Answer:
Total credit hours a student have = 2.5 hours.
Step-by-step explanation:
P.S - The exact question is -
Given - The tuition costs, C, for a local community college are modeled by C(h) = 250 + 200h, where h represents the number of credit hours taken. The local state university has tuition costs, S, modeled by the function S(h) = 300 + 180h.
To find - How many credit hours will a student have to take for the two tuition costs to be equal.
Proof -
If the two tuition cost are equal, then
C(h) = S(h)
⇒250 + 200h = 300 + 180h
⇒200h - 180h = 300 - 250
⇒20h = 50
⇒2h = 5
⇒h = \(\frac{5}{2}\)
⇒h = 2.5
∴ we get
Total credit hours a student have = 2.5 hours.
A student fit the line shown below to the data in the scatter plot. Which statement about the student's line is true?
A. It is a good fit because there are the same number of points above the line as below it.
B. It is a good fit because all of the points are on or below the line.
C. It is not a good fit because there are no points on the line.
D. It is not a good fit because only one point is on the line.
Answer:
C. It is not a good fit because there are no points on the line.
Step-by-step explanation:
In order for a line to be a good fit for a data set represented as a scatterplot, the line must follow the general trend of the data in the scatterplot. This line does not follow the general trend of the data on the scatterplot, thus option (C) is the best statement to describe the situation.
C. It is not a good fit because there are no points on the line.
if the grass is wet, then the grass is dry true or false?
john and Joshua completed in the 25km Gun Run marathon. John completed only 2/5 of the race because he slipped and hurt his ankle
a) How many kilometers did John still have to run in order to complete the race
b) At this stage, Joshua had reached the halfway mark. How far was John and Joshua
Answer:
otherwise I have no idea what I want and I have been a member at least I don't know if I'm just going well and you had a great
This year, you got 65% fewer pieces of Halloween candy than you got last year. You got 200 pieces last year. How much did you get this year?
a) In the sketchbox, draw a diagram to represent this situation
b) In the answer box, write a simplified equation to represent this situation. Use "y" to represent the amount of Halloween candy you got this year. Your equation should use decimals.
Answer:
Step-by-step explanation:
100-65=35
y=35 % of 200=0.35×200=70
Using a fair coin and a number cube with faces numbered 1 through 6, what is the probability of getting heads and rolling a 5?
A
1/12
B
1/6
C
1/2
D
11/12
Step-by-step explanation:
Use Multiplication Principle with states that if a event can occur n ways, and another mutually exclusive event occur p ways, then the total outcome is
\(n \times p\)
The possible ways of rolling a dice is 6 and the possible ways of flipping a coin is 2 so we have
\(6 \times 2 = 12\)
Now, we use the fact that proabliblity is
Number of favorable outcomes/ Total outcomes.
We can only get a head and a 5 once out of the set so the number of favorable outcomes is 1. Total outcomes is 12 so we have
\( \frac{1}{12} \)
A is the answer.
HELP ASP!!❤️
WILL GIVE BRAINLIEST!...
Find the slope of the line. Enter your answer in simplest form.
Answer:
\(m=\frac{-4}{3}\)
General Formulas and Concepts:
Order of Operations: BPEMDASSlope Formula: \(m=\frac{y_2-y_1}{x_2-x_1}\)Step-by-step explanation:
Step 1: Define
Point (-6, 5)
Point (3, -7)
Step 2: Find slope m
Substitute: \(m=\frac{-7-5}{3-(-6)}\)Simplify: \(m=\frac{-7-5}{3+6}\)Subtract/Add: \(m=\frac{-12}{9}\)Simplify: \(m=\frac{-4}{3}\)Answer:
the slope is -4/3
Step-by-step explanation:
m=y2-y1/x2-x1
-7-5=(-12)
3-(-6)=9
-12/9
-12/3=(-4)
9/3=3
-4/3
hope this helps :3
if it did pls mark brainliest
Question 4 of 10
The standard form of the equation of a parabola is y=x²-6x+14.
What is the vertex form of the equation?
OA y=(x-3)2 +15
OB. y = (x+3)(x-3) +5
O C. y=(x-3)2 +23
OD. y=(x-3)² +5
The vertex form of the equation is y = (x - 3)² - 4, which corresponds to option OD.
To convert the given equation from standard form to vertex form, we need to complete the square.
The vertex form of a parabola's equation is y = a(x-h)² + k, where (h, k) represents the vertex of the parabola.
Given equation: y = x² - 6x + 14
Move the constant term to the right side:
y - 14 = x² - 6x
Complete the square by adding and subtracting the square of half the coefficient of x:
y - 14 + 9 = x² - 6x + 9 - 9
Group the terms and factor the quadratic:
(y - 5) = (x² - 6x + 9) - 9
Rewrite the quadratic as a perfect square:
(y - 5) = (x - 3)² - 9
Simplify the equation:
y - 5 = (x - 3)² - 9
Move the constant term to the right side:
y = (x - 3)² - 9 + 5
Combine the constants:
y = (x - 3)² - 4
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Solve the heat equation (1) Subject to the given conditions. I think A solution of the boundary -value problem (D) - (3) need not be an infinite series. U(0,t)=0,u(1,t)=0,t>0
u(x,0)=4sin3πx+8sin6πx,0
The solution of the heat equation subject to the boundary and the initial conditions is u(x, t) = (4π/3)sin(3πx) exp(-9π^2 kt) + (8π/6)sin(6πx) exp(-36π^2 kt).
The heat equation with the given boundary conditions is:
∂u/∂t = k ∂^2u/∂x^2
where k is a constant. We can use separation of variables to solve this equation. Let:
u(x, t) = X(x)T(t)
Substituting this into the heat equation, we get:
X(x)T'(t) = k X''(x)T(t) / X(x)T(t)
Dividing both sides by X(x)T(t) and rearranging, we get:
X''(x)/X(x) = T'(t)/(kT(t))
The left-hand side depends only on x, while the right-hand side depends only on t. Since they are equal, they must be equal to a constant:
X''(x)/X(x) = -λ
T'(t)/(kT(t)) = λ
where λ is a constant. The boundary conditions u(0,t) = u(1,t) = 0 imply that X(0) = X(1) = 0. The general solution for X(x) is then:
X(x) = A sin(nπx)
where A is a constant and n is a positive integer. The eigenvalues λ are:
λ = -(nπ)^2
The general solution for T(t) is:
T(t) = B exp(-kλt)
where B is a constant. The solution for u(x, t) is then:
u(x, t) = Σ[ A_n sin(nπx) exp(-(nπ)^2 kt) ]
where the sum is taken over all positive integers n.
We can now use the initial condition u(x,0) = 4sin3πx+8sin6πx to determine the constants A_n. Since the solution only contains sine terms, we can use the Fourier sine series to expand the initial condition:
4sin3πx+8sin6πx = Σ[ A_n sin(nπx) ]
where the sum is taken over all positive odd integers for n = 3 and all positive even integers for n = 6. The coefficients A_n are:
A_3 = 4π/3
A_6 = 16π/6
Substituting these values into the solution for u(x, t), we get:
u(x, t) = (4π/3)sin(3πx) exp(-9π^2 kt) + (8π/6)sin(6πx) exp(-36π^2 kt)
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Can someone help me with this please!? its urgent!
Thank you who helped :)
Question: Explain how you would find the measure of the angle indicated.
Answer:
x=11 qqqqgugug
Step-by-step explanation:
I'm nerdy
Answer:
37 degrees
Step-by-step explanation:
All insides of triangles = 180 degrees, so...
67 degrees + 76 degrees + (x + 48) degrees = 180
67 + 76 + (x + 48) = 180
143 + x + 48 = 180
191 + x = 180
x = -11
x + 48
-11 + 48
37 degrees
Please help me !!!!i beg
Answer: The answer
is 48/50
Step-by-step explanation:
Answer:
It is 48/÷50
Step-by-step explanation:
It is 48/50.
