Step-by-step explanation:
The constant of proportionality k is given by k=y/x where y and x are two quantities that are directly proportional to each other.
this is also called the slope of the line.
based on our equation y = 5.5x
y/x = 5.5
so, C is the right answer.
3x =6 Which is the following above?Addition property of equality Subtraction property of equality Simplify Division property of equality Symmetric property of equality Distributive property
Given
3x = 6
Find
Which of the following above?
Explanation
as we have given , 3x = 6
here the property is division property of equality
as it states that when we divide the both sides of the equation by the same non - zero number , then the two sides remain equal.
3x = 6
3x/3 = 6/3
x = 2
Final Answer
Hence , the correct option is Division Property of Equality
3. When you find 420% of 85, what are you looking for?
A. A percent
B. The Part
C. The Whole
D. A ratio
Answer:
d
Step-by-step explanation:
cause its roght
Which of the following functions are isomorphisms? The groups under consideration are (R.+), and ((0,0), ). 1) Let f: (0, 0) (0,00) be defined by f(x)=x7 for all x € (0,0). 2) Let h: R-R be defined by h(x) = x + 3 for all x € R. 3) Let g: (0,00)-R be defined by g(x) Inx for all x € (0,0).
The groups under consideration are (a) Not an isomorphism. (b) Isomorphism. (c) Not an isomorphism.
(a) The function f(x) = x^7, defined on the interval (0, ∞), is not an isomorphism between the groups ((0, ∞), ×) and ((0, 0), •) because it does not preserve the group operation. The group ((0, ∞), ×) is a group under multiplication, while the group ((0, 0), •) is a group under a different binary operation. Therefore, f(x) is not an isomorphism between these groups.
(b) The function h(x) = x + 3, defined on the set of real numbers R, is an isomorphism between the groups (R, +) and (R, +). It preserves the group operation of addition and has an inverse function h^(-1)(x) = x - 3. Thus, h(x) is a bijective function that preserves the group structure, making it an isomorphism between the two groups.
(c) The function g(x) = ln(x), defined on the interval (0, ∞), is not an isomorphism between the groups ((0, ∞), ×) and (R, +) because it does not satisfy the group properties. Specifically, the function g(x) does not have an inverse on the entire domain (0, ∞), which is a requirement for an isomorphism. Therefore, g(x) is not an isomorphism between these groups.
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let f (x,y) = 1/ √ y-x^2 (a) sketch the region that is the domain of f (x). (b) sketch the level curves f (x)=k when k =1 and k =1/2.
When k = 1/2, the level curve is given by y - x² = 4. This is the equation of a shifted parabola, where the vertex is at (0,4) and the axis of symmetry is the y-axis.
(a) To sketch the domain of f(x, y) = 1/√(y - x²), first consider the restrictions:
1. The denominator cannot be zero: y - x² ≠ 0, or y ≠ x².
2. The square root cannot be negative: y - x^2 > 0, or y > x².
Thus, the domain of f(x, y) consists of all points (x, y) where y > x². This region can be sketched as a parabola opening upward (y = x²) with the region above the parabola being the domain.
(b) To sketch the level curves f(x, y) = k for k = 1 and k = 1/2, first set f(x, y) equal to k:
1. For k = 1: 1/√(y - x²) = 1, which implies y - x² = 1. The level curve for k = 1 is the graph of y = x² + 1, which is a parabola opening upward and translating one unit upward from the origin.
2. For k = 1/2: 1/√(y - x²) = 1/2, which implies y - x² = 4. The level curve for k = 1/2 is the graph of y = x² + 4, which is a parabola opening upward and translating four units upward from the origin.
These level curves can be sketched on the same graph with the domain, illustrating how the function f(x, y) behaves for the given values of k.
(a) To sketch the region that is the domain of f(x), we need to find the values of x and y that make the expression under the square root non-negative.
y - x² ≥ 0
y ≥ x²
This means that the domain of f(x) is all points (x,y) where y ≥ x². This is the region above the parabola y = x² in the xy-plane.
