Let's make the mysterious, original price not-so-mysterious by calling it x. 245.97 is 3/5 of x.
We can equation this.
245.97 = 3/5x
x = 245.97 / (3/5)
x = 409.95
The answer, I believe, is $409.95. Hope this helps!
The original price of the laptop that Tom bought is calculated using the formula for the value of a part. This leads us to an equation, $245.97 / 0.6, resulting in the original price of the laptop being $409.95.
Explanation:The subject of this question is basic mathematics, predominantly fraction and ratio. The problem states that Tom paid $245.97, which was 3/5 of the original price of the laptop. To find the original price, we can apply the formula for the value of a part, which states that the whole is equal to the part divided by the ratio representing the part. In this case, this gives us the equation $245.97 / (3/5) = Original Price.
To make this easier, we can convert the fraction 3/5 to its decimal form, which is 0.6. So, we will then have $245.97 / 0.6 = Original Price, which should give us the original price of the laptop. Completing the math, we find that the original price of the laptop is $409.95.
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Simplify the expression 20/(9-2)
Graph the function f(x)=x2.
Plot the vertex. Then plot another point on the parabola. If you make a mistake, you can erase your parabola by selecting the second point and placing it on top of the first.
Graph [tex]f(x) = x^2[/tex]
quadratic function is of the form [tex]f(x) = ax^2 + bx +c[/tex]
In our f(x) there is no x term and constant so we put 0
[tex]f(x) = 1x^2+0x+0[/tex]
The value of a=1 , b=0 and c=0
To find vertex , use formula [tex]x= \frac{-b}{2a}[/tex]
Plug in the values
[tex]x= \frac{-0}{2(1)}[/tex] =0
Now plug in x=0 in f(x) equation
[tex]f(x) = x^2[/tex]
[tex]f(0) = 0^2[/tex]=0
So vertex is (0,0)
Now we pick some number for x below and above 0
Make a table
x y=x^2
-2 4
0 0
2 4
Now plot all the points (-2,4) (0,0) and (2,4)
The graph is attached below
Based on data set 3 in appendix b, body temperatures of healthy adults have a bell-shaped distribution with a mean of 98.20°f and a standard deviation of 0.62°f. Using the empirical rule, what is the approximate percentage of healthy adults with body temperatures (a) between 97.58°f and 98.82
The empirical rule tells you 68% of the population is within 1 standard deviation of the mean. Your limits are 1 standard deviation from the mean, so your percentage is ...
... 68%
_____
98.20 - 0.62 = 97.58 . . . 1 standard deviation below the mean
98.20 + 0.62 = 98.82 . . . 1 standard deviation above the mean
Approximately 68% of healthy adults have body temperatures between 97.58°F and 98.82°F, as per the empirical rule which states that about 68% of data falls within one standard deviation of the mean in a bell-shaped distribution.
Using the empirical rule (also known as the 68-95-99.7 rule), we can determine the approximate percentage of healthy adults with body temperatures between 97.58°F and 98.82°F. The empirical rule states that for a bell-shaped distribution:
Approximately 68% of the data falls within one standard deviation of the mean.
Approximately 95% falls within two standard deviations.
Approximately 99.7% falls within three standard deviations.
Given that the mean body temperature is 98.20°F and the standard deviation is 0.62°F:
One standard deviation from the mean includes temperatures from 98.20°F - 0.62°F to 98.20°F + 0.62°F, which is 97.58°F to 98.82°F.
Therefore, approximately 68% of healthy adults have body temperatures between 97.58°F and 98.82°F according to the empirical rule.
find the range of the function f(x)=2x+7 for the domain -2,3,8
The range is the output value
f(-2) = 2(-2)+7 =3
f(3)= 2(3)+7 = 13
f(8) = 2(8)+7 = 23
The range is 3,13,23
A sequence is defined by the recursive function f(n + 1) = –10f(n).
If f(1) = 1, what is f(3)?
3
–30
100
–1,000
We are given
[tex]f(n+1)=-10f(n)[/tex]
we are given
[tex]f(1)=1[/tex]
At n=1:
we can plug n=1 into formula
[tex]f(1+1)=-10f(1)[/tex]
[tex]f(2)=-10f(1)[/tex]
[tex]f(2)=-10*1[/tex]
[tex]f(2)=-10[/tex]
At n=2:
we can plug n=2 into formula
[tex]f(2+1)=-10f(2)[/tex]
[tex]f(3)=-10f(2)[/tex]
[tex]f(3)=-10*-10[/tex]
[tex]f(3)=100[/tex]................Answer
A function assigns the value of each element of one set to the other specific element of another set. The value of f(3) is 100.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
As the recursive function is given to us, f(n + 1) = –10f(n), also the value of f(1)=1 , therefore, the value of f(2) can be written as,
[tex]f(n + 1) = -10f(n)\\\\f(1 + 1) = -10f(1)\\\\f(2)= -10 \times 1\\\\f(2)=-10[/tex]
Now, the value of f(3) can be written as,
[tex]f(n + 1) = -10f(n)\\\\f(2 + 1) = -10f(2)\\\\f(3)= -10 \times -10\\\\f(3)= 100[/tex]
Hence, the value of f(3) is 100.
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Which equation represents y = x2 − 10x + 30 in vertex form?
To complete the square, you can add (and subtract) the square of half the x coefficient.
... y = x² -10x + 30
... y = (x² -10x +25) + (30 -25)
... y = (x -5)² +5
Solve the inequality:
|x+3|<1
This can be "unfolded" to ...
... -1 < x+3 < 1
Subtracting 3 gives the solution:
... -4 < x < -2
Which situation can be modeled by the inequality 5 + 10w ≥ 45? 50 pts!!!
Final answer:
The inequality models a situation where you have at least 45 dollars and you are adding $10 for each additional unit.
Explanation:
The inequality 5 + 10w ≥ 45 can be modeled by a situation where you have at least 45 dollars and you are adding $10 for each additional unit. Let's solve it step by step:
1. Subtract 5 from both sides of the inequality: 10w ≥ 40.
2. Divide both sides by 10: w ≥ 4.
The solution to the inequality is w ≥ 4. This means that the situation being modeled is where you have at least 4 units of something.
Courtney would like to buy a new ca in 4 years. It is estimated that a new car will cost her 25,000 and that she will get 13,000 for her used car provided she takes good care of it. Based on these estimates, what is the least amount she should save each month in order to pay cash for her new car?
4 years=48 months
A new car costs 25,000, but she will get 13,000 for her used car as long as she takes good car of it. If she takes good care of her used car and gets 13,000 for it, she will only need to save 12,000 total. We can divide 12,000 by 48 to find out how much Courtney should save minimum each month to afford her new car. 12,000/48=250
You can check to see if this is correct by multiplying 48*250=12,000. Paying 250 for each month of the 48 months will equal the $12,000 that Courtney needs.
Courtney needs to save at least $250 per month to afford her new car in 4 years.
I hope this helps :)
Courtney should save at least $250 per month for the next 4 years to be able to pay cash for the new car after considering the amount she'll receive from selling her used car.
Courtney needs to save money to buy a new car in 4 years. The estimated cost of the new car is $25,000, and she expects to get $13,000 for her used car. To find out the least amount she should save each month, we will subtract the expected amount from the sale of her used car from the cost of the new car, and then divide by the number of months in 4 years (48 months).
The calculation is as follows:
Total amount needed = Cost of New Car - Sale of Used Car
= $25,000 - $13,000
= $12,000
Monthly savings required = Total amount needed \/ Number of months
= $12,000 \/ 48
= $250
Therefore, Courtney should save at least $250 per month to pay cash for her new car in 4 years.
13x + 5 + 17x -4.5 + x explain why this is wrong show your
18x + 17x - 4.5 + x work
35x - 4.5 + x
30.5x + x
31.5x
The answerer is combining terms in x with constants
that is, 13x + 5 ≠ 18x
13x + 5 + 17x - 4.5 + x
= (13x + 17x + x ) + 5 - 4.5 ← collecting like terms
= 31x + 0.5 ← correct simplification
combining terms in x with constants
13x + 5 ≠ 18x
13x + 5 + 17x - 4.5 + x
= (13x + 17x + x ) + 5 - 4.5 <--- collecting like terms
= 31x + 0.5 <--- correct simplification
Use the polynomial remainder theorem to evaluate the polynomial for the given value.
f(x)=3x^3−2x^2−3x+18
What is the value of f(1) ?
f(1) = 16
to evaluate f(1) substitute x = 1 into f(x)
f(1) = 3 - 2 - 3 + 18 = 16
When 3x³ - 2x² - 3x + 18 is divided by (x - 1 ) the remainder is 16
Write the standard form of the equation of a line with slope=-4 and through the point (2, 2)
Show all work
The point-slope form of the equation of a line with slope m through point (h, k) can be written as
... y = m(x -h) +k
For your problem, where m = -4 and (h, k) = (2, 2), this becomes
... y = -4(x -2) +2
... y = -4x +8 +2 . . . . eliminate parentheses
... 4x +y = 10 . . . . . . .add 4x to put into standard form
Q##..15 Graph the equation. y= 4x - 3
Answer: Please, see the attached file.
Thanks.
Solution:
We can graph using the intercepts:
(1) y-intercept, when x=0
y=4x-3→y=4(0)-3→y=0-3→y=-3
Point=(x,y)=(0,-3)
(2) x-intercept, when y=0
y=4x-3→0=4x-3
Solving for x: Adding 3 both sides of the equation:
0+3=4x-3+3
3=4x
Dividing both sides of the equation by 4:
3/4=4x/4
3/4=x
x=3/4=0.75
Point=(x,y)=(3/4,0)=(0.75,0)
With these pair of points (0, -3) and (0.75,0) we can draw the right line
25 is the result when 8 and x are added. What is the value of x? Enter your answer in the box as a fraction in simplest form.
Its simply just 8 minus 25 to find x but there is no fraction.
Help me plz with problem I need a lot of help with it
Answer:
about 35
Step-by-step explanation:
This question is asking for an estimate, which means you round the number(s) to something convenient to perform the calculation.
Here, 47% is conveniently rounded to 50% = 50/100 = 1/2. Then 1/2 of 70 is ...
1/2·70 = 70/2 = 35
A reasonable estimate of 47% of 70 is 35.
___
As you get more sophisticated in your estimating, you can also estimate the error. This estimate is about 3% (of 70) high, so is high by 3/100·70 = 2.1. That means the real answer is 35 - 2.1 = 32.9.
You could also estimate the error as 3% of 100 = 3/100·100 = 3, so you could say the actual value is between 35-3 = 32 and 35. Since 100 is larger than 70, you know that 3% of 100 is larger than 3% of 70, so this is an over-estimate of the error.
What is 3.242424... as a mixed number
Answer:
3 8/33
Step-by-step explanation:
You want the mixed-number equivalent of the repeating decimal 3.2424....
Repeating decimalA repeating decimal fraction that starts at the decimal point can be converted to a ratio of integers by expressing the repeating digits over the same number of 9s.
Here, the two repeating digits "24" mean the fraction equivalent is ...
0.2424... = 24/99 = 8/33
The mixed number equivalent of 3.2424... is 3 8/33.
__
Additional comment
If the repeating portion does not start at the decimal point, you can use the following technique to do the conversion.
Multiply the original number by 10^n, where n is the number of repeating digits.Subtract the original number from this product. Repeating digits should cancel to zeros.Divide this difference by (10^n) -1 and simplify the resulting fraction.Effectively, this multiplies and divides the number by ((10^n) -1)/((10^n) -1). In the case here, that would be multiplication by 1 in the form 99/99.
3.242424... × 99/99 = 321/99 = 3 8/33
The "321" will be manifested on a calculator as 320.99999.... If you multiply by (100 -1) with pencil and paper, you can see that you get ...
324.2424... - 3.2424... = 321 . . . . . . repeating digits cancel
If the repeat starts somewhere else, you can still use the "fraction with equal number of 9s" technique, but with a multiplier:
3.6242424... = 3.6 + 0.0242424 ... = 3.6 + (1/10)(24/99)
= 36/10 + 8/330 = 3 103/165
<95141404393>
3.242424... as a mixed number is [tex]\(3 \frac{8}{33}\)[/tex].
To express the repeating decimal 3.242424... as a mixed number, we can first write it as an infinite geometric series.
Let x = 3.242424.... Then, multiplying x by 100 gives 100x = 324.242424...
Now, subtract x from 100x:
100x - x = 324.242424... - 3.242424...
99x = 321
Now, solve for x:
[tex]\[ x = \frac{321}{99} \][/tex]
Now, express the fraction [tex]\(\frac{321}{99}\)[/tex]as a mixed number.
[tex]\[ \frac{321}{99} = 3 \frac{24}{99} \]\\Now, simplify the fraction:\[ \frac{24}{99} = \frac{8}{33} \][/tex]
So, 3.242424... as a mixed number is [tex]\(3 \frac{8}{33}\)[/tex].
caroline has enough pumpkin seeds to cover an area of 350 square feet. her garden measures 18 feet by 22 feet. does she have enough pumpkin seeds to fill the whole garden? explain
yes
area = 18 × 22 = 396 ft²
Since 396 > 350
Caroline has more than enough to fill her garden
6 divided by the difference of a number and 2, minus 5 divided by a number plus 2, equals 5 times the reciprocal of the difference of the number squared and 4. What is the number? Please help ASAP!!!!!!!!! :(
Answer:
-20
Step-by-step explanation:
7:8:9=__:12:__ find the blanks. They are ratios PLEASE HELP
Answer: [tex]7:8:9 = 10.5:12:13.5[/tex]
Step-by-step explanation:
Suppose, [tex]7:8:9= x:12:y[/tex]
Now according to the ratio, the equations will be........
[tex]\frac{7}{8}=\frac{x}{12}\\ \\ 8x=7*12=84\\ \\ x=\frac{84}{8}=10.5[/tex]
and
[tex]\frac{8}{9}=\frac{12}{y}\\ \\ 8y=9*12=108\\ \\ y=\frac{108}{8}=13.5[/tex]
So, the ratio will be [tex]7:8:9 = 10.5:12:13.5[/tex]
The ratio is [tex]\boxed{7:8:9 = 10.5:12:13.5}[/tex].
Further Explanation:
Given:
The ratio is [tex]7:8:9[/tex] and is equal to [tex]{\text{\_\_\_}}:{\text{12}}:{\text{\_\_\_}}[/tex].
Calculation:
Consider the number in the first blank as [tex]x[/tex].
Consider the number in the second blank as [tex]y[/tex].
Therefore, the ratio is [tex]7:8:9[/tex] and is equal to [tex]{{x}}:{\text{12}}:{{y}}[/tex]
From the given equation the ratio of [tex]7:8[/tex] is equal to the ratio of [tex]x:12[/tex].
Now equate [tex]\dfrac{7}{8}[/tex] and [tex]\dfrac{x}{12}[/tex] to obtain the value of [tex]x[/tex].
[tex]\begin{aligned}\frac{7}{8} &= \frac{x}{{12}} \\ \frac{7}{8} \times 12 &= x \\ \frac{{21}}{2} &= x \\ 10.5 &= x \\ \end{aligned}[/tex]
Therefore, the value of [tex]x[/tex] is [tex]10.5[/tex].
From the given equation the ratio of [tex]8:9[/tex] is equal to the ratio of [tex]12:y[/tex].
Now equate [tex]\dfrac{8}{9}[/tex] and [tex]\dfrac{12}{{y}}[/tex] to obtain the value of [tex]y[/tex].
[tex]\begin{aligned}\frac{8}{9} &= \frac{{12}}{y} \\ \frac{9}{8} &= \frac{y}{{12}} \\ \frac{9}{8} \times 12 &= y \\ \frac{{27}}{2} &= y \\ 13.5&= y \\\end{aligned}[/tex]
Therefore, the value of [tex]y[/tex] is [tex]13.5[/tex].
Hence, the ratio is [tex]\boxed{7:8:9 = 10.5:12:13.5}[/tex].
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Answer details:
Grade: Middle School
Subject: Mathematics
Chapter: Ratio and Proportion
Keywords: number, reciprocal, fraction, ratio, equation, proportion, 7:8:9, fill blank.
Write a number that is 100 times smaller than 7,000
Use inductive reasoning to describe the pattern. Then find the next two numbers in the pattern. –9, –4, 1, 6, . . .
We are given a pattern:
-9 , -4 , 1 , 6 , ...
We have to describe the pattern and find the next two terms
-9+5= -4
-4+5= 1
1+5= 6
Hence, the numbers are found by adding five to the previous term
The next two numbers are found as:
6+5 =11
11+5 = 16
Hence, next two numbers are:
11 and 16
The overall cost of carpet and installation from a particular company is represented by the function, where x represents the square footage of the carpet.
P(x) = $2.90x + $103.00
What is the average rate of change over the interval [2,000, 2,500]?
A. $2.90 per square foot
B. $4.85 per square foot
C. $0.34 per square foot
D. $1.03 per square foot
The function is linear, so its rate of change is the same everywhere. That rate of change is the coefficient of the variable x, so is $2.90. Since the units of x are feet, and the units of P(x) are dollars, the rate of change $2.90 must be ...
... A. $2.90 per square foot
The average rate of change for the given cost function over the interval [2,000, 2,500] is calculated using the slope formula, resulting in an average rate of $2.90 per square foot, corresponding to option A.
Explanation:The question asks to find the average rate of change of the cost function P(x) = $2.90x + $103.00, where x represents the square footage of the carpet, over the interval of [2,000, 2,500 square feet]. To calculate the average rate of change, we use the formula of the slope between two points on the function:
(P(x_2) - P(x_1)) / (x_2 - x_1).
So for the interval [2,000, 2,500], we have:
(P(2500) - P(2000)) / (2500 - 2000) = (($2.90 \times 2500 + $103.00) - ($2.90 \times 2000 + $103.00)) / (2500 - 2000).
This simplifies to:
($7250 + $103 - $5800 - $103) / 500 = $1450 / 500 = $2.90 per square foot.
Therefore, the average rate of change over the interval [2,000, 2,500] is $2.90 per square foot, which corresponds to option A.
What equation results from completing the square and then factoring x^2+16x =41
A. (x+8)^2 =57
B.(x+16)^2 =57
C. (x+8)^2 =105
D. (x+16)^2 =105
C
given x² + 16x = 41
to complete the square on this equation
since the coefficient of the x² term is 1
add (half the coefficient of the x-term )² to both sides
x² + 2(8)x + 64 = 41+ 64
(x + 8 )² = 105 → C
Answer:
Option C is correct
Step-by-step explanation:
Given the equation
[tex]x^2+16x=41[/tex]
we have to find the equation results from completing the square.
For completing the square method, since the coefficient of [tex]x^2[/tex] is 1 therefore we have to divide the coefficient of x by 2 and then squaring of that value adding on both sides of equation, we get
Here coefficient of x is 16 therefore square of half the number adding both sides
[tex]x^2+16x+64=41+64[/tex]
[tex]x^2+8x+8x+64=105[/tex]
[tex]x(x+8)+8(x+8)=105[/tex]
[tex](x+8)(x+8)=105[/tex]
[tex](x+8)^2=105[/tex]
Option C is correct
You are selling raffle tickets to raise money. Each ticket costs $5. Which equation solves for the number of tickets you must sell to raise $45?
A) 45-5=x
B) x/4=45
C) 45=5+x
D) 5x=45
D. 5x = 45 because you are trying to find x, the number of tickets that must be sold to earn $45.
Answer:
5x=45
Step-by-step explanation:
In the past you paid $800 per month to rent your apartment. You now pay $ 900 per month for your rent. What is the percent increase in your rent
800 - 900 = -100. = 100/800=.125 x 100 = 12.5% increase.
multiply 3x-4y=-2 by three numbers and see if (6,5) is still a solution
I am F years old and my brother is B years older. What is the sum of our ages? What will be the sum of our ages in three years? What was the difference of our ages two year ago
a) The sum of your ages is F + (F+B) = 2F+B.
b) In 3 years, the sum of your ages will be (F+3)+(F+B+3) = 2F+B+6.
c) The difference of your ages at any time is B.
Answer:
a) The sum of your ages is F + (F+B) = 2F+B.
b) In 3 years, the sum of your ages will be (F+3)+(F+B+3) = 2F+B+6.
c) The difference of your ages at any time is B.
How are percent error and percent change similar
How many whole numbers are there, whose squares and cubes have the same number of digits?
There are the following numbers for which that holds:
{-4, -2, -1, 0, 1, 2, 4}
See table below. For larger than 5 it can be proved that the number of digits will never be the same.
x x^2 x^3
0 0 0
1 1 1
2 4 8
4 16 64
Answer:
the answer if 4 numbers
(sorry i dont have an explenation i litterally guessed it when I entered it in the RSM portal.)
Step-by-step explanation:
Suppose the roots of a polynomial are 3 4 , − 7 8 , − 3 8 , and − 1 9 . Which choice is a factor of the polynomial?
A) (x +3/4)
B) (x + 3/8)
C) (x - 7/8)
D) (x - 1/9)
Answer:
x+7/8
Step-by-step explanation:
A polynomial has roots at the points where the curve cuts the x axis.
This can also be said as values of x for which the polynomial is 0
Given that when x =a is root means, we have x-a is the factor.
Based on the above, we find when 3/4, -7/8, -3/8 and -1/9 are roots
factors are x-3/4, x+7/8, x+3/8, x+1/9
Hence answer is
B) (x + 3/8)
The other options do not match with the factors only option Bmatches.
Answer: The factor of the polynomial is [tex](x+\frac{3}{8})[/tex]
Step-by-step explanation:
We are given:
4 roots of the polynomial
Root 1: [tex]\frac{3}{4}[/tex]
The factor for this root becomes: [tex](x-\frac{3}{4})[/tex]
Root 2: [tex]\frac{-7}{8}[/tex]
The factor for this root becomes: [tex](x+\frac{7}{8})[/tex]
Root 3: [tex]\frac{-3}{8}[/tex]
The factor for this root becomes: [tex](x+\frac{3}{8})[/tex]
Root 4: [tex]\frac{-1}{9}[/tex]
The factor for this root becomes: [tex](x+\frac{1}{9})[/tex]
Hence, the factor of the polynomial is [tex](x+\frac{3}{8})[/tex]