HELP!!
Lily just paid off a $400 loan. She had to pay $60 in interest at a simple annual interest rate of 5%. How many years did Lily have this loan?
A. 2
B. 3
C. 4.5
D. 5
Answer: The correct option is (B) 3.
Step-by-step explanation: Given that Lily just paid off a $400 loan. She had to pay $60 in interest at a simple annual interest rate of 5%.
We are to find the number of years for which Lily had this loan.
Let n be the required number of years.
Also, P = $400, S.I. = $60 and r% = 5%.
Therefore, by the formula of simple interest, we have
[tex]S.I.=\dfrac{Prn}{100}\\\\\\\Rightarrow 60=\dfrac{400\times5\times n}{100}\\\\\\\Rightarrow n=\dfrac{60}{20}\\\\\\\Rightarrow n=3.[/tex]
Thus, the required number of years is 3.
Option (B) is CORRECT.
1. Miguel tosses a coin three times. which diagram represents the sample space of the three tosses?
Tree diagram can be used to represent the sample space. The correct option is option C.
What is a tree diagram?In probability, a tree diagram can be used to represent the sample space. Tree diagrams represent a series of independent events or conditional probabilities.
As it is given that the coin is tossed three times, therefore, the number of stages in the tree diagram will be three, where each time the coin is tossed will result in either heads or tails.
Now, the tree diagram of the coins can be drawn as shown below.
Further, comparing it with our diagram, the only possible option is option c where the number of levels in the tree is three and each toss result in either heads or tails.
Hence, the correct option is option C.
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logx + log(3x-13) = 1
The solutions for [tex]\log x + \log (3\cdot x - 13) = 1[/tex] are [tex]x_{1} = 5[/tex] and [tex]x_{2} = -\frac{2}{3}[/tex], respectively.
In this question, we are going to solve for [tex]x[/tex] with the help of Logarithm Properties, which are described in the image attached below.
[tex]\log x + \log (3\cdot x - 13) = 1[/tex]
[tex]\log [x\cdot (3\cdot x - 13)] = 1[/tex]
[tex]\log (3\cdot x^{2}-13\cdot x) = 1[/tex]
[tex]10^{\log(3\cdot x^{2}-13\cdot x)} = 10^{1}[/tex]
[tex]3\cdot x^{2}-13\cdot x = 10[/tex]
[tex]3\cdot x^{2}-13\cdot x -10 = 0[/tex]
This is a Second Order Polynomial, which can be solved by Quadratic Formula:
[tex]x_{1} = 5[/tex] and [tex]x_{2} = -\frac{2}{3}[/tex]
The solutions for [tex]\log x + \log (3\cdot x - 13) = 1[/tex] are [tex]x_{1} = 5[/tex] and [tex]x_{2} = -\frac{2}{3}[/tex], respectively.
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Which fraction shows a correct way to set up the slope formula for the line that passes through the points (3,7) and (5,7)?
The slope of a line through the points (3,7) and (5,7) is 0, indicating a horizontal line.
To calculate the slope of a line passing through two points, you can use the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points. In this case, the points are (3,7) and (5,7). Using the slope formula, we get:
m = (7 - 7) / (5 - 3) = 0 / 2 = 0
So, the slope of the line that passes through these points is 0, which means the line is horizontal.
Tyrone’s hourly wage is $18 and his net pay is 72% of his earnings. Tyrone spends about $1,800 on his monthly expenses. If Tyrone works 40 hours per week and has no other sources of income, what is his total monthly cash inflow? (Hint: Assume that there are 4 pay periods per month.)
$2073.60 per month
===================
To calculate Tyrone's total monthly cash inflow, we need to determine his weekly and then monthly earnings.
Calculate weekly gross income:
$18/hour * 40 hours/week = $720/weekCalculate net pay per week:
$720/week * 72% = $518.40/weekCalculate monthly cash inflow:
$518.40/week * 4 weeks/month = $2073.60/monthTyrone's total monthly cash inflow is $2073.60.
Over the past year, your friend Maura has been saving up for an epic road trip to travel across the country this summer. Her goal is to squeeze in as many sights as she can with her available budget of $2000.
Give an example of a sound financial decision Maura might make to support this goal. Why is it sound? Then give an example of a poor financial decision Maura might make considering her goal. Why is it a poor decision?
