Answers
By taking a quotient we will see that he has saved $450.
How much will he have saved across these two months?On the first month Lance earnesd $546, and on the second month he earned $354.
Adding these we get:
$546 + $354 = $900
So he earned a total of 900 dollars between April and June. And we know that he saves half of that, then the amount saved is equal to that divided by 2:
$90/2 = $450
He has saved 450 dollars.
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Related Questions
3.5 minutes into meters per second
Answers
Answer:
0.583 [the 3 goes on forever]
Step-by-step explanation:
Of the following, which are solutions to the differential equation y′′−5y′+6y=0?y=e^2ty=3e^3ty=3sin(2t)I onlyII onlyIII onlyI and II only
Answers
I and II only are solutions to the differential equation y′′ − 5y′ + 6y = 0.
Let's assume y = e^2t is the solution of the given differential equation y′′ − 5y′ + 6y = 0.
Now, put y = e^2t in the given differential equation y′′ − 5y′ + 6y = 0
(e^2t)'' - 5(e^2t)' + 6(e^2t) = 0
Now differentiate it; we get
4e^2t - 10e^2t + 6e^2t = 0
0 = 0
So, here we can see that y = e^2t satisfies the equation y′′ − 5y′ + 6y = 0.
Therefore y = e^2t is the solution of the given differential equation.
Now let's assume y = 3e^3t is the solution of the given differential equation y′′ − 5y′ + 6y = 0.
Put y = 3e^3t in the given differential equation y′′ − 5y′ + 6y = 0
(3e^3t)'' - 5(3e^3t)' + 6(3e^3t) = 0
Now differentiate it; we get
27e^3t - 45e^3t + 18e^3t = 0
0 = 0
So, here we can see that y = 3e^3t satisfies the equation y′′ − 5y′ + 6y = 0.
Therefore y = 3e^3t is the solution of the given differential equation.
Similarly, let's assume y = 3sin(2t) is the solution of the given differential equation y′′ − 5y′ + 6y = 0.
Put y = 3sin(2t) in the given differential equation y′′ − 5y′ + 6y = 0
(3sin(2t)'' - 5(3sin(2t))' + 6(3sin(2t)) = 0
Now differentiate it; we get
-24cos(2t) + 30cos(2t) + 18sin(2t) = 0
-24cos(2t) + 30cos(2t) + 18sin(2t) ≠ 0
So, here we can see that y = 3sin(2t) does not satisfies the equation y′′ − 5y′ + 6y = 0.
Therefore y = 3sin(2t) is not the solution of the given differential equation.
Hence, I and II only are solutions to the differential equation y′′−5y′+6y=0.
--The given question is incorrect; the correct question is
"Of the following, which are solutions to the differential equation y′′−5y′+6y=0?
I. y = e^2t
II. y = 3e^3t
III. y = 3sin(2t)
I only
II only
III only
I and II only"--
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Bert and Ernie are solving the inequality 2x²+5x-3
problem 3-67 when Bert has an idea. "Can't we change this into one parabola and solve our
inequality that way?", he asks.
Ernie asks, "What do you mean?"
"Can't we determine the solutions by looking at the graph of f(x)=x²+x-6?", Bert replies.
a. Where does Bert get the equation f(x)=x²+x-6?
b. Try Bert's idea. Make a sketch of the parabola and show how it can be used to solve the
original inequality.
Answers
Answer:
Step-by-step explanation:
Given equation: f(x)=x^2+x-6
The roots of the equation, set the equation equal to zero.
[tex]x^2+x-6=0\\x^2+3x-2x-6=0\\x(x+3)-2(x+3)=0\\ (x+3)(x-2)=0\\ x=-3,2[/tex]
Therefore, the roots of the equation are x=-3 and x=2
1. What's the measure of AC?
2. What is the measure of AC'
3. What is the measure of C'B'?
Answers
1. The measure of AC = 8.4
2. The measure of AC' = 6
3. The measure of C'B' = 12.6
What are parallel lines?Lines in a plane that are consistently spaced apart are known as parallel lines. Parallel lines don't cross each other.
Given:
Segment B'C' is parallel to segment BC.
A line splits a triangle's sides in the same proportion if it runs parallel to one side and crosses the other sides at two different spots.
Then,
10/4 = 6/x
x = 2.4
The measure of AC = 2.4
And,
14/8.4 = 21/y
y = 12.6
The measure of C'B' = 12.6
Therefore, all the required values are given above.
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Quetion Number 27
You are comparing price at two local torage vendor. Rent-A-Space charge a monthly fee of 22 cent per cubic foot plu 5. 5% ale tax. Store-Ur-Stuff charge a monthly fee of 25 cent per cubic foot plu 5. 5% ale tax. If you pay the Store-Ur-Stuff bill prior to the firt of the month, you will get a 4% dicount, but you will till have to pay ale tax on the pre-dicount cot. Auming you pay the bill prior to the firt of the month, what i the difference in cot between the two vendor if you are toring a total of 400 cubic feet?
Answers
The distinction in cost between the two sellers is $1.44, with Store-Ur-Stuff being savvier.
Expect you to take care of the two bills preceding the first of the month, the distinction in cost between leasing from Lease A-Space and Store-Ur-Stuff is $10. Lease A-Space would cost $88 (400 cubic feet x 22 pennies/cubic foot + 5.5% deals charge) while Store-Ur-Stuff would cost $78 (400 cubic feet x quarter/cubic foot + 4% markdown + 5.5% deals charge).
The distinction in cost between Lease A-Space and Store-Ur-Stuff can be determined as follows:
Lease A-Space: 400 cubic feet x $0.22/cubic foot = $88 in addition to burden = $92.64
Store-Ur-Stuff: 400 cubic feet x $0.25/cubic foot = $100 in addition to 4% markdown = $96 less expense = $91.20
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How does tetrahedron WXYZ looks like?
Answers
The four-sided geometric object known as a tetrahedron (WXYZ) has four triangle faces that are joined to one another at their edges. Its vertices are all linked, and its faces are all equilateral triangles.
The three-dimensional geometric structure known as a tetrahedron (WXYZ) has four triangle-shaped faces. The edges of each of the tetrahedron's faces are joined to one another. All of the faces are triangular shapes with equal sides, or equilateral triangles. The tetrahedron is a solid shape because all of its vertices are joined together. The tetrahedron's four vertices are joined to one another, forming a pyramid-like shape. The tetrahedron's four vertices are the only points that do not form the triangle faces. The tetrahedron's four faces come together to produce a point in the middle of the shape. The apex of the tetrahedron is where this point is located. The faces of the tetrahedron are all congruent, or identical, as they are a regular polyhedron.
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I need Help fjidsfidasfiajiujirufr
Answers
The x- intercepts in parabola is (1,0) and (5,0).
What do you mean by parabola?A parabola is a type of symmetrical, U-shaped curve that is a graph of a quadratic function. It is defined by the equation y = ax² + bx + c, where a, b, and c are constants. The shape of the parabola is determined by the value of the coefficient "a". If a > 0, the parabola opens upwards, and if a < 0, the parabola opens downwards.
Parabolas are used in many areas of mathematics and science, including physics, engineering, and economics. For example, they are used to model the trajectory of objects under the influence of gravity, to describe the motion of objects in space, and to analyze the behavior of systems that exhibit parabolic patterns.
The vertex of a parabola is the point that represents the highest or lowest point on the curve, and the axis of symmetry is a line that separates the curve into two congruent halves.
The x-intercepts of a parabola can be found by setting the y-value to 0 and solving for x. In this case, the y-coordinate of the x-intercepts will be 0, so we have:
y = 0
To find the x-intercepts, we can use the information given in the coordinates of the parabola: (1,0), (5,0), and (0,6).
From the coordinates (1,0) and (5,0), we can see that the x-intercepts are at 1 and 5.
From the coordinate (0,6), we can see that the y-intercept is at (0,6).
So, the x-intercepts of the parabola are (1,0) and (5,0).
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HELP HELP HELP!!!!! Mason and Jack are lifting weights. Mason uses a 19-kg bar, increasing the weight by 7 kg on each set. Jack starts with an 18-kg bar and increases by 8 kg on every set. Eventually, Mason and Jack will be lifting the same amount. A. How many sets will they have completed? B. How much weight will they be lifting then?
Answers
They will lift the same weight (which is 26 kilograms) after one set.
How many sets will they have completed when they lift the same weight?Mason starts at 19kg bar and adds 7kg after each set, so after x sets, he will be lifting:
M(x) = 19 + 7*x
And Jack starts at 18kg, and after each set adds 8kg, then in this case the linear equation is:
J(x) = 18 + 8*x
They will lift the same weight when:
M(x) = J(x)
19 + 7*x = 18 + 8*x
19 - 18 = 8x - 7x
1 = x
So they will be lifting the same weight after one set, and that is:
J(1) = 18 + 8*1 = 26
26 kilograms.
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given the quadratic function y=x^2+ax+b, the minimum value is -3, and the graph passes through point (1,1). find the values of the consists a and b.
Answers
We can use these two pieces of information to write two equations:
y = x^2 + ax + b must equal -3 when x = 0 (to find the minimum value)
y = x^2 + ax + b must equal 1 when x = 1 (to find the point that the graph passes through)
Using these two equations, we can solve for a and b:
-3 = 0^2 + a * 0 + b
b = -3
1 = 1^2 + a * 1 + (-3)
a = 1
So the values of a and b are a = 1 and b = -3
Making an inference is the first part of the process of investigating a question
using data.
OA. True
OB. False
Answers
Answer:
A. True
Making an inference is the first part of the process of investigating a question using data. Making an inference is the process of drawing a conclusion based on evidence and reasoning. It is the first step in the process of data analysis, as it allows us to make a prediction or understand the relationship between variables, before any analysis is done.
Step-by-step explanation:
a flat screen television is advertised as being 47 inches on its diagonal. if the tv is 19 inches tall, then how wide is the screen?
Answers
Answer:
42.85 inches wide
Step-by-step explanation:
You must use the Pythagorean theorem
width^2+19^2=47^2
width^2=47^2-19^2
width=square root of (2209-361)
width=square root of (1848)
width= 42.85 inches
Find the missing lengths of the sides.
Answers
W = 12
L = 8
so multiply 8 and 12
the owner of a garden supply store wants to construct a fence to enclose a rectangular outdoor storage area by using part of one side of the store, which is 270 feet long, as one of the sides of the enclosed area. there are 500 feet of fencing available for the other three sides of the enclosure. find the dimensions of the outdoor enclosure with the most area.
Answers
The dimensions of the outdoor enclosure with the most area is 250 feet and 125 feet.
One side of the store is 270 feet long
There are 500 feet of fencing available for the other three sides of the enclosure.
The Perimeter of rectangular outdoor storage = 2x + y
2x + y = 500
To maximize the area
y = 500 - 2x...............(1)
Area of rectangle;
A = xy
Now putting the value of y
A = x(500 - 2x)
Solve
A = 500x - 2x^2...................(2)
To finding the value of x differentiating on both side with respect to x.
dA/dx = 500 - 4x...................(3)
Equating dA/dx = 0
500 - 4x = 0
Subtract 4x on both side, we get
4x = 500
Divide by 4 on both side, we get
x = 125
Now putting the value of x in equation 1
y = 500 - 2(125)
y = 500 - 250
y = 250
Differentiating equation 3 again with respect to x
d^2A/dx^2 = -4 < 0 (Maximum)
Hence, for the maximum storage area
Length parallel to the store wall = 250 feet
Length perpendicular to the store wall = 125 feet
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What percentage of health care workers (including physicians) that do not wash their hands before examining patients?
A. 20%
B. 75%
C. 48%
D. 15%
Answers
Option D is correct. Around 15% of health care workers (including physicians) that do not wash their hands before examining patients.
According to a study published in the Journal of Hospital Infection, an estimated 15% of healthcare workers do not consistently wash their hands before examining patients. This is a concerning statistic, as hand hygiene is one of the most important ways to prevent the spread of healthcare-associated infections.
Handwashing helps to remove dirt, bacteria, and viruses from the skin, reducing the risk of transmitting these harmful organisms to patients. Improving hand hygiene among healthcare workers is a critical component of patient safety, and many hospitals and healthcare organizations have implemented programs to increase handwashing rates and prevent the spread of infections.
Despite these efforts, the 15% figure highlights the continued need for education and training to promote hand hygiene among healthcare workers, and to ensure that all healthcare workers understand the importance of washing their hands before and after patient interactions.