(b) To sketch the level curves f(x) = k, we need to find the equations of the curves where f(x,y) takes on a constant value of k.
1/ √ y - x² = k
√ y - x² = 1/k
y - x² = 1/k²
When k = 1, the level curve is given by y - x² = 1. This is the equation of a shifted parabola, where the vertex is at (0,1) and the axis of symmetry is the y-axis. When k = 1/2, the level curve is given by y - x² = 4. This is the equation of a shifted parabola, where the vertex is at (0,4) and the axis of symmetry is the y-axis.
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When k = 1/2, the level curve is given by y - x² = 4. This is the equation of a shifted parabola, where the vertex is at (0,4) and the axis of symmetry is the y-axis.
(a) To sketch the domain of f(x, y) = 1/√(y - x²), first consider the restrictions:
1. The denominator cannot be zero: y - x² ≠ 0, or y ≠ x².
2. The square root cannot be negative: y - x² > 0, or y > x².
Thus, the domain of f(x, y) consists of all points (x, y) where y > x². This region can be sketched as a parabola opening upward (y = x²) with the region above the parabola being the domain.
(b) To sketch the level curves f(x, y) = k for k = 1 and k = 1/2, first set f(x, y) equal to k:
1. For k = 1: 1/√(y - x²) = 1, which implies y - x² = 1. The level curve for k = 1 is the graph of y = x² + 1, which is a parabola opening upward and translating one unit upward from the origin.
2. For k = 1/2: 1/√(y - x²) = 1/2, which implies y - x² = 4. The level curve for k = 1/2 is the graph of y = x² + 4, which is a parabola opening upward and translating four units upward from the origin.
These level curves can be sketched on the same graph with the domain, illustrating how the function f(x, y) behaves for the given values of k.
(a) To sketch the region that is the domain of f(x), we need to find the values of x and y that make the expression under the square root non-negative.
y - x² ≥ 0
y ≥ x²
This means that the domain of f(x) is all points (x,y) where y ≥ x². This is the region above the parabola y = x² in the xy-plane.
(b) To sketch the level curves f(x) = k, we need to find the equations of the curves where f(x,y) takes on a constant value of k.
1/ √ y - x² = k
√ y - x² = 1/k
y - x² = 1/k²
When k = 1, the level curve is given by y - x² = 1. This is the equation of a shifted parabola, where the vertex is at (0,1) and the axis of symmetry is the y-axis. When k = 1/2, the level curve is given by y - x² = 4. This is the equation of a shifted parabola, where the vertex is at (0,4) and the axis of symmetry is the y-axis.
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Where is the graph of f(x)=4[x-3]+2 discontinuos
Answer:
Below
Step-by-step explanation:
4 [x-3] + 2 = y is not discontinuous anywhere
However 4 / [x-3] + 2 DOES have a discontinuity at x = 3 because this would cause the denominator to be zero <===NOT allowed !!
4
Of the choices below, what is the best
estimate of the length of a flute?
A 45 millimeters
B 45 centimeters
C 45 meters
Answer:
Step-by-step explanation:
45 meters is too long, 45 millimeters is too small. best choice would be 45 centimeters
Simplify the expressions below
a+2b+5+3a+b
12−a+a+12
4x−12+4x
Answer:
A. 4a + 3b + 5
B. 24
C. 8x - 12
Step-by-step explanation:
a + 2b + 5 + 3a + b
To simplify this, we'll want to group the similar terms together. In other words, put all of the a's first, then all of the b's, then just the numbers.
a + 2b + 5 + 3a + b
a + 3a + 2b + b + 5
Now, we want to add those similar terms, according to this:
a + a = 2a
So in our expression, we first have
a + 3a = 4a
then
2b + b = 3b
and finally 5, which is just... 5.
Thus, our expression simplified is:
4a + 3b + 5
Now let's do the same for the other expressions.
12 - a + a + 12
First, group them.
12 + 12 - a + a
Then, add them. Let's see, first 12 + 12:
12 + 12 = 24
Then -a + a:
- a + a = 0
24 + 0 = 24
Our 2nd expression, simplified, is just 24.
Finally,
4x - 12 + 4x
First group the x's:
4x + 4x - 12
And then add them, first 4x + 4x:
4x + 4x = 8x
And of course, -12 is just -12.
Thus, our third expression simplified is:
8x - 12
A. 4a + 3b + 5
B. 24
C. 8x - 12
restaurant is making hamburgers. The cooks use
2/3 pound of beef for each hamburger. If the cooks have 46 2/3
pounds of beef, how many hamburgers can they make?
Use pencil and paper. How does the answer change if the cooks have twice as much beef? Half as much beef? Explain your reasoning.
The cooks can make
nothing hamburgers.
(Simplify your answer. Type a whole number, proper fraction, or mixed number.)
Answer:
70.69
Step-by-step explanation:
46 2/3 divided by 2/3
46.66 divided by 0.66
The anwser is 70.69
If the cook makes twice as much beef then the number of hamburgers would be two times larger which would be 141.39.
Half as much beef would be 70.69 divided by two which is 35.34.
In the community park, there are 7 oak trees and 4 maple trees. Which ratios show the number of oak trees to the number of maple trees
There are 7 oak trees and 4 maple trees in the community park, so the ratio of oak trees to maple trees can be written as 7:4.
What is ratio?
A ratio is a way of comparing two or more quantities. It is a way of expressing the relationship between two numbers in terms of their size. A ratio can be written in different ways, such as in the form of a fraction, as a decimal, or as a whole number.
We can also write the ratio in different ways, such as:
7/4 = 1.75 oak trees for every 1 maple tree
35:20 = 35 oak trees for every 20 maple trees
14:8 = 14 oak trees for every 8 maple trees
All of these ratios represent the same proportion, which is 7 oak trees to 4 maple trees.
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Solve the problems. Write the complete proof in your paper homework and for online (only) respond to questions or statements (if any) that are parts of your proof or related to it. Given: AB = AC m∠1=m∠2 AC = 15, DC = 5 Find: BD, AB
Answer:
AB=15 BD=18
Step-by-step explanation:
AB is 15 because AB=AC and AC is 15
BD:
Using the Pythagorean Theorem
10²+15²=√325
√325=18
10 is from AB-CD
15 is the height which is AC
Answer:
BD = 5, and AB = 15 :)
A researcher at a major clinic wishes to estimate the proportion of the adult population of the United States that has sleep deprivation. How large a sample is needed in order to be 95% confident that the sample proportion will not differ from the true proportion by more than 4%?
Answer: n = 600.25 ≈ 601 ( sample size)
the minimum sample size of the adults in United State who have sleep deprivation is 601
Step-by-step explanation:
Given that;
the confidence level = 95% = 0.05
the Margin of error E = 4% = 0.04
∴ level of significance ∝ = 1 - C.L
∝ = 1 - (95/100)
= 0.05
Z∝/2 = 0.05/2 = 0.025
Z-critical value at 95% confidence level is OR level of significance at 0.025 = 1.96 (z-table)
Now to calculate the sample size, we say
n = (Z(critical) / M.E )² P ( 1 - P)
now we substitute
n = (1.96 / 0.04)² × 0.5 ( 1 - 0.5)
n = 2401 × 0.5 × 0.5
n = 600.25 ≈ 601
Therefore the minimum sample size of the adults in United State who have sleep deprivation is 601
Using the formula for the margin of error, it is found that a sample of 601 is needed.
In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(\alpha\), we have the following confidence interval of proportions.
\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)
In which
z is the z-score that has a p-value of \(\frac{1+\alpha}{2}\).
The margin of error is:
\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)
95% confidence level
So \(\alpha = 0.95\), z is the value of Z that has a p-value of \(\frac{1+0.95}{2} = 0.975\), so \(z = 1.96\).
