The original price of the game was £18. This is derived by understanding a 1/2 increase equates to a 50% increase, thus making £27 150% of the original price. To get the original price, divide £27 by 1.5.
Explanation:To solve this problem, you need to understand that an increase of 1/2 equals a 50% increase. If the game price were £27 after increasing by 50%, that means £27 represents the original price plus an additional half (50%) of the original price, in other words, it represents 150% of the original price. We can set up the equation like this:
Original Price(1.5) = £27
To solve for the original price, we divide £27 by 1.5, resulting in £18.
So, the original price of the game was £18.
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Which graph represents a vertical translation by 4 units down of the function f(x)=2x?
The equation of function which have vertical translation by 4 unit will be
f(x)= 2x - 4
To understand more, check below explanation.
Translation of function:The equation of function is given as,
[tex]f(x)=2x[/tex]
If we have to shift graph of function a unit down. then required equation will be, [tex]f(x)=2x-a[/tex]
If we have to shift graph of function b unit up. then required equation will be, [tex]f(x)=2x+b[/tex]
We have to do vertical translation by 4 units down of the function f(x)=2x.
Hence, required equator will be [tex]f(x)=2x-4[/tex]
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Jumoke is 11yrs old than Aminata in 5yrs time Jumoke will be twice as old as Aminata . Find their present ages
Answer: Jumoke is currently 16 and Aminata is currently 8
Step-by-step explanation:
Could I get brainiest please? its free :D
Jumoke is 27 and Aminata is 11.
11 + 5 = 16
16 x 2 = 32
32 - 5 = 27
27 - 11 = 16
I tried. Correct me if I'm wrong.
Perbandingan kelereng Faiz dan Bayu 4 : 11. Jumlah kelereng mereka 60 buah. Selisih kelereng keduanya adalah
The difference in the number of their marbles is 28 Buah.
The ratio of Faiz's marbles to Bayu's marbles is given as 4:11. If the total number of marbles they have is 60, you can find the number of marbles each of them has.
Let x be the common multiplier for both parts of the ratio. Then, Faiz has 4x marbles, and Bayu has 11x marbles.
The total number of marbles is the sum of their marbles:
4x + 11x = 60
Combine like terms:
15x = 60
Divide by 15 to find x :
x = 4
Now, substitute x back into the expressions for Faiz and Bayu's marbles:
- Faiz's marbles: [tex]\( 4x = 4 \times 4 = 16 \)[/tex]
- Bayu's marbles: [tex]\( 11x = 11 \times 4 = 44 \)[/tex]
The difference in the number of their marbles is [tex]\( 44 - 16 = 28 \)[/tex].
So, the correct answer is: C. 28 Buah
Complete question:
Perbandingan kelereng Faiz dan Bayu 4:11. Their total color is 60. The best color of them is ...
16 pieces
24 pieces
28 pieces
44 pieces
Brad is putting up a 10 foot diameter circular flower garden in his yard. He will put plastic edging along the flowerbed. How many feet of edging will Brad need to enclose his flower garden?
Answer:
10π feet, or about 31.42 feet
Step-by-step explanation:
Diameter = 2 times radius, so the radius is 5 feet.
The question is asking us for the circumference - the distance around the circle. Plug our radius into the formula.
C = 2πr
C = 2π(5)
C = 10π feet = about 31.42 feet
Answer:
20 Pi feet or 62.8318530718 ft
Step-by-step explanation:
Find the circumference
Pi X diameter
radius = 1/2 diameter
radius *2 = 20
20 * Pi
What is the function g(x) created from f(x) = x^2 by moving the graph left 9 units, vertically stretching it by a factor of 4, and shifting the graph up 5 units?
Given:
The parent function is [tex]f(x)=x^2[/tex]
We need to determine the function g(x) created from the function f(x) by moving the graph left 9 units, vertically stretching it by a factor of 4, and shifting the graph up 5 units.
Shift left 9 units:
The rule to shift the graph c units to the left is given by
[tex]y=f(x+c)[/tex]
where c is the positive real number.
Hence, to shift the graph 9 units to the left is given by
[tex]f(x)=(x+9)^2[/tex]
Vertical stretch by a factor of 4:
The rule to stretch the graph vertically by a factor of c is given by
[tex]y=cf(x)[/tex]
where [tex]c>1[/tex]
Hence, to stretch the graph vertically by a factor of 4, we have;
[tex]f(x)=4(x+9)^2[/tex]
Shifting 5 units up:
The rule to shift the graph c units upward is given by
[tex]y=f(x)+c[/tex]
where c is the positive real number.
