There is no solution that allows Sally to average an 85 with the given scores.
Let's start by finding the 5th score:
We know that the 4th score is 20 points less than the 5th score, so let's call the 5th score "x". Therefore, the 4th score is "x - 20".
We also know that the 5th score is 2/3 of the average of the first three scores. The average of the first three scores is (73 + 85 + 93)/3 = 83.67. So, (2/3) * 83.67 = 55.78 is the 5th score (rounded to two decimal places).
Therefore, x = 55.78/(2/3) = 83.67 is the 5th score.
Now, let's calculate the total score Sally needs to average an 85:
She already has 73 + 85 + 93 + 83.67 = 334.67 points. To average an 85 over seven tests, she needs a total of 7 * 85 = 595 points.
To find the scores she needs on the 6th and 7th tests, we can subtract the points she already has from the total points she needs:
595 - 334.67 = 260.33
So, Sally needs a total of 260.33 points on the 6th and 7th tests combined.
Let's call the 6th score "y" and the 7th score "z". We can set up an equation to solve for these two scores:
(y + z)/2 = 260.33
Multiplying both sides by 2:
y + z = 520.67
Since Sally needs to average an 85 over seven tests, the sum of all seven scores must be:
7 * 85 = 595
The sum of the first five scores is:
73 + 85 + 93 + 83.67 + 83.67 = 418.34
So, the sum of the last two scores must be:
595 - 418.34 = 176.66
Now we can set up another equation:
y + z = 176.66
We can solve this equation for one of the variables. Let's solve for "y":
y = 176.66 - z
Now we can substitute this into the first equation:
(176.66 - z + z)/2 = 260.33
176.66/2 = 260.33
88.33 = 260.33
This equation does not make sense.
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The number of milligrams of Vitamin C from 100 different gummy vitamins sold in the world was collected.
Which graphical representation would be most appropriate for the data, and why?
Box plot, because the median can easily be determined from the large set of data
Stem-and-leaf plot, because you can see the shape of the data
Histogram, because it shows each individual data point
Bar chart, because the data is categorical
The graphical representation that will be most appreciated for the data would be box plot, because the median can easily be determined from the large set of data. That is option A.
What is a box plot?The box plot is a type of graphical representation of data that gIves more than one detail about the data set such as;
minimum,first quartile,median,third quartile, andmaximum.Box plots allow you to compare multiple data sets better than others dues to the above listed features that it has.
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7 part answer pls!!
The consumption of disel in truck A in one day is 102/208 ml and the consumption of truck B is 105/196 ml. Which truck consumed more disel and by how much?
Truck B consumed 0.045 mL more diesel than Truck A.
How to obtain the consumptions of each truck?The fuel consumption for each truck is obtained applying the proportions in the context of the problem.
A proportion is applied as we are converting a fraction to decimal, dividing the numerator by the denominator, as follows:
102/208 ml = 0.49 mL -> divide 102 by 208.105/196 ml = 0.535 mL -> divide 105 by 196. -> consumed more.Hence the difference is given as follows:
0.535 - 0.49 = 0.045 mL.
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Simplify (5. 5)2+5. 75⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√+9(5. 5)2+5. 75+9 using rational numbers
The simplified expression using rational numbers is 82.25.
First, let's start by defining what a rational number is. A rational number is any number that can be expressed as a ratio of two integers, where the denominator is not zero. For example, 2/3, 5, and -7/2 are all rational numbers.
Now, let's simplify the expression using rational numbers. We can start by simplifying (5.5)² and 9(5.5)².
(5.5)² is equal to 30.25, which is a rational number because it can be expressed as 121/4.
9(5.5)² is equal to 9 times 30.25, which is equal to 272.25. This is also a rational number because it can be expressed as 109/4.
Next, let's simplify √5.75. To do this, we need to express the square root as a rational number. We can do this by rationalizing the denominator.
To rationalize the denominator, we multiply both the numerator and denominator of the expression by the conjugate of the denominator. In this case, the conjugate of √5.75 is √5.75.
So, 5.75√ can be simplified as follows:
5.75√ = 5.75√5.75/√5.75
= 5.75√5.75/5.75
= √5.75
Now, we can rewrite the expression as:
(121/4) + √5.75 + (109/4) + 5.75 + 9
Combining like terms, we get:
(121/4) + (109/4) + 15.75 + 9
Simplifying further, we get:
(230/4) + 15.75 + 9
= 57.5 + 15.75 + 9
= 82.25
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The cost of 54 tickets to a water park is $972. Each ticket costs the same amount. Which table or equation represents the relationship between the number of tickets, t and the total cost of the tickets, c?
