The class boundaries are 0.5 - 3.5, 3.5 - 6.5, 6.5 - 9.5, 9.5 - 12.5, 12.5 - 15.5.
To find the class boundaries, we need to add and subtract 0.5 from the upper and lower limits of each class interval, respectively.
Using this formula, we get the following class boundaries:
Class Boundaries:
0.5 - 3.5, 3.5 - 6.5, 6.5 - 9.5, 9.5 - 12.5, 12.5 - 15.5
To construct the less than cumulative frequency table, we need to add up the frequencies of all the classes up to each class. For example:
Less than Cumulative Frequency Table:
Ages No. of Children Cumulative Frequency
1-3 10 10
4-6 12 22
7-9 15 37
10-12 13 50
13-15 9 59
To construct the greater than cumulative frequency table, we need to subtract the frequency of each class from the total frequency and then add the resulting values up to obtain the cumulative frequency. For example:
Greater than Cumulative Frequency Table:
Ages No. of Children Cumulative Frequency
13-15 9 59
10-12 13 50
7-9 15 37
4-6 12 22
1-3 10 10
Note that the last value of the greater than cumulative frequency table is always equal to the total frequency, which in this case is 59.
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Please help me :/
You can make a 6-digit security number using the digits 1-9 and digits cannot be repeated. Show all work and formulas used in computing your answers.
a) How many numbers can you make if there are no additional restrictions?
b) How many numbers can you make if the first digit cannot be a one?
c) How many odd numbers can you make (the last digit is odd?)
d) How many numbers greater than 300,000 can you make?
e) How many numbers greater than 750,000 can you make?
Sure, I'd be happy to help you with these questions!
a) To calculate the total number of possible 6-digit security numbers, we can use the permutation formula:
nPr = n! / (n-r)!
where n is the total number of digits available (9) and r is the number of digits we are selecting (6).
So, the number of possible 6-digit security numbers without any restrictions is:
9P6 = 9! / (9-6)! = 9! / 3! = 9 x 8 x 7 x 6 x 5 x 4 = 60,480
Therefore, there are 60,480 possible 6-digit security numbers that can be made with the digits 1-9 without repeating any digits.
b) If the first digit cannot be a one, we are left with 8 choices for the first digit (since we cannot use 1) and 8 choices for the second digit (since we have already used one digit). For the remaining 4 digits, we still have 7 choices for each digit, since we cannot repeat any digits.
Using the permutation formula again, the number of possible 6-digit security numbers with the first digit not being one is:
8 x 8 x 7 x 7 x 7 x 7 = 1,322,496
Therefore, there are 1,322,496 possible 6-digit security numbers that can be made with the digits 1-9 without repeating any digits, where the first digit is not one.
c) To create an odd number, the last digit must be an odd number, which means we have 5 choices for the last digit (1, 3, 5, 7, or 9). For the first digit, we cannot use 0 or 1, so we have 7 choices. For the remaining 4 digits, we still have 8 choices for each digit (since we can use any digit).
Using the permutation formula again, the number of possible 6-digit security numbers with the last digit being odd is:
7 x 8 x 8 x 8 x 8 x 5 = 7,1680
Therefore, there are 7,1680 possible 6-digit security numbers that can be made with the digits 1-9 without repeating any digits, where the last digit is odd.
d) To create a number greater than 300,000, the first digit must be 3, 4, 5, 6, 7, 8, or 9. If the first digit is 3, we have 7 choices for the first digit (3, 4, 5, 6, 7, 8, or 9). For the remaining 5 digits, we still have 8 choices for each digit.
If the first digit is not 3, we have 6 choices for the first digit (since we cannot use 1 or 2). For the remaining 5 digits, we still have 8 choices for each digit.
Using the permutation formula again, the number of possible 6-digit security numbers greater than 300,000 is:
7 x 8 x 8 x 8 x 8 x 8 + 6 x 8 x 8 x 8 x 8 x 8 = 2,526,720
Therefore, there are 2,526,720 possible 6-digit security numbers that can be made with the digits 1-9 without repeating any digits, where the number is greater than 300,000.
e) To create a number greater than 750,000, the first digit must be 8 or 9. If the first digit is 8, we have 2 choices for the first digit (8 or 9). For the remaining 5 digits, we still have 8 choices for each digit.
If the first digit is 9, we only have one choice for the first digit (9). For the remaining 5 digits, we still have 8 choices for each digit.