What is the end behavior of the function h? H(x)=-4x+4
Answer:
Below
Step-by-step explanation:
The end behavior of a function is how it grows when it reaches both plus and - infinity.
To do that we will calculate:
● lim h(x) x=> +infinity = lim-4x+4 x=> +inf = lim -4x x=> +inf
-4 is negative so the limit will be -infinity
● lim (-4x+4) x=> -inf = lim (-4x) x=> -inf
-4 is negative, x is negative then -4x is positive. So the limit will be + inf
HELP ME ASAP PLEASEE
Answer:
true
Step-by-step explanation:
Answer:
True
Step-by-step explanation:
Start by narrowing the equasions down, add all the numbers together:
1s + 1s + 1s + 1s = 4s
4s = 4s
Both equasions are equivelent to 4s, so the answer would be True.
If you had trouble understanding that, here is another way:
First lets set a control number for s, like 3. then we are going to place the control into the equasion:
1(3) + 1(3) + 1(3) + 1(3)
4(3)
Now solve:
1(3) + 1(3) + 1(3) + 1(3) = 12
4(3) = 12
Both equasions are equivelent to 12, so the answer would be True, they are equivelent.
HELP AAAAHH ITS TIMED!!!!
The endpoints of segment are -7 and 3. Find the coordinate of the midpoint M of CD
Answer:
Step-by-step explanation:
C|___|___|___|___|___|M___|___|___|___|___|D
-7 -6 -5 -4 -3 -2 -1 0 1 2 3
mid point=-7+3/2=-4/2
M=-2
So i need help on ANOTHER question i know i might be annoying but itz because im STOOPIDD okay? ok so the question is.... which is equal to 88x102. I know it looks easy but the two is supposed to be a little tiny two so its like 10 and tiny 2. I hope you can helpppp i will give like 15 points. Well i will put 15 but they might not give 15 but anyways just pls help me i needs some help. THX :))))))))
Answer:8976
Step-by-step explanation:
A mass weighing 4 pounds is attached to a spring whose spring constant is 36 lb/ft. Find the equation of motion. (Use g = 32 ft/s2 for the acceleration due to gravity. Assume t av 2 x(t) = 12 What is the period of simple harmonic motion (in seconds)?
The period of simple harmonic motion will be 1.0433 sec
What is a simple harmonic motion?
In physics, simple harmonic motion is the repeated back-and-forth movement through an equilibrium, or Centre, position so that the maximum displacement on one side of this position is equal to the maximum displacement on the other. Each whole vibration occurs at the same time interval. The force driving the movement is always pointed in the direction of the equilibrium position and is inversely proportional to the separation from it. F = kx, where F is the force, x is the displacement, and k is a constant, is what this means. Hooke's law is the name of this relationship.
The vibration of a mass attached to a vertical spring, the other end of which is fixed in a ceiling, is an example of a simple harmonic oscillator.
So, the time period of Simple harmonic motion is
\(T=2\pi \sqrt{\frac{m}{k} }\)
where m is mass and k is spring constant
m = 4 pounds
k = 36lb/ft
\(T=2\pi \sqrt{\frac{4}{36} }\)
\(T=2\pi \sqrt{\frac{1}{9} }\)\(T=\frac{2\pi }{3} }\)
T=1.0433 sec
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How many yards are equal to 144 inches?
Twin sisters Bua and Mai turn 21 today. Their mum gives them each B12,800. Bua spends B6,200 on a new phone, $3,000 on a night out and $3,500 on a handbag. Mai decides to put the money in a savings account at 4.5% interest per year.
a) How is Bua's net worth affected by her purchases?
b) What will Mai's net worth be at the end of the year?
