Answer:
The height of the ball is the same after 1.5 seconds and 3.5 seconds. ⇒ (A)
Step-by-step explanation:
The quadratic function is represented by a parabola
The parabola is symmetric about its vertex.The average of the x-coordinates of any opposite points (points have the same y-coordinates) on the parabola is equal to the x-coordinate of its vertex point.The axis of symmetry of it passes through the x-coordinate of its vertex point.The equation of its axis of symmetry is x = h, where h is the x-coordinate of its vertex point.∵ The quadratic function modeling the height of a ball over time
∴ f(t) = at² + bt + c
→ t is the time in second, f(t) is the height of the ball after t seconds
∵ It is symmetric about the line t = 2.5
∴ The x-coordinate of its vertex is 2.5
→ That means the average of the x-coordinates of any two
opposite points belong to f(t) is 2.5
∵ The average of 1.5 and 3.5 = [tex]\frac{1.5+3.5}{2}=\frac{5}{2}=2.5[/tex]
∴ 1.5 and 3.5 have the same value of f(t)
∴ 1.5 and 3.5 have the same height
The height of the ball is the same after 1.5 seconds and 3.5 seconds.
H=L^2/f•c solve for L
Answer:
±sqrt( H *f•c)= L
Step-by-step explanation:
H=L^2/f•c
Multiply each side by fc
H *fc=L^2/f•c * fc
H *f•c=L^2
Take the square root of each side
±sqrt( H *f•c)= sqrt(L^2)
±sqrt( H *f•c)= L
what is the formula to find the volume for a sphere? I forgot
Answer:
4/3 pie r^3
Step-by-step explanation:
Answer:
The formula to find the volume (V) of a sphere with radius (r) is:
V = (4/3)πr^3
In this formula, π (pi) is a mathematical constant approximately equal to 3.14159. To find the volume of a sphere, you need to cube the radius of the sphere (multiply it by itself three times), multiply the result by 4/3, and then multiply that by π. This formula works for spheres of any size, as long as you know the radius.
Hope it help!
what is the y-intercept of the line 6x+2y=7
Question 15 3 pts Suppose the commuting time on a particular train is uniformly distributed between 20 and 50 minutes. What is the mean commuting time? 35 minutes 50 minutes 38 minutes 40 minutes Next
The mean commuting time for the particular train, assuming a uniform distribution between 20 and 50 minutes, is 35 minutes. This means that, on average, commuters can expect their commuting time to be around 35 minutes.
To calculate the mean commuting time, we need to find the average value of the uniformly distributed commuting time between 20 and 50 minutes.
In a uniform distribution, the probability density function (PDF) is constant within the range of the distribution. Since the distribution is uniform between 20 and 50 minutes, the PDF is constant over that interval.
The mean of a uniform distribution can be calculated using the formula:
Mean = (a + b) / 2
where 'a' is the lower limit of the distribution (20 minutes) and 'b' is the upper limit (50 minutes).
Plugging in the values into the formula, we get:
Mean = (20 + 50) / 2 = 70 / 2 = 35 minutes
The calculation is straightforward because in a uniform distribution, the mean is simply the average of the minimum and maximum values of the distribution.
In this case, the commuting time is equally likely to be any value between 20 and 50 minutes. So, on average, commuters can expect a mean commuting time of 35 minutes.
It is important to note that the mean represents the average value and may not necessarily reflect the most frequently occurring commuting time. In this case, there is an equal likelihood of any time within the given range.
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7 t-shirts and 5 hats costs £32.
3 t-shirts and 4 hats costs £23.
Find the cost of a t-shirt.
Find the cost of a hat
Step-by-step explanation:
Let x be the cost of t-shirts
and
y be the cost of hats
Then,
7x + 5y = £32 ..... (i)
And
3x + 4y = £23 ..... (ii)
Now,
Solving (i) and (ii) by Elimination method, we get -
[ 7x + 5y = £32 ] × 4
[ 3x + 4y = £23 ] × 5
= 28x + 20y = £128
15x + 20y = £115
- - -
_________________
13x = £13
x = £13/13
x = £1Now, substituting the value of x on equation (i)
= 7(£1) + 5y = £32
= £7 + 5y = £32
= 5y = £32 - £7
= 5y = £25
y = £25/5
y = £5Hence,
The cost of t-shirt is £1
and
the cost of hats is £5.
Which function has a range of {yl y> -10}?
O y = (x – 10 + 2
y= x -5 - 10
O y = x + 10 - 4
y= x + 7 +10
Answer:y= x + 7 +10
Step-by-step explanation:
Answer:
its y = x-5 -10
Step-by-step explanation:
b on edge 2020
write 0.131313 as a fraction
Answer:
[tex]\frac{13}{99}[/tex]
Step-by-step explanation:
We require to create 2 equations with the repeating numbers after the decimal point.
let x = 0.1313.... → (1) ( multiply both sides by 100 )
100x = 13.1313.... → (2)
Subtract (1) from (2) thus eliminating the repeating numbers
99x = 13 ( divide both sides by 99 )
x = [tex]\frac{13}{99}[/tex]
That is 0.1313.... = [tex]\frac{13}{99}[/tex]
Translate this phrase into an algebraic expression.
54 less than twice a number
Use the variable n to represent the unknown number
The answer is:
54<2n
.skskskak
What is the slope of the line that passes through the points (-6, 8)(−6,8) and (-16, 33) ?(−16,33)? Write your answer in simplest form.
Given:
A line passes through the points (-6, 8) and (-16, 33).
To find:
The slope of the line.
Solution:
If a line passes through two points, then the slope of the line is
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
The line passes through the points (-6, 8) and (-16, 33). Using the above formula, the slope of the line is
[tex]m=\dfrac{33-8}{-16-(-6)}[/tex]
[tex]m=\dfrac{25}{-16+6}[/tex]
[tex]m=\dfrac{25}{-10}[/tex]
[tex]m=-2.5[/tex]
Therefore, the slope of the line is -2.5.
Slope of the line passing through the points ( -6,8) and (-16,33) will be -2.5.
Given information:
The line passes through the points ( -6,8) and (-16,33).
It is required to find the slope of the line.
Slope of the line passing from two points [tex](x_1,y_1) \; and\; (x_2, y_2)[/tex] can be written as
[tex]m= \dfrac{y_2-y_1}{x_2- x_1}[/tex]
So, the slope of the given line can be calculated as,
[tex]m= \dfrac{33-8}{-16- (-6)}\\m = \dfrac{25 }{-10} \\m = -2.5[/tex]
Therefore the slope of given line will be -2.5.
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Consider this equation:
-2x-4+5x=8
Generate a plan to solve for the variable. Describe the
steps that will be used.
Answer:
Plan: separate the variable term from the constant term; divide by the coefficient of the variable.Steps: add 4 to both sides; collect terms; divide both sides by 3.Step-by-step explanation:
The first step is to look a the equation to see where the variable is in relation to the equal sign, and whether there are any constants on that same side of the equal sign.
Here, the variable terms are on the left, and there is a constant there, as well. The plan for solving the equation is to eliminate the constant that is on the same side of the equation as the variable, then divide by the coefficient of the variable. To find that coefficient, we need to collect terms. In summary, the plan is to ...
add 4 to both sides of the equationcollect termsdivide by the coefficient of the variable (3)Executing that plan, the steps are ...
-2x -4 +5x +4 = 8 +4 . . . . add 4
3x = 12 . . . . . . . . . . . . . . . collect terms
x = 4 . . . . . . . . . divide by 3
Answer:
The goal is to get x all alone. First combine like terms. Apply the addition property of equality to add 4 to both sides. Apply the division property of equality to divide both sides by 3. The result will be x = 4. Finally, check the solution by substituting 4 into the original equation.
Step-by-step explanation:
how do i determine the value of x?
Answer:
x=65
Step-by-step explanation:
When angles are across from eachother like that their values are the same.
so you set them equal to eachother.
120 = 2x - 10
130 = 2x add 10 to both sides
130/2 = 2x/ 2 divide both sides by 2
65 = x
Answer:
Considering that you are trying to find 'x' it is best to make an equation!
Step-by-step explanation:
To find 'x' you must first make an equation!
Since both are the same lengths, you can put these two equal to each other!
(2x - 10)° = 120°
Then solve like normal!
2x - 10° = 120°
+10° = +10°
--------------------
2x = 130°
(Then divide both sides by 2)
2x/2 = 130/2
x = 65°
find the points on the given curve where the tangent line is horizontal or vertical. (assume 0 ≤ ≤ 2. enter your answers as a comma-separated list of ordered pairs.) r = 1 − sin
The points on the given curve where the tangent line is horizontal or vertical are (0,1), (π,1), (π/2,0) and (3π/2,0).
The given curve is: r=1-sinθ
Differentiating with respect to θ, we get:
dr/dθ = -cosθ
Now, the slope of the tangent to the curve is given by tangent θ = dr/dθ.
The tangent is vertical if the slope is undefined. That is, the curve has a vertical tangent if
cosθ = 0, or θ = π/2 and θ = 3π/2.
The tangent is horizontal if the slope is 0.
That is, the curve has a horizontal tangent if cosθ = ±1 or θ = 0 and θ = π.
Hence, the required points where the tangent line is horizontal or vertical are (0,1), (π,1), (π/2,0) and (3π/2,0).
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Suppose that the height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning. After 10 hours of burning, a candle has a height of 21 centimeters. After 28 hours of burning, its height is 19.2 centimeters. What is the height of the candle after 7 hours?
Answer:
The height of the candle after 7 hours is 21.3 centimeters.
Step-by-step explanation:
From the information given you can assign the following values:
x1=10; y1=21
x2=28; y2=19.2
First, you have to find the slope using the following formula:
m=[tex]\frac{y2-y1}{x2-x1}[/tex]
m=[tex]\frac{19.2-21}{28-10}[/tex]
m=-0.1
Then, you can find the equation using the point/slope formula:
y-y1=m(x-x1)
y-21=-0.1(x-10)
y-21=-0.1x+1
y=-0.1x+22
Finally, to find the answer you need to replace the value of x that would be 7 in y=-0.1x+22:
y=-0.1(7)+22
y=-0.7+22
y=21.3
According to this, the height of the candle after 7 hours is 21.3 centimeters.
what is the y intercept of the table
-1
1.5
-3
1
Answer:
-3
Step-by-step explanation:
this is a linear equation, it goes up by 2, y intercept is when x=0 so take away 2 from -1 which is -3
Answer:
-3
Step-by-step explanation:
Your slope is 2:1 or 2 y's per 1 x...
the y-intercept is at x = 0...
you must subtract 1 from x = 1 to get x = 0...
therefore, you must subtract 2 from y = -1...
-1 - (-2) = -3
A bag contains {6} red marbles, {5} yellow marbles, and {7} green marbles. How many additional red marbles must be added to the {18} marbles alredy in the bag so that the probability of randomly drawing a red marble is {3/5}?
Answer:
[tex] \frac{6 + r}{18 + r} = \frac{3}{5} [/tex]
[tex]5(6 + r) = 3(18 + r)[/tex]
[tex]30 + 5r = 54 + 3r[/tex]
[tex]2r = 24[/tex]
[tex]r = 12[/tex]
12 additional red marbles should be added to the 18 marbles already in the bag.
Detecting nonrandomness in errors can be done using:
Multiple Choice
A. MAPs.
B. strategies.
C. correlation coefficients.
D. MSEs.
E. control charts.
The correct answer for detecting nonrandomness in errors is E. control charts. Control charts are a statistical tool used to monitor processes and detect deviations from randomness or expected behavior. They are commonly used in quality control and process improvement to identify any systematic or nonrandom patterns in the data.
Control charts help visualize data over time and compare it to predetermined control limits. If the data falls within these limits and shows a random pattern, it suggests that the process is stable and operating within acceptable limits of variation. However, if the data exhibits nonrandom patterns, such as trends, cycles, or unusual points, it indicates the presence of special causes or systematic errors in the process. By analyzing the control chart, individuals can identify the sources of nonrandomness, investigate the underlying causes, and take corrective actions to improve the process and reduce errors. Therefore, control charts provide an effective method to detect nonrandomness and ensure the quality and consistency of processes.
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What is the range of f(x)=20x+4
Answer:
All real numbers
Step-by-step explanation:
The graph of this is equation is a straight line, increasing forward and backwards in both x and y. The range is all real numbers.
Sorry for last time.
Hope this helps you.
Have a nice day.
factories ×^2+3x-4
I need help with this please.
Answer:
( x − 1 ) ( x + 4 )
Step-by-step explanation:
Answer:
[tex]\huge\boxed{(x+4)(x-1)}[/tex]
Step-by-step explanation:
[tex]\sf x^2 + 3x-4 \\\\Using \ mid \ term \ break \ formula\\\\x^2 + 4x-x -4\\\\x(x+4)-1(x+4)\\\\Using \ (x+4) \ common\\\\(x+4)(x-1)\\\\\rule[225]{225}{2}[/tex]
Hope this helped!
~AnonymousHelper1807The factory tires for your vehicle are P220/55R17 with circumference of 94.4086 inches. You have decided to purchase some used P265/65R17 with circumference of 96.0165
inches and have a friend install them for you. Since the calibration was not changed in your vehicle, when the speedometer reads 55 mph, how fast will you actually be
traveling?
Answer:
55.94 mph
Step-by-step explanation:
The speedometer is measuring the speed of the vehicle according to the initial configuration.
The number of the revolution, n, that the wheels made in 1 hour is
[tex]n=\frac {\text{Speed}}{\text{Perimeter of the wheel}}[/tex]
Let p and p' be the perimeter of the old and the new wheels respectively.
[tex]P=\pi\times 94.4086[/tex] inches,
[tex]P'=\pi\times 96.0165[/tex] inches.
Since the speedometer is not calibrated according to the new configuration, so, the perimeter of old wheel has been used for the calculation of indicated speed.
[tex]\Rightarrow n=\frac{\text{Speed}}{P}[/tex]
Actually, this number of revolutions in 1 hour is made with the new tires having perimeter P'.
So, the actual speed with new tires is
[tex]=n\times P'[/tex]
[tex]= \frac{\text{Speed}}{P}\times P'[/tex]
[tex]=\frac {55}{\pi\times 94.4086}\pi\times 96.0165[/tex]
[tex]=\frac {55} {94.4086}\times 96.0165[/tex]
[tex]=55.94[/tex] mph
So, the actual speed of traveling is 55.94 mph.
-8-x= x - 4x
Can u help me know the answer please and I need to show my work
Answer:
x= -4
Step-by-step explanation:
-8 -x= x -4x
Simplify:
[tex] - 8 - x = - 3x[/tex]
Bring all x terms to 1 side by adding x on both sides:
[tex] - 8 = - 3x + x[/tex]
Simplify:
[tex] - 8 = - 2x \\ - 2x = 8[/tex]
Divide both sides by -2:
[tex]x = \frac{8}{ - 2} \\ x = - 4[/tex]
Whats does x and y equal?
Answer:
ill help
Step-by-step explanation:
You make a tape of your friend's three favorite TV shows: a comedy, a drama and a reality
show. An episode of the comedy lasts 30 minutes, while an episode of the drama or the
reality show lasts 60 minutes. The tape can hold 360 minutes of programming. You
completely fill the tape with 7 episodes and include twice as many episodes of the drama as
the comedy. How many episodes of each show are on the tape?
Answer:
comedy = 2
drama = 4
reality = 1
Step-by-step explanation:
comedy = 30min
denote as "c"
drama = 60min
denote as "d"
reality = 60min
denote as "r"
write in English
(30min of c) + (60 min of d) + (60min of r) totals to 360 min
translate to mathematics
(30c) + (60d) + (60r) = 360
we also know that there is a total of seven episodes
so we can say
c + d + r = 7
and we also know that there are twice as many episodes of drama as there is of comedy so it can be said that
d = 2c
now there is a system of equations
30c + 60d + 60r = 360
c +d + r = 7
d = 2c
all we know have to do is simplify and solve
substitute in the second equation, into the first
c + d + r = 7
d = 2c
c + 2c + r = 7
simplify
3c + r = 7
r = 7 - 3c
substitute this into the first equation
d = 2c
r = 7 -3c
30c + 60d + 60r = 360
30c + 60(2c) + 60(7 - 3c) = 360
distribute
30c + 120c + 420 - 180c = 360
simplify
-30c + 420 = 360
-420 -420
-30c = -60
c = 2
substitute back into the other equations and solve
d = 2c
d = 2 *2
d = 4
r = 7 - 3c
r = 7 - 3 * 2
r = 7 -6
r = 1
The managing partner of an advertising agency believes that his company's sales are related to the industry sales. He uses Microsoft Excel's Data Analysis tool to analyze the last 4 years of quarterly data (i.e., n 16) with the following results:
Regression Statistics
Multiple R 0.802
R Square 0.643
Adjusted R Square 0.618
Standard Error SYX 0.9224
Observations 16
There is a moderately strong positive correlation between the company's sales and industry sales.
The statistical results from the regression analysis indicate that there is a multiple R value of 0.802. This value represents the correlation coefficient, which measures the strength and direction of the relationship between two variables. In this case, the correlation coefficient suggests a moderately strong positive correlation between the company's sales and industry sales. Additionally, the R-squared value is 0.643, which indicates that approximately 64.3% of the variability in the company's sales can be explained by the variability in industry sales. This suggests that industry sales have a significant influence on the company's sales performance. Furthermore, the adjusted R-squared value is 0.618, which takes into account the number of variables and observations in the regression analysis. It provides a more accurate measure of the model's goodness of fit. Finally, the standard error SYX is 0.9224, which represents the average distance between the actual company sales data and the predicted values based on the regression model. A lower standard error indicates a better fit of the model to the data. Overall, based on the given statistics, it can be concluded that there is a moderately strong positive correlation between the company's sales and industry sales, and industry sales significantly influence the company's sales performance.
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1. Mrs. Zappia has 24 Jolly Ranchers and 42 Tootsie Rolls. She wants to put them in bags to give to her students . What is the greatest amount of bags that mrs.Zappos can make ? How many jolly ranchers and tootosie rolls will be in each bag ?
Answer:
I would do 24÷42 =x
solve for x
x=1/75 so we simplify and we get 5
so each back will have 5
Solve each of the quadratic equations 3x=0.5x2
Answer:
[tex]3x = 1 \\ x = \frac{1}{3} [/tex]
a loan payment of $1000 was due 60 days ago and another payment of $1200 is due in 30 days. what's the single payment 90 days from now is required to pay off the two obligations if interest is to be 12% and agreed focal date is on 90 days from now?
Present value of Loan payment 1 = [tex]$1000 / (1 + (0.12/365))^{60[/tex]
Present value of Loan payment 2 = [tex]$1200 / (1 + (0.12/365))^{(-30)[/tex]
The single payment required 90 days from now to pay off the two obligations would be the total present value calculated in Step 3.
To calculate the single payment required to pay off the two obligations with a 12% interest rate, we can use the concept of present value. Present value is the current worth of a future payment, taking into account the interest rate and time.
Let's break down the given information:
Loan payment 1: $1000 due 60 days ago
Loan payment 2: $1200 due in 30 days
To find the single payment required 90 days from now, we need to calculate the present value of each payment and then add them together.
Step 1: Calculate the present value of Loan payment 1.
The time period for Loan payment 1 is 60 days ago.
To bring it to the present, we need to calculate the interest accrued for 60 days at a 12% annual interest rate.
Step 2: Calculate the present value of Loan payment 2.
The time period for Loan payment 2 is 30 days in the future.
To bring it to the present, we need to calculate the interest accrued for 30 days at a 12% annual interest rate.
Step 3: Add the present values of Loan payment 1 and Loan payment 2.
Total present value = Present value of Loan payment 1 + Present value of Loan payment 2
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When 8 is multiply by 2/3, the product is?
Answer:
8/3 or 5 1/3
Step-by-step explanation:
here's a visual tutorial I don't feel like writing, sorry
.True or False:
1. Sampling distribution of the means is a probability distribution consisting of all possible sample means of a given sample size selected from a population.
2. If the sampling distribution of the sample means approximates a normal distribution, then the population is normally distributed.
3. The mean of all possible sample means is equal to the population mean.
Answer:
1. True
2. False
3. True
Step-by-step explanation:
1. True: The sampling distribution of the means is a probability distribution that includes all possible sample means of a given sample size selected from a population. It provides information about the distribution of sample means.
2. False: The statement is incorrect. The approximation of the sampling distribution of the sample means to a normal distribution is a result of the Central Limit Theorem, which states that under certain conditions, the distribution of sample means tends to be approximately normal, regardless of the population distribution.
3. True: The mean of all possible sample means, often referred to as the expected value of the sampling distribution, is indeed equal to the population mean. This is another consequence of the Central Limit Theorem, which guarantees that the average of all possible sample means will be equal to the population mean.
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QUESTION 8 We will define a checkerboard matrix to be a square matrix A = (a,j), where dij 1 if i+j is even if i+j is odd 0 8.1 Write out the 4x4 checkerboard matrix. 8.2 Find the basis for the nullspace of A, and the nullity and rank of A. 8.3 What will be the rank and mullity of the 17x17 checkerboard matrix?
8.1. the matrix A can be written as:
A = [ 1 0 1 0 ]
[ 0 1 0 1 ]
[ 1 0 1 0 ]
[ 0 1 0 1 ]
8.2. The basis for the nullspace consists of two vectors, and the matrix has a rank of 2 and a nullity of 2.
8.3. For a 17x17 checkerboard matrix, the rank is 17 and the nullity is 0.
For an n x n checkerboard matrix, the pattern of 1s and 0s alternates along rows and columns, creating a checkerboard-like pattern.
In the case of a 4x4 checkerboard matrix, the matrix A can be written as:
A = [ 1 0 1 0 ]
[ 0 1 0 1 ]
[ 1 0 1 0 ]
[ 0 1 0 1 ]
To find the basis for the nullspace of A, we need to solve the homogeneous equation Ax = 0, where x is a column vector of unknowns. By row-reducing A, we can find that the reduced row-echelon form of A is:
[ 1 0 1 0 ]
[ 0 1 0 1 ]
[ 0 0 0 0 ]
[ 0 0 0 0 ]
From the reduced form, we can see that the columns corresponding to the pivot variables (the first two columns) form a basis for the nullspace. Therefore, the basis for the nullspace of A is:
[tex][ 1 0 0 0 ]^T[/tex]
[tex][ 0 1 0 0 ]^T[/tex]
The nullity of A, denoted as nullity(A), is the dimension of the nullspace. In this case, nullity(A) = 2.
The rank of A, denoted as rank(A), is the number of linearly independent columns in A. Since the first two columns are linearly independent, the rank(A) = 2.
For a checkerboard matrix of size 17x17, we can observe that the pattern will continue to alternate along rows and columns. Therefore, the rank of the 17x17 checkerboard matrix will be 17 (since all columns will be linearly independent), and the nullity will be 0 (since there will be no non-zero solutions to Ax = 0).
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if f(x)=4x-11,what is the value of f(5)
Answer:
9
Step-by-step explanation:
4*9-11= 36 -11 = 25
Answer:
f(5) = 9
Step-by-step explanation:
f(x) = 4x - 11
f(5) = 4(5) - 11
= 20 - 11
= 9
