Answer:
C. 22
Step-by-step explanation:
If the minimum is 187, and she earns 8.5 per hour then you just divide by 8.5
Answer:
C
Step-by-step explanation:
Erica's weekly paycheck is at least $187.
She earns $8.50 per hour.
We have to do is 187 divided by 8.5 in order to find the number of hours she worked.
187/8.5=22
She worked for at least 22 hours.
13. Consider the curve r(t) = (3t²1, t³ +7,5t + 4t²). (a) Does this curve intersect the point (11,−1,6)? If so, at what t-value? (b) Does this curve intersect the point (2,8, –1)? If so, at what t-value? (c) What vector is tangent to the curve at the point when t = 2? (d) What line is tangent to the curve at the point when t = 2?
The vector tangent to the curve at the point when t = 2 is (12, 12, 21).
(a) To check if the curve intersects the point (11, -1, 6), we need to find a t-value that makes r(t) equal to the given point. We can set up the following system of equations:
3t² + 1 = 11
t³ + 7 = -1
5t + 4t² = 6
Solving these equations, we find that t = 2 satisfies all three equations. Therefore, the curve intersects the point (11, -1, 6) at t = 2.
(b) Similarly, to check if the curve intersects the point (2, 8, -1), we set up the following system of equations:
3t² + 1 = 2
t³ + 7 = 8
5t + 4t² = -1
Solving these equations, we find that there is no t-value that satisfies all three equations. Therefore, the curve does not intersect the point (2, 8, -1).
(c) To find the vector tangent to the curve at the point when t = 2, we differentiate r(t) with respect to t:
r'(t) = (6t, 3t², 5 + 8t)
Substituting t = 2 into r'(t), we get:
r'(2) = (6(2), 3(2)², 5 + 8(2))
= (12, 12, 21)
Therefore, the vector tangent to the curve at the point when t = 2 is (12, 12, 21).
(d) To find the line tangent to the curve at the point when t = 2, we can use the point-normal form of a line. Given the point (2, 8, -1) on the line and the normal vector (12, 12, 21), we can write the equation of the line as:
(x - 2) / 12 = (y - 8) / 12 = (z + 1) / 21
This represents the line tangent to the curve at the point when t = 2.
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A(n) ___X___ is defined before observing the sample, while a(n) ___Y___ is the values of the ___X____ when evaluated at a particular sample.
Select one:
a. X = data; Y = random variable
b. X = estimator; Y = statistic
c. X = estimate; Y = estimator
d. X = estimator; Y = estimate
The correct answer is:
a. X = data; Y = random variable
In statistics, "data" refers to the collection of observations or measurements made on a particular variable or set of variables. X is typically used to represent the random variable of interest, which is defined before any data is collected.
On the other hand, a statistic is a function of the data that is used to estimate a population parameter or describe some aspect of the data. An estimator is a formula or algorithm used to calculate a statistic based on a sample of data. The values of the estimator when applied to a particular sample are called estimates.
Therefore, X is not an estimator or estimate but rather the random variable being studied, while Y represents the values of X observed in a particular sample, making it a random variable as well.
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A rental car company charges $25 per day to rent a car and $0.12 for every mile driven. Violet wants to rent a car, knowing that:
She plans to drive 125 miles.
She has at most $150 to spend.
pls help
Step-by-step explanation:
Identify the cost of 125 miles;
\(125 \times 0.12 = 15\)
$15 for 125 miles.
Subtract 150 and 15;
\(150 - 15 = 135\)
(Money remaining)
Divide 135 by 25 to identify how many days she can rent the car;
\(135 \div 25 = 5 \frac{2}{5} \)
5 2/5 decreases to 5 as you can't rent a car for 5 2/5 days.
Answer: She can drive 125 miles and rent the car for 5 days.
What is -(x + 5) distributed
Answer:
-x-5
Step-by-step explanation:
Multiply every part inside the equation by -1.
x*-1 and 5*-1
-1x+-5x
Simplify.