Hence, to shift the graph 5 units upward is given by
[tex]f(x)=4(x+9)^2+5[/tex]
Therefore, the function [tex]g(x)=4(x+9)^2+5[/tex] is created from the graph [tex]f(x)=x^2[/tex] by moving the graph left 9 units, vertically stretching it by a factor of 4 and shifting up 5 units.
Hence, the graph g(x) is [tex]g(x)=4(x+9)^2+5[/tex]
The function g(x) created from f(x) = x^2 by moving the graph left 9 units, vertically stretching it by a factor of 4, and shifting the graph up 5 units is g(x) = 4*(x+9)^2 + 5.
Explanation:To generate the function g(x) from f(x) = x^2, you will perform several transformations on it:
A horizontal shift of 9 units to the left. To do this, you change the x inside the function to (x+9). A vertical stretch by a factor of 4. To do this, you multiply the whole function by 4.A vertical shift of 5 units up. To do this, you add 5 to the entire function.So, after performing these transformations to f(x) = x^2, you get the function g(x) = 4*(x+9)^2 + 5.
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John goel is to have more then -7 dollors in hisaccount by the end of this mounth. the varible d is the nuber of dollor in johns bank account at the end of the mounth. Whrite an lineqwalatiy in terms of d that is true only if john meets hif monthy goal
Answer:
d > - 7
Step-by-step explanation:
John is to have more then -7 dollars in his account by the end of this month.
Now, the variable d is the number of dollars in John's bank account at the end of the month.
Therefore, the inequality in terms of d that is true only if John meets his monthly goal will be
d > - 7 (Answer)
A pool in the shape of a rectangular prism is being filled with water. The length and width of the pool is 24 feet and 15 feet. If the height of the water in the pool is LaTeX: 1\frac{1}{3}1 1 3feet, what is the volume of water in cubic feet
Answer:
Should be 480.
A growth medium is inoculated with 1,000 bacteria, witch grow at rate of 15% each day. What is the population of the culture 6 days after inoculation?
Answer: the population of the culture 6 days after inoculation is 2313.
Step-by-step explanation:
The growth rate is exponential. We would apply the formula for exponential growth which is expressed as
y = b(1 + r)^ t
Where
y represents the population after t days.
t represents the number of days.
b represents the initial population.
r represents rate of growth.
From the information given,
b = 1000
r = 15% = 15/100 = 0.15
t = 6 days
Therefore
y = 1000(1 + 0.15)^6
y = 1000(1.15)^6
y = 2313
A quarter is worth of a dollar. Haley needs to exchange dollar bills to get quarters to do her laundry in coin washers and dryers. How many quarters will she get for $13?
Answer:
52 quarters
Step-by-step explanation:
-We know that a quarter dollar is equivalent to $0.25
[tex]\$1=4 \ Quarters[/tex]
-Given that Haley has $13, we multiply this amount by 4 since $1 has 4 quarters to obtain the number of quarters:
[tex]Q=13\times 4\\\\=52[/tex]
Hence, Hayley will get 52 quarters.
If sec0= 25/24 find cot0
Answer:
cot θ = 24/7
Step-by-step explanation:
This will be difficult to explain without a diagram, but let's proceed.
Since sec θ = 25/24 (secant θ is equal to hypotenuse/adjacent) the hypotenuse of the triangle is 25 and the side adjacent to θ will be equal to 24. To find the opposite side-length you can use the Pythagorean theorem.
25^2 = 24^2 + a^2 (You can use either a or b as the variable)
625 = 576 + a^2 (Subtract 576 from each side)
a^2 = 49
a = 7 (The sqrt of 49 is 7 | This is the side-length of the opposite side relative to θ)
Since cotangent is always adjacent/opposite:
cot θ = 24/7
Simplify the following expression if k=-4 and n =4.
[tex] - 3( {k}^{2} + 2n)[/tex]
Answer: -72
Step-by-step explanation:
[tex]-3(k^2+2n)\\-3((-4)^2+2(4))\\-3(16+8)\\-3(24)\\-72[/tex]
Which name accurately describes the figure shown below and why?.
Answer:
the third answer is right
Step-by-step explanation:
its a rhombus because the 4 sides are of equal length and the opposite sides are parallel but there are no right angles.
in the Pythagorean Theorem, the sum of the squares of the legs is equal to the square of the
Answer:
71
Step-by-step explanation:
because the theorem is sum of the square
The answer is d. hypotenuse.