Calculate the Social Security and Medicare tax that would be applied to an annual salary of $125,000. Use $106,800 for maximum taxable earnings. (Soc Sec 6.2%, taxed up to $106,800 and Medicare 1.45%).
a. Social Security tax: $77,500.00, Medicare tax: $18,125.00 b. Social Security tax: $7,750.00, Medicare tax: $1,812.50 c. Social Security tax: $66,216.00, Medicare tax: $18,125.00 d. Social Security tax: $6,621.60, Medicare tax: $1,812.50
The calculated Social Security tax is $ 6621.60 on the maximum taxable earning, that is $106800 on the rate of 6.2% and Medicare tax is $1812.50 on the annual salary, that is $125,000 on the rate of 1.45%.
Hence option d is the correct option.
The annual salary of an individual is given as $125,000.
Medicare tax is levied on the annual salary of an individual, that is on $125,000. It is given as 1.45 % on $125,000.
The maximum taxable earnings is $106,800 and Social Security tax is levied on this $106,800. It is given as 6.2% on $106,800.
Thus, applying basic rule of percentage calculation we get,
Earnings from Social Security tax = $(6.2% of 106800)
= ${(62/100*10)(106800)
= $ 6621.60
Earnings from Medicare tax = $(1.45% of 125000)
= $(145/100*100)(125000)}
= $1812.50
Hence option d Social Security tax: $6,621.60, Medicare tax: $1,812.50 is the correct option.
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A ruler is 12 inches long. What is the length of this ruler in centimeters
Answer:
Step-by-step explanation: There are 2.54 centimeters in a inch, for every inch you need to multiply it by 2.54.
2.54 x 12 = 30.48
Answer = 30.48
A 12inch ruler is 30cm.
If you look at a ordinary see through plastic ruler one side says 12 inches and the other, 30 centimetres by one millimeter.
A number "z" when rounded to the nearest whole, is equal to
Find the upper and lower bound of "z"
In order to find the upper and lower bounds of a rounded number:
Identify the place value of the degree of accuracy stated.Divide this place value by 2 .Add this amount to the given value to find the upper bound, subtract this amount from the given value to find the lower bound.How to explain the boundThe upper and lower bounds can be found by dividing the degrees of accuracy by 2 and then subtracting and adding with the value to give the lower and upper bounds respectively.
Kindly check the above explanation inorder to know how to calculate the value as your information is incomplete
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How does one find the upper and lower bound of a variable
Compare 3/8 and 2/6
Pls help
If you do tyyy
Answer: 3/8 >2/6
Step-by-step explanation:
Each neighborhood in DMR encompasses just the vertices and edges of a bad triangle. true or false
The statement " Each neighborhood in DMR encompasses just the vertices and edges of a bad triangle" is false because a neighborhood in a Delaunay triangulation typically encompasses more than just the vertices and edges of a single bad triangle.
The statement is incorrect. A "bad triangle" refers to a specific type of triangle that can occur in a Delaunay triangulation, which is a type of triangulation used in computational geometry. A bad triangle is a triangle that violates the Delaunay condition, which requires that the circumcircle of the triangle contains no other vertices of the triangulation.
While a Delaunay triangulation can be used to partition a set of points into a set of triangles, each neighborhood in the triangulation typically encompasses more than just the vertices and edges of a single bad triangle. Instead, a neighborhood typically encompasses all of the triangles in the triangulation that share a common vertex or edge with a given triangle.
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False. Each neighborhood in DMR encompasses the vertices and edges of a Delaunay triangle, which is a good triangle.
, each neighborhood in DMR (Delaunay Mesh Refinement) does not necessarily encompass just the vertices and edges of a bad triangle. DMR is an algorithm used to refine meshes, and it can involve both bad and good triangles to ensure a high-quality mesh output. The neighborhoods can contain multiple triangles and their respective vertices and edges, depending on the refinement criteria.
False. Each neighborhood in DMR encompasses the vertices and edges of a Delaunay triangle, which is a good triangle.
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A rectangle is 21 meters long and I1 meters wide
The area of the rectangle is 231 square meters.
Calculating the areaTo find the area of a rectangle, we need to multiply its length by its width.
Given that the length of the rectangle is 21 meters and the width is 11 meters, we can find the area as:
Area = Length x Width
Area = 21 meters x 11 meters
Area = 231 square meters
Therefore, the area of the rectangle is 231 square meters.
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It is recommended to drink 8 glasses of water per day. A glass of water contains approximately 237 mL. If Carmelo drank 7 glasses, approximately how many liters of water did he drink?