-x-5
What does the pair of equations y = 1, z = 8 represent? in other words, describe the set of points (x, y, z) such that y = 1 and z = 8. a plane
The set of points (x , 1 , 8) describe a line that has constant value of y and z coordinates, i.e., is parallel to x-axis in the plane.
What is the equation of a line in a plane?The equation of a plane in R has the generic form: ax + by + cz + d = 0, where a, b, and c are the elements of the normal vector n = (a, b, c) that is perpendicular to the plane or any vector parallel to the plane.
Given: Equations of the lines:
y = 1z = 8To find: description of the points (x, y, z) in the plane.
Finding:
According to the given conditions, the lines y = 1 and z = 8 describe two lines with constant values of y and z coordinates respectively in the plane.
The set of points (x , 1 , 8) describe a line that has constant value of y and z coordinates, i.e., is parallel to x-axis and can have infinitely many values of x in the plane.
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ILL MARK BRAINLIEST please help :( 32 points too
Answer:
Hope this helps!
Step-by-step explanation:
21. 1/1000
22. 1 second
23. 0.16666666666
24. 0.1
25. 0.2
26. 5/48
27. 33.9 kilometers
You would like to study all of the numbers that are at a distance 10 or less from a number -20. Write this using absolute value notation and use the variable x
Answer:
Step-by-step explanation:
dad hates me sorry bye
Checking for approximate normality in the population is essential for constructing a valid confidence interval, particularly when dealing with small sample sizes. This ensures the accuracy and reliability of the interval in estimating the true population parameter.
It's important to check whether the population is approximately normal before constructing a confidence interval because the accuracy and validity of the interval depend on the underlying distribution of the population. Here's a step-by-step explanation:
1. A confidence interval is a range of values within which the true population parameter (e.g., mean or proportion) is likely to fall, with a certain level of confidence (e.g., 95% or 99%).
2. The process of constructing a confidence interval relies on the Central Limit Theorem, which states that, for large sample sizes, the sampling distribution of the sample mean will be approximately normal, regardless of the population distribution.
3. However, for small sample sizes, the distribution of the population needs to be approximately normal in order to obtain an accurate confidence interval. This is because the normality assumption is crucial for the proper interpretation of the interval.
4. If the population is not approximately normal, the confidence interval may not provide a reliable estimate of the true population parameter, leading to incorrect conclusions and potentially invalid results.
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What is the sum of all frequencies in a frequency distribution? and why is the sum of all relative frequencies equal to 1?
Answer:
Cumulative Frequency:
The sum of all the frequencies for all classes is equal to the number of elements in the given data and that summation is termed as the cumulative frequency which defines the number of entries of that statistical data.
The sum of relative frequencies is also equal to one, since the sum of all fractional parts must equal the whole.
Step-by-step explanation:
A vehicle was valued at $36,000 in the year 2011. The value depreciated to $12,000 by the year 2015. Assume that the car continues to drop at a constant rate. How long will it take for the car to be valued at $800?
The car will cost $ 800 after a depreciation time of approximately 6 years.
In what year does a car cost $ 800 due to depreciation?
Herein we are informed about the case of a car bought in 2011 at a cost of $ 36,000 and that depreciates linearly every year. Then, the depreciation function is described below:
c(t) = c' + m · t
Where:
c' - Initial cost of the car, in monetary unit.m - Depreciation rate, in monetary unit per year.t - Time, in years.If we know that c(0) = 36,000, c(4) = 12,000 and c(t) = 800, then the depreciation rate is:
m = (12,000 - 36,000) / (4 - 0)
m = - 24,000 / 4
m = - 6,000
800 = 36,000 - 6,000 · t
6,000 · t = 35,200
t = 35,200 / 6,000
t = 5.867
The expected depreciation time is approximately 6 years.