108/250 in simplest form in a whole number.
sin10+sin20+sin40+sin50=sin70+sin80.prove it
how is a tangent different from a chord
Answer:
A tangent is a line, ray, or line segment that intersects a circle at exactly one point (called the point of tangency) and contains no points inside the circle. A chord is a segment with both endpoints on a circle. Tangents intersect the circle at one point, while a chord intersects at two.
I've checked this answer, E counted it as correct. Hope this helped!!!
A tangent touches a circle at one point, while a chord connects any two points on the circle's circumference.
A tangent and a chord are both important concepts in geometry, but they have distinct characteristics.
A tangent is a line that intersects a circle at exactly one point, touching the circle's circumference at that point.
It never crosses the circle. Tangents are perpendicular to the radius that intersects the point of tangency.
On the other hand, a chord is a line segment connecting any two points on a circle's circumference. Unlike tangents, chords can intersect the circle at multiple points.
The diameter is a special case of a chord that passes through the center of the circle.
Hence,
Tangents touch a circle at one point, while chords connect two points on a circle's circumference.
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Paul plans to put concrete on a rectangular portion of his driveway. The portion is 12 feet long and 6 inches high. The price of concrete is $98 per cubic yard. The total cost of the concrete Paul needs is $108.89. Which of the following is closest to the width of the portion of the driveway on which Paul plans to put concrete?
[1 foot = 12inches; 1 yard = 3 feet]
3 feet
5 feet
8 feet
10 feet
Answer:
The answer is b. 5 feet
Step-by-step explanation:
Solve the equation.
6 = 2(x + 8) - 5x
A. 2/3
B. 3 1/3
C. - 2/3
D. -3 1/3
Josephine started a business selling cosmetics. She spent $4500 to obtain her merchandise, and it costs her $200 per week for general expenses. She earned $550 per week in sales. What is the minimum number of weeks it will take for Josephine to make a profit? Write an inequality to model the problem.
A.)550w > 4500 + 200w
b.)200w > 4500 + 550w
c.) 550w < 4500 + 200w
d.)200w 4500 + 550w
...?
Answer:
a
Step-by-step explanation:
Final answer:
Josephine will need at least 13 full weeks to start making a profit. The correct inequality that models this economic scenario is 550w > 4500 + 200w.
Explanation:
The minimum number of weeks it will take for Josephine to make a profit in her cosmetics business can be determined by setting up an inequality where the total earnings must be greater than the sum of the initial investment and the running costs. We define w as the number of weeks. Josephine earns $550 per week, so her earnings after w weeks are 550w. The initial investment is $4500 and the weekly expense is $200, so the total expenses after w weeks are 4500 + 200w. To make a profit, the earnings must be greater than the expenses:
550w > 4500 + 200w
To solve for w, we need to collect like terms:
550w - 200w > 4500
350w > 4500
Dividing both sides by 350:
w > 4500 / 350
w > 12.86
This means Josephine will need to work for at least 13 full weeks to make a profit.
In 2005 at camp at 450 campers five years later the number of campers rose to 750 right now when you're equation that represents the number of campers that attend camp
Final answer:
To represent the number of campers attending the camp, use the equation y = mx + c, where y represents the number of campers, m represents the rate of increase, x represents the number of years, and c represents the initial number of campers. Using the given information, solve for the rate of increase (m) and initial number of campers (c). Substitute the values in the equation to find the number of campers attending the camp right now.
Explanation:
To represent the number of campers attending the camp right now, we can use the equation: y = mx + c, where y represents the number of campers attending the camp, m represents the rate at which the number of campers increase, x represents the number of years since 2005, and c represents the initial number of campers in 2005.
From the information provided, we know that in 2005 there were 450 campers and five years later, in 2010, the number of campers rose to 750. We can use these two points to find the values of m and c.
Using the formula: (y2 - y1) / (x2 - x1) = m, we can calculate the value of m as: (750 - 450) / (2010 - 2005) = 60. Therefore, the rate of increase is 60 campers per year. Now, we can substitute the values of m and c in the equation to find the number of campers attending the camp right now. y = 60x + 450.
The linear equation representing the number of campers attending camp each year, starting from 2005 with 450 campers and increasing by 60 campers per year, is C = 450 + 60t, where C is the number of campers and t is the number of years after 2005.
