Answer:
1/4 of the pan
Step-by-step explanation:
1/3 of 3/4 = 1/4
A line passes through the points (1,1/2) and (3,2) which is the equation of the line
Answer:
The equation of the line is y = 3/4x - 1/4
Step-by-step explanation:
To find the equation of this line, start by using the two points with the slope formula to find the slope.
m(slope) = (y2 - y1)/(x2 - x1)
m = (2 - 1/2)/(3 - 1)
m = (3/2)/2
m = 3/4
Now that we have the slope, we can use that and either point in point-slope form to find the equation.
y - y1 = m(x - x1)
y - 2 = 3/4(x - 3)
y - 2 = 3/4x - 9/4
y = 3/4x - 1/4
The difference between simple and compound interest in a savings account is that ______________.
Answer:
The difference is that the simple interest gives you interest only on the deposited amount in the account while the compound interest is calculated over the deposited amount and the previous interest amount added to the deposited amount.
Step-by-step explanation:
The difference between simple and compound interest is that simple interest is calculated only on the principal amount, while compound interest is earned on past interest.
Explanation:The difference between simple and compound interest in a savings account is that simple interest is an interest rate calculation only on the principal amount, while compound interest is interest that is earned on past interest. This means that with compound interest, the total amount of savings will grow dramatically over time. To illustrate this, consider the example of putting $1,000 in a savings account with 10% interest. With simple interest, after one year, you will have $1,100. But with compound interest, if you leave the $1,100 in the account and continue to earn 10% interest, you will have $1,210 at the end of year two.
Write 765,056 in word form
Seven thousand sixty-five fifty six
Answer:
seven hundred sixty-five thousand fifty-six
Step-by-step explanation:
Your Welcome
How do you use the limit comparison test on this particular series?
Calculus series tests
Compare [tex]\dfrac1{\sqrt{n^2+1}}[/tex] to [tex]\dfrac1{\sqrt{n^2}}=\dfrac1n[/tex]. Then in applying the LCT, we have
[tex]\displaystyle\lim_{n\to\infty}\left|\frac{\frac1{\sqrt{n^2+1}}}{\frac1n}\right|=\lim_{n\to\infty}\frac n{\sqrt{n^2+1}}=1[/tex]
Because this limit is finite, both
[tex]\displaystyle\sum_{n=1}^\infty\frac1{\sqrt{n^2+1}}[/tex]
and
[tex]\displaystyle\sum_{n=1}^\infty\frac1n[/tex]
behave the same way. The second series diverges, so
[tex]\displaystyle\sum_{n=0}^\infty\frac1{\sqrt{n^2+1}}=1+\sum_{n=1}^\infty\frac1n[/tex]
is divergent.
The limit comparison test is used to determine the convergence or divergence of a series by comparing it to a known convergent or divergent series.
Explanation:The limit comparison test is used to determine the convergence or divergence of a series by comparing it to a known convergent or divergent series. The test states that if the limit of the ratio between the terms of the given series and the terms of a known convergent series is a finite positive number, then both series behave in the same way. Here is how you can use the limit comparison test step by step:
Choose a known series that converges, ideally one that is similar in nature to the given series.Take the limit of the ratio between the terms of the given series and the terms of the known convergent series.If the limit is a finite positive number, then both series converge or diverge together. If the limit is zero or infinite, the result is inconclusive.For example, if we have the series ∑(n^2)/(2^n), we can use the limit comparison test with the series ∑(1)/(2^n). Taking the limit of the ratio (n^2)/(2^n) / (1)/(2^n) as n approaches infinity, we get:
lim(n→∞) [(n^2)/(2^n)] / [(1)/(2^n)] = lim(n→∞) (n^2)/(1) = ∞
Since the limit is infinite, the result is inconclusive. Therefore, the given series does not converge or diverge using the limit comparison test.
Find the vertex of the given function. f(x) = |x + 1| - 7
Vertex is at (-1,-7), because the |x+1| moves the graph left 1 and -7 moves the graph down 7.
Answer:
the second answer is a
Step-by-step explanation:
edge 2020
Complete the square to determine the minimum or maximum value of the function defined by the expression.
x2 − 12x − 2
A) maximum value at 38 B) minimum value at 38 C) maximum value at −38 D) minimum value at −38
Answer:
Option D. minimum value at −38
Step-by-step explanation:
we have
[tex]x^{2}-12x-2[/tex]
Let
[tex]y=x^{2}-12x-2[/tex]
Complete the square
[tex]y+2=x^{2}-12x[/tex]
[tex]y+2+36=(x^{2}-12x+36)[/tex]
[tex]y+38=(x^{2}-12x+36)[/tex]
[tex]y+38=(x-6)^{2}[/tex]
[tex]y=(x-6)^{2}-38[/tex] ------> equation of a vertical parabola in vertex form
The vertex is the point [tex](6,-38)[/tex]
The parabola open upward-----> the vertex is a minimum
therefore
minimum value at −38
In a function, each x-value has ________ y-value.
Explanation:
In a function, each x-value has one y-value.
___
That is the definition of a relation that is a function.
Final answer:
Each x-value in a function has exactly one corresponding y-value. Functions map elements of the domain to unique elements in the range, which can be represented graphically and must pass the vertical line test. The derivative in calculus, such as dy/dx, reflects the rate of change between these variables.
Explanation:
In a function, each x-value has one corresponding y-value. This is a foundational concept in mathematics that defines a relationship whereby each input (or x-value) in the function produces exactly one output (or y-value). Essentially, a function maps each element of the domain to exactly one element in the range.
An example of a function is y = f(x), which could represent a linear function like y = 3x + 2. In this case, for every x-value, there is a specific y-value determined by the function's formula. So if x were 1, then y = 3(1) + 2 = 5. The graphical representation of a function, such as its curve or line on a coordinate plane, must pass the vertical line test. That means if you draw a vertical line through any point on the graph, it should intersect the graph at no more than one point, confirming that each x-value has only one y-value.
Understanding functions is pivotal in different areas of mathematics, including calculus where the derivative of a function represents the rate of change of the y-value with respect to the x-value. In the case of the linear function y = 6+3x, the derivative dy/dx is constant at 3, implying that for every unit increase in x, y will increase by 3 units.
What is the sum of the series? 5∑i=1 4i
Answer:
60
Step-by-step explanation:
∑[i=1,5] 4i = 4·1 + 4·2 + 4·3 + 4·4 + 4·5
= 4 + 8 + 12 + 16 + 20
= 60
Can someone help me...
Answer:
48.3 cm^2
Step-by-step explanation:
The area of the enclosing square is that of a square 15 cm on a side, so is ...
square area = (15 cm)^2 = 225 cm^2
The white area is that of a quarter-circle of radius 15 cm, so that area is ...
quarter-circle area = (1/4)πr^2 = (π/4)·(15 cm)^2 = 56.25π cm^2 ≈ 176.7 cm^2
Then the yellow area is the difference ...
yellow area = square area - quarter-circle area
= (225 cm^2) - (176.7 cm^2)
yellow area = 48.3 cm^2
I need help on this problem. I don’t understand it at all. Please help me.
When dealing with numbers, we find the LCM by factoring the numbers, and then choosing all the primes appearing, with the highest exponent possible.
Similarly, we will factor the polynomials first:
[tex] x^4+3x^3 = x^3(x+3)[/tex]
[tex]x^2-9 = (x+3)(x-3)[/tex]
[tex]x^3+6x^2+9x = x(x^2+6x+9) = x(x+3)^2[/tex]
The following factors emerged:
[tex]x,\ x^3[/tex] We will choose [tex]x^3[/tex] because it has the higher exponent[tex]x-3[/tex][tex]x+3,\ (x+3)^2[/tex] We will choose [tex](x+3)^2[/tex] because it has the higher exponent.So, the LCM is
[tex]x^3(x-3)(x+3)^2[/tex]
which number is an irrational number
I’m pretty sure it’s A
Answer: A
Step-by-step explanation:
micah has 10 more fish than cella has. together, micah and cella have 34 fish. how many fish does micah have
Answer:
22 fish
Step-by-step explanation:
cella has 12 fish. micheal has ten more 12+10=22. combind 22+12=34
Answer:
22 fish
Step-by-step explanation:
Please help! The following three shapes are based only on squares, semicircles, and quarter circles. Find the perimeter and the area of each shaded part.
Answer:
perimeter = (18 +9π) cm
area = (81 -20.25π) cm^2
Step-by-step explanation:
The perimeter of the shaded area is the circumference of the circle added to two sides of the square. The circumference of the circle is π times the diameter, so the perimeter is ...
p = 2(9 cm) + π(9 cm) = (18 +9π) cm
___
The area of the shaded portion is the difference between the area of the square and the area of the circle. The area of the square is the square of the diameter. The area of the circle is π/4 times that value.
A = (9 cm^2) + (π/4)(9 cm^2) = (81 +20.25π) cm^2
_____
Comment on circle area
The formula you often see is ...
A = πr^2 . . . . r is the radius
since r = d/2, where d is the diameter, this can also be written as ...
A = π(d/2)^2 = (π/4)d^2
Here, the diameter of the circle is the same as the side length of its enclosing square, so the area of the circle is π/4 times the area of the enclosing square.
Answer:
Area= [tex]81-\frac{81}{4}\pi[/tex]
Perimeter= [tex]9\pi +18[/tex]
The coordinates A(0,0), B(0,3), C(4,3) and D(4,0) are graphed and connected together. What 3 dimensional shape will be created when this shape is rotated about the y-axis?
a cube would be formed as ABCD form a square when graphed
tabia stores her hair bands in a cube shaped container. the cube has a volume of 64 cubic inches. What is the lenght of the edges of the cube?
Answer:
The length of the edge of the cube = 4 inches
Step-by-step explanation:
* Lets describe the cube
- It has 6 faces all of them are squares
- It has 8 vertices
- It has 12 equal edges
∵ The volume of any formal solid = area of the base × height
∵ The base of the cube is a square
∴ Area base = L × L = L² ⇒ L is the length of the edge of it
∵ All edges are equal in length
∴ Its height = L
∴ The volume of the cube = L² × L = L³
* Now we have the volume and we want to find the
length of the edges
∵ Its volume = 64 inches³
∴ 64 = L³
* Take cube root to the both sides
∴ ∛64 = ∛(L³)
∴ L = 4 inches
* The length of the edge of the cube = 4 inches
The length of the edges of the cube is 4 inches.
Given that the volume V is 64 cubic inches, we can set up the equation:
[tex]\[ a^3 = 64 \][/tex]
To solve for a , we take the cube root of both sides:
[tex]\[ a = \sqrt[3]{64} \][/tex]
The cube root of 64 is 4, since [tex]\( 4^3 = 4 \times 4 \times 4 = 64 \).[/tex]
Therefore, the length of the edges of the cube is 4 inches.
An animal shelter spends $4.50 per day to care for each bird and $6.50 per day to care for each cat. Kaylee noticed that the shelter spent $96.00 caring for birds and cats on Thursday. Kaylee found a record showing that there were a total of 16 birds and cats on Thursday. How many birds were at the shelter on Thursday
Answer:
4
Step-by-step explanation:
Let b represent the number of birds. Then the cost of care for b birds and 16-b cats was ...
4.50b +6.50(16-b) = 96.00
-2.00b = -8.00 . . . . . . . . . . . . simplify, subtract 104
b = 4 . . . . . . . . . . . . . . . . . . . . .divide by -2
The number of birds at the shelter on Thursday was 4.
Will give brainliest if you show your work and answer completely!!!
Rick is a real estate agent and makes 7% commission on his total sales. He sells a home that worth $150,000. What is his commission?
which of the following could be side lenths of a right triangle? A.) 0.9cm, 1.2cm, 1.5cm B.) 0.9cm, 1.5 cm, 1.5cm C.) 0.9 cm, 1.2cm, 1.8cm D.) 0.9cm, 0.6cm, 1.5cm
Answer:
The answer A
Step-by-step explanation:
B: You need a side that is longer than 2 equal sides. B is incorrect.
A: Try
9^2 + 12^2 = 15^2 if that works, A will work.
81 + 144 = 225
This works. I used these numbers because they were easier to see.
0.9^2 + 1.2^2 = 1.5^2
0.81 + 1.44 = 2.25
2.25 = 2.25
That is the answer A
But we have to check the other two.
C:
0.9^2 = 0.81
1.2^2 = 1.44
1.8^2 = 3.24 This won't work. 3.24 is just too big.
D:
0.9^2 = 0.81
0.6^2 = 0.36
1.5^2 = 2.25 It's too far away.
Which are the maximum values ? I will add a picture please help
Answer:
58 at the point (9,8)
7 at the point (1, 1)
Step-by-step explanation:
The maximum points will be found in the vertices of the region.
Therefore the first step to solve the problem is to identify through the graph, the vertices of the figure.
The vertices found are:
(1, 10)
(1, 1)
(9, 5)
(9, 8)
We look for the values of x and y belonging to the region, which maximize the objective function [tex]f(x, y) = 2x + 5y[/tex]. Therefore we look for the vertices with the values of x and y higher.
(1, 10), (9, 5), (9, 8)
Now we substitute these points in the objective function and select the one that produces the highest value for f (x, y)
[tex]f(1, 10) = 2(1) + 5(10) = 52\\\\f(9, 5) = 2(9) + 5(5) = 43\\\\f(9, 8) = 2(9) + 5(8) = 58[/tex]
The point that maximizes the function is:
[tex](9, 8)[/tex] with [tex]f(9, 8) = 58[/tex]
Then the value that produces the minimum of f(x, y) is (1, 1)
[tex]f(1, 1) = 2(1) + 5(1) = 7[/tex]
Adriana collects rainwater in a large barrel that weights 10 pounds. When there are 10 gallons of water in the barrel, the total weight of the barrel and the water is 93.4 pounds. When there are 20 gallons of water, the total weight is 176.8 pounds. Which equation and graph match this situation?
Answer:
A. y = 8.34x + 10
Step-by-step explanation:
The first choice is appropriate to the situation where y=10 when x=0 and where y increases by 83.4 when x increases by 10.
___
The equation of selection D is the same and is also appropriate, but the graph does not match the equation. The equations of the other choices are incorrect, as are the graphs.
The linear equation which represents the data is : y = 8.34x + c. Hence, correct option is A.
The linear equation for the graph can be expressed in the form :
y = bx + c b = slope ; c = interceptb = change in y / change in x
Change in y :
176.8 - 93.4 = 83.4Change in x :
20 - 10 = 10Hence , slope , b = (83.4 /10) = 8.34
The value of the intercept, c ;
93.4 = 8.34(10) + c
93.4 = 83.4 + c
c = 10
Hence, the linear equation is :
y = 8.34x + 10Learn more on linear equation : https://brainly.com/question/30884929
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Please hurry I will mark brainliest and 20 points
simplify sqrt0.08^12
a.(0.08)^6
b.(0.8)^6
c.(0.16)^6
d.(0.12)^8
Answer:
a) (0.08)^6
Step-by-step explanation:
Given in the question,
[tex]\sqrt{0.08^{12} }[/tex]
As we know that
[tex]\sqrt{x} = x^{1/2}[/tex]
So,
[tex]\sqrt{0.08^{12}[/tex] = [tex]0.08^{12(1/2)}[/tex]
[tex]0.08^{12/2}[/tex]
[tex]0.08^{6}[/tex]
PLEASE HELP I'M VERY CONFUSED!
find all natural number solutions for each congruence.
1. y + 3 ≡ 2 mod 4
2. 3 - y ≡ 5 mod 9
Answer:
1. y = 4n -1
2. y = 9n -2
Step-by-step explanation:
1. For some integer n, numbers that are congruent to 2 mod 4 are ... 4n+2. Then you have ...
y + 3 = 4n +2 . . . . next, subtract 3 from both sides
y = 4n -1 . . . . values of y are natural numbers for all natural numbers n
___
2. Similarly, ...
3 - y = 9n +5
3 - 9n - 5 = y . . . . . add y-9n-5
-9n -2 = y . . . . . . . . collect terms
For every integer n, there is also an integer -n. For our purpose, we're only interested in those values of n that make -9n be positive. Rather than require n be negative so -9n is positive, we can require n be positive and use the expression 9n for the multiple of 9.
We want y a natural number, so we can write this as ...
y = 9n -2 . . . . for natural numbers n
To find the natural number solutions for congruences, we use algebraic manipulation to simplify the equation and find values that satisfy the congruence. For the given congruences, the natural number solutions are y = 3, 7, 11, 15, ... and y = 7, 16, 25, ..., respectively.
Explanation:1. To find the natural number solutions for the congruence y + 3 ≡ 2 mod 4, we need to find all values of y that satisfy the given congruence.
Subtracting 3 from both sides of the congruence, we have y ≡ -1 mod 4. Since we are looking for natural number solutions, we can rewrite this as y ≡ 3 mod 4.
The natural number solutions for this congruence are y = 3, 7, 11, 15, ...
2. For the congruence 3 - y ≡ 5 mod 9, we need to determine the natural number solutions for y that make the congruence true.
Subtracting 3 from both sides, we have -y ≡ 2 mod 9. Multiplying both sides by -1, we get y ≡ -2 mod 9. Rewriting this as y ≡ 7 mod 9, the natural number solutions for y are y = 7, 16, 25, ...
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simplify 6/4-√5
___+___
Answer:
3 - 2√5
-------------
2
Step-by-step explanation:
These two expressions have different denominators, and thus use of the LCD is necessary. The LCD is 4.
Thus, we have:
6/4 - (4/4)√5, or
6 - 4√5
-------------
4
This can be reduced to:
3 - 2√5
------------- (answer)
2
Betsy works as waitress. Today she worked an 8 hour shift, and was paid $ 92.00. Plot a graph of the amount Betsy earns against the time she works for. Then find how much Betsy is paid per hour. Write an equation using Y = MX + B Form.
Final answer:
To plot a graph of the amount Betsy earns against the time she works, we'll put the hours worked on the x-axis and the amount earned on the y-axis. Betsy is paid $11.50 per hour and the equation for Betsy's earnings is Y = 11.50X.
Explanation:
To plot a graph of the amount Betsy earns against the time she works, we'll put the hours worked on the x-axis and the amount earned on the y-axis. In this case, Betsy worked an 8 hour shift and was paid $92.00. So, the point on the graph would be (8, 92). To find how much Betsy is paid per hour, we can divide the total amount earned by the number of hours worked. In this case, $92.00 divided by 8 hours equals $11.50 per hour.
Using the equation Y = MX + B, where Y is the amount earned, M is the rate per hour, X is the number of hours worked, and B is the y-intercept, we can write the equation for Betsy as Y = 11.50X + 0, since she doesn't have a one-time fee.
help please, anyone thank you
Answer:
Part A: A (6 , 11) , B (5 , 6) , C (7 , 1) , D (0 , 8)
Part B: A (-6 , -11) , B (-5 , -6) , C (-7 , -1) , D (0 , -8)
Step-by-step explanation:
* Lets study the reflection about the two axes X and Y
- The distance between the point and the axes of reflection =
the distance between its image and the axes
- The point and the its image are on opposite sides of the axes
- If a point (x , y) reflected about x axis, that means the point
will move vertically
- Moving vertically means we will change the sign of the y-coordinates
∴ The image of (x , y) after reflection about x-axis is (x , -y)
- If a point (x , y) reflected about y axis, that means the point
will move horizontally
- Moving horizontally means we will change the sign of the x-coordinates
∴ The image of (x , y) after reflection about x-axis is (-x , y)
* Now lets use the explanation above to solve our problem
- At first lets right the original point of the quadrilateral ABCD
∵ A (-6 , 11) , B (-5 , 6) , C (-7 , 1) , D (0 , 8)
Part A: The y-axis is the line of reflection
- Lets change the signs of x-coordinates in all points
∴ The new points after reflection about y-axis is:
A (6 , 11) , B (5 , 6) , C (7 , 1) , D (0 , 8)
- Note: The point D does not change because x-coordinate is 0
and there is no sign for the 0
Part B: The x-axis is the line of reflection
- Lets change the signs of y-coordinates in all points
∴ The new points after reflection about x-axis is:
A (-6 , -11) , B (-5 , -6) , C (-7 , -1) , D (0 , -8)
Please help ASAP
(k+5)(k−5)=k^2 −25
Eleanor says that k+5 is a factor of k^2-25
Isabel says that k^2 -25 is divisible by k+5
Who is correct?
Answer:
both are
Step-by-step explanation:
A number, or a polynomial, is "divisible" by a "factor." Since (k+5) is a factor of (k^2-25), (k^2-25) is divisible by (k+5). Both Eleanor and Isabel are correct in their description.
1. A claim states that a specific crimes occurs in the given proportions shown in the table for October through March. Use the frequencies from randomly selected crimes to find the test statistic using a 0.01 significance level needed to test the claim.
A. 15.086
B. 9.843
C. 6.683
D. 749.500
(plus other questions in attached)
Answer:
C. 6.683
Step-by-step explanation:
Find the area between 1.10 and 1.60 standard deviation above the mean.
Answer:
about 0.08087
Step-by-step explanation:
The statistics functions of your graphing calclulator can help you with that. It is a good idea to learn to use them.
An equal number of students from two Algebra 1 classes at Bozeman School were randomly selected and asked how many hours per week they spend studying algebra.
The class with the largest median for hours spent studying is
-Mrs. Castro’s class
-Mr. Philippe’s class
-The medians are the same
The class with the largest range of hours spent studying is
-Mrs. Castro’s class
-Mr. Philippe’s class
-The ranges are the same
The class with the largest IQR for hours spent studying is
-Mrs. Castro’s class
-Mr. Philippe’s class
-The IQRs are the same
Answer:
Largest Median: Same
Largest Range: Castro
Largest IQR: Castro
Step-by-step explanation:
With a box-and-whisker plot, the box represents the upper and lower quartiles, the vertical line inside the box represents the median, and the lines on either side of the box show the high and low of the range.
Largest Median: Medians are the same because the verticle line inside the boxes is at 7 for both
Largest Range: Ms Castro's Class- the lines on either side of the box for Ms Castro go from 1-10 while the other class only goes from 4-10.
Largest IQR (interquartile range) Ms. Castro's class: their IQR goes from 5-8 while the other class only goes from 6-8
Answer:
same median and CASTRO CASTRO just took the TYS on algebra nation
Step-by-step explanation:
Create a second equation so the system has no solution. y=3/4x-4
Answer:
y=3/4 *x
Step-by-step explanation:
1. the given equation is the equation of line in slope-interception form (y=kx+b), where 3/4 is 'k' and (-4) is 'b'.
2. if the system of the two equations has no solution, it means, the 2d line is parallel to the given one, then 'k' of the 2d line is the same value.
3. common view of the equation of the 2d line is y=3/4 *x+b, where 'b' is number. For example, y=3/4x; y=3/4 *x+1; y=3/4 *x-5/8, etc.
One example of a linear function that generates a system without a solution is given by:
[tex]y = \frac{3}{4}x + 5[/tex]
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.If two equations have the same slope but different intercepts, they never intersect each other, that is, a system without solutions is generated. Hence, one possible example in this problem is given by:
[tex]y = \frac{3}{4}x + 5[/tex]
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