Bua's net worth is reduced by B12,700 due to her purchases. At the end of the year, Mai's net worth will be B13,376 after earning interest on her savings.
a) Bua's net worth is affected by her purchases as she spent a total of B6,200 on a new phone, B3,000 on a night out, and B3,500 on a handbag. Her total expenses amount to B12,700, which is deducted from the B12,800 she received from her mum. Therefore, Bua's net worth after her purchases is B100.
b) Mai decides to put her B12,800 in a savings account that earns 4.5% interest per year. At the end of the year, her net worth will increase due to the interest earned. The formula to calculate the future value of an investment with compound interest is:
Future Value = Present Value * (1 + interest rate)^time
Plugging in the values:
Future Value = B12,800 * (1 + 0.045)^1
Future Value = B13,376
Therefore, at the end of the year, Mai's net worth will be B13,376.
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The sales tax for an item was $37.80 and the cost $420 before tax find a sales tax rate rate your answer as a percentage
Step 1
State the for the sales tax rate
\(\frac{sales\text{ tax}}{cost\text{ of item before tax}}\)where
\(\begin{gathered} \text{sales tax=\$37.80} \\ \cos t\text{ of the item before tax=\$420} \end{gathered}\)Step 2
Get the sales tax rate in percentage by substitution
\(\begin{gathered} =\frac{37.80}{420}=0.09 \\ \text{Convert to percentage} \end{gathered}\)\(\begin{gathered} 0.09\times100=9^{}\text{\%} \\ \end{gathered}\)if it satisfies the hypotheses, find all numbers c that satisfy the conclusion of the mean value theorem. (enter your answers as a comma-separated list. if it does not satisify the hypotheses, enter dne).
The Mean Value Theorem (MVT) is a theorem in calculus that relates the derivative of a function to the average rate of change of the function over a given interval.
The Mean Value Theorem states that if a function f is continuous on the closed interval [a, b] and differentiable on the open interval (a, b), then there exists a number c in (a, b) such that:
f'(c) = (f(b) - f(a)) / (b - a)
To find all numbers c that satisfy the conclusion of the Mean Value Theorem, we need to check if the hypotheses of the theorem are satisfied, i.e. if the function is continuous on the closed interval and differentiable on the open interval.
Without the specific function and interval provided, we cannot determine all numbers c that satisfy the conclusion of the Mean Value Theorem. Please provide more information so we can help you better.
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Please help!!!!!!!!!!!!!!!!!
Hi there!
\(\large\boxed{t = 12.60 \text{ days}}\)
We can solve this by setting the equation equal to 150:
\(150 = \frac{230}{1 + 56.5e^-0.37t}\)
Cross-multiply and divide:
\(150 (1 + 56.5e^{-0.37t})= 230\)
Divide both sides by 150:
\(1 + 56.5e^{-0.37t} = 1.5333\)
Isolate for t by subtracting both sides by 1 and dividing by 56.5:
\(56.5e^{-0.37t} = 0.5333\)
\(e^{-0.37t} = 0.0094395\)
Take the natural log to solve for t:
\(ln (0.0094395) = -0.37t\)
\(-4.6628522 = -0.37t\)
Divide both sides by -0.37:
t = 12.60 days.
Show all your work as needed for full credit. Just writing the answer will not earn full credit on some problems. Find each indicated value.
Data set: 114 126 118 112 120 122 112 110 112 114 118 128 110 114 116 1) 111;
Find the percentile for the data value 111.
The percentile for the data value 111 is 37.5 or 37.5th if you round down.
A percentile is a measure that represents a specific percentage of data points that fall below it in a dataset. The nth percentile in a dataset is defined as the value that is greater than n% of the data points. The percentile is a useful tool for determining how a given data point compares to the rest of the data.
For example, if a student scored in the 90th percentile on a standardized test, it means that they scored higher than 90% of all the other students who took the test. How to find the percentile? The formula for finding the percentile rank of a data point in a dataset is given as follows:
P = (number of data points below the given value / total number of data points) × 100
where:
P is the percentile rank expressed as a percentage. The number of data points below the given value is the number of data points in the dataset that are less than the given value.
The total number of data points is the total number of data points in the dataset. Using the given data set, we can calculate the percentile for the data value 111 as follows: There are 6 data points in the dataset that are less than 111.
Therefore, the number of data points below the given value is 6. The total number of data points in the dataset is 16.
Therefore, the total number of data points is 16. The percentile rank of 111 in the dataset is:
P = (number of data points below the given value / total number of data points) × 100P = (6 / 16) × 100P = 37.5.
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The percentile for the data value 111 is 13.33%.
The given data set is: 114, 126, 118, 112, 120, 122, 112, 110, 112, 114, 118, 128, 110, 114, 116.
For finding the percentile for the data value 111, firstly, we need to find the rank of this value among the other data values.
To do this, we can sort the data set in ascending order:
110, 110, 112, 112, 112, 114, 114, 116, 118, 118, 120, 122, 126, 128
The data value 111 is not present in the given data set.
Therefore, we can find its rank by taking the average of the ranks of the two data values between which it would lie.
111 would lie between the data values 110 and 112. These two values have ranks 1 and 3 respectively.
Therefore, the rank of 111 would be:
Rank of 111 = (1 + 3)/2
= 2
This means that the value 111 is at the 2nd position when the data set is sorted in ascending order.
Now we can use the following formula to find the percentile of the data value 111:
Percentile = (Number of values below the given data value / Total number of values) × 100
We can see that there are 1 + 1 = 2 values below 111. (Two values because the data value 110 is repeated.)
The total number of values in the data set is 15.
Therefore, Percentile = (2/15) × 100
= 13.33%
Therefore, the percentile for the data value 111 is 13.33%.
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Which of the following equations is non-linear?
a. x + 5y = y + 15
b. x + 15x + 30x - 15 = 10y - 15
c. 11x = 5y + 10 - x
d. 3x + 1 = -4x + 12 -2y 2
A ladder leans against a brick wall. The foot of the ladder is 6 feet from the wall. The length of the ladder is 9 feet. Find to the nearest tenth of a degree, the angle of elevation the ladder makes with the ground.
Answer:
Step-by-step explanation:
We can use trigonometry to solve this problem. Let's draw a right triangle to represent the situation:
|\
| \
h | \ 9 ft
| \
| \
| \
-------
6 ft
Here, h represents the height on the wall where the ladder touches. We want to find the angle of elevation θ.
Using the right triangle, we can write:
sin(θ) = h / 9
cos(θ) = 6 / 9 = 2 / 3
We can solve for h using the Pythagorean theorem:
h^2 + 6^2 = 9^2
h^2 = 9^2 - 6^2
h = √(9^2 - 6^2)
h = √45
h = 3√5
So, sin(θ) = 3√5 / 9 = √5 / 3. We can solve for θ by taking the inverse sine:
θ = sin^-1(√5 / 3)
θ ≈ 37.5 degrees
Therefore, to the nearest tenth of a degree, the angle of elevation the ladder makes with the ground is 37.5 degrees.
Factor by grouping: 16x³ +28x² - 28x - 49 = 0
A) (4x²-7) (4x + 7) = 0
B (4x² + 7) (4x + 7) = 0
C(4x² + 7) (4x - 7) = 0
D (4x² - 7) (4x - 7) = 0
Factor by grouping: 16x³ +28x² - 28x - 49 = 0 is (4x² - 7) (4x - 7) = 0
What is factoring by grouping?Large polynomials can be divided into groups based on a common factor. As a result, we may factor each distinct group and then merge like words. We refer to this as factoring by grouping.
We have the equation,
16x³ +28x² - 28x - 49 = 0
In order to solve the equation by using factor by grouping:
We find common terms in between,
So, we arrange the terms,
16x³ +28x² - 28x - 49 = 0
4x² (4x - 7) -7 (4x - 7) = 0
Here, we have common term (4x-7).
Factor out the common binomial.
(4x² - 7) (4x - 7) = 0
Therefore, (4x² - 7) (4x - 7) = 0 is the factor.
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Emma bought two televisions at 2500 cedis each. One got slightly damaged during transportation. He sold the undamaged one at 3000 cedis and sold the damaged one at 2200 cedis. Calculate the percentage profit made by Emma.
Answer:
90%
Step-by-step explanation:
cost price of both tv = 2500
sale price of undamaged = 3000
sale price of damaged = 2200
sale price of both tv = 5200
profit = sale price - cost price
profit = 5200 - 2500
profit = 2700
profit percentage = profit × 100 ÷ cost price
profit percentage = 2700 × 100 ÷ 2500
profit percentage = 90%
Jean and sally drive toward each other from places that are 445 miles apart. Jean averages 43 mph by Sally averages 46 mph. If they both are driving at 9 AM and at what time would they meet
If they both were driving at 9 AM, Jean and Sally, based on their average driving speeds, would meet at 14:00 hours or 2:00 P.M.
What is the average speed?The average speed is the quotient of the total distance traveled and the time interval.
As a scalar quantity, the average speed is represented by its magnitude.
From the distance, speed, and time formula, we can determine the time when Jeann and Sally will meet.
Time = Distance/Speed
Total distance covered = 445 miles
Jean's average driving speed = 43 mph
Sally's average driving speed = 46 mph
Combined average driving speed = 89 mph
Time used to cover the distance = 5 hours (445/89)
The time they started driving = 9 AM
Time they will meet = 2 PM (9 AM + 5 hours) or 14:00 hours
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When dragons on planet Pern lay eggs, the eggs are either green or yellow. The biologists have observed over the years that 39% of the eggs are yellow, and the rest green. Next spring the lead scientist has permission to randomly select 66 of the dragon eggs to incubate. Consider all the possible samples of 66 dragon eggs. What is the usual number of yellow eggs in samples of 66 eggs
Answer: The usual number of yellow eggs in the selected sample is 26.
Step-by-step explanation:
It is given that there are 2 types of dragon eggs: Yellow and green
Observation says that 39% of the eggs are yellow.
When selected at random for incubation:
Number of eggs selected are = 66
To evaluate the number of yellow eggs, we must calculate 39% of 66 eggs
\(\Rightarrow \frac{39}{100}\times 66\\\\\Rightarrow 25.74\approx 26\)
Hence, the usual number of yellow eggs in the selected sample is 26.
A right triangle has a leg of length 14 yards and a hypotenuse of
length 42 yards. Find the length of the other leg. Provide an answer
accurate to the nearest tenth.
The length of the other leg is approximately 40.99 yards.
What is triangle ?A triangle is a polygon that has three sides, three angles, and three vertices. It is a fundamental shape in geometry and is used in many different areas of mathematics, science, and engineering.
Triangles are classified based on the relative lengths of their sides and the size of their angles. A scalene triangle has no sides of equal length, an isosceles triangle has two sides of equal length, and an equilateral triangle has all three sides of equal length. Triangles can also be classified based on the size of their angles, with acute triangles having all angles less than 90 degrees, obtuse triangles having one angle greater than 90 degrees, and right triangles having one angle equal to 90 degrees.
According to given information :We can use the Pythagorean theorem to find the length of the other leg of the right triangle. The Pythagorean theorem states that for a right triangle with legs of lengths a and b and hypotenuse of length c, we have:
\(a^2 + b^2 = c^2\)
In this case, we know that one leg has a length of 14 yards and the hypotenuse has a length of 42 yards, so we can write:
\(14^2 + b^2 = 42^2\)
Simplifying and solving for b, we get:
b = sqrt(42² - 14²)
b = sqrt(1680)
b ≈ 40.99 yards (rounded to the nearest hundredth)
Therefore, the length of the other leg is approximately 40.99 yards.
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Find the value of each variable. The dot represents the center of the circle.
Answer:
Step-by-step explanation:
By the inscribed angle theorem, \(a=21, b=42\)
So, since angles in a triangle add to 180 degrees, the angle vertical to c is \(180-21-42=117\), and thus \(c=117\)