Based on the given information, Trey can fit 160 plastic cubes inside the box.
What is volume of cube?
The volume of a cube is calculated by cubing the length of any one side of the cube. In other words, if a cube has sides of length "s", then its volume "V" is V = s³
To calculate the number of plastic cubes that can fit inside the box, we need to first calculate the volume of the box and the volume of each plastic cube. Then, we can divide the volume of the box by the volume of each plastic cube to get the total number of cubes that can fit inside.
The volume of the box is:
4 ft x 2.5 ft x 2 ft = 20 cubic feet
The volume of each plastic cube is:
(1/2 ft) x (1/2 ft) x (1/2 ft) = 1/8 cubic feet
To find out how many plastic cubes can fit inside the box, we can divide the volume of the box by the volume of each plastic cube:
20 cubic feet ÷ (1/8 cubic feet) = 160
Therefore, Trey can fit 160 plastic cubes inside the box.
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Is 2 x5/8 the same of 10 x1/8
Answer:
Step-by-step explanation:
[tex]2\times \frac{5}{8} = \frac{2}{1} \times\frac{5}{8}= \frac{10}{8}[/tex]
[tex]10\times \frac{1}{8} =\frac{10}{1} \times \frac{1}{8}= \frac{10}{8}[/tex]
So yes they are the same.
The acceleration, in feet per second per second, of an object is given by the acceleration function a(t)=2sint+1. The initial velocity is v(0)=0 and the initial position is s(0)=3. Find the equation of the velocity function. Find the position function and the average value of the position function from time t = 2 seconds to t = 5 seconds. Show all your work.
Help pls
Using the derivative of the velocity, the average value of the position function from t = 2 seconds to t = 5 seconds is 14.5.
What is the position and average value of the position function from t = 2 to t = 5?Given:
Acceleration function, a(t) = 2sin(t) + 1
Initial velocity, v(0) = 0
Initial position, s(0) = 3
To find:
Velocity function, v(t)
Position function, s(t)
Average value of the position function from t = 2 seconds to t = 5 seconds
Solution:
We know that acceleration is the derivative of velocity, and velocity is the derivative of position. So we can find the velocity and position functions by integrating the acceleration function.
Velocity function:
[tex]v(t) = \int a(t) dt\\v(t) = \int (2sin(t) + 1) dt\\v(t) = -2cos(t) + t + C1[/tex]
We know that the initial velocity, v(0) = 0. Substituting this value in the above equation, we get:
[tex]0 = -2cos(0) + 0 + C1\\C1 = 2[/tex]
Therefore, the velocity function is:
[tex]v(t) = -2cos(t) + t + 2[/tex]
Position function:
[tex]s(t) = \int v(t) dt\\s(t) = \int (-2cos(t) + t + 2) dt\\s(t) = 2sin(t) + \frac{1}{2} t^2 + 2t + C2[/tex]
We know that the initial position, s(0) = 3. Substituting this value in the above equation, we get:
[tex]3 = 2sin(0) + 0 + 0 + C2\\C2 = 3\\[/tex]
Therefore, the position function is:
[tex]s(t) = 2sin(t) + \frac{1}{2} t^2 + 2t + 3[/tex]
Average value of the position function from t = 2 seconds to t = 5 seconds:
We can find the average value of the position function using the following formula:
[tex]Avg = (1/(b-a)) * \int(a,b) f(t) dt[/tex]
Here, a = 2 and b = 5. So, substituting the values in the above formula, we get:
[tex]Avg = (1/(5-2)) * \int(2,5) (2sin(t) + \frac{1}{2} t^2 + 2t + 3) dt\\Avg = \frac{1}{3} * [ -2cos(t) + 1/6 t^3 + t^2 + 2t ] \eval(2,5)\\[/tex]
[tex]Avg = \frac{1}{3} * [ (-2cos(5) + 1/6 (5^3) + 5^2 + 25) - (-2cos(2) + 1/6 (2^3) + 2^2 + 22) ]\\Avg = 14.5[/tex]
Therefore, the average value of the position function from t = 2 seconds to t = 5 seconds is 14.5.
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Please see the attached
A restaurant borrows $15,700 for two months from a nearby bank. For this loan, the neighbourhood bank charges simple interest at a yearly rate of 10%. Suppose a month is one-twelfth of a year.
a) $218.06 in interest will be due after two months.
b) In the event that the restaurant doesn't pay, the balance due after two months is $15,918.06.
a) To find the interest that will be owed after 2 months, we first need to calculate the monthly interest rate:
r = (10%)/12 = 0.00833333...
We can use the formula for simple interest to find the interest owed:
I = Prt
where P is the principal (the amount borrowed), r is the interest rate per period, and t is the time in periods. Since the loan is for 2 months, we have t = 2/12 = 1/6 years.
Substituting the values, we get:
I = 15700 * 0.00833333... * (1/6) = 218.0555...
Rounding to the nearest cent, the interest owed after 2 months is $218.06.
b) The total amount owed after 2 months is the sum of the principal and the interest. Using the same values as above, we have:
The total amount owed = Principal + Interest
= 15700 + 218.0555...
= 15918.0555...
Rounding to the nearest cent, the amount owed after 2 months is $15,918.06.
The complete question is:-
A restaurant borrows $15700 from a local bank for 2 months. the local bank charges simple interest at an annual rate of 10% for this loan. assume each month is 1/12 of a year. answer each below. do not round any intermediate computations, and round your final answers to the nearest cent, if necessary, refer to the lists of financial formulas.
a) find the interest that will be owed after 2 months.
b) assuming the restaurant doesn't make any payments, find the amount owed after 2 months.
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The ratio of monthly income to the monthly saving of a family is 9:2. If the
saving is Rs 4,320, find the income and expenditure of the family.
Step-by-step explanation:
Let's assume that the monthly income of the family is x.
From the problem statement, we know that the ratio of monthly income to the monthly saving is 9:2.
Therefore, we can write:
x/4320 = 9/2
To solve for x, we can cross-multiply:
2x = 9*4320
2x = 38,880
x = 19,440
So, the monthly income of the family is Rs 19,440.
To find the monthly expenditure, we can subtract the monthly savings from the monthly income:
Monthly expenditure = Monthly income - Monthly saving
Monthly expenditure = 19,440 - 4,320
Monthly expenditure = 15,120
Therefore, the monthly expenditure of the family is Rs 15,120
Seven different single-digit numbers are written in the circles of the diagram shown with one number in each circle. The product of the three numbers in each of the three lines of three numbers is the same. Which number is written in the circle containing the question mark?
Answer:
Without an image or a more detailed description of the diagram, it's difficult to provide an exact answer to this problem. However, we can use some logical reasoning to try to solve it.
Let's assume that the three lines of three numbers are arranged in a Tic-Tac-Toe grid, like this:
CSS
Copy code
A B C
D E F
G H I
We know that the product of the three numbers in each line is the same. Let's call this product "P". Then we can write:
CSS
Copy code
A * B * C = P
D * E * F = P
G * H * I = P
If we divide the second equation by the first equation, we get:
CSS
Copy code
(D * E * F) / (A * B * C) = 1
Since all the numbers are single-digit, this means that either D or F is equal to A, B, C, or 1. If D or F is equal to 1, then E is also equal to 1, which means that the entire middle row is filled with 1s, and that cannot be the case since all the numbers are different.
Therefore, we can assume that either D or F is equal to one of the numbers in the top row. Without further information, we cannot determine which one it is, but we know that the product of the numbers in the bottom row must be divisible by the product of the numbers in the top row. This means that the number in the circle containing the question mark must be a factor of this product, and it must be different from all the other numbers in the diagram.
Again, without more information, we cannot determine the exact number in the circle containing the question mark, but this logic should help narrow down the possibilities.
Step-by-step explanation:
Riley is dividing a batch of 7 1/2 cups of salsa into equal servings that are 3/4 cup each. Select all of the expressions that can be used to find the number of servings Riley will have.
Thus, from the all given expressions, the number of servings Riley will ve using is 15/2 ÷ 3/4.
Explain about the mixed fraction?Once kids have a firm grasp on proper fractions, they are introduced to mixed numbers and incorrect fractions. A mixed number combines an integer (whole number) and a fraction. It is also sometimes referred to as a mixed fraction (part of a whole number).
The composite number's fractional component needs to be a legal fraction (less than one whole). The numerator (top number) of a correct fraction is less than its denominator (bottom number),
Given data:
Total batch of cup of salsa = 7 1/2Serving cup size = 3/4 each cupConvert the mixed fraction 7 1/2 in the proper fraction:
= 7 1/2
= (7*2 + 1)/2
= 15/2
Number of serving cups = Total amount of salsa / Serving cup size
Number of serving cups = 15/2 ÷ 3/4
Thus, from the all given expressions, the number of servings Riley will ve using is 15/2 ÷ 3/4.
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Complete question:
Riley is dividing a batch of 7 1/2 cups of salsa into equal servings that are 3/4 cup each. Select all of the expressions that can be used to find the number of servings Riley will have.
2/15 ÷ 3/415/2 ÷ 3/42/15 ÷ 4/515/2 ÷ 4/315/2 ÷ 3/4In a recent year and author wrote 191 check, use the poisson distribution to find the probability that on a random select today he wrote at least one check
The probability that on a random select today he wrote at least one check is 0.407
How to solveLet X be the no.of checks the author wrote in a day
Average,
u = 191 checks per year
191/365
= 0.5233/ day
X~Poisson ( u- 0.5233)
The p.m.f of X is given by
P(X=x) =
The probability that, on a randomly selected day, he wrote at least one check = P(
= 1 - P( X < 1)
= 1 - P(X=0)
= 1 - e^-0.5233 x 0.5233^0/0!
= 1 - e^-0.5233 x 1/
= 1 - 0.59256
= 0.407
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Can you solve this question?
A) f'(x)=?
B) slope at x=2: ?
slope at x=3: ?
C) tangent line at x=2: y= ?
tangent line at x=3: y= ?
D) value(s) of x=?
A. The derivative of f'(x) = 26x + 5is 26x + 5
B. Slope at x = 2 is 57
Slope at x = 3 is 83
c. The equation of the tangent line at x = 3 is y - 122 = 83(x - 3), or y = 83x - 179.
D. The value of x where the tangent line is horizontal is x = -5/26.
How to calculate the value(A) f'(x) = 26x + 5.
It should be noted that to find the derivative of f(x), we apply the power rule and the constant multiple rule:
f'(x) = d/dx (13x²+5x)
= d/dx (13x²) + d/dx (5x)
= 26x + 5
(B) ain this case, to find the slope of the graph of f(x) at x = 2 and x = 3, we plug these values into the derivative:
Slope at x = 2: f'(2) = 26(2) + 5 = 57
Slope at x = 3: f'(3) = 26(3) + 5 = 83
(C) Based on the information, to find the equation for the tangent line at x = 2 and x = 3, we use the point-slope form of a line:
Tangent line at x = 2:
We know the slope is 57, and the point (2, f(2)) is on the line.
Plugging in x = 2 to f(x) gives us f(2) = 13(2)² + 5(2) = 58.
So the equation of the tangent line at x = 2 is y - 58 = 57(x - 2), or y = 57x - 56.
Tangent line at x = 3:
We know the slope is 83, and the point (3, f(3)) is on the line.
Plugging in x = 3 to f(x) gives us f(3) = 13(3)² + 5(3) = 122.
So the equation of the tangent line at x = 3 is y - 122 = 83(x - 3), or y = 83x - 179.
D. In order to find where the tangent line is horizontal, we need to find where the slope is equal to zero. Setting f'(x) = 0 and solving for x gives:
f'(x) = 26x + 5 = 0
x = -5/26
Therefore, the only value of x where the tangent line is horizontal is x = -5/26.
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Three students need to produce a prime factorization of
48. Donna states that the first factors in the tree should
be 6 and 8. Larry states that the first factors in the tree
should be 4 and 12. Trish states that the initial factors of
48 do not affect the prime factorization. Explain why Trish
is correct.
Answer:
students need to produce a prime factorization of 48. Donna states that the first factors in the tree should be 6 and 8. Larry states that the first factors in the tree should be 4 and 12. Trish states that the initial factors of 48 do not affect the prime factorization. Explain why Trish is correct.Trish is correct because the initial factors of 48 do not affect the prime factorization. Prime factorization is the process of breaking down a composite number into its prime factors. The prime factors of a number are those factors that are prime numbers. The prime factorization of 48 is 2 x 2 x 2 x 2 x 3, which means that 48 can be expressed as a product of these prime factors. The order in which we choose the initial factors to start the prime factorization does not affect the result, as long as we continue to break down the resulting factors into their prime factors until we cannot break them down any further. Therefore, Trish is correct that the initial factors of 48 do not affect the prime factorization.
Trish is correct because the prime factorization of 48 will be the same regardless of which factors are chosen as the initial factors in the tree.
To see why, let's look at the prime factorization of 48:
48 = 2 × 2 × 2 × 2 × 3
No matter which factors are chosen as the initial factors, the same prime factors will eventually be found.
For example, if Donna's method is used, we could start with 6 and 8:
6 = 2 × 3
8 = 2 × 2 × 2
Then we could continue to factor each of these numbers until we reach prime factors:
6 = 2 × 3
8 = 2 × 2 × 2
= 2 × 2 × 2 × 3
= 2³ × 3
Now we have found all of the prime factors of 6 and 8, and we can combine them to get the prime factorization of 48:
48 = 2 × 2 × 2 × 2 × 3
If Larry's method is used, we could start with 4 and 12:
4 = 2 × 2
12 = 2 × 2 × 3
Then we could continue to factor each of these numbers until we reach prime factors:
4 = 2 × 2
12 = 2 × 2 × 3
= 2² × 3
Now we have found all of the prime factors of 4 and 12, and we can combine them to get the prime factorization of 48:
48 = 2 × 2 × 2 × 2 × 3
As we can see, the same prime factors are found regardless of which factors are chosen as the initial factors in the tree. Therefore, Trish is correct that the initial factors of 48 do not affect the prime factorization.
Which of these would you expect to have a positive correlation? Check all that apply. HINT: There are two correct selections. Question 1 options: The number of TV shows you watch and the age of your car The shoe size of that adult and the salary they earn The value of a car and the age of the car The pages of a book you read and the time you spend reading that book A person's years of experience at a job and their salary A person's grade on a test and the number of missed homework assignments leading up to that test
a bakery has 3 types of pie.. apple, cherry, and peach. there are 4 times as many apple pie as peach pie. what is a possible percentages for each type of pie
Answer:
Apple Pie = 66.67%
Cherry Pie = 16.67%
Peach Pie = 16.67%
A possible distribution of pie percentages could be 66.67% apple, 16.67% cherry, and 16.67% peach.
Step-by-step explanation:
Let's assume that the bakery has 1 peach pie. Then, according to the problem statement, the bakery has 4 apple pies.
So, the total number of pies is 1 + 4 + 1 = 6.
To find the percentage of each type of pie, we need to divide the number of each type of pie by the total number of pies and multiply by 100%.
Percentage of apple pies: (4/6) x 100% = 66.67%
Percentage of cherry pies: (1/6) x 100% = 16.67%
Percentage of peach pies: (1/6) x 100% = 16.67%
Therefore, a possible distribution of pie percentages could be 66.67% apple, 16.67% cherry, and 16.67% peach.
It is important to note that this is just one possible distribution based on the information given in the problem. If we were given different information, such as the total number of pies, the percentages could be different.
Please answer fast!!
Answer:
Look at the green dot
Step-by-step explanation:
find the sum of money that amounts to Rs- 3450 in 4 monts at the rate of 4½ %. per annam.
Answer:
To find the sum of money that amounts to Rs- 3450 in 4 months at the rate of 4.5% per annum, we can use the formula for simple interest:
Simple Interest = (Principal * Rate * Time) / 100
Where,
Principal = the sum of money borrowed or invested
Rate = the rate of interest per annum
Time = the time period in years
Since the time period given is 4 months, we need to convert it to years by dividing it by 12:
Time = 4/12 years = 1/3 years
Now, we can plug in the given values and solve for Principal:
Simple Interest = (Principal * Rate * Time) / 100
3450 = (Principal * 4.5 * 1/3) / 100
3450 * 100 = Principal * 4.5 * 1/3
11500 = Principal * 1.5
Principal = 11500 / 1.5
Principal = 7666.67 (rounded off to two decimal places)
Therefore, the sum of money that amounts to Rs- 3450 in 4 months at the rate of 4.5% per annum is Rs- 7666.67.
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An algebraic expression is described as 14 more than the product of
3 and the difference of z and 9. What is the value of this expression
when z = 17?
The value of the expression is 38 when z = 17.
What is the value of this expression when z = 17?Given that, an algebraic expression is described as 14 more than the product of 3 and the difference of z and 9.
First, we write the expression:
The difference of z and 9 means we subtract 9 from z. We then take this result and multiply it by 3.
Finally, we add 14 to the product of 3 and the difference of z and 9.
3(z - 9) + 14
Where z represents the value that we want to substitute into the expression.
Substituting z = 17, we get:
3(z - 9) + 14
3(17 - 9) + 14
3(8) + 14
24 + 14
38
Therefore, the value of the expression is 38.
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You have a 1
-gallon paint can in the shape of a cylinder. One gallon is 231
cubic inches. The radius of the can is 3
inches. What is the approximate height of the paint can? Use 3.14
for pi.
Answer:
Step-by-step explanation:
Average movie prices in the United States are, in general, lower than in other countries. It would cost $78.50 to buy three tickets in Japan plus two tickets in Switzerland. Three tickets in Switzerland plus two tickets in Japan would cost $74.10. How much does an average movie ticket cost in each of these countries?
The average movie ticket cost in Switzerland and Japan each of these countries is 46.97.
Let's assume that the average cost of a movie ticket in Japan is x, and the average cost of a movie ticket in Switzerland is y.
According to the problem statement, we can write two equations based on the given information:
3x + 2y = 78.5 ...(1)
2x + 3y = 74.1 ...(2)
We can solve these equations simultaneously to find the values of x and y. Here's how:
Multiply equation (1) by 2 and equation (2) by 3, then subtract equation (1) from equation (2):
(2x + 3y) - 2(3x + 2y) = 74.1 - 2(78.5)
Simplifying this equation, we get:
-y = -109.3
Therefore, y = 109.3.
Now substitute y = 109.3 into either equation (1) or (2) and solve for x:
3x + 2(109.3) = 78.5
Simplifying this equation, we get:
3x = -140.9
Therefore, x = -46.97.
However, we cannot have negative ticket prices.
Therefore, the average cost of a movie ticket is 46.97.
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solve the equation 25a=10a squared
Answer: The answer is [tex]\frac{5}{2}[/tex].
Step-by-step explanation:
We are given
25a = 10[tex]a^{2}[/tex].
First, we divide both sides by a
25 = 10a
Then we divide both sides by 10
[tex]\frac{5}{2}[/tex] = a
Suppose that f(4)=2, g(4)=5, f'(4)=6, g'(4)=-3, f'(5)=8, and g'(2)=10.
Find h'(4) where
(a) h(x)=f(x)g(x)
(b) h(x)= g(x)/f(x)+g(x)
(c) h(x)=f(g(x))
please help
(a) Using the product rule for h(x) = f(x)g(x), h'(4) = 24
(b) Using the quotient rule, for h(x) = g(x) / (f(x) + g(x)), h'(4) = -33/49.
(c) Using chain rule for h(x) = f(g(x)), h'(4) = 80.
What is the solution of the functions?
We can use the product rule, quotient rule, and chain rule to find the derivatives of the functions h(x).
(a) h(x) = f(x)g(x)
Using the product rule, we have:
h'(x) = f'(x)g(x) + f(x)g'(x)
At x = 4, we have:
h'(4) = f'(4)g(4) + f(4)g'(4) = 6(5) + 2(-3) = 24
Therefore, h'(4) = 24.
(b) h(x) = g(x) / (f(x) + g(x))
Using the quotient rule, we have:
h'(x) = [g'(x)(f(x) + g(x)) - g(x)f'(x)] / (f(x) + g(x))^2
At x = 4, we have:
h'(4) = [g'(4)(f(4) + g(4)) - g(4)f'(4)] / (f(4) + g(4))^2
= [(-3)(2 + 5) - 5(6)] / (2 + 5)^2
= -33 / 49
Therefore, h'(4) = -33/49.
(c) h(x) = f(g(x))
Using the chain rule, we have:
h'(x) = f'(g(x))g'(x)
At x = 4, we have:
h'(4) = f'(g(4))g'(4)
= f'(5)(10)
= 8(10)
= 80
Therefore, h'(4) = 80.
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The mean per capita income is 21,699
dollars per annum with a standard deviation of 835
dollars per annum.
What is the probability that the sample mean would be less than 21583
dollars if a sample of 399
persons is randomly selected? Round your answer to four decimal places.
The probability that the sample mean would be less than 21583 dollars if a sample of 399 persons is randomly selected is approximately 0.0826 or 8.26% (rounded to four decimal places).
What is probability?
Probability is a way to gauge how likely something is to happen. It is a number between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty that the occurrence will occur.
We can use the central limit theorem (CLT) to approximate the sampling distribution of the sample mean. According to CLT, if we have a large enough sample size (n≥30), the sampling distribution of the sample mean will be approximately normal, regardless of the underlying distribution of the population.
The mean of the sampling distribution of the sample mean is the same as the population mean, which is given as μ = 21699 dollars per annum. The standard deviation of the sampling distribution of the sample mean is equal to the standard error of the mean (SEM), which is calculated as follows:
SEM = σ/√n, where n is the sample size, and is the total standard deviation.
With the numbers from the problem substituted, we obtain:
SEM = 835/√399 = 41.767
Now, we need to find the probability that the sample mean would be less than 21583 dollars. We can standardize the sample mean using the standard normal distribution as follows:
z = (x - μ) / SEM, where the sample mean is x.
Substituting the values, we get:
z = (21583 - 21699) / 41.767 = -1.389
Using a standard normal distribution table, we can find that the area to the left of z=-1.389 is 0.0826.
Therefore, the probability that the sample mean would be less than 21583 dollars if a sample of 399 persons is randomly selected is approximately 0.0826 or 8.26% (rounded to four decimal places).
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does anyone know how to find the particular solution for this nonhomogeneous equation:
y"+3y'-3y=3xe^-1
Using the equations, the particular solution is y_p(x)=-3x+1+2e⁻ˣ.
What are non-homogeneous differential equations?As we already know, homogeneous equations have zero on the right side of the equation. Thus, it is said that non-homogenous differential equations are those with a function on the right side of their equation.
We are given a non-homogeneous differential equation in the form:
y′′+3y′-3y=3xe^-1
The differential equation is called non-homogeneous because it is known to have a non-zero right-hand side.
To solve this differential equation, we first need to find the complementary function, which is the solution to the corresponding homogeneous differential equation y′′+3y′-3y=0.
We then take the first and second derivatives of y_p(x) and substitute them into the differential equation, y′′+3y′-3y=3xe^-1 and simplify.
This leads to the system of equations:
a + 3c = 3
a + 3b - 3c = 0
a + b + 3c = 1
Solving this system of equations, we find that a=-3, b=1, and c=2. Therefore, the particular solution is y_p(x)=-3x+1+2e⁻ˣ.
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This set of equations can be solved, and the results show that a=-3, b=1, and c=2. As a result, the specific answer is [tex]y_{p(x)} =-3x+1+2e^{-x}[/tex].
What are non-homogeneous differential equations?Homogeneous equations, as we already know, have "0" on the right side of the equation. Therefore, it is said that differential equations with a function on the right side of the equation are non-homogenous differential equations.
A non-homogeneous differential equation of the following shape is provided to us:
[tex]y^{''} +3y^{'} -3y=3xe^{-1}[/tex]
Since the right-hand side of the differential equation is known to be non-zero, it is referred to as non-homogeneous.
Finding the complementary function, which is the answer to the related homogeneous differential equation [tex]y^{''} +3y^{'} -3y=0[/tex], is the first step in solving this differential equation.
The differential equation [tex]y^{''} +3y^{'} -3y=3xe^{-1}[/tex] is then simplified by taking the first and second derivatives of [tex]y_{p(x)}[/tex] and substituting them into
the equation.
This results in the formulae system:
a + 3c = 3
a + 3b - 3c = 0
a + b + 3c = 1
This set of equations can be solved, and the results show that a=-3, b=1, and c=2. As a result, the specific answer is [tex]y_{p(x)} =-3x+1+2e^{-x}[/tex].
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The attendance at Longwood middle school his first football game of the season is 437 people eat it at the second game is 4 to 76 people determine the approximate percent increase in attendance between the first and second game round your answer to the nearest 10th%
Approximate percent increase in attendance between the first and second game is 8.9%.
What is the approx. percentage increase in attendance between the first and second football games?
To calculate the percent increase in attendance between the first and second game, we can use the formula:
percent increase =
[(new value - old value) / old value] x 100%
where the old value is the attendance at the first game and the new value is the attendance at the second game.
Substituting the given values, we get:
percent increase = [(476 - 437) / 437] x 100%
percent increase = (39 / 437) x 100%
percent increase ≈ 8.92%
Rounding to the nearest tenth percent, we get the approximate percent increase in attendance between the first and second game as 8.9%.
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help me please i need help im fsilinh
Answer:
b. 1/4
Step-by-step explanation:
Probability of rolling even number = 3/6 = 1/2
Probability of tails = 1/2
Multiplying these two probabilities, we have 1/4.
If an item has an original price of $90 and has been discounted 30%, what is the sale price
Answer: 63 US$
Step-by-step explanation:
A train moves southward at 400 km/hr. How long will it take to make a 1,200 km trip?
Answer:
3 hours
Step-by-step explanation:
1200/400=3
simplify 300/25 fraction with steps
Following the basic principles and theory of simplifying fraction it is visible that this question follows the, the basic calculations involving the basic mathematics
Therefore the , let us take the given numerator that is 300 and then divide it using the denominator that is 25 ,
so, when we divide 300 /25 we get, the answer as12
because, when we divide both the numerator and denominator with 5 (because 25 and 300 are a divisible by 5 and are also multiples of )
we clearly see that 300 is divisible by 5 and the answer comes out to be 12.
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Find the vertex and the
�
x- and
�
y-intercepts of the equation
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=
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2
−
2
�
−
8
y=x
2
−2x−8
Then, use the points to graph the parabola.
a) What is the vertex of the parabola? Enter your answer as an ordered pair.
Vertex
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b) Identify the
�
x-intercept(s) of the parabola. Enter your answers as ordered pairs. Use a comma to separate answers as needed. If there are none, enter
None
None.
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x-intercept
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c) Identify the
�
y-intercept of the parabola. Enter your answer as an ordered pair.
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y-intercept
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d) Use the points you found to graph the parabola.
Answer:
Step-by-step explanation:
As seen in earlier sections, the process of completing the square is a useful tool in finding noninteger values of quadratic equations, especially intercepts. When a quadratic equation of the
form f (x) = ax2
+ bx + c is put through the process of completing the square it yields an
equation of the form f (x) = a(x – h)2
+ k . The conversion of the equation to this form will
yield critical information about the equation’s characteristics before you begin to graph it.
1.) The value of h is the distance left (if negative) or right (if positive) the graph
translates from the standard position.
2.) The value of k is the distance up (if positive) or down (if negative) the graph
translates from the standard position.
3.) The values of h and k, when put together as an ordered pair, give the vertex i.e.
(h, k).
4.) The equation x = h is the formula for the axis of symmetry.
The following example demonstrates how to find the following critical information of the
equation:
a.) vertex
b.) axis of symmetry
c.) y intercept (if any)
d.) x intercepts (if any)
Example 1: Find the vertex, axis of symmetry, x-intercept(s), and y-intercept and gr
which of the statements is true for the two division problems below? A: (x^2-3x-18)÷(x-6) or B: (x^3-x^2-5x-3)÷(x^2+2x+1)
A equals (x+3) and b equals (x-3)
A and b both equal (x+3)
a and b both equal (x-3)
a equals (x-3) and b equals (x+3)
A equals (x+3) and b equals (x-3) the statement that is true for the two division problems is that a equals factor (x+3) and b equals (x-3).
For the first division problem, [tex](x^2-3x-18)[/tex]÷(x-6), the quotient is (x+3). To solve for the quotient, you first need to factor the numerator, which is (x-6)(x+3). Then, you need to divide the numerator by the denominator, which is (x-6). The quotient is (x+3). For the second division problem, [tex](x^3-x^2-5x-3)/(x^2+2x+1)[/tex], the quotient is (x-3). To solve for the quotient, you first need to factor the numerator, which is (x+1)(x-3). Then, you need to divide the numerator by the denominator, which is [tex](x^2+2x+1)[/tex]. The quotient is (x-3). Therefore, the statement that is true for the two division problems is that a equals (x+3) and b equals (x-3).
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13. Higher Order Thinking Name two rays with the same endpoint in the figure below. Do they form an angle? Explain.
The two rays with the same endpoint in the figure below are AB and BC. Although they share a common endpoint (B), they do not form an angle since they are collinear and lie on the same line. Two non-collinear rays that share an endpoint create an angle. In this case, AB and BC lie on line AC and do not form an angle.
An angle is formed by two rays that originate from a common endpoint. In the given figure, AB and BC share the same endpoint (B), but they do not form an angle since they lie on the same line. A line is an infinite set of points that extends in both directions, while a ray is a portion of a line that starts at a particular point and extends infinitely in one direction. When two rays share a common endpoint, they form an angle only if they are not collinear, i.e., they do not lie on the same line. In this case, since AB and BC lie on line AC, they do not form an angle. Therefore, AB and BC are collinear and do not form an angle.
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Sin ² 20 +Sin² 40° +Sin ²80 simplify
Answer:
The answer is 1.5
Step-by-step explanation:
You just calculate in calculator and you will get the answer as 1.5
3. In triangle ABC, 4A is a right angle, and m<B = 45°. What is the length of BC? If your answer is not an integer, leave it in simplest radical form.
A. 18 ft.
B. 18√2
C. 18√3
D. 36
what is the answer? thank you