The amounts, using proportions, are given as follows:
Tip: $10.93.Total cost of the meal: $65.58.What is a proportion?A proportion represents a fraction relative to a total amount, and this fraction is combined with the basic arithmetic operations, especially multiplication and division, to find the desired amounts in the context of the problem from which the fraction was built.
The tip is of 20% of the total bill of $54.65, hence it's value is given as follows:
Tip = 0.2 x 54.65 = $10.93.
(because 0.2 is the decimal equivalent to the percentage of 20%, then it is multiplied by the total amount to find the desired amount).
The total cost of the meal is given by the sum of the bill of the meal plus the tip, hence:
Total Cost = 54.65 + 10.93 = $65.58.
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Find f(x) +g(x) if f(x)=10-3 and g(x)=-x+3
Answer:
10 - x
Step-by-step explanation:
Since f(x) = 10 - 3, we can replace the "f(x)" in the equation with "10 - 3". Likewise, we can replace the "g(x)" in the equation with "-x + 3" because g(x) = -x + 3:
10 - 3 - x + 3
7 - x + 3
10 - x
Shawn had some nickels in a jar. He put 147 nickels in the jar. Now there are 435 nickels in the jar. How many nickels were in the jar at the start?
Responses
A 288288
B 218218
C 312312
D 398398
Answer:
A
288 nickels
Step-by-step explanation:
There are now 435 nickels, after he put in 147. To find the answer, we need to find what the amount of nickels was before Shawn put in the 147. So, we need to subtract 147 from 435.
435 - 147 = 288
So, there were 288 nickels in the jar at the start.
Davis digs a hole at a rate of 3/4 feet every 10 minutes. After digging for 40 minutes, Davis places a bush in the hole that fills exactly 7/8 feet of the hole.
Relative to ground level, what is the elevation of the hole after placing the bush in the hole?
Enter your answer as a simplified fraction. NOT MIXED NUMBER
The elevation of the hole after placing the bush in the hole is 17/8 feet
How calculate the elevation of the hole after placing the bush in the hole?
Given: Davis digs a hole at a rate of 3/4 feet every 10 minutes
After digging for 40 minutes, Davis places a bush in the hole that fills exactly 7/8 feet of the hole
This involves subtraction and multiplication of fractions
Since the rate of digging = 3/4 feet every 10 minutes
Thus, after digging for 40 minutes, the depth will be:
3/4 × 4 = 3 feet
If Davis places a bush in the hole that fills exactly 7/8 feet of the hole, the remaining depth or elevation will be:
3 feet - 7/8 feet = 17/8 feet
Therefore, after placing the bush in the hole, the elevation of the hole is 17/8 feet
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What is the slope of a line perpendicular to the line whose equation is 6x + 2y = -32. Fully simplify your answer.
The slope of a line is m=−3
The slope of a line indicates its steepness. The slope is determined mathematically as "increase over run" (change in y divided by change in x).
Given that
the slope of 6x+2y=−32:
slope using the standard form:
slope m of a line of the form Ax+By=C equals –A/B
A=6, B=2
m=−6/2
simplify
m=−3
Therefore the slope of a line is m=−3
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In Cedarburg, the library is due south of the courthouse and due west of the community
swimming pool. If the distance between the library and the courthouse is 12 kilometers and
the distance between the courthouse and the city pool is 13 kilometers, how far is the library
from the community pool?
kilometers
The library is 5 kilometres far from the community pool.
According to the Pythagoras theorem, the square of the hypotenuse of a triangle, which has a straight angle of 90 degrees, equals the sum of the squares of the other two sides. Look at the triangle ABC, where BC² = AB² + AC² is present. The base is represented by AB, the altitude by AC, and the hypotenuse by BC in this equation.
The distance between the courthouse and the library is 12 kilometres and the distance between the courthouse and the city pool is 13 kilometres. Let the distance between the library and the community pool be x and it can be observed that the Courthouse, library and Community hall form a sort of right-angled triangle
So, using Pythagoras theorem, we get
[tex]13^2=x^2+12^2\\x^2=169-144\\x^2=25\\x=5 km[/tex]
So, the library is 5 kilometres far from the community pool.
Therefore, the distance between the library and the community pool is 5 kilometres.
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Please help me please
The value of all the missing angles is in the measure of m∠1 = 88°, m∠2 = 42°, and m∠3 = 113°.
We know that,
Sum of all angles of triangle = 180°.
Therefore, m∠3 + 42° + 25° = 180°.
m∠3 = 180° - 67°
m∠3 = 113°
Vertical angles: Vertical angles are the angles that are opposite to each other when two lines cross.
We know that,
Vertical or opposite angles have equal measures.
So, 42° and m∠2 are vertical or opposite angles.
Therefore, the value of m∠2 = 42°.
Similarly, for m∠3, We know that,
Sum of all angles of triangle = 180°.
∴ ∠1 + ∠2 + 50° = 180°.
=> ∠1 + 42° + 50° = 180°
=> m∠1 = 88°.
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Find the value of the variables in the figure. Explain your reasoning.
The value of the variables in the figure is x = 60 degrees and y = 10 degrees.
From the figure:
x + 120 = 180 (since consecutive interior angles equal to 180)
x = 180 - 120
x = 60 degrees.
3y + 40 + 3x - 70 = 180(since supplementary angles = 180)
3y + 3x - 30 = 180
3(y + x) = 180 + 30
y + x = 210/3
y + x = 70
substitute x value
y + 60 = 70
y = 70 - 60
y = 10 degrees.
Therefore the value of the variables in the figure is x = 60 degrees and y = 10 degrees.
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a fruit basket contains apples, oranges, and tangerines in the ratio 3:2:5, respectively. what is the total number of apples, oranges, and tangerines in the fruit basket?
The total number of apples, oranges, and tangerines in the fruit basket is in the ratio 10 or 10x
In mathematics, a ratio is a comparison of two or more numbers that indicates their sizes in relation to each other.
A ratio compares two quantities by division, with the dividend or number being divided termed the antecedent and the divisor or number that is dividing termed the consequent.
We know that : the ratio of apples : oranges : tangerines = 3 : 2 : 5.
The total number of apples, oranges, and tangerines in the fruit basket is the total number of ratio, that is 3 + 2 + 5 = 10.
Because of the question is not contain information about the number of pieces, we can describe the dividend with x (or unknown value). So, the total number of apples, oranges, and tangerines in the fruit basket with ratio, that is 10 or 10x.
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Show that there exist a rational number a and an irrational number b such that a^b is irrational.
Answer:
In explanation below.
Step-by-step explanation:
Presumably, the proof you have in mind is to use a=b=2–√a=b=2 if 2–√2√22 is rational, and otherwise use a=2–√2√a=22 and b=2–√b=2. The non-constructivity here is that, unless you know some deeper number theory than just irrationality of 2–√2, you won't know which of the two cases in the proof actually occurs, so you won't be able to give aa explicitly, say by writing a decimal approximation.
if the point D (8. -5) is reflected over the y axis, the coordinates of D would be
If the point D (8. -5) is reflected over the y-axis, the coordinates of D' would be: (-8, -5).
What is a reflection?A reflection can be defined as a type of transformation which moves every point of the object by producing a flipped but mirror image of the geometric figure.
In Geometry, a reflection over the y-axis (y = x) is given by this transformation rule (x, y) → (-x, y).
By applying a reflection over the y-axis to point D, the coordinates of the vertices of point D' include the following:
(x, y) → (-x, y)
Point D = (8, -5) → Point D' = (-8, -5)
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8x + 5° + 3x + 8° =90
Solve for x pls <3
Answer: x=7°
Combine like terms and divide.
8x+5°+3x+8°=90°
(8x+3x)+(5°+8°)=90°
11x+13°=90°
-13° -13°
11x=77°
[tex]\frac{11x}{11} =\frac{77}{11}[/tex]
x=7°
Given the perimeter of 225 ft. Solve for x and then find the indicated side lengths.
Answer:
X=14
Side GF: 41 ft
Side FE: 58 ft
Side DE: 98 ft
Side DG: 28 ft
Step-by-step explanation:
(13+2x)+(4x+2)+(7x)+(X+14)
6x+15+8x+14
14x+29=225
-29. -29
14x=196
/14. /14
X=14
Fill in 14 for x for each side
13+2(14)
13+28
Side GF: 41 ft
4(14)+2
56+2
Side FE: 58 ft
7(14)
Side DE:98 ft
14+14
Side DG: 28 ft
Hopes this helps please mark brainliest
Dora is paid a salary of $50,000per year. How much would she be paid if she's weekly
Answer:
about 958 dollars
Step-by-step explanation:
50,000÷52.1429 is about 958 dollars weekly
1-8: MathXL for School: Practice & Problem Solving
0 Assignment is past due (10/27/22 11:59pm)
Question Help
The populations of Cities A and B are 3.7 x 105 and 2,115,000, respectively. The population of City C is twice the population
of City B.
The population of City C is how many times the population of City A?
1.8.PS-15
The population of City C is times the population of City A.
(Round the final answer to the nearest whole number as needed. Round all intermediate values to the nearest tenth as needed.)
Answer:
11
Step-by-step explanation:
You want the ratio of the populations of city C and city A, given city C is 2 times the 2,115,000 population of city B, and city A's population is 3.7×10⁵.
EvaluationThe ratio of interest is ...
2B/A = 2(2115000)/(3.7×10⁵)
A calculator provides an easy answer to the value of this expression. (See attached.)
City C is about 11 times the population of City A.
__
Additional comment
If you want to work this out "by hand", you will need to find the quotient of ...
4230000/370000 = 423/37 = 11 17/37 ≈ 11
because 17/37 < 1/2.
In just two days it will be seven days after three days before Halloween. What is the date today ?
Answer:
November 2nd
Step-by-step explanation:
Halloween = Oct. 31
3 days before Halloween (Oct. 31) is Oct. 28
7 days after that it is Nov. 4
2 days before is November 2nd
18 POINTS AND WILL MARK BRAINLIEST PLS HELP ME IT WAS DUE LAST WEEK
Answer:
B
Step-by-step explanation:
y intercept is 500 so that is how much was in the tank when it started
And slope is -9 which is the steady decline in water
Hopes this helps
Answer: i'm writeing this so you can mark the other person brainliest
Step-by-step explanation:
if amy has 17 apples and gave 9 to jacob how may does amy hve if she goes to the store and buys 78 more?
Answer:You should have learnt this in kindergarten yet you're in high school, the answer is 86
Evaluate 1/2x^4 – 3/4x² for x = 2.
Answer:
[tex]-\frac{5}{32}[/tex]
Step-by-step explanation:
[tex]\frac{1}{2(2)^4}-\frac{3}{4(2)^2} \\\frac{1}{32} - \frac{3}{16} = -\frac{5}{32}[/tex]
I need help please!!!!!!!
the slope of the given point is m=9
(06.02)
Match the verbal expression (term) with its algebraic expression (definition).
Match
Term
A variable cubed
Quotient of some number and three
Product of an unknown value and three
Three less than a variable
Three more than some number
Definition
A) 3a
B) b + 3
C) z + 3
D) y - 3
E) x³
The values of the statements are x³, b ÷ 3, 3a, y-3, z+3.
What is an Expression?
An expression is a mathematical statement which consists of variables, constants and mathematical operators.
Hence the answer is, the statements are:
A variable cubed : x³
Quotient of some number and three: b ÷ 3
Product of an unknown value and three : 3a
Three less than a variable : y-3
Three more than some number : z+3
Hence the answer is, the values of the statements are x³, b ÷ 3, 3a, y-3, z+3.
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Boden's account has a principal of $600 and a simple interest rate of 3.5%. Complete the number line. How much money will be in the account after 4 years, assuming Boden does not add or take out any money?
Answer:$84
Step-by-step explanation:
$84 dollars because 3.5 percent of 600 is 21 so if we do 21x4=$84 well atleast that't what i think
Henry drinks 1/2 of a bottle of soda. Sasha then drinks 1/3 of the soda that is left in the bottle. There is now 6 ounces of soda in the bottle. How many ounces of soda were there in the full bottle?
Answer: There were 18 oz. in the full bottle.
Step-by-step explanation:
If there are 6 oz. left, and Sasha drank 1/3 of half the bottle, then that means she drank 3 oz, since 6 is 2/3 of 9, which means that half of the bottle was 9 oz. 9 oz. is half of 18 oz, which means that there were 18 ounces in the full bottle.
What is the slope of the line represented by the equation 2x-5y=9
The slope of the line represented by the equation 2x - 5y = 9 is 2/5 .
In the question ,
it is given that ,
the equation of the line is 2x - 5y = 9 .
we know that the equation of the line is represented as y = mx + c ,
where slope of the equation is "m" .
So , rewriting 2x - 5y = 9 in the form of y = mx + c ,
w get ,
2x - 5y = 9
5y = 2x - 9
dividing both sides of the equation 5y = 2x - 9 by 5 ,we get
y = 2/5x - 9/5
y = (2/5)x - 9/5
the slope is = 2/5 .
Therefore , The slope of the line represented by the equation 2x - 5y = 9 is 2/5 .
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A certain brand of coffee comes in two sizes. An 11.5-ounce package costs 3.19. A 30.6-ounce package costs 7.98. Find the unit price for each size. Then state which size is the better buy based on the unit price. Round your answers to the nearest cent.
The size that is the better one is 30.6-ounce package costs 7.98.
How to calculate the cost?The 11.5-ounce package costs 3.19. The price per package will be:
= 3.19 / 11.5
= 0.27
A 30.6-ounce package costs 7.98. The cost per package will be:
= 7.98 / 30.6
= 0.26
In this case, it should be noted that the cheaper one.is the better buy. This was illustrated as the 30.6-ounce package costs 7.98.
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g if you randomly select 850 credit card users, what interval will contain the sample proportion for 95% of samples of that size?
The Confidence interval is (0.85,1.05) which contain the sample proportion for 95%of samples size.
Confidence interval is an interval with a confidence level. Confidence interval is always constructed on basis of sample , p = sample statistic - margin of error to sample statistic + margin of error
Confidence interval for a proportion are calculated using the following formula:
p= ( p' - Z√p'(1-q')/n , p'+ Z √p'(1-p')/n ) ---(1)
where, p' ---> sample proportion for sucess
1-p' -----> sample proportion for failure
Z --> Z-value (statistic value)
n---> sample size
we have given that,
sample size ( n)=850 , sample proportion (p') = 0.95 and population proportion= 0.75
a) mean of sample of proportion is same as poplution proportion i.e 0.75 ..
1 -p' = q' = 0.05
Using the formula for margin of error ,
M .E = Z √ p'q'/n ---(2)
as the Z-value for given proportion is 13.46
putting all values in equation( 2) we get,
M.E = 13.45 √0.95×0.05/850 = 0.1005
Now, we shall calculate the confidence interval for given data
confidence interval (p)
= ( 0.95 - 0.100 , 0.95 + 0.100)
p= ( 0.85 , 1.05)
Hence,confidence interval(CI) is (0.85, 1.05).
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Complete Question:
75% of all credit card users carry a balance from month to month. a. If you randomly select 850 credit card users and will compute the sample proportion that carry a balance from month to month, what is the mean of the sample proportion? b. If you randomly select 850 credit card users, what interval will contain the sample proportion for 95% of samples of that size?
a) 6x(3x+5)-2x(9x-2)=17
b) 2x(3x -1)-3x(2x+11)-70=0
Answer:
a). 18x+30 - 18x+4=17
18x-18x 30+4 =17
34=17
[tex](a) \: { \pink{ \boxed{ \blue{ \sf{x = \frac{13}{30}}}}}}[/tex]
[tex](b) \: { \pink{ \boxed{ \blue{ \sf{x = -2}}}}}[/tex]
Step-by-step explanation:
[tex](a){ \red{ \sf{6x(3x + 5) - 2x(9x - 2) = 17}}}[/tex]
[tex]{ \red{ \sf{ { \cancel{18x}^{2} + 30x \: { \cancel { - 18x}^{2} + 4 = 17}}}}} [/tex]
[tex]{ \red{ \sf{30x + 4 = 17}}}[/tex]
[tex]{ \red{ \sf{30x = 17 - 4}}}[/tex]
[tex]{ \red{ \sf{30x = 13}}}[/tex]
Divide both the sides by 30 then,
[tex]{ \red{ \sf{ \cancel {\frac{30}{30}}}}}{ \red{ \sf{x} = \frac{13}{30}}} [/tex]
[tex]{ \red{ \boxed{ \green{ \sf{x = \frac{13}{30}}}}}} [/tex]
[tex](b) { \red{ \sf{2x(3x - 1) - 3x(2x + 11) - 70 = 0}}}[/tex]
[tex]{ \red{ \sf{ { \cancel{6x}^{2} - 2x}}}} \: \: { \red{ \sf{ \cancel { - 6x}^{2} - 33x - 70 = 0}}} [/tex]
[tex]{ \red{ \sf{ - 2x - 33x - 70 = 0}}}[/tex]
[tex]{ \red{ \sf{ - 35x - 70 = 0}}}[/tex]
[tex]{ \red{ \sf{ - 35x = 70}}}[/tex]
Divide both the sides by -35 then,
[tex]{ \red{ \sf{ \cancel {\frac{ - 35}{ - 35}}}x}}= { \red{ \sf{ { - \frac{ \cancel{70} ^{2} } { \cancel{35_{1} }}}}}}[/tex]
[tex]{ \red{ \boxed{ \green{ \sf{x = -2}}}}}[/tex]
Jacob reduced the size of a painting to a width of 3. 2 inches. What would be the new height if the painting was originally 42. 88 inches in width and 33. 5 inches tall?.
The new height of painting by Jacob will be 2.5 inches.
The ratio and proportion will be used to relate the original and reduced dimensions of painting. The original width and height = 42.88/33.5. Let us assume the new height be x. So, new width and height = 3.2/x. Equating these two fractions -
42.88/33.5 = 3.2/x
Rewriting the equation according to x
x = (3.2 × 33.5) ÷ 42.88
Performing multiplication in numerator
x = 107.2 ÷ 42.88
Performing division on Right Hand Side of the equation
x = 2.5
Thus, the new height will be 2.5 inches.
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Please answer this question, URGENT 50 POINT
Answer: Use your brain aka 12 and 7
Step-by-step explanation:isn't this urgent?
Fall Math Benchmark
1. For the scenario given, explain in words your process for solving the problem.
Two rectangular walls need to be painted. They are each 12 feet high and 23 feet
wide. It costs $1.50 per square foot for paint. How much will it cost to paint the
walls?
The amount that it will cost to paint the walls, given the cost per square foot and the dimensions of the rectangular walls is $828
How to find the cost?First, find the area of the rectangular walls by the formula for the area of a rectangle which is:
= Length x Width
The area of the rectangles is therefore:
= 12 x 23
= 276 feet ²
The area of the two rectangular walls is:
= 276 + 276
= 552 feet ²
The cost to paint the walls is:
= Area of walls x cost per square feet to paint
= 552 x 1.50
= $828
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princeton pretzels picks a package box A 6in 7in 6in box B 3in 8in 9in calculate the volume of each box answer
Answer:
box a - 252 inches squared (6 x 7 x 6)
box b - 216 inches squared (3 x 8 x 9)
Step-by-step explanation: