1--4 = 5
-6 -6 = 12
5^2 = 25
12^2 = 144
144+25 = 169
sqrt(169) = 13
distance = 13
What are the discontinuities of the function f(x) = the quantity of x squared plus 5 x plus 6, all over 2 x plus 16. ?
Answer:
Step-by-step explanation:
Since f(x) = (x^2 + 5x + 6) / (2x + 16)
For discontinuities, they can be found at where the slope does NOT exist
Take the derivative of f(x):
f'(x) = (x^2 + 16x + 34) / 2(x+8)^2
Apparently, when x= -8, f'(x) is NOT defined
Therefore, the discontinuity is uniquely located at x = -8
The average annual salary of the employees of a company in the year 2005 was $80,000. It increased by the same factor each year and in 2006, the average annual salary was $88,000. Let f(x) represent the average annual salary, in thousand dollars, after x years since 2005. Which of the following best represents the relationship between x and f(x)?
f(x) = 88(0.88)x
f(x) = 88(1.1)x
f(x) = 80(0.88)x
f(x) = 80(1.1)x
Answer: [tex]f(x) = 80 ( 1.1 ) ^x[/tex]
Step-by-step explanation:
Let the function that shows the average annual salary after x years since 2005 is,
[tex]f(x) = ab^x[/tex] ----- (1)
Where a and b are any unknown numbers.
For x = 0,
[tex]f(0) = ab^0= a[/tex]
But According to the question,
The average annual salary of the employees of a company in the year 2005 was $80,000.
Therefore, f(0)=80000 dollars.
⇒ a = 80000
From equation (1),
[tex]f(x) = 80000 b^x[/tex] ------- (2)
Now again according to the question,
In 2006, the average annual salary was $88,000
But the average annual salary in 2006 is [tex]f(1) = 80000 b^1[/tex]
⇒ [tex] 80000 b^1=88000[/tex]
⇒ b = 1.1
Putting the value of b in equation (2),
The average annual salary after x years since 2005 is,
[tex]f(x) = 80000 (1.1)^x[/tex] dollars
Or [tex]f(x) = 80 (1.1)^x[/tex] thousand dollars
Thus, Fourth Option is correct.
A store had 235 MP3 players in the month of January. Every month ,30% of the MP3 players were sold and 50 new MP3 players were stocked in the store. Witch recursive best represents the number of MP3 players in the store f(n) after n months?
Solve the following system of equations by substitution. 3x + 2y = -12 x = 2 A. (2, -9) B. (-2, -3) C. (3, 2) D. (2, 3)
find the solution of the system of equations 2x-4y=32 2x-8y=48
Each of the four outside walls of the large wooden box shown above is to be covered with waterproof plastic that comes in 3-foot-wide rolls. The plastic does not overlap. What is the total length, in feet, of plastic, needed to cover the four walls?
A) 21 ft
B) 42 ft
C) 63 ft
D) 84 ft
E) 126 ft
Explain too, thanks.
the age of two groups of yoga students are shown in the following dot plot
What is the range of y=sec x
The values where cos(x) is equal to 0 are excluded from the domain of the function y=sec(x)=1cos(x), or the values 2+n for all integers n. The function's range is either y<=1 or y>=1.
What is domain?The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x).
here, we have,
we know that "secant function" mean:
Its root is the Latin verb secare, which means "to cut." Any line that intersects a circle twice is referred to as a secant line, and you can conceive of this line as slicing the circle in half. The distance from the origin to the point where the tangent line intersects the x-axis is the secant function.
now, the identity of the sec is:
1/cos(x) = sec(x) Cot (x) = 1/Tan (x)
To know more about domain visit:-
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The following data show the height, in inches, of 11 different garden gnomes:
2 9 1 23 3 7 10 2 10 9 7
After removing the outlier, what does the mean absolute deviation of this data set represent?
A, On average, the height of a garden gnome varies 3.2 inches from the mean of 7 inches.
B, On average, the height of a garden gnome varies 3.6 inches from the mean of 6 inches.
C, On average, the height of a garden gnome varies 3.2 inches from the mean of 6 inches.
D, On average, the height of a garden gnome varies 3.6 inches from the mean of 7 inches.
Which number is equivalent to the fraction 18/5
F^(-1) when f(x)=2x-7/3
Jared flipped a fair coin 50 times. He expected half of his tosses to land on heads, but he only got heads 15 times. If he increased the number of times he flipped the coin to 500, he should expect the number of heads to be-
Simplify (−34.67)0.
−34.67
−1
0
1
Answer:
The answer is 1.
Im sorry I forgot the step by step explanation, but I had this in a quuiz a while ago and the answer is 1.
The averge temperature in Fairbanks, Alaska, in november is 2°F above zero. Write thiis temperture as an integer
Answer: Answer is 2
Step-by-step explanation:
Last year, Raul estimated that he would need 480 night lights, but he sold 420 night lights. This year, he bought 425 night lights and only sold 375. Which set of statements about the percent errors for the two years is true
Answer:
The answer is C in edg.
A decorator adds vases to a mantle to decorate. She wants to use 2 matching green vases, 3 matching blue vases, and 4 matching white vases. Find the total number of arrangements of vases that can be made.
288
140
1,260
362,880
Answer:
1,260
Step-by-step explanation:
Because it seemed right and I'm pretty sure it is
What value does 4 represent in the number 487.009
when multiplying two or more fractions, you should?