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I need help PLEASE PEOPLE!!
Answers
Answer: 3
Step-by-step explanation:
22.5% of 40= 9 which is the amount for cats
30% of 40= 12 which is the amount for dogs.
12-9=3
find the slope of the line passing through the points(-3 -8) and (4 ,6)
Answers
Answer:
below
Step-by-step explanation:
For the slope, m, between two lines
m = (y1-y2) / (x1-x2) it does not matter which point you assign as 1 or 2
m = (-8-6) / ( -3 - 4) = -14 / -7 = 2
what is the unsigned decimal equivalent (with 5 digits after the decimal point, truncated, e.g., 12.34567) of the following unsigned base 9 value? 1101.101
Answers
The decimal equivalent of 1101.101 in base 9 is 729.1184.
The decimal equivalent of an unsigned base 9 value is simply the number represented in the decimal system.
To find the decimal equivalent of 1101.101 in base 9, we need to convert each digit to its decimal equivalent.
First, we'll convert the whole number portion of 1101.101.
1101 in base 9 is equivalent to
=> 9³ + 1 = 729
Now, we'll convert the fractional portion.
The first digit after the decimal point, 1, represents 1/9.
The next digit, 0, represents 0/9².
The last digit, 1, represents 1/9³.
Adding these values together, we get
=> 729 + 1/9 + 1/729 = 729.1184
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Hey can you please help me what is 2 1/5 x 1 1/4 as a simplest form?
Answers
Answer: 2 3/4.
Step-by-step explanation: To multiply the mixed numbers, we need to first make them into improper fractions. To make 2 1/5 into an improper fraction, we multiply the whole number 2 by the denominator, 5, and add that to the numerator 1, giving us 11/5. We do the same for 1 1/4, giving us 5/4. 5/4 x 11/5 equals 55/20. 55/20 simplifies to 2 3/4.
Solve the system using the substitution method.
10x - 16y = 17
3x + 3y = 9
Answers
if ₱60,000.00 was deposited in a bank and became ₱61,625.00 at the end of 150 days, find the interest rate using exact and ordinary days.
Answers
Days exactly: The rate of interest is 4.17%. The interest rate of amount is 4.21% on regular days.
I = P x R x T/365, where I is the interest, P is the principal, R is the rate, and T is the duration, can be used to determine the interest rate using exact days.
I = 61625 - 60000 = 625, P = 60000, R =?, and T = 150 are the numbers used in this calculation. The formula for 625 reads as follows: 625 = 60000 x R x 150/365. By multiplying both sides by 365/150, we may find R. As a result, R = 625 x 365/90000 = 4.17%.
I = P x R x T/360, where I is the interest, P is the principal, and R is the rate of return, can be used to get the interest rate using regular days.T stands for time, and R represents the rate. I = 61625 - 60000 = 625, P = 60000, R =?, and T = 150 are the numbers used in this calculation. The formula for 625 reads as follows:
625 = 60000 x R x 150/360. By dividing both sides by 360/150, we may find R. As a result, R = 625 x 360/90000 = 4.21%.
I = P x R x T/365, which means that R = I x 365/P x T = 625 x 365/60000 x 150 = 4.17%. Exact days
I = P x R x T/360 on typical days, which means that R = I x 360/P x T is 625 x 360/60000 x 150, or 4.21%.
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Mr. Gabriel borrowed $1860 to buy a computer. He will pay $71.30 per month for 30 months. Find the simple intresr rate for his loan.
Answers
The simple interest rate for his loan could be 6%
How to calculate simple interest amount?If the initial amount (also called as principal amount) is P, and the interest rate is R% annually, and it is left for T years for that simple interest, then the interest amount earned is given by:
[tex]I = \dfrac{P \times R \times T}{100}[/tex]
Given that Mr. Gabel borrowed $1860 to buy a computer. He will pay $71Mr. Gabel borrowed $1860 to buy a computer. He will pay $71.30 per month for 30 months.
To Find the simple interest rate for his loan.
P= 1860R= x
T= 30 months = 2.5 years
I = $279
Therefore, I= prt
279 = 1860 (r)(2.5)
279 = 4650r
0.06 = r
r = 6%
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14. Steve has a $50 gift certificate from the local bookstore. He was planning to spend the entire amount by purchasing 3 hard-cover books and 4 paperback books. However, he bought only 2 hard-cover books and 3 paperback books, and he still has $15.50 left on the gift certificate. Find the cost of a hard-cover book and the cost of a paperback book.
Answers
Answer:Let x be the cost of a hard-cover book and y be the cost of a paperback book.
We know that Steve spent 2 hard-cover books and 3 paperback books. So we can write the equation as:
2x + 3y = 50 - 15.5
2x + 3y = 34.5
We also know that he was planning to buy 3 hard-cover books and 4 paperbacks, so we can write another equation as:
3x + 4y = 50
Now we have a system of two equations with two unknowns:
2x + 3y = 34.5
3x + 4y = 50
We can use the first equation to eliminate one variable by multiplying both sides by 2 and then subtracting 3y:
4x + 6y = 69
3x + 4y = 50
x = 19.5
Now we can substitute this value of x into the second equation and find the value of y:
3(19.5) + 4y = 50
58.5 + 4y = 50
4y = -8.5
y = -2.125
Therefore, the cost of a hard-cover book is $19.5 and the cost of a paperback book is $-2.125.
Note that the cost of a paperback book is a negative value which is not possible in this case. It means that the given information does not have a solution.
Step-by-step explanation:
Sydney i cutting the crut from the edge of her andwich. The dimenion, in centimeter, of the andwich i hown. A rectangle labeled andwich. The right ide i labeled 2 x quared 9. The bottom ide i labeled 2 x quared 8. Which expreion repreent the total perimeter of her andwich, and if x=1. 2, what i the approximate length of the crut?
Repone
4x217; 21. 8 centimeter
4 x quared plu 17 ; 21 point 8 centimeter
8x234; 43. 6 centimeter
8 x quared plu 34 ; 43 point 6 centimeter
8x234; 45. 52 centimeter
8 x quared plu 34 ; 45 point 5 2 centimeter
4x217; 22. 76 centimeter
Answers
The total perimeter will be 4x^+17 and length be 22.76 cm
As per the data given in the questions,
We have, the shape of the sandwich be rectangular.
We know that, perimeter of the rectangle can be determined by using formula: 2(l+b),
where, l = length of the rectangle
and, b = breadth of the rectangle
The expression for the perimeter of the sandwich would be:
2 (2x^2 + 9) + 2 (2x^2 + 8)
= 4x^2 + 26
Now for finding the length of the crust,
we will put the value of x=1.2,
So, the value of the approximate length of the crust would be:
=4x^2 + 26
= 4 * 1.2^2 + 26
= 22.76 centimetres.
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can someone please help me(20 points will give brainliest!!!)
Answers
Answer: A: 50,000
Answer: B: 55
Step-by-step explanation:
You can use ratio proportions to answer this problem
10/10,000 = 50/x
Cross multiply: 10x/10 = 500,000/10
x = 50,000
You can use ratio proportions to answer this problem
10/10,000 = x/55,000
Cross mupltipy: 10,000x/10,000 = 550,000/10,000
x = 55
May or may not be correct
solution a is prepared using a stock solution with a concentration of 0.300 m by a dilution factor of 10. what is the concentration of solution a?
Answers
The concentration of solution A after dilution by a factor of 10 would be 0.0300 M.
The dilution factor is defined as the ratio of the final volume to the initial volume of the solution.
If a solution is diluted by a factor of 10, it means that the final volume of the solution is ten times greater than the initial volume. As a result, the concentration of the solute in the final solution will decrease by a factor of 10.
Therefore, if the initial concentration of the stock solution is 0.300 M, then the concentration after dilution by a factor of 10 of solution A would be
= 0.300 M / 10
= 0.0300 M
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Please help ASAP the question is in the picture
Answers
The data represent a quadratic function.
What is a quadratic equation?
A quadratic equation is a second-order polynomial equation with a single variable such as x, where ax²+bx+c=0. with a ≠ 0 . Given that it is a second-order polynomial equation, the algebraic fundamental theorem ensures that it has at least one solution. Real or complicated solutions are both possible.
To calculate the second difference,
select 3 consecutive y-values, and then subtract the first y-value from the second and the second y-value form the third. Then find the difference of these two resulting values . If all second differences are equal, the data represent a quadratic function.
1) -7,-5, -1
second y value - first y-value = 2
third y value - second y value = 4
difference of these two resulting values = 2
2) -5,-1,5
second y value - first y-value = 4
third y value - second y value = 6
difference of these two resulting values = 2
The data represent a quadratic function.
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In a circle with radius 4, an angle intercepts an arc of length 8\pi8π. Find the angle in radians in simplest form.
Answers
The required Angle in radian in simplest form is 2π.
What is circle?A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the centre.
Explain angle in radian with arcs of circle.The centre angle of one radian (s = r) subtends an arc length of one radius. One radian has the same value for all circles because they are all alike. The central angle of a circle is measured by its arc, which is 360 degrees, and its radian measure, which is 2 radians.
According to question:Radius = 4 unit, arc = 8π
We know that
angle = arc/radius
angle = 8π/4
angle = 2π radian.
Thus, required angle in radian is 2π.
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find a parametrization of the tangent line to ()=(ln()) −10 10 at the point =1.
Answers
The tangent line to the curve y = ln(x) - 10 at the point (1, -9) is parametrized by x = t and y = t - 10
To find the tangent line to the curve y = ln(x) - 10 at the point (1, -9), we need to find a parametrization of the line. We can do this by finding the slope of the tangent line and the point at which the tangent line intersects the y-axis.
First, we find the slope of the tangent line by taking the derivative of the function y = ln(x) - 10 at x = 1:
dy/dx = d/dx ln(x) = 1/x
So, the slope of the tangent line at (1, -9) is m = 1/1 = 1.
Next, we find the y-intercept of the tangent line. This can be found by using the point-slope form of a line:
y - y1 = m(x - x1)
Substituting in the values for m, x1, and y1, we get:
y - (-9) = 1(x - 1)
Simplifying, we find:
y + 9 = x - 1
y = x - 10
So, the y-intercept of the tangent line is -10.
Putting everything together, we find that the parametrization of the tangent line to the curve y = ln(x) - 10 at the point (1, -9) is given by:
x = t
y = x - 10 = t - 10
So, the tangent line to the curve y = ln(x) - 10 at the point (1, -9) is parametrized by x = t and y = t - 10.
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Use the Midpoint Rule with n = 4 to approximate the area of the region bounded between the curves y = sin2(πx/4) and y = cos2(πx/4) for 0 ≤ x ≤ 1.
Answers
The area of the region bounded between the given curves is =0.640675 unit square.
The center point of a straight line can be located using the midpoint formula. You may occasionally need to determine the difference between two specific numbers. The average of the two numbers is what you find there. In a similar way, we obtain the halfway number (or point) between two coordinates using the midpoint formula in coordinate geometry.
The midpoint rule states that you can calculate the area under a curve by using the formula:
[tex]M_n=\frac{b-a}{2}[f(\frac{(x_0+x_1)}{2})+f(\frac{x_1+x_2}{2})+....+f(\frac{x_{n-1}+x_n}{2})][/tex]
In our case a=0 ,b=1 ,n=4
[tex]x_0=0 ,x_1=1/4,x_2=1/2, x_3=3/4\ and \ x_4=1[/tex]
Therefore, we have-
[tex]M_4=\frac{1}{4}[f(\frac{1}{8})+f(\frac{3}{8})+f(\frac{5}{8})+f(\frac{7}{8}][/tex]
now to evalute f(x),
[tex]f(x)=cos^{2}(\frac{\pi x}{4})-sin^{2}(\frac{\pi x}{4})\\ \\f(x)= cos(\frac{\pi x}{2})\\\\f(1/8)=cos(\frac{\pi}{16})=0.9807\\\\f(3/8)=0.8314\\\\f(5/8)=0.5555\\\\f(7/8)=0.19509[/tex]
hence the value of integral is equal to -
M4= 2.56279÷4=0.640675
The area of the region bounded between the given curves is =0.640675 unit square.
learn more about the midpoint formula,
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There are 32 Year 11 pupils in a rugby club, out of a total of 85 pupils.
Write this proportion as a percentage.
Give your answer correct to 1 decimal place when appropriate. 26% of an amount.
Answers
Answer:
32/85=26/100
Step-by-step explanation:
