Antoine and Tess have a disagreement over how to compute a 15% gratuity on $46.00. Tess says, “It is easy to find 10% of 46 by moving the decimal point one place to the left to get $4.60. Do that twice. Then add the two amounts to get $4.60 + $4.60 = $9.20 for the 15% gratuity.”
Tess is correct about figuring 10% but he added 2 of them together which is like adding 10% +10% which is 20% not 15%.
he should have taken 1/2 of the 4.60 for 5% since 5 is half of 10
half of 4.60 = 2.30
then add that to the 4.60
4.60 +2.30 = 6.90 is 15%
Answer:Tess 20%
Step-by-step explanation:
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.
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.
You have a 5" by 7" photo that you would like to have enlarged to fit an 8" by 10" frame. Would the two photographs be similar? Explain
F^(-1) when f(x)=2x-7/3
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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 statement is always true about an isosceles triangle A.it has 1 right angle B.it has 2 congruent angles C.it has no sides that are congruent D.the sum of all 3 angles in 360 degrees
It has 2 congruent angles, is always true about an isosceles triangle
What is Isosceles Triangle?
A triangle with two equal sides is said to be isosceles. Also equal are the two angles that face the two equal sides. In other terms, an isosceles triangle is a triangle with two sides that are the same length.
Angles of Isosceles Triangle:Contrary to the equal sides, two of the isosceles triangle's three angles have equal measures. One of the angles is therefore not equal. Assume that if we are given the measure of an unequal angle, we can quickly determine the other two angles using the angle sum property.
Properties of Isosceles Triangle:Since this triangle's two sides are equal, the base of the triangle is the side that is not equal.
The triangle's two equal sides' opposing angles are always equal.
The vertex (topmost point) of an isosceles triangle is where the altitude of the triangle is calculated.
The third angle of a right isosceles triangle is 90 degrees.
Hence, the answer (b) it has 2 congruent angles
Learn more about the Isosceles Triangle here:
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Why can't irrational numbers be whole numbers
Mr. Rifkin had 240 digital and manual cameras. After donating 82 digital cameras and 26 manual cameras, he had 3 times as many digital cameras as manual cameras left. How many digital cameras did he have first?
Mr. Rif-kin initially had 181 digital cameras.
Let's denote:
- [tex]\( x \)[/tex] as the initial number of digital cameras.
- [tex]\( y \)[/tex] as the initial number of manual cameras.
According to the given information:
1. Mr. Rif-kin had a total of 240 digital and manual cameras initially:
[tex]\[ x + y = 240 \][/tex]
2. After donating 82 digital cameras and 26 manual cameras, he had 3 times as many digital cameras as manual cameras left:
[tex]\[ (x - 82) = 3(y - 26) \][/tex]
We can set up a system of equations with these two equations and solve for [tex]\( x \)[/tex] and [tex]\( y \)[/tex].
1. From Equation 1:
[tex]\[ y = 240 - x \][/tex]
2. Substituting [tex]\( y \)[/tex] from Equation 1 into Equation 2:
[tex]$\begin{aligned} & x-82=3((240-x)-26) \\ & x-82=3(214-x) \\ & x-82=642-3 x \\ & 4 x=724 \\ & x=181\end{aligned}$[/tex]
Now that we have found [tex]\( x \)[/tex], we can find [tex]\( y \)[/tex] using Equation 1:
[tex]$\begin{aligned} & y=240-x \\ & y=240-181 \\ & y=59\end{aligned}$[/tex]
So, Mr. Rif-kin initially had [tex]\( 181 \)[/tex] digital cameras and [tex]\( 59 \)[/tex] manual cameras.
The complete question is here:
Mr. Rif-kin had 240 digital and manual cameras. After donating 82 digital cameras and 26 manual cameras, he had 3 times as many digital cameras as manual cameras left. How many digital cameras did he have at first?
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)
The two jar are geometrically similar.The height are 25cm and 10cm.The diameter of the larger jar is 7.5cm.Find the diameter of the smaller jar.
25/10 = 7.5/x
75/25x
x=75/25 = 3
diameter of smaller jar = 3 cm
The net of square pyramid is shown below. What is the surface area of the pyramid ?
At Wayne College, 3/4 of the students are enrolled in an art class. Of the students enrolled in an art class, 1/4 are enrolled in a painting class. What fraction of the students at Wayne College are enrolled in a painting class?
Use <,>,or = to compare 0.36 and 0.4.
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.
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
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
How many toothpicks are used to create Figure 10? Describe how you found the answer.
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
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]
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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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
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:
John read the first 114 pages of a novel, which was 3 pages less than 1/3 of the novel. Write an equation to determine the total number of pages (p) in the novel. And find the total number of pages in the novel
Answer:
351
Step-by-step explanation:
If we add 3 pages to 114, we get a number that is [tex]\frac{1}{3}[/tex] the total number of pages in the novel (p). Thus, we can write:
[tex]114+3=\frac{1}{3}p[/tex]
Solving for p gives us the total number of pages in the novel. So:
[tex]114+3=\frac{1}{3}p\\117=\frac{1}{3}p\\p=\frac{117}{\frac{1}{3}}\\p=117*3=351[/tex]
Thus, total number of pages in the novel is 351.
Which expression is equivalent to 6(14)? 6(10 + 4) 6(10 + 14) 6(1 + 40) 6(10 + 40)
2
4-(28 divided 7)+111
What is the slope of a line that is perpendicular to the line whose equation is 8y−5x=118y−5x=11?
Answer:
The slope of a line that is perpendicular to the line whose equation is [tex]8y-5x=11[/tex] is [tex]m=-\frac{8}{5}[/tex]
Step-by-step explanation:
Given : Equation [tex]8y-5x=11[/tex]
To find : What is the slope of a line that is perpendicular to the line whose equation is given?
Solution :
First we find the slope of the given line,
The general slope form of line is [tex]y=mx+b[/tex] where m is the slope of the line and b is the y-intercept.
Re-write the given equation into general form,
[tex]8y-5x=11[/tex]
Take 5x to another side,
[tex]8y=5x+11[/tex]
Divide both side by 8,
[tex]y=\frac{5}{8}x+\frac{11}{8}[/tex]
On comparing with general form,
The slope of the line is [tex]m=\frac{5}{8}[/tex]
We know,
When two line are perpendicular one slope is negative reciprocal of another.
If the slope of line is [tex]m=\frac{5}{8}[/tex]
Then the slope of perpendicular line on this line is [tex]m=-\frac{8}{5}[/tex]
Therefore, The slope of a line that is perpendicular to the line whose equation is [tex]8y-5x=11[/tex] is [tex]m=-\frac{8}{5}[/tex]
The Moon is about 240,000 miles from the Earth what is the distance written as a whole number multiplied by a power of 10
A cylindrical well is 25 meters deep and has a diameter of 1.8 meters. Approximately how many cubic meters of soil were dug out to make the well?
(Use π = 3.14.)
10.17 cubic meters
21.19 cubic meters
63.59 cubic meters
70.65 cubic meters
Answer:
The answer is C. 63.59 cubic meters
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Please help me!! find the solution of this system of equations -x + 5y=-18 5x - 9y= 10