In this problem:
There is no previous estimate, hence \(\pi = 0.5\) is used.The minimum sample size is n for which M = 0.04, hence:\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)
\(0.04 = 1.96\sqrt{\frac{0.5(0.5)}{n}}\)
\(0.04\sqrt{n} = 1.96(0.5)\)
\(\sqrt{n} = \frac{1.96(0.5)}{0.04}\)
\((\sqrt{n})^2 = \left(\frac{1.96(0.5)}{0.04}\right)^2\)
\(n = 600.25\)
Rounding up, a sample of 601 is needed.
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Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. Simplify the expression 8 2 + 9 ( 12 ÷ 3 × 2 ) − 7. Explain each of your steps
the simplified expression is 129.
To simplify the expression 8² + 9(12 ÷ 3 × 2) - 7, we follow the order of operations, which is:
Parentheses (do the calculations inside parentheses first)
Exponents (do the calculations involving exponents)
Multiplication and Division (do these operations from left to right)
Addition and Subtraction (do these operations from left to right)
Using these rules, we can simplify the expression step by step as follows:
8² + 9(12 ÷ 3 × 2) - 7 (Apply parentheses first)
= 8² + 9(4 × 2) - 7 (Evaluate 12 ÷ 3 as 4 and then 4 × 2 as 8 inside the parentheses)
= 8² + 9(8) - 7 (Evaluate 9 times 8 as 72)
= 64 + 72 - 7 (Evaluate 8² as 64)
= 129 (Perform the final subtraction and add the remaining terms)
Therefore, the simplified expression is 129.
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What is Cauchy-Schwarz inequality?
The Cauchy-Schwarz inequality is a mathematical theorem that states that for any two sequences of real numbers, the sum of the product of the corresponding terms of the sequences is less than or equal to the product of the sums of the sequences.
In other words, it gives a bound on the dot product of two vectors in terms of their lengths. The Cauchy-Schwarz inequality is used in various fields of mathematics, including analysis, linear algebra, and optimization, and has numerous applications, for example in probability theory, statistics, and quantum mechanics.
In summary, the Cauchy-Schwarz inequality provides a powerful tool for bounding the dot product of two vectors in terms of their lengths, and has wide-ranging applications in various branches of mathematics and related fields.
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HELP PLS!! 50 POINTS
Answer:
5 ^ (1/12)
Step-by-step explanation:
5 ^ 1/3
-----------------
5 ^ 1/4
When we divide exponents with the same base, we subtract the exponents
5 ^ (1/3 -1/4)
Getting a common denominator
5 ^ ( 4/12 - 3/12)
5 ^ (1/12)
Answer:
\(\Huge \boxed{5^{\frac{1}{12}}}\)
\(\rule[225]{225}{3}\)
Step-by-step explanation:
\(\displaystyle \sf \frac{5^{\frac{1}{3}} }{5^{\frac{1}{4}} }\)
When dividing same bases, we subtract the exponents.
\(\displaystyle \sf 5^{\frac{1}{3}- \frac{1}{4} }\)
Making exponents have the same denominator.
\(\displaystyle \sf 5^{\frac{4}{12}- \frac{3}{12} }\)
Subtracting exponents.
\(\displaystyle \sf 5^{\frac{1}{12}}\)
\(\rule[225]{225}{3}\)
plss help me due now
Answer:
B
Step-by-step explanation:
Hi!!
since they both equal y so we can set these equations equal to each other
60x+30=70x
-60x. -60x
30=10x
/10. /10
3=x
3 hours is x and now we can fill in x to find y
y=70(3)
y=210
210 miles so B is the correct answer
Hopes this helps please mark brainliest
What is a example of an irrational ?
Answer:
The example of irrational are; 0.3030030003..... , 22/7 and others.
Step-by-step explanation:
I don’t know what it is
15 ft. x 8 ft=
Answer:
The answer is 120 sq. ft.
for which (if any) of the three dependent variables in this data set (gender, age, ethnicity) would you report the standard deviation?
Gender and ethnicity are categorical variables and therefore, the standard deviation cannot be calculated for variables.
