0( Since, f(0)=f(0+0)
That is,
f(0)=f(0)+f(0)
By using property (1)
Also,
f(0)=2f(0)
That is,
2f(0)-f(0)=0
That is,
f(0)=0 )
Also,
f(2)=f(1+1)
That is,
f(2)=f(1)+f(1) ( By using property (1) )
i.e.
f(2)=2f(1)
That is,
f(2)=2k
Similarly for any m ∈ N
f(m)=f(1+1+1+...+1)
That is,
f(m)=f(1)+f(1)+f(1)+ ....... +f(1) (m times)
That is,
f(m)=mf(1)
That is,
f(m) = [tex]mk[/tex]
Now,
f(1) = [tex]f(\frac{1}{n} +\frac{1}{n} +......\frac{1}{n} )[/tex]
f(1) = [tex]f(\frac{1}{n} )+f(\frac{1}{n} )+......f(\frac{1}{n} )[/tex]
f(1) = n [tex]f(\frac{1}{n} )[/tex]
f(1) = k
[tex]f(\frac{1}{n} )[/tex] = k * [tex]\frac{1}{n}[/tex]
Also,
when x∈ Q
[tex]x = \frac{p}{q}[/tex]
Then,
[tex]f(\frac{p}{q})[/tex] = [tex]f(\frac{1}{q} )+ f(\frac{1}{q} )+ .....f(\frac{1}{q} )[/tex]
[tex]f(\frac{p}{q})[/tex] = p * [tex]f(\frac{1}{q} )[/tex]
[tex]f(\frac{p}{q})[/tex] = [tex]p\frac{k}{q}[/tex]
[tex]f(\frac{p}{q})[/tex] = [tex]k\frac{p}{q}[/tex]
So,
[tex]f(x) = kx[/tex] for all x belongs to Q
Now, as we know that:
Q is dense in R.
So Э x∈ Q' such that Э a seq < [tex]x_{n}[/tex] > belonging to Q such that:
< [tex]x_{n}[/tex] > ⇒[tex]x[/tex]
Now, we know that: Q'=R
This means that:
Э α ∈ R
such that Э sequence [tex]a_{n}[/tex] such that:
[tex]a_{n}[/tex] belongs to Q,
[tex]a_{n}[/tex] ⇒ [tex]\alpha[/tex]
[tex]f(a_{n} )= ka_{n}[/tex]
( since [tex]a_{n}[/tex] belongs to Q )
Let f is continuous at x=α
This means that:
[tex]f(a_{n} )[/tex] ⇒ [tex]f(\alpha )[/tex]
k [tex]a_{n}[/tex] ⇒ [tex]f(\alpha )[/tex]
k [tex]a_{n}[/tex] ⇒ k [tex]\alpha[/tex]
This means that:
[tex]f(\alpha )[/tex] = k [tex]\alpha[/tex]
This means that:
f(x) = [tex]kx[/tex] for every x∈ R
Therefore,
Let f be a function defined on all of that satisfies the additive condition is, f(x) = [tex]kx[/tex] for every x∈ R.
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1.24) George rides his bike to his friend's house that is 5 kilometers from his house. If he rides
his bike at an average speed of 15 km/h, how long will it take him to get to his
friend's house?
t=d
Answer:
5 km / 15 km/h = 0.3333 hours
Step-by-step explanation:
This is calculated by dividing the distance he has to travel (5 km) by his average speed (15 km/h) and then converting the result to minutes.
0.3333 hours x 60 minutes/hour = 20 minutes
You can paint 75 square feet of a surface every 45 minutes. Determine how long it takes you to paint a wall with the given dimensions.
9ft x 9ft
Answer: 48.6 minutes
Step-by-step explanation:
First find the total square feet:
9 x 9 = 81
Next, divide this by the increments give:
81 / 75 = 1.08
Now, the increments were each 45 minutes, so multiply this by the product:
45 x 1.08 = 48.6
Jordan went to the store with $90.He wants to purchase a leather jacket for $45,a hat for $10,and the rest on jeans.Each pair of jeans costs $35.Write an inequality for the number of jeans he can purchase
Answer:
x <= 1.
Step-by-step explanation:
Let x be the number of jeans Jordan can purchase.
We know that the total cost of the leather jacket, hat and jeans is $45 + $10 + $35x = $45 + $10 + $35x.
We also know that the total cost cannot exceed the amount of money Jordan has, which is $90.
So we can write the inequality: $45 + $10 + $35x <= $90
Solving for x, we get: $35x <= $35
x <= 1
So the number of jeans Jordan can purchase is x <= 1.
Match each expression with the type of factoring that applies. Question 11 options: 3x3 + 15x2 + 2x + 10 x3 + 27 2x2 + 6x x2 - 25 x2 + 6x + 8 x3 - 1 1. GCF (greatest common factor) 2. Unfoil 3. Difference of Squares 4. Difference of Cubes 5. Sum of Cubes 6. Grouping
Expressions → Type of factoring
3x³ + 15x² + 2x + 10 → Grouping
x³ + 27 → Sum of cubes
2x² + 6x → Greatest common factor
x² - 25 → Difference of squares
x² + 6x + 8 → Unfoil
x³ - 1 → Difference of cubes
What is factorization?'Factor' is a term used to express a number as a product of any two numbers. Factorization is a method of finding factors for any mathematical object, be it a number, a polynomial or any algebraic expression. Thus, factorization of an algebraic expression refers to finding out the factors of the given algebraic expression.
Given expressions
3x³ + 15x² + 2x + 10Using grouping method
= (3x³ + 15x²) + (2x + 10)
= 3x²(x + 5) + 2(x + 5)
Factoring out common term
= (x+5)(3x² + 2)
x³ + 27It can be written as
= x³ + 3³
Which is sum of cubes
2x² + 6xit can be written as
= 2x.x + 2x.3
GCF (greatest common factor) = 2x
= 2x (x + 3)
x² - 25It can be written as
= x² - 5²
which is difference of squares
x² + 6x + 8= x² + 4x + 2x + 8
= x(x + 4) + 2(x + 4)
= (x + 4) (x + 2)
Which is unfoil.
x³ - 1it can be written as
= x³ - 1³
which is difference of cubes.
Hence, the factoring of expressions 3x³ + 15x² + 2x + 10, x³ + 27, 2x² + 6x, x² - 25, x² + 6x + 8, x³ - 1 refers to grouping, sum of cubes, greatest common factor, difference of squares, unfoil and difference of cubes respectively.
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Which graph shows the solution to the system of linear equations? y = 2x − 2 4x − 2y = 4 Coordinate plane with one line that passes through the points 0 comma negative 2 and 1 comma 0. Coordinate plane with one line that passes through the points 0 comma negative 1 and 1 comma 1 and another line that passes through the points 0 comma negative 2 and 1 comma 0.
This is false, hence, the portion of the graph which does not contain (0, 0) is shaded.
What is inequalities?A connection in mathematics that compares two numbers or other mathematical expressions in an unequal way is known as an inequality. It is most frequently used to compare the sizes of two numbers on the number line. A relationship between two expressions or values that is not equal to each other is known as inequality in mathematics. So inequality emerges from an imbalance.Given the inequalities :
y ≥ 2x + 1
y ≤ 2x - 2
From y ≥ 2x + 1 ;
Since the inequality sign is ≥, a solid line is used to draw the straight line graph of y ≥ 2x + 1
From :
y = mx + c
Where, m = slope ; c = intercept
Hence, a straight line graph with ;
Intercept, c = 1 (where the line crosses the y-intercept)
Slope, m = 2
Consider a point, which isn't on the line ;
Take point (0,0) and use it to test the inequality :
0 ≥ 2(0) + 1
0 ≥ 0 + 1
0 ≥ 1
Since this is untrue, the area of the graph that does not contain (0, 0) is shaded.
From : y ≤ 2x - 2
Since the inequality sign is ≤, a solid line is used to draw the straight line graph of y ≤ 2x - 2
Graph the line y ≤ 2x - 2, with ;
Intercept, c = - 2
Slope = 2
Consider a point, which isn't on the line ;
Take point (0,0) and use it to test the inequality y ≤ 2x - 2:
0 ≤ 2(0) - 2
0 ≤ 0 - 2
0 ≤ - 2
This is untrue, hence the area of the graph that doesn't include (0, 0) is shaded.
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One professional basketball player typically attempts eight free throws per game. Let X represent the number of free throws made out of eight. The distribution for X is shown in the table.
A 2-column table with 9 rows. Column 1 is labeled number of free throws made with entries 0, 1, 2, 3, 4, 5, 6, 7, 8. Column 2 is labeled Probability with entries 0.002, 0.008, 0.04, 0.12, 0.23, 0.28, 0.21, 0.09, 0.02.
What is the probability that the basketball player will make at least six free throws out of the eight attempts?
0.11
0.21
0.30
0.32
The likelihood that the basketball player will convert at least six of his or her eight free throw tries is 0.32.
What is meant by probability ?The simple definition of probability is the likelihood that something will occur. We can discuss the probabilities of different outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics refers to the study of events subject to probability.
The ratio of all potential cases to the number of cases that are favorable to an event determines its likelihood when there is no reason for us to believe that any one of these circumstances will happen more frequently than any other, making them all equally likely.
The likelihood that an event will occur is quantified by probability. The probability of an event is the relative frequency throughout time of that event. Probabilities are all numbers between 0 and 1, inclusive—that is, any numbers between 0 and 1.
Therefore, the correct answer is option d) 0.32.
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Help asap I need this by today!!!
Answer:33
Step-by-step explanation:
49-16=33
Using Pythagoras theorem, the altitude a is √33.
What is Pythagoras theorem?The Pythagorean theorem, a cornerstone of Euclidean geometry, connects the side lengths of a right triangle via the straightforward formula a² + b² = c². Ancient scholars and architects from Babylon, Egypt, China, and India were aware of the connection.
While Pythagoras lived and wrote between 569 and 475 BCE, the work that bears his name first appeared on clay Babylonian tablets around 1800 BCE. Early Chinese scholars were also aware of the Pythagorean theorem, and it was mentioned in ancient Indian sacred texts that dealt with the construction of altars.
To solve a,
We can see a right triangle forming by those 3 squares
Lets take theirs sides as the base, altitude and hypotenuse
Hypotenuse = 7
Base = 4
Altitude = to find
Using Pythagoras theorem
[tex]a^2 + b^2 = c^2[/tex]
[tex]\Rightarrow a = \sqrt{c^2 - b^2 }[/tex]
[tex]\Rightarrow a = \sqrt{7^2 - 4^2 }[/tex]
[tex]\Rightarrow a = \sqrt{49 - 16 }[/tex]
[tex]\Rightarrow a = \sqrt{33 }[/tex]
Thus, Using Pythagoras theorem, the altitude a is √33.
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X-6y=24 find the slope
The slope of the linear equation perpendicular to:
x - 6y = 24
is a = -6.
How to find the slope of the perpendicular line?A general line can be written in the slope-intercept form as:
y = a*x + b
Where a is the slope and b is the y-intercept.
Particularly, two lines are perpendicular if the product between their slopes is equal to -1.
Here we want to find a line perpendicular to:
x - 6y = 24
First, we need to find the slope of this line.
x - 6y = 24
-6y = -x + 24
y = (-1/6)*-x - 24/6
y = (1/6)*x - 3
The slope is 1/6, then if the slope of the perpendicular line is a, the slope must be a solution of:
a*(1/6) = -1
a = -6
The slope of the perpendicular line is -6.