Here's why:
The Pythagorean Theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides (the legs).
So, if you have a right triangle with legs of length a and b, and hypotenuse of length c, the equation would be: a^2 + b^2 = c^2.
Therefore, the sum of the squares of the legs (a^2 + b^2) is equal to the square of the hypotenuse (c^2).
The other options are incorrect because:
a. shorter leg: The theorem doesn't differentiate between the lengths of the legs, it simply states that the sum of their squares is equal to the square of the hypotenuse.
b. longer leg: Same as above, the theorem doesn't consider the individual lengths of the legs, just their squares.
c. sum of the angles: The Pythagorean Theorem deals with the sides of a right triangle, not its angles. The sum of the angles in any triangle is always 180 degrees.
Complete Question:
In the Pythagorean Theorem, the sum of the squares of the legs is equal to the square of the
a. shorter leg
b. longer leg
c. sum of the angles
d. hypotenuse
WILL GIVE 20 POINTS PLEASE HELP ME
The number of visitors to the Railroad Museum during 24 randomly selected hours is shown here. Construct a stem and leaf plot for the data.
67 62 38 73 34 43 72 35 53 55 58 63
47 42 51 62 32 29 47 62 29 38 36 41
Constructing a frequency distribution table for visitor numbers with a range of 29 to 73 and class intervals of 10 provides a clear overview, facilitating analysis and interpretation of the data.
Construct a frequency distribution table for the given data, with explanations:
1. Find the range of the data:
The lowest number of visitors is 29.
The highest number of visitors is 73.
The range is 73 - 29 = 44.
2. Determine the appropriate class intervals:
Choose a class interval width that will create a reasonable number of classes, typically between 5 and 10.
Consider the range of the data and aim for intervals that are easy to interpret.
In this case, a class interval width of 10 would be suitable, resulting in 5 classes:
29-38
39-48
49-58
59-68
69-78
3. Create the table:
Draw a table with three columns:
Class Interval
Tally (optional)
Frequency
4. Tally the data (optional):
Go through each data point and mark a tally mark in the appropriate class interval. (This is helpful for visual counting, but not strictly necessary.)
5. Count the frequencies:
Count the number of data points that fall into each class interval and record those numbers in the frequency column.
Complete question:
The number of visitors to the Railroad Museum during 24 randomly selected hours is shown here. 67 62 38 73 34 43 72 35 53 55 58 63 47 42 51 62 32 29 47 62 29 38 36 41 The error in the data is 1. a) Construct a frequency distribution table
The winner of a raffle will receive a 21- foot outboard boat. If 3000 raffle tickets were sold and you purchased 20 tickets, what are the odds against your winning the boat
149 : 1 is the odds against your winning the boat.
Step-by-step explanation:
It is given that,
The winner of a raffle will receive a 21-foot outboard boat.
Total raffle tickets were sold = 3000 tickets Number of tickets you purchased = 20 ticketsThe odds against any event is the ratio of the unfavorable outcomes to the favorable outcomes.
The number of possible outcome that you will win ⇒ 20
The number of possible outcomes that others wins ⇒ 3000-20 = 2980
To find the odds against your winning the boat :
Number of possible outcomes that one of the others wins : Number of possible outcome that you will win.
⇒ 2980 : 20
⇒ 149 : 1
Therefore, the odds against your winning the boat is 149 : 1
Which equation is true for the value b=2 ?
A circle has a radius of 32 inches. Find the circumference of the circle to the nearest tenth. Use 3.14 for PI.
The calculation of the circumference of a circle with a radius of 32 inches, using 3.14 for PI, gives a result of 201.0 inches.
Explanation:The subject of this question involves calculating the circumference of a circle. The formula used to find the circumference of a circle is 2πr, where r is the radius of the circle. Here, π is approximated to 3.14 as given in the question, and the radius r is given as 32 inches.
Substituting the given values into the formula, we get circumference = 2 * 3.14 * 32 = 200.96 inches. Thus, the circumference of the circle to the nearest tenth is "201.0 inches."
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How many 3.15 pound containers can you make with 37.8 pounds of raisins?
Answer:
12 (3.15 pound) containers.
Step-by-step explanation:
37.8 divided by 3.15 equals 12 (3.15 pound) containers.
Find the measures of an interior angle and an exterior angle of a regular 16-gon
Answer:
2520°
Step-by-step explanation:
The sum of the angles in any triangle is 180°
shape. sides. triangles. sum int angles.
triangle. 180×1=180°
quad. 180×2=360°
pentagon. 180×3=540°
n-sides. n( n−2) 180(n−2)
16-sides. 180×14=2520°
Histidine has 3 nitrogens. arrange the indicated nitrogens in decreasing order of basicity (1 = most basic, 3 = least basic). if there are fewer than 3 nitrogens in the molecule, leave that answer space blank. if two nitrogens have the same basicity, give them the same number. histidine
Answer:
Nitrogen 7 = 1 ---- Most Basic
Nitrogen 1 = 2
Nitrogen 3 = 3 ------ Least Basic
Step-by-step explanation:
The basicity of amino acids is as a result f the unshared pair of electrons in the Nitrogen atoms.
Part of the rule of basicity of organic compounds(amino acids) posits that:
The more unstable an electron pair is, the more basic it is.
From the diagram attached below;
Nitrogen 7 posses and unstable electron due to the lone pair of electron in the NH₃⁺ which renders it most basic .
Nitrogen 1 and 3 are in ring form thereby they are less basic But nitrogen 1 is more basic compared to nitrogen 3 because lone pair on Nitrogen 1 is not involved in resonance unlike Nitrogen 3 that is resonance stabilized (i.e alternating by a resonance effect).
Another phenomenon to deduce the basicity of Histidine is the effect of hybridization.
Basicity of Organic Compounds increases with decreasing s character.
Therefore, the trend of basicity is as follows: sp³ > sp² > sp
Because in sp; the lone pairs are most stable, hence least basic
And in sp³; the lone pairs are least stable; hence most basic.
Therefore; From the diagram attached below:
Nitrogen 7 = 1 ---- Most Basic
Nitrogen 1 = 2
Nitrogen 3 = 3 ------ Least Basic
What is the equation of the line with the same slope as the equation x-4y=3 and the y-intercept(0,-8)?
Answer:
Answer:y = 1/4x -8Step-by-step explanation:First find the slope of the linex-4y =3Subtract x from each sidex-4y -x = -x+3-4y = -x+3Divide each side by -4-4y/-4 = -x/-4 +3/-4y = 1/4 x -3/4This is in the form y= mx+b where the slope is m and the y intercept is bThe slope is 1/4We want the same slopey = 1/4x +bwe know the y intercept is -8y = 1/4x -8.
Step-by-step explanation:
Flying with the wind a plane went 383 mph. Flying into the same wind the plane only went 319 mph. Find the speed of the wind and the speed of the plane in still air.
Answer:
The speed of the wind is 32 mph and the speed of the plane in still air is 351 mph.
Step-by-step explanation:
Let the speed of the plane be Vp and the speed of the wind be Vw. In the first situation, the wind is exerting force towards the same direction as the plane so we can say that Vp + Vw = 383 mph. In the second situation, the forces are opposite of each other, so the equation can be written as Vp - Vw = 319 mph.
If we solve them together, we get the result of 2Vp = 702 mph which means that the speed of the plane is Vp = 351 mph. If we put Vp into one of the equations and solve for Vw then the speed of the wind can be found as Vw = 32 mph.
I hope this answer helps.
What is the expression of 8 more than a number x
"more" means added to, or addition. So 8 more than 'x' is:
x + 8
SOLVE X/5+3=2
A)-5
B)25
C)5
D)-1/5
Answer:
b 25
Step-by-step explanation:
Answer:
A)-5 if its without parenthasis around 5+ 3
Step-by-step explanation
2 minus 3 is -1 and -1 times 5 is -5
Plz help! Question in picture. What is the slope?
You have a wire that is 74 cm long. You wish to cut it into two pieces. One piece will be bent into the shape of a square. The other piece will be bent into the shape of a circle. Let A represent the total area of the square and the circle. What is the circumference of the circle when A is a minimum
Answer:
32.55 cm
Step-by-step explanation:
Let x = the length of wire that becomes a circle.