The standard deviation is a measure of the spread or dispersion of the data around the mean. In other words, it tells us how far each data point in a set is from the average of the set.
When we analyze data, it's important to understand how much variation there is in the data, and the standard deviation is one way to do this.
When it comes to the three dependent variables in the data set (gender, age, and ethnicity), it is important to understand that the standard deviation is only calculated for numerical data.
However, age is a numerical variable, and the standard deviation can be calculated for it.
To find the standard deviation of the ages, we need to first find the mean of the ages and then subtract each age value from the mean and square the result.
Next, we add up all the squared deviations and divide by the number of ages minus one. Finally, we take the square root of the result, and that gives us the standard deviation of the ages in the data set.
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Hector is building a metal sculpture in the shape of an equilateral triangle. After he divides ametal bar into 3 equal pieces, Hector figures each side of the triangular sculpture can be atmost 9 feet long.Let x represent the perimeter of the triangular sculpture. Which inequality describes theproblem?
One of the properties of an equilateral triangle is that all the sides are equal
From the statement given, each of the lengths of the triangle is at most 9 feet long means that each of the lengths is less than or equal to 9 feet
This can be represented mathematically as
\(\begin{gathered} l\leq9ft \\ \text{Where l is the length} \end{gathered}\)The perimeter of an equilateral triangle is the addition of the three equal lengths i.e.
\(l+l+l=\text{ 3l}\)If x represents the perimeter, then
Solve for x in the equation x2 - 4x-9= 29.
Plz help! Question is below!
Answer:
16
Step-by-step explanation:
Answer:
16
Step-by-step explanation:
8 x 1/2=
8/1 x 2/1 = 16
-3/2 divided by 1/4
Answer:
-6
Step-by-step explanation:
Answer:
-6
Step-by-step explanation:
When you divide fractions, you multiply the inverse.
So, -3/2 divided by 1/4 is -3/2 x 4/1 = -12/2
Simplified = -6
Hope this helps:)
help me with number 9 which is DEF one, please
Answer:
x = 9
DE = 13
EF = 36
DF = 28
Step-by-step explanation:
DF = EF
7x - 35 = 4x - 8
3x = 27
x = 9
DE = x + 4 = 9 + 4 = 13
EF = 4x - 8 = 4(9) - 8 = 36
DF = 7x - 35 = 7(9) - 35 = 28
In parallelogram ABCD, AB is three more than twice the measure of BC. If the perimeter of the parallelogram is 18 units and all angles are right. Calculate the measure of BD.
The value of line BD in parallelogram ABCD is 2units
What is a parallelogram?A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides of a parallelogram are equal in length, and the opposite angles are equal in measure. The Sum of all the interior angles of a parallelogram equals 360 degrees.
The perimeter of a parallelogram is 2(l+w)
if BD is x
AB = 3+2x
P= 2(3+2x+x)
18= 2(3+3x)
divide both sides by
9= 3+3x
subtract 3 fromboth sides
6= 3x
x = 2units
therefore BD= 2units.
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The area of a triangle is found by multiplying half of the measure of its base by its height. the area of the following right triangle is 18 square centimeters.
To find the area of a triangle, we use the formula: Area = 0.5 * base * height. Given that the area of the right triangle is 18 square centimeters, we can use this information to find the values of the base and height.
Let's denote the base of the triangle as 'b' and the height as 'h'. We are given that the area of the right triangle is 18 square centimeters, so we can write the equation as 0.5 * b * h = 18. To find the values of 'b' and 'h', we need additional information. If we are provided with either the base or the height, we can solve for the other unknown. Without any further details, it is not possible to determine the exact values of the base and height.
However, we can explore different scenarios based on the given area of 18 square centimeters. For example, if the base is 6 centimeters, the height would be 6 centimeters as well (0.5 * 6 * 6 = 18). Similarly, if the base is 9 centimeters, the height would be 4 centimeters (0.5 * 9 * 4 = 18).