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pls help me in this exercise
Answer:
a = 15 , b = [tex]\frac{2}{9}[/tex]
Step-by-step explanation:
the equation of proportion is
y = kx ← k is the constant of proportion
to find k substitute x = 0.7, y = 2.1 , values from the table into the equation
2.1 = 0.7k ( divide both sides by 0.7 )
3 = k
y = 3x ← equation of proportionality
then using x = 5
a = 3 × 5 = 15
using y = [tex]\frac{2}{3}[/tex]
[tex]\frac{2}{3}[/tex] = 3b ( multiply both sides by 3 to clear the fraction )
2 = 9b ( divide both sides by 9 )
[tex]\frac{2}{9}[/tex] = b
which of the following are quadratic functions?
A. y= 5x-3/2+x^2
B. y= x^2+5x-2
C. y=-x+2
D. y= x-1/x
The quadratic equation are y= 5x-3/2+x^2, y= x^2+5x-2 and y= x-1/x.
What is quadratic equation?it's a second-degree quadratic equation which is an algebraic equation in x. Ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form. A non-zero term (a 0) for the coefficient of x2 is a prerequisite for an equation to be a quadratic equation. The x2 term is written first, then the x term, and finally the constant term is written when constructing a quadratic equation in standard form. In most cases, the numerical values of letters a, b, and c are expressed as integral values rather than fractions or decimals.
Here,
A. y= 5x-3/2+x^2
It has a degree is 2, So quadratic equation.
B. y= x^2+5x-2
It has a degree is 2, So quadratic equation.
C. y=-x+2
It has a degree is 1, So it's not quadratic equation.
Hence the value of k is 0.33.
D. y= x-1/x
y = x² -1/x
It has a degree is 1, So it's not quadratic equation.
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Search fields jason makes 8 gallons of punch he serves some punch in 1 pint containers now he has 12 pints of punch how many pints of punch did jason serve
The amount of pints of punch that Jason served is; 52 pints
How to solve Algebra Word Problems?Algebraic word problems are defined as the questions that require translating sentences to equations, then solving those equations. and a single variable.
We are given that;
Amount of punch made = 8 gallons
Amount of punch left after serving = 12 pints
Now, conversion of pints to gallon is;
1 pint = 0.125 gallons
Thus;
12 pints = 1.5 gallons
Thus;
Amount of pints served = 8 - 1.5 gallons
= 6.5 gallons
Converting to pints gives 52 pints
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Suppose you have a pint of grape juice and a pint of milk. You pour 1 tablespoon of the grape juice into the milk and mix it up. Then you pour 1 tablespoon of this mixture back into the grape juice. Which liquid is more contaminated?
The answer is pint of milk
What is a mixture?A mixture refers to the mix that is derived as a result of mixing two or more items or substances in a certain ratio or proportion.
Given here: 1 tablespoon of grape juice is mixed into the milk and 1 tablespoon of this mixture is mixed with grape juice.
Thus the milk is more contaminated as the latter mixture contains some amount of grape juice and as a result the grape juice mixture is not contaminated to the extent of the pint of milk.
Hence, The answer is pint of milk
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Can somebody please tell me how do we solve these questions? Thank you.
Answer:
D
Step-by-step explanation:
26+169=0
The company Sea Esta has 12 members on its board of directors. In how many different ways can it elect a president, vice-president, secretary and treasurer?
The company Sea Esta can elect a president, vice-president, secretary and treasurer in 495 different ways.
What is Combination in Mathematics?
In mathematics, a combination is a way of selecting a certain number of items from a larger set of items, without regard to the order in which the items are selected. It is a way to count the number of distinct subsets of a given size from a larger set.
The formula for combination is:
(n!) / (r! * (n-r)!)
The company Sea Esta has 12 members on its board of directors, and they need to elect a president, vice-president, secretary, and treasurer. The number of ways to elect these four positions is determined by using the formula of combination, which is:
Where n is the total number of options (in this case, the number of board members) and r is the number of positions to be filled (in this case, 4).
So, the number of ways to elect a president, vice-president, secretary, and treasurer is:
(12!) / (4! * (12-4)!) = (1211109) / (4321) = 495
Therefore, the company Sea Esta can elect a president, vice-president, secretary and treasurer in 495 different ways.
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A bag contains k blue beads and 4 red ones, If the probability of randomly picking a blue bead from it is 1/3, find the value of k
Answer:
[tex]k = 2[/tex]
Step-by-step explanation:
[tex]\textrm{P(blue \;bead)} = \dfrac{\textrm{Number of blue beads}}{\textrm{Total number of beads}}\\\\\textrm {Number of blue beads } = k\\\\\textrm{Total number of beads } = k + 4\\\\[/tex]
[tex]\textrm{P(blue \;bead)} = \dfrac{k}{k+4}\\\\[/tex]
[tex]\textrm{We are given this probability as } \dfrac{1}{3}\\\\\textrm{So,}\\\\\dfrac{k}{k+4} = \dfrac{1}{3}\\\\[/tex]
Cross-Multiplying this equation we get
[tex]k\cdot 3 = 1 \cdot (k + 4)\\\\\longrightarrow 3k = k + 4\\\\3k - k = 4\\\\2k = 4\\\\k = 2\\\\[/tex]
Please help me I have a test on this soon and need a better understanding !!!
Answer and explanation: The equation for the slope-intercept form is y=mx+b. M represents the slope and b is y-intercept/when x= 0.
We have to arrange the given equation into the form y=mx+b.
3x+2y=-14, We want to somehow isolate y.
2y=-14-3x, We can move all the terms that don't have y to the right
y=(-14-3x)/2, We can get rid of the 2 by dividing by 2 on both sides
y=-7-(3/2)x, We can distribute the division by 2 to both terms on the right
y=-(3/2)x-7, We can now just rearrange the terms
The equation is now in the form y=mx+b as -3/2 is m and -7 is b. Your answer to the first question is A.
For part B, we can use the equation for part A. We know m or the slope is -3/2 so our answer is also A.
l =240, w= l ÷ 3, A = I ×W, A= ?
Using the substitution method, we know that the values of A is 19,200.
What is the substitution method?The substitution method is typically used in mathematics to solve an equation system.
In this approach, you solve the equation for one variable first, then you enter its value into the other equation.
So, we know that:
I = 240
W = I / 3
A = I * W
A = ?
Now, keep substituting the values to get A as follows:
I = 240
W = 240/3
W = 80
A = I * W
A = 240 * 80
A = 19,200
Therefore, using the substitution method, we know that the values of A is 19,200.
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need help with that answer
For you to make 5 pecan pies, it would be necessary to buy 1.9 pounds of pecans.
How many grams are there in a cup of pecans?Based on the information displayed on the label 1 cup of pecans is equal to 99 grams.
How many pounds do you need for 5 pecan pies?We know 1 pecan pie requires 1 3/4 cups or 1.75 cups (3/4 = 0.75)
1.75 x 5 = 8.75 cups in total
Now, let's calculate this in grams:
8.75 x 99 = 866.22 grams
Finally, let's calculate the pounds
1 pound = 453
x = 866.22
x = 866.22 / 453 = 1.9
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what is the average (mean) value of 3t^3-t^2
To calculate the average (mean) value of a function, you need to find the area under the curve of the function, divide it by the interval over which the function is defined, and then find the value of the function at the midpoint of the interval.
In this case, the function is 3t³ - t² and we need to find an interval to calculate the average (mean) value. A common interval used for this calculation is from 0 to 1.
The area under the curve of the function from 0 to 1 can be found by integrating the function from 0 to 1. However, to keep it simple, we can also use the definite integral of the function from 0 to 1, which is:
∫ (3t³ - t²) dt = 3t⁴/4 - t³/3 | from 0 to 1
= (3/4) - (1/3) = 1/4
So, the average (mean) value of the function 3t³ - t² over the interval 0 to 1 is: 1/4 ÷ 1 = 1/4
And the value of the function at the midpoint of the interval, which is 0.5, is: 3(0.5) ³ - (0.5) ² = 3/8 - 1/4 = -1/32
So, the average (mean) value of the function 3t³ - t² over the interval 0 to 1 is -1/32.
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Examine the triangle below, solve for x and y, rounded to two decimal places.
X=
y=
X
30° 16
y
The value of x and y in right angle triangle is 16√2 and 16
What is a Right Angle Triangle ?
A right triangle is a triangle having one right angle or two perpendicular sides. It is also referred to as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or previously rectangled triangle. The relationship between the sides and various angles of the right triangle serves as the basis for trigonometry.
The Pythagorean theorem, often known as Pythagoras' theorem, in Euclidean geometry relates the three sides of a right triangle. This statement states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.
In the triangle 2 angles are 90° and 45° respectively.
The third angle is = 180°+90°-45°=45°
The triangle is issosceles triangle
So the side which is not x is 16.
Now by using Pythagoras Theorem
x = √16^2+16^2 = 16√2
The value of x is 16√2
The value of y is y^2 + 16^2 = 16√2^2
y^2 = 512 - 256
y^2 = 256
y = 16
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image! i’ll put the answers here
A. 2.5
B. 3
C. 5
D. 9.5
Answer:
Text are too tiny for me to see sorry
Answer:
2.5
Step-by-step explanation:
P=29
w+w=4+4=8(rule of perimeter is 2w+2L)
29-8=21
21-16=5(L+L=8+8=16)
5 will be over 2 since it's for the 2 sides so 5÷2=2.5
your welcome
Please help I’m so confused!!!
Part (a)
[tex]\lim_{h \to 0} \frac{(h-1)^5+1}{h} \\ \\ =\lim_{h \to 0} \frac{5(h-1)^4}{1} \\ \\ =\boxed{5}[/tex]
Part (b)
[tex]y+1=5(x+1) \\ \\ y+1=5x+5 \\ \\ \boxed{y=5x+4}[/tex]
If you dissolved 50 g of sugar in 30 g of water, what would the sugar concentration be? 5%
The percentage of concentration of sugar in water will be 166.67%.
What is concentration?Concentration is the ability to focus on a single task or activity for an extended period of time. It requires both mental and physical effort, and involves staying attentive and motivated. Concentration helps us achieve our desired outcomes and complete tasks more efficiently. It also improves our ability to retain information, allowing us to better understand and remember what we have learned. Practicing concentration can lead to improved mental health, increased productivity, and better problem solving skills.
50/30 = x/100
30x = 100 × 50
30x = 5000
x = 166.67 %
Thus, The percentage of concentration of sugar in water will be 166.67%.
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√18y5
Simplify completely
Answer:
3✓2y5. ok. ksksmsmsmsksksksjsksSuppose you know that ZS and ZY are complementary, and that mZS=2(mZY) -30°. Find mZY.
On solving the provided question we can say that the Measure of complementary angles ∠ZY is 40 degrees.
What is complementary angle?When the sum of the measurements of two angles is 90 degrees, they are said to be complimentary.For instance, the angles of 30 and 60 degrees are supplementary. A supplementary angle is two angles combined to make a 180 degree angle, while a supplemental angle is two angles combined to make a 90 degree angle. Two angles are referred to as complimentary if their total is 90 degrees. Alternatively said, a right angle is created by the complementary angles (90 degrees).
Since ∠ZS and ∠ZY are complementary,
∠ZY+∠ZS=45 We also have another relation which says
∠ZS=2∠ZY -30
Substituting 2. in 1. gives
∠ZY+2∠ZY -30=90
3∠ZY=120
∠ZY=40
Hence the measure of angle is 40 degrees.
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