If the parent function f(x) = (2x − 3)3 is transformed to g(x) = (-2x + 3)3, which type of transformation occurs?
find the equation of a line containing the given point and slope (10,5); m=9/20
Calculator Reference A mountaineer climbed 1,000 feet at a rate of x feet per hour. He climbed an additional 5,000 feet at a different rate. This rate was 10 feet per hour less than twice the first rate. Which expression represents the number of hours the mountaineer climbed?
Answer: The expression that represents the number of hours the mountaineer climbed is given by
[tex]\dfrac{1000}{x}+\dfrac{2500}{x-5}[/tex]
Step-by-step explanation:
Since we have given that
Distance covered by mountaineer = 1000 feet
Speed at which he climbed = x feet per hour
Time taken by him would be
[tex]\dfrac{1000}{x}[/tex]
Additional distance covered by him = 5000 feet
Speed at which he climbed this time = 2x-10
So, Time taken is given by
[tex]\dfrac{5000}{2x-10}\\\\\\=\dfrac{5000}{2(x-5)}\\\\\\=\dfrac{2500}{x-5}[/tex]
Hence, the expression that represents the number of hours the mountaineer climbed is given by
[tex]\dfrac{1000}{x}+\dfrac{2500}{x-5}[/tex]
How do you solve this
The scores on a final exam were approximately normally distributed with a mean of 82 and a standard deviation of 11. If 85 students took the exam, and above a 60 is a passing grade, how many students failed the exam?
In this case, we can use the z statistic to find for the proportion of students who failed the exam. The formula for z score is given as:
t = (x – u) / s
where,
x = the sample score = 60
u = sample score mean = 82
s = standard deviation = 11
Substituting all given values into the equation:
t = (60 – 82) / 11
t = - 2
Based from the standard proportion distribution tables for z, this corresponds to:
P = 0.0228
This means that 2.28% of the students failed the exam or equivalent to:
failed students = (0.0228) * 85 = 1.938
approximately 2 students failed the exam
Answer:
2 students failed the exam
Step-by-step explanation:
The table shows the outputs y for different inputs x:
Input
(x) 3 7 11 15
Output
(y) 4 6 8 10
Part A: Do the data in this table represent a function? Justify your answer. (3 points)
Part B: Compare the data in the table with the relation f(x) = 5x – 21. Which relation has a greater value when x = 11? (2 points)
Part C: Using the relation in Part B, what is the value of x if f(x) = 99? (5 points)
(10 points)
Answer:24
Step-by-step explanation:
At Ron's Roller Rink, the number of customers has been decreasing at a steady rate of 5% per year. If there were 900 skaters per week in 2010, what is a good estimate for the number of skaters per week in 2006?
How often is the number of house representatives assigned to states reallocated? every 2 years every 6 years every 10 years never?
The members of the executive branch are the president, vice president and the cabinet. The president holds all the power for this branch of the government and the other members report to the president. The legislative branch writes up and votes on laws. This is called legislation. The legislative branch also known as congress has two parts: the House of Representatives and the senate. Other powers of the congress include declaring war, confirming presidential appointments for groups like the Supreme Court and the cabinet and investigating power. According to Article 1, Section 2, Clause 1, the House of Representatives shall constitute members every 2 years by the people of the state.
If p is a positive integer,then p(p+1)(p-1) is always divisible by?
I am not quite sure what the choices are, but the answer to that problem is:
If p is a positive integer, then p(p+1)(p-1) is always divisible by “an even number”.
The explanation to this is that whatever number you input to that equation, the answer will always be an even number. This is due to the expression p(p+1)(p-1) which always result in a even product.
For example if p=3, then (p+1)(p-1) becomes (4)(2) giving you a even number.
And if for example if p=2, then (p+1)(p-1) becomes (3)(1) which gives an odd product, but we still have to multiply this with p therefore 2*3 = 6 which is even product. The outcome is always even number.
Answer: From the choices, select the even number
Final answer:
If p is a positive integer, p(p+1)(p-1) is always divisible by 3.
Explanation:
If p is a positive integer, then p(p+1)(p-1) is always divisible by 3.
This can be proven by applying the property of divisibility by 3. According to this property, a number is divisible by 3 if and only if the sum of its digits is divisible by 3.
In the expression p(p+1)(p-1), the three terms p, (p+1), and (p-1) represent three consecutive numbers. Since the sum of the digits of any consecutive numbers is always divisible by 3, the expression is always divisible by 3.
PLEASE HELP!!!!!! The line of symmetry for the quadratic equation y = ax 2 - 8x - 3 is x = 2. What is the value of "a"?
A) -2
B) -1
C) 2
Explain why we need more than one digit to express certain quantities
Poisson suppose you have 5 cakes made ready to sell. what is the probability that you will sell out?
A new crew of painters can paint a small apartment in 12 hours. AN EXPERIENCED crew can paint the small apartment in 6 hours. How many hours does it take to paont the apartment when the two crews work together?
When Sharon began shopping this morning, she had $40.00. She purchased five paperback books and had lunch. The books were all the same price, and lunch cost $3.25. She now has $7.00 left over. What was the price of each of the books? A. $5.95 B. $6.60 C. $7.35 D. $8.75
Jonathan bought a new computer for $1,728 using the electronics store's finance plan. He will pay $96 a month for 18 months. Which equation can Jonathan use to find out how much money he still owes after each month of the plan?
Answer:
[tex]y=1728-96x[/tex]
Step-by-step explanation:
Given : Cost of computer = $1728
He will pay $96 a month for 18 months.
To Find: Which equation can Jonathan use to find out how much money he still owes after each month of the plan?
Solution:
He pays per month = $96
Let the number of months be x
So, He pays in x months = 96x
Since the total Cost of computer is $1728
So, amount left to be paid = [tex]1728-96x[/tex]
Let y be the unpaid amount after x months
So, equation becomes : [tex]y=1728-96x[/tex]
Hence An equation can Jonathan use to find out how much money he still owes after each month of the plan is [tex]y=1728-96x[/tex]
3/10, 0.222, 3/5, 0.53 in order from greastest to least
You invest $9000 with a 6% interest rate compounded semiannually. After 9 yrs, how much money is in your account?
Convert 5.6 liters to milliliter
5,600 ml
560 ml
0.056 ml
0.0056
a rectangular floor is 18 feet long and 12 feet wide. what is the area of the floor in square yards
1 yard = 3 feet
18/3 =6
12/3=4
6*4 = 24 square yards
A medium sized apple weighs 130 grams. How many apples are there in 1 kilogram?
Answer:
7
Step-by-step explanation:
A square picture with a side length of 4 inches needs to be enlarged. The final area needs to be 81 square inches.
Which equation can be used to solve for x, the increase in side length of the square in inches?
x2 + 4x – 81 = 0
x2 + 4x – 65 = 0
x2 + 8x – 65 = 0
x2 + 8x – 81 = 0
Answer:
[tex]x^2+8x-65=0[/tex]
Step-by-step explanation:
Side length of square = 4 inches
Let x be the increase in length
So, New length = x+4
Area of square = [tex]Side^2[/tex]
Area of enlarged square = [tex](x+4)^2[/tex]
Using identity : [tex](a+b)^2=a^2+b^2+2ab[/tex]
Area of enlarged square = [tex]x^2+16+8x[/tex]
We are given that The final area needs to be 81 square inches.
So, [tex]x^2+16+8x=81[/tex]
[tex]x^2+16+8x-81=0[/tex]
[tex]x^2+8x-65=0[/tex]
So, Option C is true
Hence equation can be used to solve for x, the increase in side length of the square in inches is [tex]x^2+8x-65=0[/tex]
The upper leg length of 20 to 29-year-old males is normally distributed with a mean length of 43.7 cm and a standard deviation of 4.2 cm. a random sample of 9 males who are 20 to 29 years old is obtained. what it the probability that the mean leg length is less than 20 cm? 0.1894 pratically 0 0.2134 0.7898
The probability that the mean leg length is less than 20 cm is practically 0.
Explanation:To find the probability that the mean leg length is less than 20 cm, we can use the sampling distribution of the sample mean. The sampling distribution of the sample mean is approximately normal when the sample size is large enough. In this case, the sample size is 9, which is smaller than 30 but still reasonably large, so we can assume that the sampling distribution of the sample mean follows a normal distribution.
We can standardize the sample mean using the formula:
z = (x - μ) / (σ / sqrt(n))
Where:
z: the z-scorex: the value of the sample meanμ: the population meanσ: the population standard deviationn: the sample sizeSubstituting the given values:
z = (20 - 43.7) / (4.2 / sqrt(9))
z = -23.7 / (4.2 / 3)
z = -23.7 / 1.4
z ≈ -16.93
Looking up the z-score in a standard normal distribution table, we find that the probability of getting a z-score less than -16.93 is practically 0. Therefore, the probability that the mean leg length is less than 20 cm is practically 0.
Find the component form of v given the magnitudes of u and u + v and the angles that u and u + v make with the positive x-axis. u = 1, θ = 45° u + v = 2 , θ = 90°
If f(x) = 2x2 + 1 and g(x) = x2 – 7, find (f – g)(x).
Answer: The required value is
[tex](f-g)(x)=x^2+8.[/tex]
Step-by-step explanation: The given functions are:
[tex]f(x)=2x^2+1,\\\\g(x)=x^2-7.[/tex]
We are given to find the value of [tex](f-g)(x).[/tex]
We know that, if s(x) and t(x) are any two functions of a variable x, then we have
[tex](s-t)(x)=s(x)-t(x).[/tex]
Therefore, we have
[tex](f-g)(x)\\\\=f(x)-g(x)\\\\=(2x^2+1)-(x^2-7)\\\\=2x^2+1-x^2+7\\\\=x^2+8.[/tex]
Thus, the required value is
[tex](f-g)(x)=x^2+8.[/tex]
Answer:
3x2 - 6 its the answer
Please help quick !!
In a certain grocery store, strawberries cost $5.92 per pound ( 5.92 dollars/lb ). what is the cost per ounce?
Answer:
$,37 dollars per ounce of strawberries
Step-by-step explanation:
We have to remember that there are 16 ounces in one pound so in order to calculate the cost per ounce, we just divide the cost per pound by 16:
5,92/16= ,37
SO the cost per ounce of strawberries when the price per pound is 5,92 dollars will be 0,37 dollars.
What is the next number in the series? 71 62 53 44 35 ?
The leader of the group brought 8.03 ounces of trail mix. The hikers only ate 5.26 ounces of the trail mix. How much trail mix was left?
What is the answer to this question?
The value of y is inversely proportional to the value of x. When y=40, x=5. What is the value of y when x=8
Answer: 64
Step-by-step explanation:
i put it into math-way