Using the permutation formula again, the number of possible 6-digit security numbers greater than 750,000 is:
2 x 8 x 8 x 8 x 8 x 8 + 1 x 8 x 8 x 8 x 8 x 8 = 262,144
Therefore, there are 262,144 possible 6-digit security numbers that can be made with the digits 1-9 without repeating any digits, where the number is greater than 750,000.
Consider the following planes. 5x - 3y + z = 2, 3x + y - 5z = 4 Find parametric equations for the line of intersection of the planes. (Use the parameter t.) (x(t), y(t), z(t)) = Find the angle between the planes. (Round your answer to one decimal place.)
the cross product of the normal vectors of the planes will give you the direction vector of the line.
(5,−3,1)×(3,1,−5)=(14,28,14)
Which we can scale down to (1,2,1)
Now we need a point on the line. By inspection we can see that (1,1,0) lies in both planes.
Sometimes it it not that easy. But it is usually pretty easy to find a point in at least one plane and then travel along some line in that plane until we intersect the line in question.
Vector form of the line L:(x,y,z)=(1,2,1)t+(1,1,0)
In parametric form x=t+1,y=2t+1,z=t
The parametric equations are (x(t), y(t), z(t)) = (17/34 + 11t/34, 22/34 - 5t/34, 57/34 + 7t/34), where t is a parameter. The angle between the planes is 93.7 degrees.
To find the line of intersection of the planes, we can set the two equations equal to each other and solve for x, y, and z in terms of a parameter t. We can begin by eliminating one variable, say z.
From the first equation, we have z = 2 - 5x + 3y, and substituting this into the second equation gives 3x + y - 5(2 - 5x + 3y) = 4. Simplifying this equation, we get 22x - 14y - 23 = 0. Solving for y in terms of x, we get y = (22/14)x - (23/14).
Substituting this into the first equation and solving for z, we get z = (17/14)x + (57/14). Therefore, we have x = (17/22) + (11/22)t, y = (22/14) - (5/14)t, and z = (17/14)x + (57/14) + (7/22)t. These are the parametric equations for the line of intersection of the planes.
To find the angle between the planes, we can find the angle between their normal vectors.
The normal vector to the plane 5x - 3y + z = 2 is (5, -3, 1), and the normal vector to the plane 3x + y - 5z = 4 is (3, 1, -5). Using the dot product formula, we have cosθ = (5)(3) + (-3)(1) + (1)(-5) / sqrt(5² + (-3)² + 1²) sqrt(3² + 1² + (-5)²), which simplifies to cosθ = -19/34.
Taking the inverse cosine of this value, we get θ = 93.7 degrees, rounded to one decimal place. Therefore, the angle between the planes is approximately 93.7 degrees.
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the height and age of each child in a random sample of children was recorded. the value of the correlation coefficient between height and age for the children in the sample was 0.8 . based on the least-squares regression line created from the data to predict the height of a child based on age, which of the following is a correct statement? responses on average, the height of a child is 80% of the age of the child. on average, the height of a child is 80% of the age of the child. the least-squares regression line of height versus age will have a slope of 0.8 . the least-squares regression line of height versus age will have a slope of 0.8 . the proportion of the variation in height that is explained by a regression on age is 0.64 . the proportion of the variation in height that is explained by a regression on age is 0.64 . the least-squares regression line will correctly predict height based on age 80% of the time. the least-squares regression line will correctly predict height based on age 80% of the time. the least-squares regression line will correctly predict height based on age 64% of the time.
The least-squares regression line of height versus age will have a slope of 0.8 . Was true statement option (2)
The correlation coefficient (r) measures the strength and direction of a linear relationship between two variables, in this case, height and age. A correlation coefficient of 0.8 indicates a strong positive linear relationship between height and age. The slope of the least-squares regression line represents the change in the height of a child for each one-unit increase in age.
Therefore, a slope of 0.8 indicates that for each one-year increase in age, the expected increase in height is 0.8 units. The other options are not correct or relevant based on the given information.
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Full Question: the height and age of each child in a random sample of children was recorded. the value of the correlation coefficient between height and age for the children in the sample was 0.8 . based on the least-squares regression line created from the data to predict the height of a child based on age, which of the following is a correct statement?
responses on average,
the height of a child is 80% of the age of the child. on average, the height of a child is 80% of the age of the child. the least-squares regression line of height versus age will have a slope of 0.8 . the least-squares regression line of height versus age will have a slope of 0.8 . the proportion of the variation in height that is explained by a regression on age is 0.64 . the proportion of the variation in height that is explained by a regression on age is 0.64 .PLEASE HELP WILL MARK BRANLIEST!!!
The number of bracelets that can be made using all the colors one time only is 720.
Given that Diana is making bracelet with 6 different colors we need to find the number of bracelets that can be made using all the colors one time only,
Since there are 6 beads so, the number of bracelets can be made = 6!
= 720
Hence the number of bracelets that can be made using all the colors one time only is 720.
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One measure of student success for colleges and universities is the percent of admitted students who graduate. Studies indicate that a key issue in retaining students is their performance in so-called gateway courses. These are courses that serve as prerequisites for other key courses that are essential for student success. One measure of student performance in these courses is the DFW rate, the percent of students who receive grades of D, F, or W (withdraw). A major project was undertaken to improve the DFW rate in a gateway course at a large midwestern university. The course curriculum was revised to make it more relevant to the majors of the students taking the course, a small group of excellent teachers taught the course, technology (including clickers and online homework) was introduced, and student support outside the classroom was increased. The following table gives data on the DFW rates for the course over three years. In Year 1, the traditional course was given; in Year 2, a few changes were introduced; and in Year 3, the course was substantially revised.
Year DFW Rate Number of Students Taking Course
Year 1 42. 1% 2408
Year 2 24. 3% 2325
Year 3 19. 4% 2126
1. Do you think that the changes in this gateway course had an impact on the DFW rate? (Use α = 0. 1. )
2. State the null and alternative hypotheses.
3. State the Ï2 statistic, degrees of freedom, and the P-value.
Yes. The null hypothesis is that the changes in the course did not have a significant impact on the DFW rate. The chi-squared statistic is 44.63, with 2 degrees of freedom, and the p-value is less than 0.001.
1. Yes, it is likely that the changes in the gateway course had an impact on the DFW rate, as the rate decreased from 42.1% in Year 1 to 19.4% in Year 3.
2. The null hypothesis is that the changes in the course did not have a significant impact on the DFW rate, while the alternative hypothesis is that the changes did have a significant impact on the rate.
3. The chi-squared statistic is 44.63, with 2 degrees of freedom, and the p-value is less than 0.001. This indicates that there is a significant relationship between the year the course was given and the DFW rate, providing evidence to reject the null hypothesis in favor of the alternative hypothesis that the changes made to the course had a significant impact on the DFW rate.
The p-value of less than 0.001 indicates strong evidence against the null hypothesis, as it is less than the significance level of 0.1.
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πα d Find dx f-'(4) where f(x) = 4 + 2x3 + sin (*) for –1 5151. = 2
After plugging the derivatives of f(x) we get, dx f-'(4) = f'(√(2/3)) = 4 + cos(Ф)
To find dx f-'(4), we need to take the derivative of f(x) and then solve for x when f'(x) equals 4.
First, let's find the derivative of f(x):
f'(x) = 6x² + cos(Ф)
Next, we need to solve for x when f'(x) equals 4:
6x² + cos(Ф) = 4
cos(Ф) = 4 - 6x²
Now, we can use the given value of πα d to solve for x:
πα d = -1/2
α = -1/2πd
α = -1/2π(-1)
α = 1/2π
d = -1/2πα
d = -1/2π(1/2π)
d = -1/4
So, we have:
cos(Ф) = 4 - 6x²
cos(πα d) = 4 - 6x² (substituting in the given value of πα d)
cos(-π/2) = 4 - 6x² (evaluating cos(πα d))
0 = 4 - 6x²
6x² = 4
x² = 2/3
x = ±√(2/3)
Since we're looking for the derivative at x = 4, we can only use the positive root:
x = √(2/3)
Now, we can plug this value of x back into the derivative of f(x) to find dx f-'(4):
f'(√(2/3)) = 6(√(2/3))² + cos(Ф)
f'(√(2/3)) = 4 + cos(Ф)
dx f-'(4) = f'(√(2/3)) = 4 + cos(Ф)
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Write the algebraic expression that matches each graph.
Graph inserted below via image.
Answer: 7
Step-by-step explanation:
Answer:
y=|x-2|-2
Step-by-step explanation:
Go onto desmos and you can ask it to graph an equation to test your answers.
Stephanie took her family out to Texas Roadhouse and is getting ready to pay the dinner bill. The bill is $57. 50. If she plans on leaving an 18% tip, what is the total dinner cost?
To calculate the total dinner cost, we need to add the bill amount to the tip amount.
The tip amount is 18% of the bill amount:
Tip = 0.18 x $57.50 = $10.35
Therefore, the total dinner cost is:
Total Cost = Bill Amount + Tip Amount
Total Cost = $57.50 + $10.35
Total Cost = $67.85
So, the total dinner cost including the 18% tip is $67.85.
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9) The profit from a business is described by the function P(x) = -3x² + 12x + 75, where xis the number of items made, in thousands, and P(x) is the profit in dollars. How many items will maximize the profit? А 1,000 4,000 B 2. 000 D 6,000
The number of items that will maximize the profit is 2000. Thus, the correct answer is option c.
To calculate the maximum profit that can be earned we have to differentiate the equation and find the value of x
dP/dx = 1/dx (-3x² + 12x + 75)
= -6x + 12
Calculating dP/dx = 0
0 = -6x + 12
6x = 12
x = 2
Next, we calculate the next differential of the equation:
It comes out to be -6
Since it is smaller than zero, the value of x calculated is the maxima.
The maxima = 2
Thus, the item that will maximize the profit comes out to be 2000 as x is the number of items made in thousand.
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Find the exact values of sin 2u, cos2u, and tan2u using the double-angle formulas cot u= square root 2, pi < u < 3pi/2
sin 2u = -1/2, cos 2u = -1/2, tan 2u = 1, because cot u = sqrt(2) and the range of u is between pi and 3pi/2.
How to find the trigonometric function?
Given cot u = sqrt(2) and the range of trigonometric of u, we can determine the values of sine, cosine, and tangent of 2u using the double-angle formulas. First, we can find the value of cot u by using the fact that cot u = 1/tan u, which gives us tan u = 1/sqrt(2). Since u is in the third quadrant (i.e., between pi and 3pi/2), sine is negative and cosine is negative.
Using the double-angle formulas, we can express sin 2u and cos 2u in terms of sin u and cos u as follows:
sin 2u = 2sin u cos u
cos 2u =[tex]cos^2[/tex] u - [tex]sin^2[/tex] u
Substituting the values of sine and cosine of u, we get:
sin 2u = 2*(-sqrt(2)/2)*(-sqrt(2)/2) = -1/2
cos 2u = (-sqrt(2)/2[tex])^2[/tex] - (-1/2[tex])^2[/tex] = -1/2
To find the value of tangent of 2u, we can use the identity:
tan 2u = (2tan u)/(1-[tex]tan^2[/tex] u)
Substituting the value of tan u, we get:
tan 2u = (2*(1/sqrt(2)))/(1 - (1/sqrt(2)[tex])^2[/tex]) = 1
Therefore, sin 2u = -1/2, cos 2u = -1/2, and tan 2u = 1.
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THE ANSWER IS NOT 81!!!
The measures of the angles of a triangle are shown in the figure below solve for X
Which values from the set {-8, -6, -4, -1, 0, 2} satisfy this inequality? -1/2x + 5>7
The values that satisfy the inequality -1/2x + 5>7 are -8 and -6.
To determine which values from the set {-8, -6, -4, -1, 0, 2} satisfy the inequality -1/2x + 5 > 7, we first need to isolate the variable x. Start by subtracting 5 from both sides of the inequality:
-1/2x > 2
Now, multiply both sides by -2 to solve for x. Remember that when you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality sign:
x < -4
Now we can see that the inequality is asking for all values of x that are less than -4. Looking at the given set {-8, -6, -4, -1, 0, 2}, we can identify the values that satisfy this condition:
-8 and -6 are the values that are less than -4.
Therefore, the values from the set {-8, -6, -4, -1, 0, 2} that satisfy the inequality -1/2x + 5 > 7 are -8 and -6.
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help I want to get this done
Answer:
j: 0, m: (-4)
Step-by-step explanation:
RECALL:
Rational function is the func. expressed by polynomials p(x) and q(x) as:
p(x)/q(x) where q(x) is non-zero
j(m+4) must be non zero, or
j(m+4)≠0
j≠0 and m+4≠0
j≠0 and m≠(-4)
Suppose the surface area for a can having a particular volume is minimized when the height of the can is equal to 22 cm. If the surface area has been minimized, what would you expect the radius of the can to be? (Round your answer to the nearest tenth if
necessary. You do not need to include the unit.)
If the surface area of a can with a particular volume is minimized when the height of the can is 22 cm, we would expect the radius of the can to be the same as the height, given that a cylinder has the smallest surface area when its height and radius are equal.
The surface area of a can with height h and radius r can be given by the formula:
A = 2πr² + 2πrh
The volume of the can is given by:
V = πr²h
If we differentiate the surface area with respect to r and equate it to zero to find the critical point, we get:
dA/dr = 4πr + 2πh(dr/dr) = 0
Simplifying this expression, we get:
2r + h = 0
Since we know that the height of the can is 22 cm, we can substitute h = 22 in the equation to get:
2r + 22 = 0
Solving for r, we get:
r = -11
Since the radius of the can cannot be negative, we discard this solution. Therefore, the radius of the can should be equal to its height, which is 22 cm.
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Please hurry I need it asap
Answer:
13 units
Step-by-step explanation:
To find the distance between the two points, use the distance formula.
[tex]\sqrt{(x-x)^{2}+(y-y)^{2} }[/tex]
Plug in the point values.
[tex]\sqrt{(-8--3)^{2}+(-6-6)^{2} }[/tex]
Simplify the parenthesis.
[tex]\sqrt{(5)^2+(-12)^2}[/tex]
Get rid of the parenthesis.
[tex]\sqrt{25+144}[/tex]
Simplify.
[tex]\sqrt{169}[/tex]
Solve.
13 units
What is the probability of drawing the Ace of Diamonds from a deck of cards, putting it back in the deck, shuffling the deck, and then drawing the Ace of Clubs?
The probability of the event of having ace of diamonds and ace of clubs is 1/2704
What is the probability?A probability event can be defined as a set of outcomes of an experiment. In other words, an event in probability is the subset of the respective sample space.
In a standard deck of cards, we have 52 cards of which 4 are aces. The probability of drawing the first ace of diamonds will be 1/52. Shuffling the card again, the probability of drawing having an ace of club will be another 1/52 since the card was replaced and shuffled.
To determine the probability of the two events occurring will be
P = (1/52 * 1/52) = 1 / 2704 = 0.0003698
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MATH HELPPP ASAPP !! NEEDA PASS BY 8 AM TOMORROW
The lateral surface area of the rectangular prism is given as follows:
L = 60 cm².
How to calculate the lateral surface area?The lateral surface area of a rectangular prism of length l, width w and height h is given by the equation presented as follows:
L = 2 ( l + w ) h
The dimensions for this problem are given as follows:
l = 3 cm, w = 2 cm and h = 6 cm.
Hence the lateral surface area of the rectangular prism is given as follows:
L = 2 x (2 + 3) x 6
L = 60 cm².
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Simplify the following using appropriate properties :
(a) [1/2 x 1/4 ]+[1/2 x6]
(b) [1/5 x 2/15] - [1/5 x 2/15]
I need step by step explanation please will mark as brainliest if you give good explanation
Step-by-step explanation:
(a) [1/2 x 1/4] + [1/2 x 6]
First, we can simplify each term separately:
1/2 x 1/4 = 1/8
1/2 x 6 = 3
Now, we can add these two simplified terms:
1/8 + 3 = 3 1/8
Therefore, [1/2 x 1/4] + [1/2 x 6] simplifies to 3 1/8.
(b) [1/5 x 2/15] - [1/5 x 2/15]
Both terms are the same, so when we subtract them, the result will be zero:
[1/5 x 2/15] - [1/5 x 2/15] = 0
Therefore, [1/5 x 2/15] - [1/5 x 2/15] simplifies to 0.
Find the points on the curve y - 2x - 4x2 - 11 at which the tangent is parallel to the line = 8x - 3.
The point on the curve y = -4x² - 2x - 11 where the tangent is parallel to the line 8x - 3 is (-1, -13).
To find the points on the curve where the tangent is parallel to the line, we need to find where the derivative of the curve is equal to the slope of the line.
The given curve is: y = -4x² - 2x - 11
The derivative of this curve is: y' = -8x - 2
The slope of the given line is: 8
We want to find the points where the derivative of the curve is equal to the slope of the line:
-8x - 2 = 8
Solving for x, we get:
x = -1
Now, we can plug this value of x back into the original equation to find the corresponding value of y:
y = -4(-1)² - 2(-1) - 11
y = -13
Therefore, the point on the curve where the tangent is parallel to the line 8x - 3 is (-1, -13).
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In 2016, Dave bought a new car for $15,500. The current value of the car is $8,400. At what annual rate did the car depreciate in value? Express your answer as a percent (round to two digits between decimal and percent sign such as **. **%). Use the formula A(t)=P(1±r)t
The car depreciated at an annual rate of approximately 45.81%.
In 2016, Dave bought a new car for $15,500, and its current value is $8,400. To find the annual depreciation rate, we'll use the formula A(t) = P(1 ± r)t, where A(t) is the future value, P is the initial value, r is the annual rate, and t is the time in years.
Here, A(t) = $8,400, P = $15,500, and t = 1 (one year). We are solving for r, the annual depreciation rate.
$8,400 = $15,500(1 - r)¹
To isolate r, we'll first divide both sides by $15,500:
$8,400/$15,500 = (1 - r)
0.541935 = 1 - r
Now, subtract 1 from both sides:
-0.458065 = -r
Finally, multiply both sides by -1 to find r:
0.458065 = r
To express r as a percentage, multiply by 100:
0.458065 x 100 = 45.81%
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The car depreciated at an annual rate of 12.2%.
How to find depreciated value of car?The car depreciated in value over time, so we want to find the rate of decrease. We can use the formula:
A(t) = P(1 - r)t
where A(t) is the current value of the car, P is the original price of the car, r is the annual rate of depreciation, and t is the time elapsed in years.
We can plug in the given values and solve for r:
$8,400 = $15,500(1 - r)⁵
Dividing both sides by $15,500, we get:
0.54 = (1 - r)⁵
Taking the fifth root of both sides, we get:
(1 - r) = 0.878
Subtracting 1 from both sides, we get:
-r = -0.122
Dividing both sides by -1, we get:
r = 0.122
Multiplying by 100 to express as a percentage, we get:
r = 12.2%
Therefore, the car depreciated at an annual rate of 12.2%.
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Can you guys help me on this algebra work? thankscompare b(x) = 6x^2 to f(x)compare m(x) = -1/3x^2 - 4
b(x) = 6x² and m(x) = -1/3x²- 4 have similarities and differences as quadratic functions with different coefficients and signs.
How do b(x) and m(x) compare?We can look at the similarities and differences to compare b(x) = 6x² and m(x) = -1/3x² - 4
Similarities:Both b(x) and m(x) are quadratic functions, which means they have an x² term.
They both have a constant term, with b(x) having a constant of 0 and m(x) having a constant of -4.
Differences:The coefficients of the x² term are different: b(x) has a coefficient of 6, while m(x) has a coefficient of -1/3.
The signs of the coefficients are different: b(x) has a positive coefficient, while m(x) has a negative coefficient.
Overall, b(x) and m(x) have some similarities in their form as quadratic functions, but their coefficients and signs are different, which means they will have different shapes and behaviors.
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The value of y varies directly with x. which function represents the relationship between x and y if y = 18/5 when x = 24
The function that represents the relationship between x and y is y = 3/20 x
Since y varies directly with x, we can write the relationship between x and y as
y = kx
where k is the constant of proportionality.
y = 18/5 when x = 24
Substituting these values into the equation, we get:
18/5 = k(24)
Simplifying this equation, we get:
k = (18/5) / 24
k = (18/5 × 24)
k = 18/120
We can simplify this expression to:
k = 3/20
Therefore, the function that represents the relationship between x and y is y = 3/20 x
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Polina is designing a new sandbox for her local playground. Polina knows she needs `1894` cubic inches of sand to fill the sandbox up `10` inches. If Polina wanted to fill the sandbox up `3` more inches to the top, how much more sand would she need?
Answer:
568.2 in
Step-by-step explanation:
To find this we first have to divide 1894/10 then we get 189.4 which we multiply by 3 to find how much more sand we need.
Which expression is equivalent to 1/4(8 - 6x + 12)?
The expression that is equivalent to 1/4(8 - 6x + 12) is 2 - 3x/2 + 6
What are algebraic expressions?
Algebraic expressions are simply defined as those mathematical expressions that are composed of terms, variables, their coefficients, their factors and constants.
These mathematical expressions are also comprised of arithmetic operations.
These operations are listed thus;
BracketParenthesesAdditionSubtractionMultiplicationDivisionFrom the information given, we have that;
1/4(8 - 6x + 12)
expand the bracket, we have;
8 - 6x + 12/4
Divide in group, we have;
8/4 - 6x/4 + 12/4
Divide the values
2 - 3x/2 + 6
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pls help me with this question quick
If the eastbound train travels at 75 miles per hour, it will take the two trains 2.8 hours to be 476 miles apart.
To solve the problem, we can use the formula:
distance = rate × time
Let's call the time it takes for the two trains to be 476 miles apart "t".
The westbound train travels at a rate of 95 miles per hour, so in time "t" it will travel a distance of 95t miles. Similarly, the eastbound train travels at a rate of 75 miles per hour, so in time "t" it will travel a distance of 75t miles.
To find the total distance between the two trains after time "t", we add the distances traveled by each train:
95t + 75t = 476
Combining like terms and solving for "t", we get:
170t = 476
t = 2.8 hours
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A regular hexagon is shown. What is the measure of the radius, c, rounded to the nearest inch? use the appropriate trigonometric ratio to solve. 6 in. 10 in. 14 in. 24 in.
The measure of the radius of the hexagon rounded to the nearest inch is 14 inches.
The problem presents a hexagon with a central angle of 60º, and the task is to calculate its radius. To do so, we can use the trigonometric relationship between the radius, apothem, and an angle. The apothem is a line segment from the center of a polygon perpendicular to one of its sides. For a regular hexagon, the apothem length is equal to the radius, which we want to find.
The trigonometric relationship for this case is cos(30) = a/c, where a is the apothem and c is the radius. By rearranging the equation to solve for c, we get c = a/cos(30).
Substituting the value of 12 inches for the apothem, we get c = 12/cos(30). Using a calculator, we can find that cos(30) = 0.866, so c = 12/0.866 = 13.855 inches.
To round to the nearest whole number, we get c = 14 inches.
Correct Question :
A regular hexagon is shown. What is the measure of the radius, c, rounded to the nearest inch? use the appropriate trigonometric ratio to solve. 6 in. 10 in. 14 in. 24 in.
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6. Which of the following equations would have no
solution?
F. 13 - 7x = -7x + 13
G.1/3(6x + 9) = 12
H. 1/4(8x + 4) = 2x - 4
J. -10x + 5 = 3 - 10x + 2
Answer: F, H, and J all have no real solution. The only equation that has a solution is
Step-by-step explanation: Use foil method.
Please help with the 2nd one
Answer:
Step-by-step explanation:
1807
You are setting the combination on a three-digit lock. You want to use the numbers 123 but you don't care what order they are in.
6 different permutations using the number 1 , 2 , 3 can be masde for the lock .
Given,
1 , 2 , 3 numbers to be used for a three digit lock .
There are 3 options for the first digit, 2 options for the second digit, and 1 option for the third digit.
To find the total number of permutations, we can use the formula for permutations:
Permutations of n items taken r at a time, which is n!/(n-r)!.
Here,
In this case,
n is 3
r is 3,
So the total number of permutations is 3!/(3-3)! = 3! = 3 x 2 x 1 = 6.
Hence,
So, you can make 6 different permutations using the numbers 1, 2 and 3 in any order.
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Scientists estimate that the mass of the sun is 1. 9891 x 10 kg. How many zeros are in this
number when it is written in standard notation?
A 26
B 30
C 35
D 25
There are 26 zeros in this number when it is written in standard notation. The correct answer is option (A). The mass of the sun is estimated to be 1.9891 x 10³⁰kg. To determine the number of zeros in this number when written in standard notation, we need to first convert it to standard form.
In standard form, the number is expressed as a decimal between 1 and 10 multiplied by a power of 10. To convert the given number to standard form, we move the decimal point 30 places to the right because the exponent is positive 30. This gives us 1989100000000000000000000000000. As we can see, there are 27 digits in this number. Therefore, there are 27-1=26 zeros in this number when it is written in standard notation.
In conclusion, the answer is A, 26. This type of question is commonly asked in science and engineering, where large or small numbers are expressed in scientific notation for convenience. Understanding how to convert between scientific notation and standard form is important for anyone studying or working in these fields.
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