Explanation:In 2005, there were 450 campers at a camp. Five years later, the number of campers increased to 750. To represent the growth in the number of campers, we can write a linear equation. Assuming the number of campers increases at a constant rate each year, we first find the rate of increase.
Rate of increase per year = (Number of campers in 2010 - Number of campers in 2005) / (2010 - 2005)
Rate of increase per year = (750 - 450) / (5)
Rate of increase per year = 300 / 5 = 60 campers per year
Let's denote C as the number of campers and t as the number of years after 2005. The equation that represents the number of campers is:
C = 450 + 60t
This equation indicates that starting with 450 campers in 2005, every year there are 60 more campers attending the camp.
Determine if the equations are intersecting, parallel, or coincident. bx - ay = 2 ax + by = 3
Answer:
Intersecting
Step-by-step explanation:
After having singled out y on one side of both equations you should have.
Y=b/a• x - 2/-a
And
Y= -a/b • x + 3/b
As you can see they have opposite reciprocals which is an intersection
You invest $2000 in a bank account that has 5% annual interest rate, compound ed continously. how much will you have in 5 years?
If the sum of a number and 6 is multiplied by 5, the result is same as 9 times the number decreased by 2. find the number.
Laura was making a recipe that said the ingredients were for 6 people, but she needed to make it for 8 people. the recipe called for 2 2/3 cups of milk and 1/4 cup oil. how many of these liquid ingredients did she need for 8 people?
Answer:
[tex]3\frac{5}{9}[/tex] cups of milk and [tex]\frac{1}{3}[/tex] cups of oil for 8 people .
Step-by-step explanation:
Cups of milk for 6 people = [tex]2 \frac{2}{3} =\frac{8}{3}[/tex]
Cups of milk for 1 people = [tex]\frac{\frac{8}{3}}{6}=\frac{4}{9}[/tex]
Cups of milk for 8 people = [tex]\frac{4}{9} \times 8= \frac{32}{9}[/tex]
Cups of oil for 6 people = [tex]\frac{1}{4}[/tex]
Cups of oil for 1 people = [tex]\frac{\frac{1}{4}}{6}= \frac{1}{24}[/tex]
Cups of oil for 8 people = [tex]\frac{8}{24}=\frac{1}{3}[/tex]
Hence [tex]3\frac{5}{9}[/tex] cups of milk and [tex]\frac{1}{3}[/tex] cups of oil for 8 people .
What is the solution to the following bernoulli de?
\[t^2 dy/dx+y^2=ty\]
Use substitution to solve the system
5x+4y=12
Y=2x-10
Is 89 prime or composite
Answer:
Prime
Step-by-step explanation:
A prime number is a number that has only one factor. A composite number is a number that has more than one factor.
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Given the equation Square root of 2x plus 1 = 3, solve for x and identify if it is an extraneous solution.
^ I really don't understand this topic, whatsoever. Could someone help?
By squaring both sides and solving for [tex]\(x\),[/tex] we find [tex]\(x = 4\)[/tex] as the solution, which is not extraneous upon substitution into the original equation.
To solve the equation [tex]\(\sqrt{2x + 1} = 3\),[/tex] we need to isolate[tex]\(x\).[/tex] Here's how:
1. Square both sides of the equation to eliminate the square root:
[tex]\[ (\sqrt{2x + 1})^2 = 3^2 \][/tex]
[tex]\[ 2x + 1 = 9 \][/tex]
2. Subtract 1 from both sides to isolate [tex]\(2x\)[/tex]:
[tex]\[ 2x = 9 - 1 \][/tex]
[tex]\[ 2x = 8 \][/tex]
3. Divide both sides by 2 to solve for [tex]\(x\)[/tex]:
[tex]\[ x = \frac{8}{2} \][/tex]
[tex]\[ x = 4 \][/tex]
Now, we have [tex]\(x = 4\)[/tex]. To determine if it's an extraneous solution, we need to check if it satisfies the original equation.
Substitute [tex]\(x = 4\)[/tex] into the original equation:
[tex]\[ \sqrt{2(4) + 1} = 3 \][/tex]
[tex]\[ \sqrt{9} = 3 \][/tex]
[tex]\[ 3 = 3 \][/tex]
Since the equation holds true, [tex]\(x = 4\)[/tex]is a valid solution, not an extraneous one.
Therefore, the solution to the equation [tex]\(\sqrt{2x + 1} = 3\) is \(x = 4\),[/tex]and it is not an extraneous solution.
Eric reflected parallelogram ABCD across the x-axis. If angle A is 125° and angle B is 55°, what is the degree measurement of angle A'?
Answer:
Angle A= Angle A' = 125°
Step-by-step explanation:
We have given that : Eric reflected parallelogram ABCD across the x-axis.
If angle A is 125° and angle B is 55°
To find : Degree measurement of angle A'
Solution :
As it is reflected parallelogram , and by property of reflection it form congruent parallelogram
since it is congruent then measures of angle remain same
by this statement the measure of angle of parallelogram ABCD
remain same or equal to parallelogram A'B'C'D'
⇒Angle A= angle A' = 125°
Suppose that a drop of mist is a perfect sphere and that, through condensation, the drop picks up moisture at a rate proportional to its surface area. Show that under these circumstances the drop's radius increases at a constant rate. ...?
From the given condition, the rate of change of radius is constant.
What is rate of change?How quickly something evolves over time is referred to as its rate of change (ROC).
Given:
Suppose that a drop of mist is a perfect sphere and that, through condensation, the drop picks up moisture at a rate proportional to its surface area.
Let V be the volume of the sphere & S be the surface area.
According to the question,
dV/dt = kS
Since,
V = 4/3πr³
dV/dt = 4πr²dr/dt
S = 4πr²
Putting these values to the above expression,
4πr²dr/dt = k4πr²
dr/dt = k
Therefore, the rate of change of radius is constant.
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The area of a rectangle is 70 square inches and the length of the rectangle is 3 inches longer than the width.
The area of a rectangle is found by multiplying the length times the width.
Which equation models this situation?
w(w+3)=70w(w+3)=70
w + 3 = 70
3w = 70
w + 3w = 70
The correct equation to model the rectangle's area where the length is 3 inches more than the width and the area is 70 square inches is W(W + 3) = 70, which simplifies to W^2 + 3W = 70.
Explanation:The student is asking for the correct equation to model a rectangle's area where the length (L) is 3 inches more than the width (W), and the area is 70 square inches. To find an equation that models the situation, we need to express L in terms of W. Since L is 3 inches more than W, we can write L as W + 3. The area (A) of a rectangle is found by multiplying the length by the width, so A = L x W.
Therefore, the equation that models this situation is W(W + 3) = 70. To see why, let's insert the expression for L into the area formula:
A = L x W = (W + 3) x W
This simplifies to:
A = W^2 + 3W
Since we know the area A is 70 square inches, we substitute and get the equation:
W^2 + 3W = 70
Which is the correct model for the given situation.
Suppose f(π/3) = 3 and f '(π/3) = −7,
and let
g(x) = f(x) sin x
and
h(x) = (cos x)/f(x).
Find the h'(x)
To find h'(x), differentiate the function h(x) = (cos x)/f(x) using the product rule.
Explanation:To find h'(x), we need to differentiate the function h(x) = (cos x)/f(x).
First, let's find the derivative of cos x, which is -sin x.
Next, we need to find the derivative of f(x). Since f(π/3) = 3 and f '(π/3) = −7, we know the slope of the tangent line at x = π/3 is -7.
Using the product rule, we can now differentiate h(x) = (cos x)/f(x) as follows:
h'(x) = [f(x)(-sin x) - cos x(f '(x))]/[f(x)]^2
If x = a + bi and y = –a – bi, x + y = 0
Answer:
inverse property
{-4y-11x=36
{20=-10x-10y
A square sheet of art paper has an area of 625 square inches. what is the minimum side length of an easel that supports the whole sheet of paper?
a.-25
b.25
c.15
d.35(-25 or 25?)
Are the graphs of −5y=2x+3 and y=25x+4 parallel, perpendicular, or neither?
The graphs of the system of equations −5y=2x+3 and y=25x+4 are neither parallel nor perpendicular.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
The system of equations is:
−5y=2x+3 and y=25x+4
The slope of parallel graphs is the same. The reciprocal slopes of a perpendicular are opposite.
These equations are neither because they have slopes of 25 and -2/5.
Thus, the graphs of the system of equations −5y=2x+3 and y=25x+4 are neither parallel nor perpendicular.
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Factor -9x^2-36x-36 please.