What is the value of x in this equation: 4x + 5 = 3x + 4? Solve the equation using the algebra tiles. x =
Answer:
Solution of the equation 4x + 5 = 3x + 4 is:
x= -1
Step-by-step explanation:
We are given a equation:
4x + 5 = 3x + 4
We have to solve the equation for x
4x+5=3x+4
subtracting both sides by 4
4x+5-4=3x+4-4
4x+1=3x
subtracting both sides by 4x
4x|+1-4x=3x-4x
1= -x
⇒ x= -1
Hence, solution of the equation 4x + 5 = 3x + 4 is:
x= -1
In a box-and-whisker plot, the interquartile range is a measure of the spread of the middle half of the data. Find the interquartile range for the data set: 10, 3, 7, 6, 9, 12, 13
5. Suppose a railroad is 2 km long, and it expands on a hot day by 50 cm in length. Approximately how high would the center of the rail rise above the ground? (Hint: Convert all measurements to meters BEFORE calculating any values)
To find the height at which the center of a railroad rail would rise due to expansion, convert all measurements to meters and use the formula h ≈ ΔL / 8. For expansion of 50 cm, the rail would rise approximately 6.25 cm.
The student has asked how high the center of a 2 km long railroad rail would rise when it expands by 50 cm on a hot day. First, we need to convert all measurements to meters: the railroad is 2000 m long, and it expands by 0.50 m. To find the height that the rail would rise, we can consider the rail as forming an arc of a circle after expansion.
We have the original length of the rail as the diameter of the circle and the expanded length as a slightly longer arc of the same circle. As the increase in length due to expansion is very small compared to the original length, we can use the approximation that the height of the rise is equal to the arc's excess length divided by 8 (h ≈ ΔL / 8).
Applying this formula: h ≈ 0.50 m / 8 = 0.0625 m or 6.25 cm. This approximation works under the assumption that the bend in the rail is mild, as it would be in reality due to the small degree of expansion.
Why can't irrational numbers be whole numbers
How many 60 degree angles does it take to make a full turn??
Answer:
6
Step-by-step explanation:
60x 6 =360
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Solve for x: the quantity of x plus 4 all over 2 = 7.
x = 3
x = 5
x = 6
x = 10
Use a calculator to evaluate 8 · cos30° rounded to four decimal places.
Answer:
The value of 8 cos 30° rounded to four decimal places = 6.9282
Step-by-step explanation:
Here we need to find the value of 8 cos 30° rounded to four decimal places.
Using the calculator to find the value
8 cos 30° = 6.9282032302755
Rounding the number to four decimal places, we will get
8 cos 30° = 6.9282
The value of 8 cos 30° rounded to four decimal places = 6.9282
Which expression shows a sum of three terms?
3x
3 + x
x3
x + 3 + x
Part A: Solve −np − 90 < 30 for n. Show your work. (4 points) Part B: Solve 5m − 3h = 45 for h. Show your work. (6 points)
A bag contains nickels, quarters and pennies. If a handful of coins brings in five nickels, 3 quarters, and nine pennies, how much money is expected to be in the bag if 90 coins are in the bag?
The expected amount of money in the bag if 90 coins are in the bag is [tex]\(\$5.78\)[/tex].
We need to determine the total value of the coins in the bag based on the given handful and then extrapolate that to the total number of coins in the bag.
First, let's calculate the value of the coins in the handful:
The value of five nickels is [tex]\(5 \times 5\)[/tex] cents = 25 cents.
The value of three quarters is [tex]\(3 \times 25\)[/tex] cents = 75 cents.
The value of nine pennies is [tex]\(9 \times 1\)[/tex] cent = 9 cents.
Adding these values together gives us the total value of the handful:
[tex]\[25 + 75 + 9 = 109 \text{ cents}\][/tex]
Next, we need to find out the ratio of each type of coin in the handful. We have a total of [tex]\(5 + 3 + 9 = 17\)[/tex] coins in the handful.
The ratios for each type of coin are as follows:
Nickels: [tex]\(\frac{5}{17}\)[/tex]
Quarters: [tex]\(\frac{3}{17}\)[/tex]
Pennies: [tex]\(\frac{9}{17}\)[/tex]
Now, let's calculate the expected number of each type of coin in the bag, given that there are 90 coins in total:
Expected nickels: [tex]\(90 \times \frac{5}{17}\)[/tex]
Expected quarters: [tex]\(90 \times \frac{3}{17}\)[/tex]
Expected pennies: [tex]\(90 \times \frac{9}{17}\)[/tex]
Using these ratios, we can calculate the expected number of each coin type:
Expected nickels: [tex]\(90 \times \frac{5}{17} \approx 26.47\)[/tex], but since we can't have a fraction of a coin, we'll consider 26 nickels.
Expected quarters: [tex]\(90 \times \frac{3}{17} \approx 15.88\)[/tex], rounding to 16 quarters.
Expected pennies: [tex]\(90 \times \frac{9}{17} \approx 47.65\)[/tex], rounding to 48 pennies.
Finally calculate the total expected value in the bag by multiplying the number of each type of coin by its value:
Value of expected nickels: [tex]\(26 \times 5\)[/tex] cents = 130 cents
Value of expected quarters: [tex]\(16 \times 25\)[/tex] cents = 400 cents
Value of expected pennies: [tex]\(48 \times 1\)[/tex] cent = 48 cents
Adding these values together gives us the total expected value in the bag:
[tex]\[130 + 400 + 48 = 578 \text{ cents}\][/tex]
To convert the total value from cents to dollars, we divide by 100:
[tex]\[578 \text{ cents} \div 100 = \$5.78\][/tex]
A triangle has one side that measures x, and the other two sides each measure 4 inches less than x. The perimeter is 19 inches.
What is the measure of x?
Answer: Simplified version of the answer above: (x = 9) is the correct answer.
Step-by-step explanation: