By evaluating the function, we conclude that f(10) = -7
How to evaluate the function f(x)?
Here we know that:
g(x) = 2x - 8
And f(x) = 5 - g(x).
Then we can write:
f(x) = 5 - (2x - 8) = 5 - 2x + 8 = -2x + 13
Now we want ot evaluate it in x = 10, this means replace the variable by the number 10.
f(10) = -2*10 + 13 = -20 + 13 = -7
Then, we conclude that f(10) = 7
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From the diagram below, we can tell that ___.
Answer: b. the two triangles are similar by SAS
Step-by-step explanation:
These two triangles (ABC and ADE) both share angle A. This means that one angle is congruent.
Next, we will look at the sides. Triangle ADE has side lengths of 6, 9, and x. Triangle ABC has side lengths of 8+6, 12+9, y. Let us see how these side lengths compare.
[tex]\frac{8+6}{12+9} =\frac{14}{21} =0.6666[/tex]
[tex]\frac{6}{9} = 0.6666[/tex]
THey are similar. This means the triangles can be prooven similar with SAS.
9 The cost of a mobile phone call is 30 cents plus 20 cents per minute.
a Find the possible cost of a call if it is:
i shorter than 5 minutes ii longer than 10 minutes
b For how many minutes can the phone be used if the cost per call is:
i less than $2.10 ii greater than or equal to $3.50
Using a linear function, we have that:
a) The costs are:
i. C(x) < $1.3.
ii. C(x) > $2.3.
b) The times are:
i. Less than 9 minutes.
ii. At least 16 minutes.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.In this problem, the y-intercept is of 0.3, while the slope is of 0.2, hence the cost for a call of x minutes is:
C(x) = 0.3 + 0.2x.
For calls shorter than 5 minutes, the costs are:
C(x) < 0.3 + 0.2 x 5
C(x) < $1.3.
For calls longer than 10 minutes, the costs are:
C(x) > 0.3 + 0.2 x 10
C(x) > $2.3.
The cost is less than $2.10 for calls of less than x minutes, found as follows:
0.3 + 0.2x < 2.1
0.2x < 1.8
x < 9.
The cost is greater or equal to $3.50 for calls of at least x minutes, found as follows:
0.3 + 0.2x >= 3.5
0.2x >= 3.2
x >= 16.
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suppose sin(A)=-0.78. use the trig identity sin^2(A)+cos^2(A)=1 and the trig identity tan(A) = sin(A)/cos(A) to find tan(A) in quadrant IV. round to the ten-thousandth.
a. -0.2039
b. 1.3941
c. 0.8671
d. -1.2464
In quadrant IV, [tex]\cos(A)[/tex] is positive. So
[tex]\sin^2(A) + \cos^2(A) = 1 \implies \cos(A) = \sqrt{1-\sin^2(A)} \approx 0.6258[/tex]
Then by the definition of tangent,
[tex]\tan(A) = \dfrac{\sin(A)}{\cos(A)} \approx \dfrac{-0.78}{0.6258} \approx \boxed{-1.2465}[/tex]
A group of friends wants to go to the amusement park. They have $284.25 to spend on parking and admission. Parking is $9.25, and tickets cost $27.50 per person, including tax. How many people can go to the amusement park?
Answer:
7
Step-by-step explanation:
The start this question by looking at two important things, how much money we have and how much money it costs per person. The friends have a total of $284.25 and we don't know how much it costs per person. To find this we must set up an equation and solve it!
Because each person must pay for parking and a ticket, we can find the cost for one person by adding the parking and ticket cost together.
$9.25 + $27.50 = $36.75
Now that we have solved this equation, we know that it costs $36.75 for one person. To find how many total people can go we dived the total amount of money we have by how much it costs per person. Let's call the number of people that can go 'p'.
p = [tex]\frac{284.25}{36.75}[/tex]
Once we simplify/solve this equation we get 7 [tex]\frac{36}{49}[/tex] so essentially, we get the whole number 7 and a long decimal, but the only important part is the 7. We take the whole number from our answer which is 7.
We now know the answer: 7.
Let's check our work!
7 * 36.75 = 257.75
284.25 - 257.75 = 26.5
26.5 < 36.75 so we are correct!
The final answer is 7!
Have an amazing day!
Geometry: complete this proof, ASAP!!!!!!!!!!!!!!!! It’s urgent
Answer:
1. AC is perpendicular to BD
1. Given
2. ACB is a right angle
2. Definition of perpendicular lines
3. Triangle ACB is a right triangle
3. Definition of right triangles
4. Angles 1 and 3 are complementary
4. Interior angles of a triangle add up to 180 degrees (Triangle Interior Angle Sum Theorem), and m<ACB = 90 degrees (definition of right angles), so m<1 + m<3 = 90 degrees (subtraction property of equality). By the definition of complementary angles, angles 1 and 3 are complementary.
I’m gonna ask this question again can someone help me solve this and leave in terms of pi
The equation of the circumference of a circle in terms of [tex]\pi[/tex] is [tex]2\pi r[/tex] or [tex]\pi d[/tex].
The circumference for a circle with diameter 10 is [tex]10\pi[/tex].
The circumference for a circle with diameter 19 is [tex]19\pi[/tex].
The circumference for a circle with diameter 30 is [tex]30\pi[/tex].
The circumference for a circle with diameter 16 is [tex]16\pi[/tex].
Relatively easy, right?
The equation of the area of a circle in terms of [tex]\pi[/tex] is [tex]\pi r^2[/tex].
The area of a circle with radius 5 is [tex]25\pi[/tex].
The area of a circle with radius 9.5 is [tex]90.25\pi[/tex].
The area of a circle with radius 15 is [tex]225\pi[/tex].
The area of a circle with radius 8 is [tex]64\pi[/tex].
Hope this helped!
(By the way, I don't know why you're using hard formulas for trying to find the radius or diameter. The diameter is simply twice the radius, and the radius is simply half the diameter.)
Answer:
Circumference = 10[tex]\pi[/tex], 19[tex]\pi[/tex], 30[tex]\pi[/tex], 16[tex]\pi[/tex]
Area = 25[tex]\pi[/tex], 90.25[tex]\pi[/tex], 225[tex]\pi[/tex], 64[tex]\pi[/tex]
Step-by-step explanation:
For the first row we have the radius which is 5, the diameter is 10. The formula for circumference is 2[tex]\pi[/tex]r. So for this one its gonna be 2[tex]\pi[/tex]5 or 10[tex]\pi[/tex]
radius = 5
diameter = 10
circumference = 2[tex]\pi[/tex]5 or 10[tex]\pi[/tex]
area = [tex]\pi[/tex][tex]5^{2}[/tex] or 25[tex]\pi[/tex]
for the second row
radius = 9.5
diameter = 19
circumference = 2[tex]\pi[/tex]9.5 or 19[tex]\pi[/tex]
area = [tex]\pi[/tex][tex]9.5^{2}[/tex] or 90.25[tex]\pi[/tex]
for the third row
radius = 15
diameter = 30
circumference = 2[tex]\pi[/tex]15 or 30[tex]\pi[/tex]
area = [tex]\pi[/tex][tex]15^{2}[/tex] or 225[tex]\pi[/tex]
for the fourth row
radius = 8
diameter = 16
circumference = 2[tex]\pi[/tex]8 or 16[tex]\pi[/tex]
area = [tex]\pi[/tex][tex]8^{2}[/tex] or 64[tex]\pi[/tex]
someone help please!
See attachment for the graph of the functions y = x + 2, y = 2x and y = -x
How to complete the tables and plot the graphs?Equation 14
The equation is given as:
y = x + 2
When x = 0, we have
y = 0 + 2 = 2
When x = 1, we have
y = 1 + 2 = 3
When x = 2, we have
y = 2 + 2 = 4
So, the complete table is
x y
0 2
1 3
2 4
See attachment for the graph of the function y = x + 2
Equation 15
The equation is given as:
y = 2x
When x = 0, we have
y = 2 * 0 = 0
When x = 1, we have
y = 2 * 1 = 2
When x = 2, we have
y = 2 * 2 = 4
When x = 3, we have
y = 2 * 3 = 6
So, the complete table is
x y
0 0
1 2
2 4
3 6
See attachment for the graph of the function y = 2x
Equation 16
The equation is given as:
y = -x
When x = -3, we have
y = 3
When x = -1, we have
y = 1
When x = 1, we have
y = -1
When x = 3, we have
y = -3
So, the complete table is
x y
-3 3
-1 1
1 -1
3 -3
See attachment for the graph of the function y = -x
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help me with this question
Answer: A) 23,00
Step-by-step explanation:
A=23,00
B=8,600
C=12,00
D=3,600
The angle measurements in the diagram are represented by the following expressions. \qquad \blueD{\angle A=7x + 40^\circ}∠A=7x+40 ∘ start color #11accd, angle, A, equals, 7, x, plus, 40, degrees, end color #11accd \qquad\greenD{\angle B=3x + 112^\circ}∠B=3x+112 ∘ start color #1fab54, angle, B, equals, 3, x, plus, 112, degrees, end color #1fab54 Solve for xxx and then find the measure of \blueD{\angle A}∠Astart color #11accd, angle, A, end color #11accd: \blueD{\angle A} =∠A=start color #11accd, angle, A, end color #11accd, equals ^\circ ∘
⟨A = 7•x + 40° and ⟨B = 3•x + 112°
From a possible diagram of the question, ⟨A = ⟨B, which gives;
x = 18°⟨A = 166°How can the value of x and the measure of ⟨A be found?Given;
⟨A = 7•x + 40°
⟨B = 3•x + 112°
In the diagram from a similar question posted online, we have;
⟨A and ⟨B are corresponding anglesCorresponding angles formed by parallel lines having a common transversal are congruent, therefore;
⟨A and ⟨B are congruentWhich gives;
⟨A = ⟨B7•x + 40° = 3•x + 112°
7•x - 3•x = 112° - 40° = 72°
7•x - 3•x = 4•x = 72°
x = 72° ÷ 4 = 18°
Therefore;
x = 18°Which gives;
⟨A = 7•x + 40°
⟨A = 7 × 18 + 40° = 166°
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Answer:d
Step-by-step explanation:
khan
If (a2b−3c)34a−1b4c5=apbqcr What is the value of p+2q?
Use BODMAS and algebra to arrive at the values of P = 5/2, q = -25/4 and r = -9/2.
Then substitute the values of p and q into p+2q to get -10
Selim is ordering concrete spheres to place as barriers in the city park. The spheres cost $2 per square foot, and Selim can spend $20 per sphere. What is the maximum diameter of the spheres he can purchase?
Answer:
1.78 feet.
Step-by-step explanation:
If they cost $20 each and its $2 per square foot, the area of the spheres
is 20 / 2 = 10 ft^2.
Area of sphere = 4 π r^2 = 10 (where r = the radius)
---> r^2 = 10 / 4π
= 0.796
---> r = 0.892 ft
So the diameter = 2 * r
= 1.78 feet to nearest hundredth.
1. General term for -2, -5, -8, -11
2. General term for 22, 20, 18, 16
The general terms for the given arithmetic sequences are given as follows:
1. [tex]a_n = -2 -3(n - 1)[/tex]
2. [tex]a_n = 22 - 2(n - 1)[/tex]
What is an arithmetic sequence?In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.
The general term of an arithmetic sequence is given by:
[tex]a_n = a_1 + (n - 1)d[/tex]
For sequence 1, given by -2, -5, -8, -11, the first term and the common ratio are given as follows:
[tex]a_1 = -2, d = -3[/tex]
Hence the general term that defines sequence 1 is presented below:
[tex]a_n = -2 -3(n - 1)[/tex]
For sequence 2, represented by 22, 20, 18, 16, the first term and the common ratio are given as follows:
[tex]a_1 = 22, d = -2[/tex]
Hence the general term that defines sequence 2 is presented below:
[tex]a_n = 22 - 2(n - 1)[/tex]
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Simplify[tex](\frac{16}{81}x^{16}\right))^{\frac{1}{2}}[/tex]
Answer:
[tex]\sf \dfrac{4}{9}x^8[/tex]
Step-by-step explanation:
Law of exponents:[tex]\sf (a*b)^m = a^m *b^m\\\\(a^m)^n =a^{m*n}[/tex]
16 = 4 *4 = 4²
81 = 9 *9 = 9²
[tex]\sf\left (\dfrac{16}{81}x^{16}\right)^{\frac{1}{2}}= \left(\dfrac{4^2}{9^2}x^{16}\right)^{\frac{1}{2}}[/tex]
[tex]\sf =\dfrac{4^{2*\frac{1}{2}}}{9^{2*\frac{1}{2}}}*x^{16*\frac{1}{2}}\\\\=\dfrac{4}{9}x^8[/tex]
a green grocer had 623 oranges. He packed them in cartons, which could only take 11 oranges or 12 oranges respectively, and no oranges remained. How many cartons had 12 oranges only?
Answer:51 crates could have 12 oranges and one crate could hold 11 oranges.
Step-by-step explanation: 623 / 12 is 51.9... 51 x 12 is 612. 612 + 11 is 623 math checks out.
Simplify.
2[(8 ÷ 4)-(-5)] + 6
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textsf{Equation:}[/tex]
[tex]\mathsf{2[(8 \div 4)-(-5)] + 6}[/tex]
[tex]\huge\textsf{Solving:}[/tex]
[tex]\mathsf{2[(8 \div 4)-(-5)] + 6}[/tex]
[tex]\mathsf{= 2[((2 - (-5)] + 6}[/tex]
[tex]\mathsf{= 2(7) + 6}[/tex]
[tex]\mathsf{= 2 \times 7 + 6}[/tex]
[tex]\mathsf{= 14 + 6}[/tex]
[tex]\mathsf{= 20}[/tex]
[tex]\huge\textbf{Therefore, your answer should be: }[/tex]
[tex]\huge\boxed{\frak{20}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]
Given:▪ [tex] \sf{2[(8 ÷ 4)-(-5)] + 6}[/tex]
First, we will start with the division:
[tex]\longrightarrow \sf{2[(2) − (−5)] +6}[/tex]
Now we will resolve what is inside the bracket:
[tex]\longrightarrow \sf{2[2+5] +6}[/tex]
[tex]\longrightarrow \sf{2 \times 7 +6}[/tex]
Now we will solve the multiplication:
[tex]\longrightarrow \sf{14 +6= 20}[/tex]
[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]
[tex] \bm{2[(8 ÷ 4)-(-5)] + 6 = \boxed{\bm {20}}}[/tex]
My car uses 8.5L of petrol per 100km travelled. If petrol costs $2.05 per litre, how much will the petrol cost for my trip?
Answer:
$0.17425/Km
Step-by-step explanation:
8.5L/100Km*$2.05/L
= $0.17425/Km
ANSWER MY QUESTION AND I WILL MARK YOU BRAINLYIST
The following are the distances (in miles) to the nearest airport for 11 families. 9, 11, 11, 16, 16, 24, 28, 30, 34, 42, 45 Notice that the numbers are ordered from least to greatest. Give the five-number summary and the interquartile range for the data set. Five-number summary
Minimum:
Lower quartile:
Median:
Upper quartile:
Maximum:
Interquartile range:
Here is the five-number summary:
Minimum: 9
Lower quartile: 11
Median: 24
Upper quartile: 34
Maximum: 45
Interquartile range: 23
What is the five-number summary?The minimum number is the smallest number in the dataset. The minimum number is 9. The maximum number is the largest number in the dataset. The maximum number is 45.
The first quartile, third quartile and the interquartile range are used to measure dispersion.
The first quartile : 1/4(n + 1)
1/4 x (12) = 3rd term = 11
The third quartile : 3/4 x (n + 1)
3/4 x (12) = 9th term = 34
Interquartile range = third quartile - first quartile
34 - 11 = 23
Median can be described as the number that occurs in the middle of a set of numbers that are arranged either in ascending or descending order
Median = 25
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18 PTS!! What is the 400th term of the sequence below when using the explicit formula
aₙ=a₁+(n-1)•d?
79, 82, 85, 88,...
A. 1273
B. 1279
C. 1276
D. 1282
Answer:
[tex]\huge\boxed{\sf a_{400}=1276}[/tex]
Step-by-step explanation:
Sequence:79, 82, 85, 88, ....
Explicit formula:[tex]a_n=a_1+(n-1)d[/tex]
Where,
[tex]a_n = a_{400[/tex] (the term that is to be found)[tex]a_1 = 79[/tex] (the first term)[tex]n = 400[/tex][tex]d = 3[/tex] (difference between first and second term)Put the givens in the above formula
[tex]a_{400}=79 +(400-1)3\\\\a_{400}=79 + 399\times3\\\\a_{400}=79+ 1197\\\\a_{400}=1276\\\\\rule[225]{225}{2}[/tex]
which fraction is greater 3/6 or 6/10
Answer:
6/10
Step-by-step explanation:
3/6 = 0.5
6/10 = 0.6
0.6>0.5
Then
6/10 is greater than 3/6
Alice and Bob are currently 1000 feet apart and are both running directly
toward each other at a constant speed of 10 feet per second. A bird starts in the same
position as Alice and flies directly toward Bob at a speed of 20 feet per second. When the
bird reaches Bob, it turns around immediately and starts flying toward Alice at the same
speed, turning around immediately when it reaches Alice, and repeating this procedure until
Alice and Bob meet. When Alice and Bob finally meet, what is the total distance that the
bird has flown, in feet?
The distance the bird has flown by the time Alice and Bob meet is 40 feet.
Given that the distance between Alice and Bob is 1000 feet and their running speed is 10 feet per second and the speed of bird is 20 feet per second.
Distance equals speed multiplied by time.
Distance between Alice and Bob=1000 feet.
Distance between the bird and Bob=1000 feet.
Speed of Alice and Bob=10 feet per second.
The combined speed of Alice and Bob=20 feet per second.
Since the two are running directly toward each other the distance each will cover at the meeting point is 50 feet (1000/20)
The time covered at the meeting point=20 second (1000/50)
Speed of the bird=20 feet per second.
The distance covered by the bird towards Bob at their meeting point is 40 feet(20 feet*20 seconds).
Hence the distance the bird has flown by the time Alice and Bob meet is 40 feet.
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Given u=(-12,-5) and v=(3,9) what is proj v u?
[tex]\frac{(-12)(3)+(-5)(9)}{3^2 + 9^2} \langle 3, 9 \rangle \\ \\ =-\frac{9}{10} \langle 3, 9 \rangle \\ \\ =\langle -\frac{27}{10}, -\frac{81}{10} \rangle[/tex]
So, the correct answer is Option 1.
PLEASE HELP IM DTUCK
Answer:
Future Amount ≈ 32
Step-by-step explanation:
substitute x = 8 into the given formula , that is
future amount = 16[tex](1.09)^{8}[/tex] = 16 × 1.99256.. ≈ 32 ( nearest whole number )
If a system reliability of 0. 998 is required, what reliability of two components in series is required?
The reliability of two components in series is 0.996.
To find the reliability of the engine, we need all the two components to work. Each components has a reliability of 0.998, so to find the reliability of the engine we need to find the probability of all two components working.
Reliability is defined as the probability that a product, system, or service will perform its intended function adequately for a specified period of time, or will operate in a defined environment without failure.
We can find this probability multiplying all the ten reliabilities:
P = 0.998^2 = 0.996004
Rounding to three decimal places, we have P = 0.996
The reliability of the engine is 0.996.
Hence,
The reliability of two components in series is 0.996.
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An industrial machine produces widgets, but it has a 0.07 defective rate. what is the probability that the machine produces fewer than 5 defective widgets in a production run of 100 items?
The probability that the machine produces fewer than 5 defective widgets in a production run of 100 items is 0.10
What is the probability?A probability refers to the ratio of favorable events to the n number of total events.
Also, it means the chance that a particular event (s) will occur expressed on a linear scale from 0 to 1 which can also be expressed as a percentage between 0 and 100%.
Given data
An industrial machine produces 5 widgets.
It has a 0.07 defective rate.
Defective rate fewer than 5
Total Probability = P of 4 defective + P for 3 defective + P for 2 defective + P for 1 defective.
Total Probability = 4/100 + 3/99 + 2/98 + 1/97
Total Probability ≈ 0.10
Therefore, the required probability for fewer than 5 defective rate is 0.10
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2. Solve for x.
9
6
8
X
Answer:
I think the answer is 12 because 8/6 is 1.3333.... Continously so the smaller traingel is 1.33333 times smaller then the bigger one. So you jus do 9 x 1.3333... To get the bigger angels side
If zeba were younger by 5 years than what she really is then the square of her age would have been 11 more than five times her actually age. What is her age now?
Answer:
I am not 100% confident, but I think that she is 11.
Step-by-step explanation:
Answer:
14 years old
Step-by-step explanation:
Define the variable
Let x be the actual age of Zeba (in years).
Create an equation using the give information and the variable x:
[tex](x - 5)^2=5x+11[/tex]
To find Zeba's age now, solve the equation for x.
Expand the brackets:
[tex]\implies x^2-10x+25=5x+11[/tex]
Subtract 5x from both sides:
[tex]\implies x^2-10x+25-5x=5x+11-5x[/tex]
[tex]\implies x^2-15x+25=11[/tex]
Subtract 11 from both sides:
[tex]\implies x^2-15x+25-11=11-11[/tex]
[tex]\implies x^2-15x+14=0[/tex]
Factor the found quadratic
To factor a quadratic in the form [tex]ax^2+bx+c[/tex], find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex], then rewrite [tex]b[/tex] as the sum of these two numbers:
[tex]\implies x^2-14x-x+14=0[/tex]
Factor the first two terms and the last two terms separately:
[tex]\implies x(x-14)-1(x-14)=0[/tex]
Factor out the common term (x - 14):
[tex]\implies (x-1)(x-14)=0[/tex]
Apply the zero product property:
[tex]\implies (x-1)=0 \implies x=1[/tex]
[tex]\implies (x-14)=0 \implies x=14[/tex]
Therefore, Zeba's age now is either 1 or 14 years.
As the question states "If Zeba were younger by 5 years" then 1 must be an extraneous solution since 1 - 5 = -4 and Zeba cannot be -4 years old.
Therefore, Zeba's age now is 14 years old.
Check
Given the actual age of Zeba is 14 years old.
Therefore, If Zeba were younger by 5 years, she would be 9 years old as: 14 - 5 = 9
The square of 9 is: 9² = 81.
5 times her actual age: 5 × 14 = 70
81 is 11 more than 70, hence verifying that her actual age is 14 years old.
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The perimeter of a rectangle is 320 feet. Find the length and width if the length is an odd integer and the width is 5 times the next consecutive odd integer.
The length is 25 feet and the width is 135 feet
What are consecutive odd integers?
Consecutive odd integers differ by 2. If x is an odd integer, then x + 2, x + 4 and x + 6 are consecutive odd integers.
How to find the perimeter of the rectangle?
⇒Perimeter of rectangle = 2(l+w)
The perimeter of a rectangle is 320 feet
let the length of a rectangle is x
The next consecutive odd integer is x+2
width = 5(x+2)
=5x+10
2(length + width) = 320
l+w=160
x+5x+10=160
6x=150
x=25
length = 25 feet
width = 5(25+2)=135 feet
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The limits of the class intervals are
The lower and the upper class limit are as follows
interval lower limit upper limit
10-14 10 14
15-19 15 19
20-24 20 24
25-29 25 29
This is further explained below.
What is the class limit?Generally, The lower class limit and the upper-class limits are just the minima and maximum values that are allowed in each class, respectively: The gap that exists between the upper-class limit and the lower class limit is referred to as the class interval.
In conclusion, The lower and the upper class limit are as follows
interval lower limit upper limit
10-14 10 14
15-19 15 19
20-24 20 24
25-29 25 29
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PLS HELP. I tried and cant figure it out.
Answer:
I x² +12x I = -32
Step-by-step explanation:
Absolute value equation:
x = -4 ; x = -8
x + 4 = 0 and x + 8 = 0
(x +4)(x + 8) = 0
x*x + x*8 + 4*x + 4*8 = 0
x² + 4x + 8x + 32 = 0
x² + 12x + 32 = 0
Absolute value equation:
I x² + 12x I = -32
What number should go in the space? Multiplying by 1.36 is the same as increasing by _________%.
The required percentage increase is 36%. So, a number increased by 36% is the same as the number multiplied by 1.36.
How to calculate the percentage increase of a number?The formula for calculating the percentage increase of a number is
%increase = 100 × (Final - initial)/initial
Calculation:Consider the number as 'x'
The result when the number is multiplied by 1.36 is 1.36x
So, the percentage increase is calculated as follows:
%increase = 100 × (Final - initial)/initial
Where Initial = x and Final - 1.36x
⇒ %increase = 100 × (1.36x - x)/x
⇒ %increase = 100 × x(1.36 - 1)/x
⇒ %increase = 100 × 0.36
⇒ %increase = 100 × 36/100
∴ %increase = 36
Thus, when a number is multiplied by 1.36, the result obtained is equal to the 36% increase in the number.
Learn more about the percentage increase here:
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