In summary, the area of a right triangle is found by multiplying half of the measure of its base by its height. With the given information of an area of 18 square centimeters, we can explore different combinations of base and height values that satisfy the equation 0.5 * base * height = 18. The specific values of the base and height would depend on additional information or constraints provided.
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Please someone tell me the answer of these questions
Answer:
VERTICALLY OPP ANGLES
Step-by-step explanation:
Which real-world scenario involves a right triangle? a triangular bathroom tile with side lengths of 6 inches, 8 inches, and 12 inches a triangular bike path with lengths of 5 miles, 12 miles, and 13 miles a triangular plot of land with side lengths of 10 yards, 10 yards, and 15 yards a triangular street sign with side lengths of 3 feet, 3 feet, and 3 feet
Answer:
The bike path
Step-by-step explanation:
A right triangle has a hypotenuse that can be found using the formula
a^2 + b^2 = c^2 where c is the hypotenuse
The street sign is obviously not correct because a hypotenuse is longer than the sides. The bathroom tile isn't correct either because 6^2 + 8^2 = 100, or 10 after you take the square root. That leaves the bike path.
Checking to make sure:
5^2 + 12^2 = c^2
25 + 144 = √169
√169 = 13
The scenario from the given scenarios involving a right triangle is: "A triangular bike path with lengths of 5 miles, 12 miles, and 13 miles", as the sides satisfy the Pythagoras theorem.
When do three given line segments form a right triangle?Any three line segments can form a right triangle only when they satisfy the Pythagoras Theorem, according to which, the square of the largest side in a right triangle is equal to the sum of the squares of the other two sides, that is, a² = b² + c², where a is the largest side, and b and c are the two other sides.
How to solve the given question?In the question, we are asked to identify from the given scenarios, the case that involves a right triangle.
We know that for three segments to be a right triangle, they need to satisfy the Pythagoras Theorem. So we check every scenario with the theorem:
A triangular bathroom tile with side lengths of 6 inches, 8 inches, and 12 inches: This is not a right triangle as it doesn't satisfy the Pythagoras theorem as (12² = 144) ≠ (6² + 8² = 36 + 64 = 100).A triangular bike path with lengths of 5 miles, 12 miles, and 13 miles: This is a right triangle as it satisfies the Pythagoras theorem as (13² = 169) ≠ (12² + 5² = 144 + 25 = 169).A triangular plot of land with side lengths of 10 yards, 10 yards, and 15 yards: This is not a right triangle as it doesn't satisfy the Pythagoras theorem as (15² = 225) ≠ (10² + 10² = 100 + 100 = 200).A triangular street sign with side lengths of 3 feet, 3 feet, and 3 feet: This is not a right triangle as it doesn't satisfy the Pythagoras theorem as all the sides are equal, so it is an equilateral triangle.∴ The scenario from the given scenarios involving a right triangle is: "A triangular bike path with lengths of 5 miles, 12 miles, and 13 miles", as the sides satisfy the Pythagoras theorem.
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Complete the equation to make a true statement.
Enter your answer in the box.
Applying the power of power rule, the completed equation is given as follows:
\(x^{10} = (x^5)^2\)
How to use the power of power rule?The power of a power rule is used when a single base is elevated to multiple exponents, and states that simplified expression is obtained keeping the base, while the exponents are multiplied.
Hence the missing exponent for this problem is obtained as follows:
2x = 10
x = 10/2
x = 5.
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A widget manufacturer's expense function is
E = 6.00 q + 11,000
What are the variable costs to produce one widget?
The variable costs to produce one widget is 6.00
How to determine the variable costsFrom the question, we have the following parameters that can be used in our computation:
E = 6.00 q + 11,000
The variable cost is the slope of the relation
Using the above as a guide, we have the following:
Fixed cost = 11000
Variable cost = 6.00
The above parameters mean that
The variable cost is 6.00
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You have a standard deck of cards. What is the probability of drawing a heart or a face card?
Answer:
3/4
Step-by-step explanation: