A mean is an arithmetic average of a set of observations. The amount that Jack has to earn in tips on Sunday if he wants to average $19 a day is $25.
What is Mean?A mean is an arithmetic average of a set of observations. it is given by the formula,
[tex]\rm Mean=\dfrac{\text{Sum of all obervation}}{\text{Number of observation}}[/tex]
As it is given that Jack makes $12 on Monday, $14 on Tuesday, $18 on Wednesday, $16 on Thursday, $26 on Friday and $22 on Saturday. And we need to know how much he should earn on Sunday, so the average is $19. Therefore, we can write,
[tex]\rm Mean=\dfrac{\text{Sum of all obervation}}{\text{Number of observation}}[/tex]
[tex]19 = \dfrac{12+14+18+16+26+22+x}{7}\\\\133 = 108 + x\\\\133-108=x\\\\x = 25[/tex]
Hence, the amount that Jack has to earn in tips on Sunday if he wants to average $19 a day is $25.
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Julia uses a scale to weigh three identical stacks of coins.
• The scale has a maximum percent error of 3%.
• The scale says the weight of the first stack of coins is 10.0 ounces.
• The scale says the weight of the second stack of coins is 10.3 ounces
Rounded to the nearest tenth of an ounce, what is the greatest possible amount that the scale could say for the weight of the third stack of coins?
A. 9.7 ounces. b .10.0 ounces c.10.3 ounces D. 10.6 ounces
Answer: 10.6
Step-by-step explanation: it has a .3% increase each time, therefore it would be D. 10.6
The rectangular prism below has a total surface area of 158 in^2. Use the net below to determine the missing dimension, x
A. 6 in
B. 8 in
C. 12in
D. 10 in
Answer:
b
Step-by-step explanation:
In an amphitheater, there are 20 seats in the front row, 23 seats in the second row, 26 seats in the third row, and so on, in an arithmetic sequenc A) Write an explicit formula to find an. The number of seats in the nº row.
B) The last row in the amphitheater has 83 seats in it. How many rows a seats are there?
C) Write an expression using sigma notation that represents the total number of seats in the amphitheater.
D) Evaluate this expression. How many total seats are there?
For the given arithmetic sequence we have:
A) [tex]A_n = 20 + (n - 1)*3[/tex]B) 22 rows.C) [tex]\sum_{n = 1\ to\ 22} (20 + (n - 1)*3)[/tex]D) There are 1,133 seats in total.How to write the formula for the sequence?
We know that we have 20 seats on the front row, and then we add 3 more on each row, so the formula will be:
[tex]A_n = 20 + (n - 1)*3[/tex]
This gives the number of seats on the n-th row.
B) The last row has 83 seats, then we need to solve:
[tex]A_n = 20 + (n - 1)*3 = 83\\\\(n - 1)*3 = 83 - 20 = 63\\\\n - 1 = 63/3 = 21\\\\n = 21 + 1 = 22[/tex]
So we conclude that there are 22 rows.
C) The total number of seats will be:
[tex]\sum_{n = 1\ to\ 22} (20 + (n - 1)*3)[/tex]
D) Instead of using the sum above (we should add 22 terms) we use the general formula for the sum of N terms in an arithmetic sequence:
[tex]S_N = (N/2)*(2A_1 + (N - 1)*d)[/tex]
In this case, we replace N by 22, and d is the common difference of the sequence, which we know is equal to 3, so we wil have:
[tex]S_{22} = (22/2)*(2*20+ (22 - 1)*3) = 11*(40 + 21*3) = 1,133[/tex]
There are 1,133 seats in total.
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Rationalise the equation :
[tex] \frac{y ^{2} }{ \sqrt{x^{2} + y {}^{2} } + x} [/tex]
Answer:
[tex]\sqrt{x^2+y^2}-x[/tex]
Step-by-step explanation:
[tex]\textsf{Mulitply by}\quad\dfrac{\sqrt{x^2+y^2}-x}{\sqrt{x^2+y^2}-x}:[/tex]
[tex]\implies \dfrac{y^2}{\sqrt{x^2+y^2}+x} \times \dfrac{\sqrt{x^2+y^2}-x}{\sqrt{x^2+y^2}-x}[/tex]
[tex]\implies \dfrac{y^2(\sqrt{x^2+y^2}-x)}{(\sqrt{x^2+y^2}+x)(\sqrt{x^2+y^2}-x)}[/tex]
[tex]\implies \dfrac{y^2(\sqrt{x^2+y^2}-x)}{(\sqrt{x^2+y^2})^2-x^2}[/tex]
[tex]\implies \dfrac{y^2(\sqrt{x^2+y^2}-x)}{x^2+y^2-x^2}[/tex]
[tex]\implies \dfrac{y^2(\sqrt{x^2+y^2}-x)}{y^2}[/tex]
[tex]\textsf{Cancel the common factor}\:y^2:[/tex]
[tex]\implies \sqrt{x^2+y^2}-x[/tex]
Rationalising the denominator of the given fraction means we need to multiply both the numerator and the denominator of the fraction by the conjugate of the expression in the denominator. For example:
[tex]\;\longrightarrow\dfrac{1}{a+b}[/tex]
Here the conjugate of denominator of the expression is a - b. So we need to multiply both the numerator and denominator with the fraction.
[tex]\;\longrightarrow \dfrac{1}{a+b} \times \dfrac{a-b}{a-b}[/tex]
Hence, this is what the rationalization means.
Elucidation:We have been given and equation and we have been asked to rationalise the equation.
The conjugate of the denominator of the given equation is √(x² + y²) - x. Therefore;
[tex]\implies \dfrac{y^2}{\sqrt{x^2+y^2}+x} \times \dfrac{\sqrt{x^2+y^2}-x}{\sqrt{x^2+y^2}-x}[/tex]
[tex]\implies \dfrac{y^2(\sqrt{x^2+y^2}-x)}{(\sqrt{x^2+y^2}+x)(\sqrt{x^2+y^2}-x)}[/tex]
[tex]\implies \dfrac{y^2(\sqrt{x^2+y^2}-x)}{(\sqrt{x^2+y^2})^2-x^2}[/tex]
[tex]\implies \dfrac{y^2(\sqrt{x^2+y^2}-x)}{x^2+y^2-x^2}[/tex]
[tex]\implies \dfrac{y^2(\sqrt{x^2+y^2}-x)}{y^2}[/tex]
[tex]\implies \boxed{\sqrt{x^2+y^2}}[/tex]
Hence, this is our required solution for this question.
Find the slope of the line y=5x+4y=5x+4.
Answer:
[tex]\huge\boxed{\sf Slope = m = 5}[/tex]
Step-by-step explanation:
Given slope equation:
y = 5x + 4
Comparing it with the standard form of slope equation
y = mx + b
Where m is slope and b is y-intercept
Hence,
by comparing both equation, we get:
Slope = m = 5
[tex]\rule[225]{225}{2}[/tex]
how can i simplify 11 to the 6th power over 11 to the 4th power?
Answer:
11² = 121
Step-by-step explanation:
When you divide powers with the same base, subtract the exponents.
[tex] \dfrac{11^6}{11^4} = 11^{6 - 4} = 11^2 = 121 [/tex]
Answer:
121
Step-by-step explanation:
11 to the 6 power = 1771561
11 to the 4 power = 14641
1771561/14641 = 121
what are ordered pairs
Answer:a pair of elements a, b having the property that (a, b) = (u, v) if and only if a = u, b = v.
[tex]5 = \frac{x}{3} + 2[/tex]
step by step please.
Answer:
9
Step-by-step explanation:
Given equation:
[tex]5 = \dfrac{x}{3} + 2[/tex]
To determine the solution (x) of the equation, we need to isolate it. To do this, we can subtract 2 both sides of the equation.
[tex]\implies 5 - 2 = \dfrac{x}{3} + 2 - 2[/tex]
[tex]\implies 3 = \dfrac{x}{3}[/tex]
To further isolate "x", we can use cross multiplication.
[tex]\implies 3 \times 3 = x[/tex]
Finally, simplify the expression on the left-hand-side to obtain the value of x.
[tex]\implies \boxed{9 = x}[/tex]
Which expression is equivalent to 5/8?
A. 8÷5
B. 8×5
C. 5÷8
D. 5×8
A fraction is equavalent to the top number divided by the bottom number.
5/8 is equivalent to 5 ÷ 8
Answer: C. 5 ÷ 8
Keith bought a tree for his backyard. The graph shows the height of the tree after a certain number of years.
A. At what rate is the tree growing?
B. Write an equation for the graph.
C. Is the graph proportional?
Answer:18
Step-by-step explanation:
Its is 18 caycausecause the arrow is pointing next to it
1
A storage container measures 3 ft by 6 ft and is 5 ft high. What is the volume of this container in cubic yards?
Answer:
3 1/3 yd^3
Step-by-step explanation:
Volume of a rectangular prism: L*W*H
ft. = 1/3 yd.
3/3 = 1 yd.
6/3 = 2 yd.
5/3 = 1 2/3 yd.
1*2*1 2/3
=2* 1 2/3
=2 4/3
= 3 1/3 yd.^3
2. a) How many months is one
quarter of a year?
Answer:
3
Step-by-step explanation:
A quarter is equal to four and since 12 divided by 4 = 3, 3 months is a quarter of a year
Have a great day!
Round to the nearest tenth if necessary.
Find the distance between the two points.
(2, 5) and (–1, –5)
Distance formula: sqrt((x2-x1)^2 + (y2-y1)^2)
distance = sqrt((-1 -2)^2 + (-5-5)^2)
distance = sqrt(109)
Distance = 10.44
Convert 0.54. to a decimal In base 3
Answer:
what does a this mean? .54 is a decimal
What is the end behavior of the function f of x equals 3 times the cube root of x?
As x → –∞, f(x) → –∞, and as x → ∞, f(x) → ∞
As x → –∞, f(x) → ∞, and as x → ∞, f(x) → –∞
As x → –∞, f(x) → 0, and as x → ∞, f(x) → 0
As x → 0, f(x) → –∞, and as x → ∞, f(x) → 0
[tex]f(x) = 3 \sqrt[3]{x} [/tex]
[tex]lim f(x) = 3 \sqrt[3]{ - \infty } = - \infty \\ x = > - \infty [/tex]
[tex]limf(x) = 3 \sqrt[3]{ \infty } = \infty \\ x = > \infty [/tex]
Answer:
As x → –∞, f(x) → –∞, and as x → ∞, f(x) → ∞.
Step-by-step explanation:
I got it right on the test.
FREE BRAINLIEST IF CORRECT: Write the following without the absolute value sign: |a^2| if a>0
Answer:
Step-by-step explanation:
When you square a number, whether it's positive or negative, the square is always positive. That is, a2 is positive whether a is positive or negative. Examples:
12 = 1 x 1 = 1
(-1)2 = (-1) x (-1) = 1
52 = 5 x 5 = 25
(-5)2 = (-5) x (-5) = 25
Since the answer is always positive, you don't need the absolute value signs: |a2| = a2.
hope this helps can i get brainly pls
A cone has a height of 6 yards and a radius of 3 yards. What is its volume? Use 3.14 and round your answer to the nearest hundredth.
Answer:
V = 56.52
Step-by-step explanation:
Formiula
V = (1/3) * pi * r^2 * h
Givens
pi = 3.14
r = 3 yard
h = 6 yards
Solution
V = (1/3) * 3.14 * 3^2 * 6 Multiply 1/3 * 6
V = 2 * 3.14 * 9
V = 56.52
the sign below shows the length of a trail park 3 1/4miles what is the length , in feet of the trail
Answer: 17160 feet
Step-by-step explanation: Convert 3.25miles to feet. Multiply by 5280
Expand and fully simplify 3(x + 1) + 2(3x + 4)
Answer:
[tex]\Large\boxed{\sf{9x+11}}[/tex]Step-by-step explanation:
Given:
Isolate the term of x from one side of the equation.
Use the distributive property.
DISTRIBUTIVE PROPERTY:
[tex]\Longrightarrow: \sf{A(B+C)=AB+AC}[/tex]
Each term within the parentheses can be multiplied by a factor outside the parentheses.
3(x+1)
3*x=3x
3*1=3
Rewrite the expression down.
3x+3
3x+3+2(3x+4)
Multiply expand.
2(3x+4)
2*3x=6x
2*4=8
6x+8
3x+3+6x+8
Combine like terms.
3x+6x+3+8
Add the numbers from left to right.
3+8=11
3x+6x+11
Add.
Solutions:
3x+6x=9x
[tex]\Longrightarrow: \boxed{\sf{9x+11}}[/tex]
Therefore, the final answer is 9x+11.I hope this helps. Let me know if you have any questions.
Find the value of x.
Step-by-step explanation:
9x+5x+71+139+92=540
14x+302=540
14x=540-302=238
x=238/14
x=17
Matthew and Anthony each have a video game collection. The number of video games in Matthew’s collection can be represented by x. The number of video games in Anthony’s collection is 5 times the number in Matthew’s collection. The total number of video games in both collections is 72. What is x, the number of video games in Matthew’s collection?
The number of video games in Matthew’s collection is 12
To solve the problem, we need to know what simultaneous equations are
What are simultaneous equations?These are a pair of equations which contain two variables.
Now, let
x = number of video games in Matthew's collection and y = number of video games in Anthony's collection.Given that the number of video games in Anthony’s collection is 5 times the number in Matthew’s collection, we have that y = 5x (1)
Also, the total number of video games in both collections is 72.
So, x + y = 72 (2)
Substituting equation (1) into (2), we have
x + 5x = 72
6x = 72
x = 72/6
x = 12
So, the number of video games in Matthew’s collection is 12
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what are the solutions to the equation -5x2 + 3x = -9
Answer: Move terms to the left side−52+3=−9−5x2+3x=−9−52+3−(−9)=0−
Common factor−52+3+9=0−5x2+3x+9=0−(52−3−9)=0
Divide both sides by the same factor−(52−3−9)=0−(5x2−3x−9)=052−3−9=0
Solution=3±321 over 10
Step-by-step explanation:
Answer: 1/3 as an equation
Step-by-step explanation: file attached
The Hiking Club plans to go camping in a State park where the probability of rain on any given day is 17%. What is the probability that it will rain on at least four of the five days they are there? Round your answer to the nearest thousandth.
Answer: 30%
Explanation: Every day is 30%.
- Jackson
Can someone help me find the value of y and how to my got it
Explanation:
The tickmarks tell us that sides HG and FG are the same length. The triangle is isosceles. Directly from this, we know that the opposite angles F and H are congruent. Both are 4y-7 degrees.
Angle G is 90 degrees because of Thales' Theorem. This is because HF is the diameter of the circle. It's also the hypotenuse of the right triangle.
For any triangle, the three interior angles always add to 180 degrees.
F+G+H = 180
(4y-7) + (90) + (4y-7) = 180
8y + 76 = 180
8y = 180-76
8y = 104
y = 104/8
y = 13
percent discount
A $98.00 power inverter is on sale for $78.40
Answer: 20%
Step-by-step explanation:
98 - 78.40 = $19.6
Discount is 19.6/98 = 0.2
Percentage = 0.2 × 100/ 1
M is the point (3, -3) and N is the point (7,5). P is a point on the line MN such that MP = 1/3MN. - (a) Find the position vector of P. (b) Calculate the magnitude of MN
Answer:
[tex]P=\left(\dfrac{13}{3},-\dfrac{1}{3}\right)[/tex]
[tex]|\overrightarrow{MN}|=4\sqrt{5}[/tex]
Step-by-step explanation:
Part (a)
[tex]x_P=\dfrac13(x_N-x_M)+x_M=\dfrac13(7-3)+3=\dfrac{13}{3}[/tex]
[tex]y_P=\dfrac13(y_N-y_M)+y_M=\dfrac13(5-(-3))+(-3)=-\dfrac13[/tex]
[tex]\implies P=\left(\dfrac{13}{3},-\dfrac{1}{3}\right)[/tex]
Part (b)
The magnitude of MN is the distance between points M and N.
Using the distance between two points formula, where
[tex](x_1,y_1)=(3,-3)[/tex] and [tex](x_2,y_2)=(7,5)[/tex]
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]\implies |\overrightarrow{MN}|=\sqrt{(7-3)^2+(5-(-3))^2}[/tex]
[tex]\implies |\overrightarrow{MN}|=4\sqrt{5}[/tex]
A game show contestant has answered 37 out of 44 trivia questions correctly so far. Solve the
90
equation
100
-
37 + 1 to find the number of consecutive questions the contestant needs to answer correctly to
44 + y
raise the correct answer percentage to 90%
Answer:
The contestant needs to answer the next 26 consecutive questions correctly.
Step-by-step explanation:
[tex] \frac{37 + x}{44 + x} = \frac{9}{10} [/tex]
[tex]9(44 + x) = 10(37 + x)[/tex]
[tex]396 + 9x = 370 + 10x[/tex]
[tex]x = 26[/tex]
The contestant needs to answer the next 26 consecutive questions correctly.
What is proportion?Proportion is an equation that defines that the two given ratios are equivalent to each other.
In other words, the proportion states the equality of the two fractions or the ratios.
In proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other.
Given that, a game show contestant has answered 37 out of 44 trivia questions correctly so far.
We need to solve an equation given to find the number of consecutive questions the contestant needs to answer correctly,
So, the equation is,
37+x / 44 + x = 90/100
37+x / 44 + x = 9/10
10(37+x) = 9(44+x)
370+10x = 396+9x
x = 26
Hence, the contestant needs to answer the next 26 consecutive questions correctly.
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If 140 people were surveyed, how many preferred crab?
If 140 people were surveyed, from the given table, the number of people that preferred crab is; 42
How to work with percentages?We are given;
Total sample size; n = 140
Now, from the table we see the percentages that preffered each seafood.
Percentage that preferred Shrimp = 24%
Percentage that preferred Crab = 30%
Percentage that preferred Fish = 36%
Percentage that preferred Neither = 10%
Thus;
Number that preferred Crab = 30% * 140
Number that preferred Crab = 42 people
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Please help me solve this with steps
Answer:
x = 1.5 or 3/2
Step-by-step explanation:
First, expand the equation.
(2x - 3)² = 0
(2x - 3)(2x - 3) = 0
In similar equations, we would solve for both pairs of parenthesis. However, since the equations inside both are the same, we only need to solve for ONE of them, bringing one correct answer.
2x - 3 = 0
Add 3 to both sides.
2x = 3
Divide both sides by 2.
x = 3/2 or 1.5.
Step-by-step explanation:
Mark me brainliest please i really need itEli and Samantha work at a dry cleaners ironing shirts. Eli can iron 20 shirts per hour, and Samantha can iron 35 shirts per hour. Samantha worked 2 more hours than Eli and they ironed 400 shirts between them. Write a system of equations that could be used to determine the number of hours Eli worked and the number of hours Samantha worked. Define the variables that you use to write the system.
Answer:
Step-by-step explanation:
I did this before. I'm 14 :D
E-
y=20x
Eli ironed 2 more hours and got 400 shirts.
S-
y=35x
Let x be the number of shirts ironed.
400/20x = 20.
20-2=18.
That means she ironed 360 shirts prior.
If both of them were at the same speed of 18 by (let x represent). Then Samantha ironed 630 shirts while Eli ironed 360 shirts, but ironed 2 more hours which got him to get 400 shirts.