H. 3,059 L
B. 16. 59L
C. 1,359 L
D. 1,659 L
Answer:
d Because I just took the test and got it right
12 If the domain of the function f(x) = 2X²-8 is {- 2, 3, 5}, then
the range is
(1) {-16, 4, 92}
(2) {-16, 10, 42}
(3) {0, 10, 42}
(4) {0, 4, 92}
#6 write it in y=MX+B
Simplify. 3x5/6 A.15/6 B.23/6 C.2 2/1 D. 3 5/6
Therefore, expression 3x5/6 simplifies to 3 5/6.
What is expression?In mathematics, an expression is a combination of symbols and/or numbers that represents a quantity or a mathematical relationship between quantities. Expressions can be simple or complex, and can involve arithmetic operations, algebraic operations, functions, and variables. Expressions can be evaluated, simplified, and manipulated using mathematical rules and operations to obtain new expressions or values.
Here,
To simplify 3x5/6, we can rewrite it as (3/1) × (5/6). Multiplying the numerators and denominators, we get:
(3/1) × (5/6) = 15/6
= 2 3/6
Since 3/6 can be simplified to 1/2, we have:
2 3/6 = 2 1/2
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Following the logic shown in the proof above, describe the missing answer for "Reason 3".
A
SAS
B
AAS
C
SSA
D
ASA
Based on the given options and the information provided, the missing answer for "Reason 3" is option D, ASA.
The proof mentioned is based on the fact that the two triangles have two pairs of congruent angles and one pair of congruent sides.
This corresponds to the criteria for the ASA postulate, which states that if two triangles have two pairs of congruent angles and one pair of congruent sides, then the triangles are congruent.
Therefore, by using the ASA postulate, we can conclude that the two given triangles are congruent.
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Martiza's car has 16 gallons of gas in the tank. She uses 3/4 of the gas. How many gallons of gas does Martiza use?
Answer:
12
Step-by-step explanation:
4 x 4= 16 so 4 x 3=12 and 3/4 = 4 x 3
Whitney rolls a ball down a ramp that is 18 feet long. If the ball descends two feet each second what integer represents the amount of time in seconds the ball takes to reach the end of the ramp
The integer that represents the amount of time in seconds the ball takes to reach the end of the ramp is 9.
What integer represents the amount of time in secondsTo find the amount of time in seconds it takes for the ball to reach the end of the ramp, we need to divide the total distance by the rate of descent.
The total distance the ball needs to travel is 18 feet, and it descends 2 feet each second.
Therefore, the time it takes for the ball to reach the end of the ramp can be calculated as follows:
time = distance / rate
time = 18 feet / 2 feet/second
time = 9 seconds
So, the integer is 9.
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the length of a staff meeting in hours is a random variable having the following probability density function 5(x-.5)^5 calculate the expected length of a staff meeting
The expected length of a staff meeting is approximately 12.5 minutes.
what is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.
To calculate the expected length of a staff meeting, we need to find the mean of the probability density function given.
The formula for finding the expected value or mean of a continuous random variable with probability density function f(x) is:
E(X) = ∫ x f(x) dx over the range of the variable
Using this formula, we can find the expected length of a staff meeting as follows:
E(X) = ∫ x f(x) dx over the range of the variable
= ∫ 0 to 1 x [tex]5(x-0.5)^{5}[/tex] dx (since the length of a meeting can't be negative)
= 5 ∫ 0 to 1 x[tex](x-0.5)^{5}[/tex] dx
Now we can use integration by parts or substitution to solve the integral. For simplicity, we can use substitution, with u = x - 0.5 and du = dx:
E(X) = 5 ∫ -0.5 to 0.5[tex]5(x-0.5)(u)^{5}[/tex] du
= 5 ∫ -0.5 to 0.5 [tex](u^6 + 0.5u^5)[/tex] du
= 5 [(1/7)[tex]u^7\\[/tex] + (1/10)[tex]u^6[/tex]] evaluated at -0.5 and 0.5
= 5 [(1/7)[tex](0.5)^7[/tex] + (1/10)[tex](0.5)^6[/tex] - (1/7)[tex](-0.5)^7[/tex] - (1/10)[tex](-0.5)^7[/tex]]
≈ 0.2083 hours or 12.5 minutes
Therefore, the expected length of a staff meeting is approximately 12.5 minutes.
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Veneta wants to buy a new couch. Her brother just bought a couch for $1,250. Veneta wants to spend within $188 of this price. What are the highest and lowest amounts Veneta is willing
Answer:
highest: $1,438
lowest: $1,062
Step-by-step explanation:
The highest and lowest points are adding $188 and subtracting $188 from her brother's amount.
So, to find the highest point, add $188 to $1,250, which is $1,438.
To find the lowest point, subtract $188 from $1,250, which is $1,062.
Hope this helps ;)
You are at a Riverdogs game and want to tip your server 15%. If your bill was $12, how much tip do you leave?
Answer: $1.80
Step-by-step explanation: 15% of 12 is 1.8
apply the half-angle identities for sine and cosine to rewrite or evaluate the following expression.
[tex]tan(\frac{11\pi}{12} )[/tex]
Answer: We can use the halfangle formula for the tangent to answer this question. Using this formula we get that [tex]$\tan\left(\frac{11\pi}{12}\right) = \sqrt{3} - 2[/tex].
Step by Step Explanation: The half angle formula for tangent is [tex]$\tan\left(\frac{A}{2}\right) = \frac{\sin(A)}{1+\cos(A)}[/tex] . So
[tex]$\tan\left(\frac{11\pi}{12}\right)[/tex]
[tex]$= \frac{\sin(\frac{11\pi}{6})}{1+\cos(\frac{11\pi}{6})}[/tex]
[tex]$= \frac{\sin(2\pi - \frac{\pi}{6})}{1+\cos(2\pi - \frac{\pi}{6})}[/tex]
[tex]$ = \frac{-\sin(\frac{\pi}{6})}{1+\cos(\frac{\pi}{6})}[/tex]
[tex]$= \frac{-1/2}{1 + \sqrt{3}/2}[/tex]
[tex]$= -\frac{1}{2+\sqrt{3}}[/tex]
[tex]$= - \frac{2-\sqrt{3}}{(2+\sqrt{3})(2-\sqrt{3})}[/tex]
[tex]= - \frac{2 -\sqrt{3}}{4-3}}[/tex]
[tex]= \sqrt{3} -2[/tex]
What are the half angle identitiesThese are some of the common halfangle identities:
[tex]\cos(A/2) = \sqrt{\frac{1+\cos(A)}{2}[/tex]
[tex]\sin(A/2) = \sqrt{\frac{1-\cos(A)}{2}[/tex]
[tex]\tan(A/2) = \frac{\sin(A)}{1+\cos(A)} = \frac{1 - \cos(A)}{\sin(A)}[/tex]
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679/1327+677-x/1329+675-x/1331+
673-x/1333=4
The value of x after simplifying the given equation is approximately 1295.6.
To solve for x in the equation
(679/1327) + (677-x)/1329 + (675-x)/1331 + (673-x)/1333 = 4
We can start by simplifying the fractions and combining like terms
679/1327 + (3x - 1010)/((1329)(1331)(1333)) = 4
Multiplying both sides by (1327)(1329)(1331)(1333), we get
(679)(1329)(1331)(1333) + (3x - 1010)(1327)(1331)(1333) = 4(1327)(1329)(1331)(1333)
Expanding the products and simplifying, we get
(679)(1329)(1331)(1333) + (3x)(1327)(1331)(1333) - 1010(1327)(1331)(1333) = 4(1327)(1329)(1331)(1333)
Adding 1010(1327)(1331)(1333) to both sides, and dividing both sides by (3)(1327)(1331)(1333), we get
x ≈ 1295.6
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PLEASE HELP I HAVE TO SUBMIT SOON!!!
She needs 74.25 ft² of glass to cover the pyramid.
How to obtain the surface area of the pyramid?To obtain the surface area of any prism, we combine the areas of all the parts that compose the prism.
The pyramid in this problem is composed as follows:
Square base with side length of 5.5 ft.Four triangles with base 5.5 ft and height of 4 ft.The area of the square base is given as follows:
As = 5.5² = 30.25 ft².
The area of the four triangles is given as follows:
At = 4 x 1/2 x 5.5 x 4
At = 44 ft².
Hence the surface area of the pyramid is given as follows:
S = As + At
S = 30.25 + 44
S = 74.25 ft².
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find the surface area of the trapezoid
Hence ,the surface area of the trapezoid is 173 [tex]ft^{2}[/tex] .
What is the trapezoid?In geometry, a quadrilateral with at least one set of parallel sides is referred to as a trapezium in American and Canadian English, or a trapezium in British and other forms of English. In Euclidean geometry, a trapezium is a convex quadrilateral by definition. The bases of the trapezium are the parallel sides.
What is the surface area of trapezoid?The amount of space that a trapezoidal prism is surface takes up is known as its surface area. A three-dimensional solid called a trapezoidal prism is composed of two trapezoids on opposing faces connected by four rectangles known as the lateral faces. You will learn how to determine the surface area of a trapezoidal prism, as with all three-dimensional shapes.
We know that ,surface area of trapezoid is,
Surface Area= [tex]\frac{1}{2}[/tex] x (sum of the lengths of the parallel sides) x perpendicular distance between parallel sides
In given figure,
∵ value of parallel sides is 10 ft and 13 ft ,
So, the sum of the lengths of the parallel sides= 10+13=23 ft
∵ perpendicular distance between parallel sides= 15 ft
∴ The Surface Area of trapezoid = [tex]\frac{1}{2}[/tex] x (sum of the lengths of the parallel sides) x perpendicular distance between parallel sides
⇒The Surface Area of trapezoid = [tex]\frac{1}{2}[/tex] x 23 x 15
⇒The Surface Area of trapezoid = [tex]\frac{1}{2}[/tex] x 345
⇒The Surface Area of trapezoid = 172.5 [tex]ft^{2}[/tex] ≅ 173 [tex]ft^{2}[/tex]
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I need help asap
Solve the equation for x.
2/3x - 1/9x +5=20
X=_______
Answer:
The answer for x is 27
Step-by-step explanation:
2x/3-1x/9+5=20
2x/3-x/9=20-5
6x-x/9=15
5x/9=15
multiply both sides by 9
5x/9×9=15×9
5x=15×9
divide both sides by 5
5x/5=15×9/5
x=3×9
x=27
Answer:
Step-by-step explanation:
A rectangle has a diagonal of length of 60 inches and the diagonal creates angles of
30 degrees and 60 degrees in the corners of the rectangle. Determine the area of the rectangle in
simplified radical form.
Let's call the length of the rectangle "l" and the width "w". We know that the diagonal of the rectangle is 60 inches, and that it creates angles of 30 degrees and 60 degrees in the corners of the rectangle.
Using trigonometry, we can relate the sides of the rectangle to its diagonal and the angles formed by the diagonal. Specifically, we can use the sine and cosine functions to relate the sides to the angles:
sin(30) = w/60 and cos(30) = l/60
sin(60) = l/60 and cos(60) = w/60
Simplifying each equation, we get:
w = 30√3 and l = 30
Therefore, the area of the rectangle is:
Area = l x w = (30)(30√3) = 900√3 square inches.
Hence, the area of the rectangle in simplified radical form is 900√3 square inches.
Let x=-[tex]\frac{16\pi }{3}[/tex]
Part A: Determine the reference angle of x. (4 points)
Part B: Find the exact values of sin x, tan x, and sec x in simplest form. (6 points)
The reference angle of x can be found to be 13π/3.
The exact values of sin x, tan x, and sec x in simplest form:
sin x = √3/2tan x = √3sec x = -2How to find the reference angle ?Since our angle x = (10π) / -3 is in the third quadrant, we subtract π to get the reference angle:
reference angle = |x - π| = |(10π) / -3 - π| = |-13π/3|
The reference angle is 13π/3.
sin x = sin(reference angle) = sin(13π/3)
sin(π/3) = √3/2
So, sin x = √3/2
tan x = tan(reference angle) = tan(13π/3)
tan(π/3) = √3
So, tan x = √3
sec x = 1 / cos x = 1 / cos(reference angle) = 1 / cos(13π/3)
cos(π/3) = 1/2
So, sec x = 1 / (-1/2) = -2.
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9 didvided by 5 and 1 /7th
Answer:
7/4
Step-by-step explanation:
i am sooo sure that the answer is 1.75
Convert the following percents to decimals.
.825% =
Answer:
0.00825
Step-by-step explanation:
Move the decimal point two places to the left to go from a percentage to a decimal.
a) Work out the bearing of A from B.
b) Work out the bearing of B from A.
(Hint: bearings are written with three digits.)
306°
54°
126°
N
B
234⁰
Not drawn accurately
a).The bearing of point A from B is 234°.
b). The bearing of point B from point A is 054°.
What is bearing?Bearing is usually measured in degrees, with 0° indicating the reference direction (usually North), and increasing clockwise to 360°. It refers to the direction or angle between a reference direction and a point or object.
The bearing of point A from B is the angle measured from the north of B to the straight line distance between A and B which is 234°. While the bearing of point B from point A is the angle measure starting from the north of A to the straight line distance between A and B which is 054°.
Therefore, the bearing of point A from B is 234° while the bearing of point B from point A is 054°.
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