The solution for the expression 2^(x) − 2^(−x) = 5 is x = log2(10)
Substitute 2^(−x) for 5 and solve for x, which is log2(10).
The given expression ,
2^(x) − 2^(−x) = 5
2^(x) = 5 + 2^(−x)
2^(2x) = (5 + 2^(−x))^2
2^(2x) = 25 + 10*2^(−x) + 2^(−2x)
25 + 10*2^(−x) + 2^(−2x) = 2^(2x)
25 − 2^(2x) = 10*2^(−x) − 2^(−2x)
25 − 2^(2x) = 10*2^(−x) − 2^(−2x) + 2^(2x)
25 = 10*2^(−x) + 2^(2x) − 2^(−2x)
25 = 10*2^(−x) + 2^(−2x) (2^(2x) - 2^(−2x))
25/(2^(−2x) (2^(2x) − 2^(−2x))) = 10*2^(−x)
25/(2^(2x) − 2^(−2x)) = 10*2^(−x)
2^(x) = 10
x = log2(10)
Substitute 2^(−x) for 5 and solve for x, which is log2(10).
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if your heart rate is 120 beats per minute during strenuous exercise, what is the time per beat in units of seconds? 0.2 s/beat 0.4 s/beat 0.5 s/beat 0.6 s/beat
Therefore ,the heart beat the time per beat in units of seconds is 0.5s/beat.
A well-formed equation in algebra unites two variables with the equals sign to indicate the equality of the two terms. An equation, for instance, is any well-formed formula that consists of two expressions joined by the equals sign in English. An équation, on the other hand, is described as consisting of one or more variables in French.
Here,
Given: your heart rate is 120 beats per minute during strenuous exercise
Thus to calculate time per beat in units of seconds
We,
time per second per beat = total second in a minute /heart rate
time per second per beat =60/120
time per second per beat =1/2
time per second per beat = 0.5 s/beat
Therefore ,the heart beat the time per beat in units of seconds is 0.5s/beat.
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Johnny just became a personal trainer and is finalizing his pricing plans. One plan is to charge $74 for the initial consultation and then $64 per session. Another plan is to charge $20 for the consultation and $66 per session. Johnny realizes that the two plans have the same cost for a certain number of sessions. What is that cost? How many sessions is that?
The cost when the two plans are the same is $1802. The number of sessions where the plans would be the same is 27.
What is the cost and the number of sessions?The linear equation that represents the total cost of the first plan: initial consultation + charge per session x number of sessions)
= $74 + $64s
The linear equation that represents the total cost of the second plan: $20 + $66s
When the two plans are the same, the two linear equations would be the same.
$20 + $66s = $74 + $64s
In order to determine the value of s, take the following steps:
Combine similar terms:
$66s - $64s = $74 - $20
Add similar terms:
$2s = $54
Divide both sides of the equation is $2
s = $54 / 2
s = 27
Total cost when s is 27: $20 + $66(27)
$20 + 1782 = $1802
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If f(x) = x ^ 2 is vertically stretched by a factor of 7 to g(x) what is the equation of g(x) ?
The expression is vertically stretched by a factor of 7 then the equation for g(x) will be 7x².
What is an equation?Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.
This relationship is illustrated by the left and right expressions being equal. The left-hand side equals the right-hand side is a basic, straightforward equation.
As per the given information in the question,
f(x) = x²
It is stretched vertically by a factor of 7.
So, k = 7
The equation for vertical expansion is,
y = k(f(x))
Then, the equation will be,
g(x) = 7x²
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If f(7) = 22, then f^-1(22) = [?]
The required value of the given inverse function f⁻¹(22) will be 7.
What is an inverse function?The inverse function is defined as a function obtained by reversing the given function.
Given that f(7) = 22
To determine the value of the given inverse function f⁻¹(22)
An inverse function's main objective is to show the value that occurs in a specific function value. Which means :
If we have f(x) and f⁻¹(x), then
if f(a) = b then f⁻¹(b) = a
As per the given question, we have
⇒ f(7) = 22 then f⁻¹(22) = 7
Therefore, the required value of the given inverse function f⁻¹(22) will be 7.
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Hexagon K is a scaled copy of hexagon J.
What scale factor takes hexagon J to hexagon K?
The scale factor 5/2 takes hexagon J to hexagon K.
What is Hexagon?
Hexagon AB, a publicly traded international information technology company with its headquarters in Stockholm, Sweden, was established in 1992 and is a leader in hardware and software for virtual reality. The Stockholm Stock Exchange has Hexagon's B share on its list of major corporations.
From the given two Hexagon's K and L, the Hexagon K is copy to Hexagon K.
The scale factor = the ratio of edges
Scale factor = 20/8 = 30/12 = 5/2
Hence, the scale factor 5/2 takes hexagon J to hexagon K.
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Complete question:
Complete question is attached below.
how large a sample is needed in exercise 9.2 if we wish to be 96% confident that our sample mean will be within 10 hours of the true mean?
A sample of at least 68 bulbs is needed to be 96% confident that our sample mean will be within 10 hours of the true mean.
We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.96}{2} =0.02[/tex]
Now, we have to find z in the Z table as such z has a p value of [tex]1-\alpha[/tex] .
So it is z with a p value of 1-0.02 = 0.98, so z= 2.055
Now, find the margin M as such
[tex]M = Z*\frac{\sigma }{\sqrt{n} }[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
In this problem, we have that:
[tex]\sigma = 40 , M = 10\\\\M = Z*\frac{\sigma}{\sqrt{n} } \\\\10 = 2.055*\frac{40}{\sqrt{n} } \\\\\sqrt{n} = 8.22\\\\n= 67.6[/tex]
Hence , a sample of at least 68 bulbs is needed to be 96% confident that our sample mean will be within 10 hours of the true mean.
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for a two-factor study with 2 levels of factor a, 2 levels of factor b, and a separate sample of 10 participants in each treatment condition, the two means for level a1 are 4 and 1, and the two means for level a2 are 3 and 2. for these data, what is the value of ss between treatments?
As per the two factor study, the value of s is 60.
Two factor study
In math, two factor study defined as an experimental design in which data is collected for all possible combinations of the levels of the two factors of interest.
Given,
Here we have that for a two-factor study with 2 levels of factor a, 2 levels of factor b, and a separate sample of 10 participants in each treatment condition, the two means for level a1 are 4 and 1, and the two means for level a2 are 3 and 2.
And we need to find the value of s between treatments.
As per the given question, we have identified that the values,
Number of participants = 10
And we also know that, level a1 are 4 and 1, and the two means for level a2 are 3 and 2.
So, based on the two factor method, the value of s calculated as,
Here we have to multiple factors first,
=> 3 x 2 = 6
And then multiply that by n = 10,
=> 6 x 10 = 60
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A student who obtained a percentile rank of 75 on an achievement test is best characterized as having?
A student who obtained a percentile rank of 75 on an achievement test is best characterized as having scored higher than 75% of the test takers.
What is percentile rank?
A percentile rank describes a student's performance in relation to other students in the same grade and subject who made up the specific norm group. The percentile rank of a student indicates whether their score was equal to or higher than the percentage of students in the norm group.
The percentage of scores in a frequency distribution that are lower than a given score is known as the percentile rank of that score in statistics.
A percentile rank of 75 indicates that the student outperformed 75% of the other students in his or her norm group, and 25% of the students outperformed your student.
Hence, a student who obtained a percentile rank of 75 on an achievement test is best characterized as having scored higher than 75% of the test takers.
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Forty-seven more girls than boys are
enrolled in Kennedy Junior High.
There are 2597 students in Kennedy.
How many of them are girls?
Answer:
Step-by-step explanation:
2,637
a ______________ is a distribution of scores where a straight line can be visualized in the middle of a maze of cases running from one corner to another.
A linear relationship is a distribution of scores where a straight line can be visualized in the middle of a maze of cases running from one corner to another.
What does the term "linear relationship " mean?
A statistical word used to express a straight-line relationship between two variables is a linear relationship (or linear association).
Graphs and mathematical equations of the form y = mx + b can both be used to represent linear relationships.
Why are relationships linear and nonlinear?
Plotting a linear relationship on a graph results in a straight line, whereas plotting a nonlinear relationship results in a curve.
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Which graph represents the solution set to 2x+3y<6
On solving the provided graph question, we got to know that - the area below the line will be taken into account.
what are graphs ?
Graphs are visual representations or charts used in mathematics to methodically express data or values. A relationship between two or more objects is frequently represented by a point on a graph.
Given : equation 2x + 3y ≤ 6
Out of the options provided, we must select the graph that displays the graph of the solution set for the equation 2x + 3y 6.
Consider the given equation 2x + 3y ≤ 6
We first find the points where the equation cut x- axis and y-axis.
Thus,
[tex]For x - axis put y = 0 ,\\We get 2x + 3(0) \leq 6 =2x \leq 6 x \leq 3\\Thus, point (3,0)\\For y - axis put x = 0 ,\\We get 2(0) + 3y \leq 6 = 3y \leq 6 = y \leq 2\\Thus, point (0,2)[/tex]
For each region, we select a test point, determine the values of x and y there, and then determine whether or not the inequality is satisfied.
Take into account the point (0, 0), and inequality becomes,
[tex]2(0) + 3(0) \leq 6 = 0 \leq 6 (true)\\[/tex]
So, the area below the line will be taken into account.
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what is 3km/minute=??mi/hour PLEASE ANSWER
It means 3 km in 1 minutes.
I think this is a speed of an object which shows that it can run or walk 3km in 1 minutes.
hope you understand.
Which of the following graphs matches the inequality 3x − 2y > 4? The graph shows a solid line, which crosses the y-axis at negative 2 and the x-axis at 4 thirds, with shading above the line. The graph shows a solid line, which crosses the y-axis at negative 2 and the x-axis at 4 thirds, with shading below the line. The graph shows a dashed line, which crosses the y-axis at negative 2 and the x-axis at 4 thirds, with shading above the line. The graph shows a dashed line, which crosses the y-axis at negative 2 and the x-axis at 4 thirds, with shading below the line.
For inequality we get graph attached in solution. So, Option (b) is correct i.e. we will get solid line, which crosses the y-axis at negative 2 and the x-axis at 4 thirds, with shading below the line.
How to solve inequality?Take these actions:
Place "y" on the left and the remaining variables on the right in the equation.Plot the "y=" line (make it a solid line for y or y, and a dashed line for y or y>).Place a shade above or below the line depending on whether the value is larger or less than (y> or y).For given equation 3x-2y> 4
Step 1: Add 2y to both sides. Our equation becomes
3x>4+2y
Step 2: Now subtract 4 from both sides and divide both sides by 2. After that we will get
(3x/2)-2>y
Step 3: Plot y=3x/2 -2 on graph.
Step 4: Shade all region below line plotted in step 3.
Image is attached for graph:
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To graph the system of inequalities:
y ≤ −5x + 2
y < 3x − 1.5
We can start by graphing the boundary lines for each inequality:
For y ≤ −5x + 2, the boundary line is y = -5x + 2, which has a slope of -5 and a y-intercept of 2. Since the inequality includes "less than or equal to," we will use a solid line to represent the boundary.
For y < 3x − 1.5, the boundary line is y = 3x - 1.5, which has a slope of 3 and a y-intercept of -1.5. Since the inequality is "less than" and not "less than or equal to," we will use a dashed line to represent the boundary.
Next, we need to determine the shading for each inequality:
For y ≤ −5x + 2, we shade below the solid line because y is less than or equal to the other side of the inequality.
For y < 3x − 1.5, we shade below the dashed line because y is less than the other side of the inequality.
Based on the given options, the correct answer is:
The graph shows a solid line that passes through 0 comma 2 and 1 comma negative 3, with shading below the line. There is also a dashed line that passes through 0 comma negative 1.5 and 1 comma 1.5, with shading below the line.
Find the smallest positive integer which has the same number of factors as 2022.
Using HCF to determine the integer with smallest number of factors, the value is 24
What is LCMHCF stands for Highest Common Factor. It is the largest positive integer that divides two or more given numbers without leaving a remainder.
In this problem, we are asked to find number that will have the same number of factors as 2022, we can start by listing all factors of 2022.
The HCF of 2022 are
2022 : 1, 2, 3, 6, 337, 674, 1011, 2022
The factors of 24 are : 1, 2, 3, 4, 6, 8, 12, 24
24 has 8 factors, which is the same number of factors as 2022. 24 is the smallest positive integer with 8 factors.
From the explanation above, the smallest integer with same number of factors as 2022 is 24.
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If g=2 r=3 and t=11 solve
(2t+3g) divided by 4
The results of the evaluation of the given expression; (2t+3g) divided by 4 as required is; 7.
What is the result of the evaluation of the expression?It follows from the task content that the result of the evaluation of the given expression is to be determined according to the information provided.
Therefore, since the expression to be evaluated is; ( 2t + 3g ) / 4.
Where; g = 2, r = 3 and t = 11.
Therefore, we have;
( 2(11) + 3(2) ) / 4
= ( 22 + 6 ) / 4
= 28 / 4
= 7.
Therefore, the result of the expression evaluation is; 7.
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Jesse has an expression:
x² - x - 6
Why would Jesse want to factor this expression to get the following expression?
(x - 3)(x + 2)
A. To find the coefficients.
B. To find the discriminant.
C. To find the order.
D. To find the x-intercepts.
Jesse wants to factor the expression To find the x-intercepts.
Quadratic Expression:An expression containing a variable having the largest power of two is called a quadratic expression. The power of the expression should be two, not greater or lower.
Coefficients:A coefficient is a multiplication factor in a polynomial, series, or statement in mathematics; it is often a number.
Discriminant:The concept used to find the number of solutions of a quadratic equation is known as Discriminant. The expression that appears under the square root in the quadratic formula is named Discriminant.
X- intercept :The value of the x coordinate at the point where the graph intersects the x-axis, or alternatively, the value of the x coordinate at the point where the value of the y-coordinate equals zero, is the x-intercept for any curve.
Here we have
x² - x - 6 is factorized as (x - 3)(x + 2)
If we take (x - 3)(x + 2) = 0
=> (x - 3) = 0 (x + 2) = 0
=> x = 3 x = -2
This means x values are x-intercept
Therefore,
Jesse wants to factor the expression To find the x-intercepts.
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Which digit should be put in the empty box so that the resulting number is between seven lakh three thousand and seven lakh four thousand?
A. 0
B. 1
C. 3
D. 4
What is the answer please say
Answer:
c) ♣ + 25
Step-by-step explanation:
♦ + 20 = ♣
♦ + 45 = ♦ + (20+25)
=> ♦ + 45 = ♣ + 25
The solution of the equation is C
How to solve equations?The equations can be solved as follows:
let
x = the quadrilateral shape
y = flower shaped figure
Hence, let's replace it in the equation
x + 20 = y
Let's find x + 45
Therefore,
x + 20 = y
x = y - 20
Let's substitute the value of x in the second equation
x + 45
y - 20 + 45
y + 25
Recall y is the flowered shaped figure. Therefore, the answer is C.
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the price of an book is $10. to buy the book. Rosie must also pay 6% sales tax. Rosie wants to know the total price of the book including sales tax.
Turn a percent into a decimal by moving the decimal point two to the left.
10 x 6% = 10 x .06
10 x .06 = .60
Sales tax: 60 cents
Total price: $10.60
Quadrilateral STUV is similar to quadrilateral WXYZ. Find the measure of side XY.
Figures are not drawn to scale.
Answer:
11.4
Step-by-step explanation:
Given these quadrilaterals are similar, all we have to do is divide 21 (ST) by 5.7 (WX). That should give us 3.6842105263, which is the scale factor. To find the length of XY, we have to divide UT (the side similar to XY) by the scale factor. UT = 42, and 42/3.6842105263 = 11.4
Answer:
11.4
Step-by-step explanation:
BRAINLIEST TO BEST SOLUTION! The question is attached. THANK YOU FOR YOUR HELP!
Answer: not sure on this problem too
Step-by-step explanation:
sorry, can't really help!
The area of the circle is 66.50cm²
How to calculate the area of the circle?A circle is an object in which all distances are equal from the center.
In a circle, the length of the two tangents are equal.
From the figure, BP=CP
Also, the angles between a tangent and a radius is = 90⁰
⇒<OCP=90⁰
<PCB=<PBC=(180-60)/2 = 120/2 = 60⁰
Using cosine rule,
p²=b²+c²-2bccosP
p²=8²+8²-2*8*8*cos60
p²=64+64-128*0.5
p²=128-64
p²=64
Take the square root of both sides to get
p=√64=8
Note that CB=8 .....................(given)
Cx=8/2=4cm
Using trigonometric ratio
CosC = Adjacent/Hypotenuse
Cos30 = 4/CO
CO = 4/cos30
CO = 4/0.8660
CO = 4.6cm
CO = radius (r)
Area of circle = пr²
Area = 22/7 * 4.6 * 4.6
Area = 66.50 cm²
In conclusion, the area of the circle is 66.50cm²
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Use these clues to find the number.
It is an even number.
* It is greater than 6 and less than 12.
* It has a 0 in the ones place.
Answer:
10
Step-by-step explanation:
0 in the 0nes place but less than 12. more than 6. so it has to be 10.
I’m stuck here I need help
The coordinates of the end point of the line AC is C(8.6) using the section formula.
Explain the section formula?The coordinates of such a point which divides an line segment internally or externally in certain ratio can be found using the section formula. The midpoint of such a line segment can be determined using this technique as well.For the given question,
The coordinates are-
A(2, -6) C(m,n)mid point M(5,0)The formula for the mid point using the section formula is-
x(m) = x2 + x1 / 2
5 = m + 2 / 2
10 = m + 2
m = 8
y(m) = y2 + y1 / 2
0 = n - 6/ 2
0 = n -6
n = 6
Thus, the coordinates of the end point of the line AC is C(8.6) using the section formula.
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The complete question is-
Segment AC is bounded by points A(2, -6) and C(m,n). If points (5,0) is the mid point of the segment AC, find the coordinates of the point C.
calculer.
a. 3x5-(5-12)
b. 5-(3-5x6)
c. 4x(2-3x9)+7
d. 9x(-2-4x5)-3
e. 63:(2-3x7+5x2)-11
f. 48:(2-12:4-7)-4
A.
3 × 5 - (5 - 12)
= (3 × 5) - (5 - 12)
= 15 - (5 - 12)
= 15 - (-7)
= 15 + 7
= 22
B.
5 - (3 - 5 × 6)
= 5 - (3 - (5 × 6))
= 5 - (3 - 30)
= 5 - (-27)
= 5 + 27
= 32
C.
4 × (2 - 3 × 9) + 7
= 4 × (2 - (3 × 9)) + 7
= 4 × (2 - 27) + 7
= 4 × (-25) + 7
= -100 + 7
= -93
D.
9 × (-2 - 4 × 5) - 3
= 9 × (-2 - (4 × 5)) - 3
= 9 × (-2 - 20) - 3
= 9 × (-22) - 3
= -198 - 3
= -201
E.
63 ÷ (2 - 3 × 7 + 5 × 2) - 11
= 63 ÷ (2 - (3 × 7) + (5 × 2)) - 11
= 63 ÷ (2 - 21 + 10) - 11
= 63 ÷ (-9) - 11
= (63 ÷ (-9)) - 11
= -7 - 11
= -18
F.
48 ÷ (2 - 12 ÷ 4 - 7) - 4
= 48 ÷ (2 - (12 ÷ 4) - 7) - 4
= 48 ÷ (2 - 3 - 7) - 4
= 48 ÷ (-8) - 4
= (48 ÷ (-8)) - 4
= -6 - 4
= -10
Rewrite the following equation in logarithmic form.
e^a=95/73
The logarithmic form of e^a = 95/73 is [tex]loge_{\frac{95}{73} }[/tex] = a
What is natural logarithm?natural logarithm can be referred to as the power to which the base ‘e’ that has to be raised to obtain a number called its log number. Here e is the exponential function. It was initially discovered in the 17th century by John Napier, who discovered and conceptualized the theory of logarithms. Before looking into the key difference between ln and log, let’s understand the definition of log and ln.
if e^a = 95/73
means that the natural logarithm of 95/73 is the number a
so that we have
a = [tex]loge_{\frac{95}{73} }[/tex]
In conclusion the logarithmic form of the expression is a = [tex]loge_{\frac{95}{73} }[/tex]
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The graph shows the proportional relationship between time spent filling a pool, x, and the amount of water in the pool, y.
What does the point (5, 100) represent? At ____ minutes, there are _____ gallons of water in the pool.
What the point (5, 100) represent is that: At 5 minutes, there are 100 gallons of water in the pool.
How to interpret the ordered pair?The graph missing in the complete question is added at the end of this solution as an attachment
From the question, we have the following parameters that can be used in our computation:
The graph is a proportional relationship x = time spent filling a pooly = the amount of water in the poolThis means that the point (5, 100) represents
(x, y) = (5, 100)
So, we have
x = 5 and y = 100
Recall that
x = time spent filling a pooly = the amount of water in the poolSo, it means that there are 100 gallons of water in the pool after 5 minutes
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simplify this please help
Answer:
48/7
Step-by-step explanation:
8/7/6
= 8 × 1/7/6
= 8× 6/7
48/7
veterinarians often use nonsteroidal anti-inflammatory drugs (nsaids) to treat lameness in horses. a group of veterinary researchers wanted to find out how widespread the practice was in the united states. they obtained a list of all veterinarians treating large animals, including horses. they sent questionnaires to all the veterinarians on the list. such a survey is called a census. the response rate was 40%. which statement is correct?
All veterinarians that responded to the questionnaire were included in the sample.
Which of the subsequent claims is true?All veterinarians who responded to the survey made up the sample.the total number of veterinarians in the US who treat horses and other large animals.Non-steroidal anti-inflammatory medicines are frequently prescribed by veterinarians to treat lameness in horses.Researchers in the field of veterinary medicine were interested in learning how prevalent the practise was in the country.They were given a list of all vets who cared for horses and other large animals.All the veterinarians on the list received questionnaires.A census is the name given to such a survey.Complete Question : Veterinarians often use non-steroidal anti-inflammatory drugs to treat lameness in horses. A group of veterinary researchers wanted to find out how widespread the practice was in the United States. They obtained a list of all veterinarians treating large animals, including horses. They sent questionnaires to all the veterinarians on the list. Such a survey is called a census. The response rate was 40%. Which of the following statement is correct?
a. The sample consisted of all veterinarians on the list and therefore equaled the target population.
b. The sample consisted of all veterinarians who returned the questionnaire.
c. The sample consisted of all veterinarians who treat horses with NSAIDs.
d. None of the choices are correct.
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How do you write 3/4 as a percent?
Answer:
0.75 or 75%
Step-by-step explanation:
I know that 2/4 is 0.5 or 50% and 1/4 is 0.25 or 25% so it goes by 25. One more than 2/4 is 3/4, which is what you are trying to find, so it would be 0.75, or 75%.
Help me please I need help
The percentage of the down payment in the purchase is 15% and the down payment of $67500 will be 45% of the purchase price.
Calculating Percentage:The ratio of the actual worth to the total value multiplied by 100 is the formula for calculating the percentage.
The percentage formula is given by
Percentage, % = (Value × 100) / Total Value.Here we have
A family buys a studio apartment for $ 150,000
The down payment paid by the family is $ 22500
a. Percentage of down payment in the purchase
From the above data,
The percentage of the down payment = [tex][ \frac{22500 }{150,000} \times 100 ][/tex]
= [tex][ \frac{22500 }{1500} ][/tex] = 15
Therefore,
The percentage of the down payment is 15%
b. The percentage of the purchase price would be a $67500 down payment?
Let x be the percentage of the down payment in the purchase amount
=> [tex]\frac{x}{100} \times $ 150,000 = 67500[/tex]
=> [tex]x \times 1500 = 67500[/tex]
=> x = 67500/1500
=> x = 45%
Therefore,
The percentage of the down payment in the purchase is 15% and the down payment of $67500 will be 45% of the purchase price.
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