1. In 2020, the populations of City A and City B were equal. From 2015 to 2020, the population of City A increased by 20% and the population of City B decreased by 10%. If the population of City A was 120,000 in 2015, what is the population of City B in 2015?
2. A chef is preparing a sauce for a steak she offers as a key dish in her menu. To prepare the sauce she needs to prepare a mix with 40% butter, with the rest being egg yolk. In the kitchen right now, she only has a sauce that has 20% butter (rest is egg yolk) and a sauce that has 50% butter (rest is egg yolk) in stock. In what ratio should she mix the 20% sauce with the 50% sauce in order to obtain the 40% sauce that she needs to prepare her famous recipe?
3. A book was on sale for 30% off its original price. If the sale price of the book was $28, what was the original price of the book? (Assuming there is no sales tax)
4. At a retail store, they needed to do surveys of 32 stores which equals 40% of all their stores. How many stores does the retailer have in total?*
Answer:
180000 people
1 : 2
$40
80 stores
Step-by-step explanation:
1.)
Population in 2020 are equal : Let population =
City A increased by 20% From 120,000 in 2015
(1 + 0.2) * 120,000 = (1.2 * 120,000) = 144,000
Hence, city A = 144,000.
Since, city A and B have equal population ; city B also has a population of 144000 in 2020.
Let population in 2015 = x
(1 - 0.2) * x = 144000
0.8x = 144000
x = 144000/0.8
x = 180,000
2.)
Let proportion of 20% butter = x and proportion of 50% butter = 1 - x
0.2x + 0.5(1 - x) = 0.4
0.2x + 0.5 - 0.5x = 0.4
-0.3x + 0.5 = 0.4
-0.3x = 0.4 - 0.5
-0.3x = - 0.1
x = 0.1/0.3
x = 0.3333
(1-x) = 1 - 0.33333 = 0.6666%
0.3333% of 20% butter
0.6666% of 50% butter
Hence ;
0.3333 : 0.6666
1 : 2
3.)
Let original price of book = x
Discount on sale = 30%
Sale price = $28
Sale price = original price * (1 - discount)
$28 = (1 - 0.3) * x
$28 = 0.7x
x = $28/0.7
x = $40
4.)
Let total number of stores = x
Store surveys needed = 32
40% of total stores = 32 stores
0.4x = 32
x = 32 / 0.4
x = 80
A G.P is such that the 3rd term minus a first term is 48. The 4th term minus 2nd term 144. Find: (i) Common ratio ii) The first term (ii) 6th term of the sequence
Answer:
Step-by-step explanation:
r is the common ratio.
Third term minus first term is 48.
a₃ - a₁ = 48
a₃ = a₁r²
a₁r² - a₁ = 48
a₁(r²-1) = 48
r²-1 = 48/a₁
Fourth term minus second term is 144.
a₄ - a₂ = 144
a₂ = a₁r
a₄ = a₁r³
a₁r³ - a₁r = 144
a₁r(r²-1) = 144
r²-1 = 144/(a₁r)
48/a₁ = 144/(a₁r)
r = 3
:::::
r²-1 = 48/a₁
a₁ = 6
:::::
a₆ = a₁r⁵ = 1458
(i) The common ratio for the given condition is 3.
ii) The first term of the sequence is 6.
iii) The 6th term of the sequence is 1458.
What is a sequence?It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.
Divergent sequences are those in which the terms never stabilize; instead, they constantly increase or decrease as n approaches infinity,
It is given that a is a geometric progression such that the 3rd term minus a first term is 48. The 4th term minus the 2nd term 144.
Each number following the first in a geometric sequence is multiplied by a particular number, known as the common ratio.
As the third term minus the first term is 48.
a₃ - a₁ = 48
a₃ = a₁r²
a₁r² - a₁ = 48
a₁(r²-1) = 48
r²-1 = 48/a₁
The fourth term minus the second term is 144.
a₄ - a₂ = 144
a₂ = a₁r
a₄ = a₁r³
a₁r³ - a₁r = 144
a₁r(r²-1) = 144
r²-1 = 144/(a₁r)
48/a₁ = 144/(a₁r)
r = 3
r²-1 = 48/a₁
a₁ = 6
a₆ = a₁r⁵ = 1458
Thus the common ratio for the given condition is 3, the first term of the sequence is 6 and the 6th term of the sequence is 1458.
Learn more about the sequence here:
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Given the flag ABCDE, determine the single rule (x,y) that creates the
transformed figure A'B'C'D'E'. Fill in your answer below in the format (x,y)--
>
WILL GIVE BRAINLIEST
Answer:
(y, -x)
Step-by-step explanation:
Rotation of 90°
(Clockwise)
(x, y) ---> (y, -x)
Rotation of 90°
(CounterClockwise)
(x, y) --> (-y, x)
Rotation of 180°
(Both Clockwise and Counterclockwise)
(x, y) ---> (-x, -y)
Rotation of 270°
(Clockwise)
(x, y) ---> (-y, x)
Rotation of 270°
(CounterClockwise)
(x, y) ---> (y, -x)
The average monthly salary of a worker is ₹8200. If there are 45 workers in a factory, then total expenditureincurred on expenditure is:
Answer: [tex]Rs.3,69,000[/tex]
Step-by-step explanation:
Given
average monthly salary of a worker is [tex]Rs.8200[/tex]
If there are 45 workers in a factory
Total expenditure is calculated by taking the product of Average monthly salary and no of workers in the factory
[tex]\Rightarrow 8200\times 45\\\Rightarrow Rs.3,69,000[/tex]
HELP. Need help on this
Answer:
what are the answers
Step-by-step explanation:
35. Graph the following system of equations and find the x-coordinate of the solution.
3x+ 3y=3
Y=-1/2x+2
x=2
x= -2
X = 3
x=0
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Answer:
(b) x = -2
Step-by-step explanation:
The graph shows the lines intersect at (x, y) = (-2, 3).
The x-coordinate of the solution is x = -2.
What is the value of cot ø= 2/3 what is the value of csc ø
Answer:
Step-by-step explanation:
cotθ = cosθ/sinθ = 2/3
sinθ = 3/√(2²+3²) = 3/√13
cscθ = 1/sinθ = √13/3
Question 7(Multiple Choice Worth 1 points)
(07.02 MC)
Jason has two bags with 6 tiles each. The files in each bag are shown below
1
2
3
4
5
6
Without looking, Jason draws a file from the first bag and then a file from the second bag What is the probability of Jason drawing the file numbered 5 from the first bag and an odd file from the second bag?
0
영
o
Answer:a.3/6
Step-by-step explanation:
Because there’s a total of 12 files in each bag which is 6 in each
help
The points (63, 121), (71, 180), (67, 140), (65, 108), and (72, 165) give the weight in pounds as a function of height in inches for 5 students in
a class. Give the points for these students that represent height as a function of weight
{(121, 63), (180, 71), (140, 67), (108, 65), (165, 72)}
{(121, 140), (180, 71), (140, 67), (108, 65), (165, 72);
{(121, 71), (180, 63), (140, 67), (108, 65), (165, 72)}
{(63, 121), (71, 180), (67, 140), 65, 108), (72, 165))
Answer:
{(121, 63), (180, 71), (140, 67), (108, 65), (165, 72)}
Step-by-step explanation:
We have:
Weight as a function of height.
Give the points for these students that represent height as a function of weight:
Inverse of the input, that is, in the (x,y) format, (x,y) -> (y,x), the coordinates are exchanged, and thus, the correct option is:
{(121, 63), (180, 71), (140, 67), (108, 65), (165, 72)}
Please help me thank you
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Answer:
y = 32.1x +779.91165 cases in 2010Step-by-step explanation:
A suitable statistics calculator can tell you the coefficients of the linear regression equation. In the attached, we put the given x- and y-values into a table and asked for the best fit equation. Rounded to tenths, the equation is ...
y = 32.1x +779.9
The year 2010 is 12 years after 1998, so we can find the desired projection using x=12.
y = 32.1×12 +779.9 = 385.2 +779.9 = 1165.1
The number of cases is projected to be 1165 in 2010.
_____
We wonder if using the button "Open Statistics Calculator" will let you solve this question yourself.
Any help would be very appreciated
Answer:
21
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp/ adj
tan 60 = x / 7 sqrt(3)
7 sqrt(3) tan 60 = x
7 sqrt(3) sqrt(3) = x
7*3 = x
21 = x
A survey of 77 teenagers finds that 30 have 5 or more servings of soft drinks a week. a. Give a 90% confidence interval for the proportion of teenagers who have 5 or more servings of soft drinks a week. b. In the general population, 30% have 5 or more servings of soft drinks a week. Is there evidence that a higher proportion of teenagers have 5 or more servings of soft drinks a week than the general population
Answer:
a) The 90% confidence interval for the proportion of teenagers who have 5 or more servings of soft drinks a week is (0.2982, 0.481).
b) 30% = 0.3 is part of the confidence interval, which means that there is no evidence that a higher proportion of teenagers have 5 or more servings of soft drinks a week than the general population.
Step-by-step explanation:
Question a:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
A survey of 77 teenagers finds that 30 have 5 or more servings of soft drinks a week.
This means that [tex]n = 77, \pi = \frac{30}{77} = 0.3896[/tex]
90% confidence level
So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3896 - 1.645\sqrt{\frac{0.3896*0.6104}{77}} = 0.2982[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3896 + 1.645\sqrt{\frac{0.3896*0.6104}{77}} = 0.481[/tex]
The 90% confidence interval for the proportion of teenagers who have 5 or more servings of soft drinks a week is (0.2982, 0.481).
Question b:
30% = 0.3 is part of the confidence interval, which means that there is no evidence that a higher proportion of teenagers have 5 or more servings of soft drinks a week than the general population.
write √3 x √6 in the form b√2 where b is an integer
Answer:
[tex]3 \sqrt{2} [/tex]
Step-by-step explanation:
[tex] \sqrt{(9 \times 2)} [/tex]
Take the square root of 9 out of the square root and leave the 2 in.
Answer:
3[tex]\sqrt{2}[/tex]
Step-by-step explanation:
Using the rules of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex] , then
[tex]\sqrt{3}[/tex] × [tex]\sqrt{6}[/tex]
= [tex]\sqrt{3(6)}[/tex]
= [tex]\sqrt{18}[/tex]
= [tex]\sqrt{9(2)}[/tex]
= [tex]\sqrt{9}[/tex] × [tex]\sqrt{2}[/tex]
= 3[tex]\sqrt{2}[/tex]
This is a list of the heights ( each nearest cm ) of 12 children
150 134 136 139 131 141
132 134 136 137 150 146
Select the type of the data.
Discrete
Continuous
Categorical
Qualitative
choose one
NO FAKE ANSWERS
FIRST MARKED BRAINLIST
qualitative
Step-by-step explanation:
b cos the question is in quality format
Answer:
cutee!
SUP???
Hiii friend :]
cuteee~!
prettyyy
which of the following tables represents an inverse variation between x and y
Answer:
I think that d is the answer
round 8 5/6 to the nearest whole number
Answer:
9
Step-by-step explanation:
8 5/6
5/6 is close to 1 so it will round up
8+1 = 9
8 5/6 rounds to 9
Answer:
[tex]9[/tex]
Step-by-step explanation:
Step 1: Round [tex]8\frac{5}{6}[/tex] to the nearest whole number
In order to round up, the fraction needs to be either 1/2 or greater than 1/2. In our case, it is greater than half therefore we will round up to 9.
Answer: [tex]9[/tex]
Which equation is true?
f of negative 10 = 1
f of 2 = negative 10
f of 0 = 6
f of 1 = negative 10
Answer:
f(0) = 6
Step-by-step explanation:
Complete question:
The function f (x) is given by the set of ordered pairs 1,0 (-10,2), (0,6) (3,17) (-2,-1) which equation is true
f(-10)=1
f(2)=-10
f(0)=6
f(1)=-10
Given the coordinate (x, y). This shows that the input function is x and the output function is y, i.e. f(x) = y
From the pair of coordinates given, hence;
f(1) = 0
f(-10) = 2
f(0) = 6
f(3) = 17
f(-2) = -1
From the following options, this shows that f(0) = 6 is correct
Answer:
f(0) = 6
Step-by-step explanation:
EDGE
Rectangle QRST with vertices Q(-3,2), R(-1,4), S(2,1), and T(0,-1)) in the x-axis
Answer:
D
Step-by-step explanation:
The coordinate of the new rectangle after the reflection across will be Q'(-3, -2), R'(-1, -4), S'(2, -1), and T'(0, 1). Then the correct option is D.
What is a transformation of a point?A spatial transformation is each mapping of feature space to itself and it maintains some spatial correlation between figures.
The reflection does not change the shape and size of the geometry. But flipped the image.
Rectangle QRST with vertices Q(-3, 2), R(-1, 4), S(2, 1), and T(0, -1).
The coordinate of the new rectangle after the reflection across is given as,
Q' = (-3, -2)
R' = (-1, -4)
S' = (2, -1)
T' = (0, 1)
The coordinate of the new rectangle after the reflection across will be Q'(-3, -2), R'(-1, -4), S'(2, -1), and T'(0, 1). Then the correct option is D.
More about the transformation of a point link is given below.
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Question 1
The perfect square among the following options is
8
Say
27
216
256
Answer:
217 is the perfect swuare i think
Find the slope, if it exists, of the line containing the points (10,-3) and (10,-8).
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
m=
Answer:
The slope is undefined.
Step-by-step explanation:
The line must pass through the points (10,-3) and (10,-8), meaning that it must be vertical. The slope of a line is undefined if the line is vertical.
The table below represents average food costs broken down by meal. If you
were planning a trip, how much should you budget for food costs per day?
Breakfast
Lunch
Dinner
$12.98
$18.95
$26.58
A. $20.00
B. $60.00
C. $80.00
D. $45.00
By taking the addition of the values in the table and overestimating a little bit, the correct option is B: $60.00
How much should you budget for food costs per day?Here we have the following table of average costs:
Breakfast $12.98Lunch $18.95Dinner $26.58Assuming you eat these 3 per day, the total cost in food per day is the sum of all the values in the table.
It gives:
Total cost: $12.98 + $18.95 + $26.58 = $48.51
Notice that these are average costs, so you should budget a little bit over that just in case, then the correct option is $60, which is the first option over the average total cost.
Learn more about additions:
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Answer:
45
Step-by-step explanation:
Simplify to the extent possible:
(logx16)(log2 x)
Answer:
Step-by-step explanation:
Use the change-of-base rule.
Which equation could represent a linear combination of the systems?
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Answer:
(b) 0 = -78
Step-by-step explanation:
Subtracting 6 times the first equation from the second will give ...
(4x +15y) -6(2/3x +5/2y) = (12) -6(15)
0 = -78
Answer:
the answer is b
Step-by-step explanation:
Which expression is equivalent to 27 + 45?
Answer:
8 x 9
Have a nice day!
Which of the following describes an angle with a vertex at Z?
A biologist is researching a newly discovered species of bacteria. At time t = 0 hours, she puts 100 bacteria into what she has determined to be a favourable growth medium. The population of bacteria doubles every 3 hours. How many bacteria are there in 6 hours? a)200 b)100 c)400 d)600
Answer:
I'm sorry but I don't know this one
Need Help this is due in 30 minutes!
Answer:
E
Step-by-step explanation:
Since all the numbers are hundredths decimals, let multiply by the power of 2 of the base 10. So let multiply the equation by
[tex]10 {}^{2} [/tex]
So our new equation is
[tex]3 3{x}^{2} + 71x - 14 = 0[/tex]
Solve by AC method
[tex]ac = - 462[/tex]
[tex]b = 71[/tex]
We must think of two numbers that
Multiply to -462 and Add to 71. Set up equation
The numbers are 77 and -6.
So our new equation is
[tex] {33x}^{2} + 77x - 6x - 14 = 0[/tex]
Solve by factoring by grouping
[tex](33 {x}^{2} + 77x) - (6x - 14)[/tex]
Factor out 11 for the first equation
[tex]11x(3x + 7) - 2(3x + 7)[/tex]
So our factors are
[tex](11x - 2)(3x + 7)[/tex]
Set each equal to zero
[tex]11x - 2 = 0[/tex]
[tex]11x = 2[/tex]
[tex]x = \frac{2}{11} [/tex]
[tex]3x + 7 = [/tex]
[tex]3x = - 7[/tex]
[tex]x = \frac{ - 7}{3} [/tex]
What is the surface area of the composite figure?
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Answer:
382 cm²
Step-by-step explanation:
The side facing is a trapezoid with bases 8 and 14 cm, and height 7 cm. Its area is ...
A = 1/2(b1 +b2)h
A = (1/2)(8 +14)(7) = 77 . . . . cm²
The perimeter of the face is ...
7 cm + 8 cm + 9 cm + 14 cm = 38 cm
The total surface area is the sum of the lateral area and the base area.
SA = LA + BA
SA = (38 cm)(6 cm) + 2×(77 cm²) = 228 cm² + 154 cm²
SA = 382 cm²
The surface area of the composite figure is 382 square centimeters.
_____
Additional comment
The lateral area is the width of a rectangular face (6 cm) times the total of all of the lengths of those faces. That total is the perimeter of the trapezoidal base (38 cm).
There are two trapezoidal bases that contribute area. The first calculation figured the area of one of them.
About 9% of the population has a particular genetic mutation. 400 people are randomly selected. Find the mean for the number of people with the genetic mutation in such groups of 400
Answer:
36 people
Step-by-step explanation:
The expected value E(X) = mean of sample = np
Where, p = population proportion, p = 9% = 0.09
n = sample size, = 400
The mean of the number of people with genetic mutation, E(X) = np = (400 * 0.09) = 36
36 people
Does the point (0, 0) satisfy the equation y = x2?
Answer:
The point is a solution
Step-by-step explanation:
y = x^2
Substitute the point into the equation and see if it is true
0 = 0^2
0=0
True