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HELP please :)
a laptop costs $899 how much will it be with a sale of 24% off
Answer:
683.24
Step-by-step explanation:
Im pretty sure PLEASE give BRAINLIEST I NEED IT
All you have to do is 899 times .24 and then get that answer and subtract
Answer:
its $683.24
as we first took out 24%of $899 i.e215.76 then we subtracted it from $899
I just need level two and three solved please
Answer:
intercepts: (0, 5/2) or (-5, 0)arbitrary point: (7, 6)Step-by-step explanation:
You want two methods of choosing points on the line with slope 1/2 through A(-1, 2).
InterceptsWriting the equation in standard form, we can find the x- and y-intercepts. To get there, we can start from point-slope form:
y -k = m(x -h) . . . . . . line with slope m through point (h, k)
y -2 = 1/2(x -(-1)) . . . . . using given slope and point
2y -4 = x +1 . . . . . . . . . . multiply by 2
x -2y = -5 . . . . . . . . . . . . add -1 -2y
Setting x=0 tells us the y-intercept is ...
0 -2y = -5
y = -5/-2 = 5/2
So, the y-intercept is (0, 5/2).
Setting y=0 tells us the x-intercept is ...
x -2(0) = -5
x = -5
So, the x-intercept is (-5, 0).
Arbitrary pointIt will be convenient to choose an arbitrary y-value to find another point on the line. We can pick y = 6, for example, Then the corresponding x-value is ...
x -2y = -5
x = -5 +2y = -5 +2(6) = 7
Another point on the line is (7, 6).
__
Additional comment
If we were to choose an arbitrary value for x, we would want it to be odd, so the corresponding y-value would be an integer. We chose to pick an arbitrary value of y so we didn't have to worry about how to make the x-value an integer.
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You are thinking of buying a new tent. Look at the dimensions given below.
What is the perimeter of the tent's porch?.
Answer:
Step-by-step explanation:
The shorter sides of the porch can be found by subtracting 2.5m from 3m to get .5m; the longer sides are found by looking at the opposite end of the tent at the rectangle with a 1 inside of it. That 1 indicates the length of the rectangle, which is the same for the porch's length. That means that the perimeter is .5+1+.5+1 which is 3m total.
show that in a class of 35 students, at least two of them have last names that begin with the same letter.
By the Pigeonhole Principle, in a class of 35 students, at least two of them have last names starting with the same letter.
To show that in a class of 35 students, at least two of them have last names that begin with the same letter, we can apply the Pigeonhole Principle.
The Pigeonhole Principle states that if you distribute n items into m containers, and n > m, then at least one container must contain more than one item.
In this case, we can think of each student's last name as an item, and the letters of the alphabet as the containers. Since there are 26 letters in the English alphabet, and we have 35 students in the class, we have more students than the number of available letters.
By applying the Pigeonhole Principle, we conclude that at least two students must have last names that begin with the same letter. This is because there are more students (35) than the number of available letters (26), so it is impossible to assign each student a unique letter as the first letter of their last name. Therefore, there must be at least one letter shared by two or more students in the class.
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as long as you are working with the same variables, it does not matter whether or not you average the data over every month versus every year; the correlation will be the same. group of answer choices true false
The given statement is true.
What is variables?
In statistical modelling, experimental sciences, and mathematical modelling, there are dependent and independent variables. Dependent variables are so named because they are researched in an experiment under the assumption or requirement that they are dependent on the values of other variables according to some rule or law.
The given statement is true.
It does not matter whether we average the data across every month or every year as long as the variables are the same; the correlation will remain the same. Since the correlation coefficient r is a unitless metric, the time variable has no effect on it.
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Someone help!!!!!! Look at the picture below
Answer:
9
Step-by-step explanation:
i can not really tell what letters are on the picture but i think it is 9
Use the information to answer the following question.
Carolyn was asked to solve the following system of equations.
Her work is shown.
Step 1: 3x – 2y = 7
Step 2: 3x – 2(x + 2) = 7
Step 3: 3x – 2x + 4 = 7
Step 4: x + 4 = 7
Step 5: x = 3
Step 6: y = x + 2
Step 7: y = 3 + 2
Step 8: y = 5
Solution: (3, 5)
Did Carolyn make an error in her work?
Yes, Carolyn did not correctly combine like terms in Step 2.
Yes, Carolyn should have substituted the x-value into the first equation in Step 6.
No, Carolyn solved the system of equations correctly.
Yes, Carolyn did not correctly distribute the negative in Step 3.
Carolyn made an error in her work because she did not correctly distribute the negative in Step 3.
System of EquationsA system of equations is the given term math for two or more equations with the same variables. The solution of these equations represents the point of the intersection.
You can solve a system of equations by the adding or substitution methods. In the addition method, you eliminate a variable, on the other hand, in the substitution method you replace a variable for the other.
The question gives:3x-2y=7 (1)y=x+2The question shows that Carolyn applies the substitution method because she replaces the variable y (equation 2) in equation 1. See the given step 2.
3x – 2y = 7
3x – 2(x + 2) = 7
3x – 2x - 4 = 7 - here it is the mistake. (Carolyn did not correctly distribute the negative).
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a car travels a distance of of 540 km in 6 hours what's his speed
Answer:
90 km per hour
Step-by-step explanation:
divide total distance by number of hours traveled :)
Lake Vostok is Antarctica's largest and deepest subsurface lake. The mean depth of the lake is believed to be 344 meters. 44 random samples of the depth of this lake were obtained. Assume the underlying distribution is normal and σ = 30 meters. Please use 3 decimal places in all calculations.
a) State the hypotheses that are required if we want to know if the mean depth of the lake is less than 344 meters. Be sure to include both the null and alternative hypotheses.
b) Find the probability of the Type II error if the true mean depth of the lake is μa = 326 meters; that is, find β(326). Assume that α = 0.01. Hint: If your numeric answer is wrong, please confirm that your hypotheses are correct before you run out tries. β(326) =?
c) Assuming that the alternative hypothesis in part a) is in the opposite direction, find the power if the true mean depth of the lake is μa = 355 meters, power(355). Assume that α = 0.01. Hint1: Because the hypotheses have changed, no steps in part b) can be reused.
State the new hypotheses that are required if we want to know if the mean depth of the lake is greater than 344 meters. Be sure to include both the null and alternative hypotheses.
power(355) = ?
d) Find the test statistic assuming that the sample mean is 337.
The test statistic when α = 0.01. = ?
The test statistic when α = 0.05. = ?
a.) The hypotheses are Null and alternative.
b.) The probability of a Type II error is: β(326) = 0.0046
c.) The power is: power(355) = 0.9599
d.) The null hypothesis at the 0.05 level of significance.
a) The hypotheses are:
Null hypothesis: The mean depth of the lake is equal to 344 meters.
Alternative hypothesis: The mean depth of the lake is less than 344 meters.
b) To find the probability of a Type II error, we need to assume that the true mean depth is 326 meters, calculate the corresponding z-score, and find the area under the curve to the right of this z-score (since the alternative hypothesis is in the left direction). Using the formula for the z-score:
z = (x - μ) / (σ / sqrt(n))
z = (344 - 326) / (30 / sqrt(44))
z = 2.63
Using a standard normal table, we find that the area to the right of 2.63 is 0.0046. Therefore, the probability of a Type II error is:
β(326) = 0.0046
c) Assuming the alternative hypothesis is now that the mean depth of the lake is greater than 344 meters, the new hypotheses are:
Null hypothesis: The mean depth of the lake is equal to 344 meters.
Alternative hypothesis: The mean depth of the lake is greater than 344 meters.
To find the power when the true mean depth is 355 meters, we need to calculate the corresponding z-score and find the area under the curve to the right of this z-score. Using the formula for the z-score:
z = (x - μa) / (σ / sqrt(n))
z = (344 - 355) / (30 / sqrt(44))
z = -1.75
Using a standard normal table, we find that the area to the right of -1.75 is 0.9599. Therefore, the power is:
power(355) = 0.9599
d) The test statistic is:
t = (x - μ) / (s / sqrt(n))
t = (337 - 344) / (30 / sqrt(44))
t = -2.15
When α = 0.01, the critical t-value is -2.695. Since -2.15 > -2.695, we fail to reject the null hypothesis at the 0.01 level of significance.
When α = 0.05, the critical t-value is -1.681. Since -2.15 < -1.681, we reject the null hypothesis at the 0.05 level of significance.
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What is the measure of the reference angle for a 102° angle?
A. 68°
B. 12°
C. 57°
D. 78°
I really need the answer fast please!
Answer:
78°
Step-by-step explanation:
The two angles have to add up to 180°
180° - 102° = 78°
Angle = 78°
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Slope of line that passes through (2,7) and (-4,19)
To calculate the slope of the line, we have that its points are A(x₁, y₁) and B(x₂,y₂), we apply the following formula:
\(\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{m=\frac{\Delta y}{\Delta x} \iff m=\frac{y_2-y_1}{x_2-x_1} } \end{gathered}$}}\)
To solve, we have that the points are:
\(\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{A(x_1=\underbrace{2} \ \ , \ \ y_1=\overbrace{7} \ ) \ and \ B(x_2=\underbrace{-4} \ \ , \ \ y_2=\overbrace{19} } \end{gathered}$}}\)
What we do to solve is that we substitute this data in the formula provided above.
\(\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{m=\dfrac{y_2-y_1}{x_2-x_1} } \end{gathered}$}}\)
\(\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{m=\frac{19-7}{-4-2} } \end{gathered}$}}\)
\(\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{m=\frac{12}{-6}=-2 } \end{gathered}$}}\)
The slope of the line that passes through (2,7) and (-4,19) is -2.really need help on these two questions for geometry, please actually answer it instead of just grabbing points and leaving :')
Answer:
Step-by-step explanation:
E and F are horizontally aligned, so the slope of EF is 0 and its length is 16-10 = 6.
G and H are horizontally aligned, so the slope of GH is 0 and its length is 16-10 = 6.
F and G are vertically aligned, so FG is vertical and its length is 10-4 = 6.
E and HG are vertically aligned, so EH is vertical and its length is 10-4 = 6.
Quadrilateral EFGH is a square.
Growth and decay how do you solve a(r)to the power of t
Solution for the question 2 :
It is given that ,
\(\begin{gathered} P_0=\text{ }800 \\ r\text{= }2\text{ \%} \\ n\text{ = 9 years} \end{gathered}\)The population after n years is given by exponential function ,
\(\begin{gathered} P(n)=P_0(1+\frac{r}{100})^n \\ \\ \\ \end{gathered}\)Population after 9 years is calculated as,
\(\begin{gathered} P(9)=\text{ 800 }\times(1+0.02)^9 \\ P(9)=\text{ 800 }\times(1.02)^9 \\ P(9)=800\text{ }\times\text{ 1.1951} \\ P(9)=\text{ }956.08\text{ }\approx\text{ 956 } \end{gathered}\)Thus the population after 9 years is 956 .
Shelly measures the dimensions of her bedroom so she can buy new carpet..
Which set of dimensions for Shelly's carpet is most reasonable?
A
B
C
D
12 feet by 10 feet
60 inches by 36 inches
20 meters by 18 meters
100 centimeters by 80 centimeters
Answer:
12 feet × 10 feet
Step-by-step explanation:
12 feet × 10 feet is the size of a modest bedroom.
60in × 36in is only 5×3 feet, more like a closet.
20×18m is around 60×54feet something like a whole studio apartment or 1-bedroom apartment.
100×80cm is like 3 feet by lessthan 3 feet like a doormat size or maybe a coat closet.
Select the correct formula for the polyatomic ion. you can find a list of common polyatomic ions by clicking here. the formula for the ammonium ion: nh3 nh4 am
The chemical formula for ammonium carbonate is (NH₄)₂CO₃. Therefore, option (C) is correct.
When heated, ammonium carbonate, also known as ()2, rapidly breaks down into ammonia and carbon dioxide. It functions as a smelling salt and a leavening agent. Ammonium carbonate, often known as baker's ammonia, was used before baking soda and baking powder as leaveners.
Sal volatile contains ammonium carbonate, and salt of hartshorn when baked emits a strong odour. At standard pressure and temperature, two processes lead to the gradual breakdown of ammonium carbonate. The pure ammonium carbonate sample will combine with different byproducts.
Upon spontaneous dissociation, ammonium carbonate can separate into ammonium bicarbonate and ammonia. which results in the addition of more ammonia, carbon dioxide, and water.
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Answer:
The formula for the ammonium ion: NH4+
The formula for the nitrate ion: NO3–
A chromate ion consists of four oxygen atoms bonded to a chromium atom. It has two extra electrons. The formula of this ion: CrO42–
Heres all three. Hope i helped
I'm a denf it so I can show because I can't send the full pic
Some of these type of quatities are vectors, they depend on directions, for instance B. The number C. adds two values, so they don't make zero, and number D. still has one galf of the gas. So the answer is number A. Veronica receives 21 and spends 21, so
George wants to invest $3,250. American Bank offers a simple interest rate of 4%, while Liberty Savings offers an interest rate of 3.75% compounded annually. How much more in interest will George earn after 8 years if he invests with Liberty Savings rather than American Bank?
Answer:
We can see that the simple interest is better
Step-by-step explanation:
We calculate the simple interest and the compound interest values
Simple interest
I = PRT/100
I is principal
R is the rate
T is the time
I = (8000 * 4 * 8)/100 = 3,840
For the compound interest, we have that;
A = I( 1 + r)^n
A is the amount in the account after the saving period
I is the amount deposited
r is the rate
n is the number of years
Substituting these, we have that;
A = 3250(1 + 0.04)^8
A = 4447.85
The interest is this amount minus the deposit
That will be;
4447.85 -3250 = 1,197.5
Let us also recall that it took the bus 36 s to cover 400 m, that the student was 200 m ahead of the bus, and it took the student 1.70 s to accelerate.
(a) What is the distance covered by the bus, from the moment the student starts chasing it and till the moment when the bus passes by the stop? You can use either equations or the v(t) graph. Give your answer in meters.
(b) What is the distance covered by the students in these 36 s (from the beginning of her race and till the bus passes by the stop)? You can use either equations or the v(t) graph. Give your answer in meters.
(c) Hence, by how much does the student miss the bus? Give the answer in meters. Use your answers from parts (a) and (b)
(c) The student misses the bus by the difference between the total distances covered by the bus and the student.
(a) To determine the distance covered by the bus from the moment the student starts chasing it until the moment the bus passes by the stop, we need to consider the relative motion between the bus and the student. Let's break down the problem into two parts:
1. Acceleration phase of the student:
During this phase, the student accelerates until reaching the bus's velocity. The initial velocity of the student is zero, and the final velocity is the velocity of the bus. The time taken by the student to accelerate is given as 1.70 s.
Using the equation of motion:
v = u + at
where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time, we can calculate the acceleration of the student:
a = (v - u) / t
= (0 -\(v_{bus}\)) / 1.70
Since the student starts 200 m ahead of the bus, we can use the following kinematic equation to find the distance covered during the acceleration phase:
s = ut + (1/2)at^2
Substituting the values:
\(s_{acceleration}\) = (0)(1.70) + (1/2)(-\(v_{bu}\)s/1.70)(1.70)^2
= (-\(v_{bus}\)/1.70)(1.70^2)/2
= -\(v_{bus}\)(1.70)/2
2. Constant velocity phase of the student:
Once the student reaches the velocity of the bus, both the bus and the student will cover the remaining distance together. The time taken by the bus to cover the remaining distance of 200 m is given as 36 s - 1.70 s = 34.30 s.
The distance covered by the bus during this time is simply:
\(s_{constant}_{velocity} = v_{bus}\) * (34.30)
Therefore, the total distance covered by the bus is:
Total distance = s_acceleration + s_constant_velocity
= -v_bus(1.70)/2 + v_bus(34.30)
Since the distance covered cannot be negative, we take the magnitude of the total distance covered by the bus.
(b) To determine the distance covered by the student during the 36 s, we consider the acceleration phase and the constant velocity phase.
1. Acceleration phase of the student:
Using the equation of motion:
s = ut + (1/2)at^2
Substituting the values:
\(s_{acceleration}\) = (0)(1.70) + (1/2\(){(a_student)}(1.70)^2\)
2. Constant velocity phase of the student:
During this phase, the student maintains a constant velocity equal to that of the bus. The time taken for this phase is 34.30 s.
The distance covered by the student during this time is:
\(s_{constant}_{velocity} = v_{bus}\) * (34.30)
Therefore, the total distance covered by the student is:
Total distance =\(s_{acceleration} + s_{constant}_{velocity}\)
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Is zero positive proof?
No, The number zero is neither positive nor negative.
Aryabhata, who is known as a great astronomer of the classic age of India was the one who invented the digit “0” for which he became immortal but later on is given to Brahmagupta.
The numbers to the right of zero on the number line are positive and those on the left side are negative.
Positive numbers are greater than 0 and located to the right of 0 on a number line. Negative numbers are less than 0 and are located to the left of 0 on a number line.
Positive and negative numbers are sometimes called signed numbers.
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The sixth term of an AP is twice the 3rd term and the first term is 3. Find the common difference and the 10th term
The common difference of the given AP is -3/2 and the 10th term will be -21/2.
What is Arithmetic progression?The difference between every two successive terms in a sequence is the same this is known as an arithmetic progression (AP).
The arithmetic progression has wider use in mathematics for example sum of natural numbers.
As per the given,
The sixth term of an AP is twice the 3rd term
a₆ = 2a₃
First term a = 3
The sixth term will be given as,
a₆ = 3 + (6 - 1)d
a₆ = 3 + 5d
The third term will be given as,
a₃ = 3 + (3 - 1)d
a₃ = 3 + 2d (2)
Since,a₆ = 2a₃
a₆ = 3 + 5d → 2a₃ = 3 + 2d
a₃ = 3/2 + d (1)
Equate the equation (1) and (2)
3 + 2d = 3/2 + d
d = 3/2 - 3
d = (3 - 6)/2 = -3/2
The 10th term will be as,
a₁₀ = 3 + (10 - 1)(-3/2)
⇒ 3 - 9 × 3/2
⇒ 3 - 27/2
⇒ -21/2
Hence "The common difference of the given AP is -3/2 and the 10th term will be -21/2".
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Robert was able to travel 292.0 miles in 4.000 hours and used 38 liters of gasoline. What was Robert's speed in feet per second
Robert's speed was approximately 107.07 feet per second.
Robert's speed in feet per second, we need to convert the distance traveled from miles to feet and the time taken from hours to seconds.
1 mile is equal to 5,280 feet. 1 hour is equal to 3,600 seconds.
Distance traveled in feet = 292.0 miles × 5,280 feet/mile
= 1,540,760 feet
Time taken in seconds = 4.000 hours × 3,600 seconds/hour
= 14,400 seconds
Now, we can calculate Robert's speed in feet per second by dividing the distance traveled by the time taken
Speed = Distance / Time
Speed = 1,540,760 feet / 14,400 seconds
Speed ≈ 107.07 feet/second
Therefore, Robert's speed was approximately 107.07 feet per second.
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