Then 74 - x = the length of wire that becomes a square
Circumference of circle + perimeter of square = 74
1. Expression for the side of the square
P = 4s = 74 - x
s = ¼(74 - x)
2. Expression for the radius of the circle
C = 2πr = x
r = x/(2π)
3. Expression for the total area
[tex]\begin{array}{rcl}\text{Total area} & = &\text{area of circle+ area of square}\\A & = & \pi r^{2} + s^{2}\\& = &\pi \left(\dfrac{x}{2 \pi}\right)^{2} + \left (\dfrac{1}{4}(74 - x)\right)^{2}\\\\ & = & \dfrac{x^{2}}{4 \pi} + \dfrac{1}{16}(5476 - 148x + x^{2})\\\\ & = & 0.07958x^{2} + 342.25 - 9.25x + 0.0625x^{2}\\A & = & 0.1421x^{2} -9.25x + 342.25 \\ \end{array}[/tex]
This is the equation of a parabola.
In standard form,
ƒ(x) = 0.1421x² -9.25x + 342.24
a = 0.1421; b = -9.25; c = 342.24
The parabola opens upwards, because a > 0. Therefore, the vertex is a minimum.
The vertex of a parabola occurs at
x = -b/(2a) = 9.25/(2 × 0.1421) = 9.25/(0.2842) = 32.55
The circumference of the circle is 32.55 cm.
The graph below shows that the area of the circle is a minimum when x = 32.55 cm
6.5% of people in the U.S. Have A- blood type. You randomly select 6 Americans and ask them if their blood type is A-. a) Find the probability that all 6 are type A-. b) Find the probability that at most 4 of them are type A-. c) Find the mean and standard deviation.
Answer:
a) 7.54189*10^-8
b) 0.99999999
c) E ( X ) = 0.39 , s ( X ) = 0.604
Step-by-step explanation:
Solution:-
- We will assume the proportion of people with A- blood group is independent and remains constant for a fairly small sample of n = 6 Americans selected at random.
- We will denote a random variable X = The number of americans out of 6 that have blood group type A-.
- The random variable is assumed to follow binomial distribution.
- The probability of success is the proportion of people in U.S that have blood group type A-, p = 0.065:
X ~ Bin ( 6 , 0.065 )
Where, r represents the number of americans out of selected 6 have blood group A-. The pmf of a binomial variate is given as:
P ( X = r ) = nCr * ( p ) ^r * ( 1 - p ) ^ ( n - r )
a) Find the probability that all 6 are type A-
- We will pmf given above and set r = 6. And evaluate the resulting probability:
P ( X = 6 ) = 6C6 * ( p )^6 * ( 1 - p ) ^ ( 0 )
= p^6
= ( 0.065 )^6
= 7.54189*10^-8
b) Find the probability that at most 4 of them are type A-
- We will pmf given above and evaluate the following expression:
P ( X ≤ 4 ) = 1 - P ( X = 5 ) - P ( X = 6 )
P ( X ≤ 4 ) = 1 - 6C5 * ( p )^5 * ( 1 - p ) ^ ( 1 ) - p^6
= 1 - 6*(0.065)^5 ( 0.935 ) - 0.065^6
= 1 - 6.50923*10^-8 - 7.54189*10^-8
= 0.99999999
c) Find the mean and standard deviation.
- The mean E ( X ) of the defined random variable distributed binomially is given by:
E ( X ) = n*p = 6*0.065 = 0.39 people
- The mean s( X ) of the defined random variable distributed binomially is given by:
s ( X ) = √n*p*q = √(6*0.065*0.935) = 0.604
What is the value of x^3*y^1 when x=5 and y=10
Answer:
1250
Step-by-step explanation:
x^3*y^1
Let x = 5 and y = 10
5^3* 10^1
PEMDAS says powers first
125 * 10
Then multiply
1250
20 pts if you answer
I REPORT UNNECESSARY ANSWERS
Answer:
C) 1/12
Step-by-step explanation:
P(2) = 1/6
P(Tail) = 1/2
1/6 × 1/2
1/12
simplify: square root 108+square root 125-square root 75
Answer:
[tex]11\sqrt{3} + 5\sqrt{5}[/tex]
Step-by-step explanation:
[tex]\sqrt{108}+\sqrt{125} - \sqrt75}[/tex]
1. [tex]\sqrt{108} = 6\sqrt{3}[/tex]\
2. [tex]\sqrt{125} = 5\sqrt{5}[/tex]
3. [tex]\sqrt{75} = 5\sqrt{3}[/tex]
4. Add [tex]6\sqrt{3} + 5\sqrt{3} = 11\sqrt{3}[/tex]
your left with [tex]11\sqrt{3}+5\sqrt{5}[/tex]
Answer:
12
Step-by-step explanation: