Answer:
33%
Step-by-step explanation:
Assuming the weight of the mixture to be 100g**, then the weight of ryegrass in the mixture would be 30g.
Also, assume the weight mixture X used in the mixture is Xg, then the weight of mixture Y used in the mixture would be (100-X)g.
So we can now equate the parts of the ryegrass in the mixture as:
0.4X + 0.25(100-X) = 30
<=> 0.4X + 25 - 0.25X = 30
<=> 0.15X = 5
<=> X = 5/0.15 = 500/15 = 100/3
So the weight of mixture X as a percentage of the weight of the mixture
= (weight of X/weight of mixture) * 100%
= (100/3)/100 * 100%
= 33%
plzzzzzzzzzz help me somebody, anybody. my questions always get skipped over!
I believe the answer is B. Hope this helps!
The variable z varies jointly as the second power of x and the third power of y. When x equals 2 and y equals 2.4, z equals 31.5. Approximate the constant of variation to the nearest hundredth.
Answer:
The constant of variation, k = 0.57
Step-by-step explanation:
We are given that z varies jointly as the second power of x (x²), and the third power of y (y³).
For a constant of variation, k, z can be written as
z = x²y³k.
We are also given
z = 31.5
x = 2
x = 2.4
31.5 = (2²)(2.4)³k
31.5 = 4×13.824k
31.5 = 55.296k
k = 31.5/55.296
= 0.57
Solve the two-step equation. − 2 3 x – 21 4 = 27 4
Answer:
Step-by-step explanation:
I'm going to assume that the problem is -23x -214 = 274
And in that case...
1. First isolate the x-value by adding 214 to both sides of the equation:
-23x = 488
2. Then, divide both sides by -23 to truly get x alone:
x = [tex]-\frac{488}{23}[/tex] or -21.22
Answer:
x = -18
Add the opposite of the constant on the left:
-2/3x = 21/4 +27/4 = 48/4 = 12
Multiply the equation by the inverse of the coefficient of x:
x = (-3/2)(12) = -18
The solution is x = -18.
Step-by-step explanation:
What is the value of p such that the line passing through (9,-1) and (6,p) has a slope of -1?
Answer:
p=2
Step-by-step explanation:
Use the slope formula
(p-(-1))/(6-9)=-1
(p+1)/-3=-1
p+1=3
p=2
Answer:
Step-by-step explanation:
Slope, m =change in value of y on the vertical axis / change in value of x on the horizontal axis represent
change in the value of y = y2 - y1
Change in value of x = x2 -x1
y2 = final value of y
y 1 = initial value of y
x2 = final value of x
x1 = initial value of x
The line passes through (9,-1) and (6,p) and the slope is 1
y2 = p
y1 = - 1
x2 = 6
x1 = 9
Therefore,
(p - - 1)/(6 - 9) = - 1
(p + 1)/- 3 = - 1
(p + 1) = - 1 × - 3
p + 1 = 3
p = 3 - 1
p = 2
You have a three year fixed rate lease of $900/month due to expire next month. Your landlord is willing to renew the three year lease with a 3% total rent increase. What is your rent over the three year life of the new lease?
Answer:
[tex]\\3 percent of 900 = 27 \\900 + 27 = 927 \\ 927 * 36 = 33372[/tex]
Step-by-step explanation:
First you have to find out the 3% of 900 (is 27)
then you add 27 to 900
then you multiply it by 3 years (36 months)
and your result is 33372 :)
The rent over the three-year term of the new lease will be $33,372, calculated with a 3% increase annually.
Step 1:
Calculate the new monthly rent after the 3% increase.
The new monthly rent will be the current rent plus 3% of the current rent.
New monthly rent = $900 + 0.03 * $900 = $900 + $27 = $927.
Step 2:
Calculate the total rent over the three-year term.
Since there are 12 months in a year and the lease is for three years, multiply the new monthly rent by the number of months in three years.
Total rent over three years = $927/month * 12 months/year * 3 years = $33,372.
So, the rent over the three-year life of the new lease will be $33,372.
A local real estate magazine used the median instead of the mean when it reported the SAT score of the average student who attends Groveland High School. A graphical display of SAT scores of students who attend Groveland High School indicated that the data were strongly skewed to the right. Which of the following explains why, in this situation, the median is a more accurate indicator of the SAT score of the average student than the mean is
Final answer:
The median is a more accurate indicator of the average student's SAT score at Groveland High School in a right-skewed distribution because it is not affected by outliers, unlike the mean.
Explanation:
The question addresses why the median is a more accurate indicator of the SAT score of the average student at Groveland High School rather than the mean when the data is strongly skewed to the right. This is because the median is the middle value that divides the number set into two equal halves, and it is not affected by outliers or extremely high scores that are present in a right-skewed distribution. In contrast, the mean is the average of all values and can be significantly influenced by outliers, leading to a value that may not accurately represent the 'central' tendency of the data. Thus, for a right-skewed data set, the median provides a better measure of center for what can be considered a typical score because it is not skewed by unusually high values.
Fill each blank with sometimes, always or never to make each statement true
a. the diagonals of a parallelogram_______ bisect each other.
b. the opposite sides of a parallelogram will_________ have different lengths
c. parallelograms are________ rectangles
Answer:
a.always
b.never
c.sometimes
Final answer:
The blank spaces in the statements regarding properties of parallelograms should be filled with 'always' for diagonals bisecting each other, 'always' for opposite sides having the same length, and 'sometimes' when referring to parallelograms being rectangles, as not all parallelograms have right angles.
Explanation:
The given question asks you to fill in the blanks with sometimes, always, or never to make each statement about a parallelogram true. Here are the completed statements with explanations:
The diagonals of a parallelogram always bisect each other.The opposite sides of a parallelogram will always have the same length. (Here 'always' is used to imply that because it's a property of parallelograms, the opposite sides will indeed be equal in length.)Parallelograms are sometimes rectangles. (This is true because rectangles are a specific type of parallelogram with right angles, but not all parallelograms are rectangles.)To understand these properties, consider that a parallelogram is a quadrilateral with opposite sides that are parallel and equal in length. Additionally, the diagonals of a parallelogram bisect each other, which means they cut each other exactly in half at the point where they cross. This property is invariant under any affine transformation, so it holds true regardless of how the parallelogram is oriented or scaled.
Someone please help.. plz dont skip me
Which of the following are ordered pairs for the equation y =x - 3?
(0,3) (-2,-1) (2,5)
(0,3) (2,1) (-2,-5)
(0,-3) (2,-1) (-2,-5)
(0,-3) (2,-1) (-2,5)
1. Graph the polar equation
2. Find each quotient and express it in rectangular form.
2(cos150°+isin150°)/ 8(cos210°+isin210°)
-0.22+0.12i
1/4[sin(-60°)+icos(-60°)]
0.12-0.22i
1/4[cos(-60°)+isin(-60°)]
3. Write the rectangular equation (x+5)^2+y^2=25 in polar form.
R= -10sin theta
R= 5
R= 5cos theta
R= -10cos theta
To graph the polar equation, plot points based on r and θ values. To express the quotient of complex numbers in rectangular form, operate division, simplify, then convert. To convert a rectangular equation to polar form, substitute x and y with their polar form.
Explanation:1. To graph the polar equation, you would plot points based on the r (magnitude/distance) and θ (angle) values from the origin (0,0). As you've not provided the specific polar equation, I cannot provide a full step-by-step explanation.
2. To divide complex numbers and express the quotient in rectangular form, you multiply the numerator and the denominator by the conjugate of the denominator, simplify, and convert the result into rectangular coordinates (x+iy) form. For example,
2(cos150° + isin150°) / 8(cos210° + isin210°)
After calculating the division, you end up with the cosine and sine of an angle in the numerator. Then, convert this to rectangular form. Unfortunately, as Brainly platform constraints, computational solutions cannot be provided through this medium.
3. To convert the rectangular equation (x+5)^2+y^2=25 in polar form, replace x = rcosθ and y = rsinθ in the equation. Then simplify the equation to get a polar equation.
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A survey of 550 male managers and 650 female managers was conducted. All 1,200 managers identified whether, for each of six characteristics, the characteristic is important to consider when hiring a new employee. For each of the six characteristics, the percent of managers surveyed who identified that characteristic as important to consider is given in the following table. SURVEY RESULTSCharacteristic Percent Work Experience 72%Proficiency in English 68%Ability to Follow Directions 65%Specific Occupational Skill 60%Computer Expertise 58%Appropriate Attire and Behaviour 55%The number of managers surveyed who identified work experience as an important characteristic to consider was approximately what percent greater than the number who identified appropriate attire and behavior as an important characteristic to consider?
A. 15%
B. 20%
C. 25%
D. 30%
E. 35%
Answer:
Correct option is (B). 20%.
Step-by-step explanation:
The number of managers is, 1200.
The percentage of managers who identified work experience as an important characteristic to consider is, P (W) = 72%.
The percentage of managers who identified appropriate attire and behavior as an important characteristic to consider is, P (AB) = 55%.
Compute the number of managers who identified work experience as an important characteristic to consider as follows:
[tex]n(W)=1200\times P(W)\\=1200\times\frac{72}{100}\\=864[/tex]
Compute the number of managers who identified appropriate attire and behavior as an important characteristic to consider as follows:
[tex]n(AB)=1200\times P(AB)\\=1200\times\frac{55}{100}\\=660[/tex]
Compute approximately what percent greater is P (W) than P (AB) as follows:
[tex]P(W>AB)=\frac{n(W)-n(AB)}{1200}=\frac{864-660}{1200}=\frac{204}{1200}=0.17\approx0.20[/tex]
Thus, the number of managers surveyed who identified work experience as an important characteristic to consider was approximately 20% percent greater than the number who identified appropriate attire and behavior as an important characteristic to consider.
Correct option is (B).
A home owner has a monthly budget of $400 to spend on their homes landscaping. If they spent 35% of their budget this month on landscaping, how much was spent?
Answer:
$140
Step-by-step explanation:
If the Monthly Budget for Landscaping=$400
and the Percentage of Landscaping Budget Spent this Month=35%
The Amount Spent on Landscaping=35% of Total Landscaping Budget
=35 percent of $400
Recall that percentage is always over 100, therefore 35%=35/100
=[tex]\frac{35}{100}X400[/tex]
=$140
The homeowner spent $140 on landscaping this month.
Answer:
$260 was spent.
Step-by-step explanation:
The main problem is about proportion, specifically direct proportion.
$400 is the total budget, wich means is 100% of the budget.
They spent 35%, so we need to substract the amount of spent budget to total budget, in order to know how much was spent, we will call it remaining budget:
total budget=100%
spent budget=35%
remaining budget=total budget - spent budget
remaining budget= 100% - 35% = 65%
remaining budget= %65
As a result of the substraction we have the percentage of remaining budget, 65%. The next step is to transform that percentage into an amount of money. To do that we use the Mathematical Rule of Three.
The Rule of Three is a method to solve direct proportion problems, when we have three quantities related to each other. For this case %100 equals $400 and %65 equals to unknown, that's the cuantitie we want to know, that is, remaining budget, as shown below:
%100 -> $400
%65 -> x
On a general form it could be understood as a relation between a-b and c-x:
a -> b
c -> x
Next we will apply the following formula
[tex]x= \frac{c*b}{a} [\tex]
For this case:
[tex]x= \frac{65*400}{100} [\tex]
[tex]x= $260[\tex]
The remaining budget is $260
An SRS of size n was taken to estimate mean body mass index (BMI) for girls between 13 and 19 years of age. The 95% confidence interval obtained had lower limit 19.5 and upper limit 26.3. Which of the following is NOT true? 1. A total of 95% of all teenage girls have BMI between 19.5 and 26.3. 2. The margin of error is 34. 3. The value z in the margin of error is 1.96. 4. A total of 95% of all SRS of size n contain the true mean BMI
Answer:
Option 1) A total of 95% of all teenage girls have body mass index between 19.5 and 26.3.
Step-by-step explanation:
We are given the following in the question:
95% confidence interval of mean body mass index (BMI) for girls between 13 and 19 years of age is:
[tex](19.5, 26.3)[/tex]
Lower limit = 19.5
Upper limit = 26.3
1. A total of 95% of all teenage girls have body mass index between 19.5 and 26.3.
The given statement is false. This is not the right interpretation for confidence interval.
2. The margin of error is 3.4
The confidence interval can be found as
[tex]\text{sample mean}\pm \text{Margin of error}[/tex]
Let x be the sample mean and y be the margin of error, thus, we can write
[tex]x - y =19.5\\x + y = 26.3\\2x =45.8 \\x = 22.9\\y = 22.9 - 19.5\\y = 3.4[/tex]
Thus, the margin of error is 3.4
Thus, the given statement is true.
3. The value z in the margin of error is 1.96.
The statement is true.
The z-multiplier for a 95% confidence interval used is 1.96
4. A total of 95% of all SRS of size n contain the true mean body mass index
The given statement is true. It is the right interpretation of 95% confidence interval.
Among the provided statements, 'A total of 95% of all teenage girls have BMI between 19.5 and 26.3' is NOT accurate. A 95% confidence interval does not indicate that 95% of the data is in that range.
Explanation:In this case, the statement that is NOT true about the confidence interval for estimating the mean body mass index (BMI) for girls between 13 and 19 years of age is: 1. A total of 95% of all teenage girls have BMI between 19.5 and 26.3.
A 95% confidence interval does not claim that 95% of the population data falls within this range. Instead, it asserts that if we were to take many samples and build a confidence interval from each sample, then about 95% of the confidence intervals would contain the true mean BMI (this is the meaning of statement 4).
Statement 2 is incorrect since the margin of error is not 34. It is calculated as (26.3 - 19.5)/2 = 3.4.
Statement 3 is correct as the value for 'z' in a 95% confidence interval is indeed 1.96. This is because 1.96 is the z-score that cuts off the top 2.5% and bottom 2.5% of data in a standard normal distribution, leaving 95% of the data in between.
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ASAP
Brianna invested $480 in an account paying an interest rate of 6 1/2% compounded continuously. Adam invested $480 in an account paying an interest rate of 6 3/4 % compounded quarterly. To the nearest hundredth of a year, how much longer would it take for Brianna's money to double than for Adam's money to double?
Answer: it would take 7 years more for Brianna's money to double than for Adam's money to double
Step-by-step explanation:
Considering Brianna's investment,
The formula for continuously compounded interest is
A = P x e (r x t)
Where
A represents the future value of the investment after t years.
P represents the present value or initial amount invested
r represents the interest rate
t represents the time in years for which the investment was made.
e is the mathematical constant approximated as 2.7183.
From the information given,
P = $480
r = 6.5% = 6.5/100 = 0.065
A = 2 × 480 = $960
Therefore,
960 = 1800 x 2.7183^(0.065 x t)
960/1800 = 2.7183^(0.065t)
2 = 2.7183^(0.065t)
Taking ln of both sides, it becomes
Ln 2 = 0.065tln2.7183
0.693 = 0.065t
t = 0.693/0.065
t = 10.66
Approximately 17 years
Considering Adam's investment, we would apply the formula for determining compound interest which is expressed as
A = P(1+r/n)^nt
Where
A = total amount in the account at the end of t years
r represents the interest rate.
n represents the periodic interval at which it was compounded.
P represents the principal or initial amount deposited
From the information given,
P = 480
A = 960
r = 6.75% = 6.75/100 = 0.0675
n = 4 because it was compounded 4 times in a year.
Therefore,.
960 = 480(1 + 0.0675/4)^4 × t
960/480 = (1 + 0.016875)^4t
960/480 = (1.016875)^4t
Taking log of both sides, it becomes
Log 2 = 4t log 1.016875
0.301 = 0.0291t
t = 0.301/0.0291
t = 10.34
Approximately 10 years
mansi shines a beam of light on a mirror. The angle between the beam and the mirror is 25°. The beam reflects off the mirror at an angle of 25°. Find the measure of the unknown angle.
Answer:
130°
Step-by-step explanation:
The diagram for the question is redrawn on the attached image. It was obtained online.
Basically, what the question is asking is for the angle between the new path of the beam and the old path if the beam continued without being reflected by the mirror.
The line of the old path of the beam of light is a straight line. And the sum of angles on straight line = 180°
25° + 25° + y° = 180°
y = 180° - 50° = 130°
Solve the following equation: -3 = 1 3/5 + m.
-2 3/5
-4 3/5
-4 2/5
-1 25
Answer:
-4 2/5
Step-by-step explanation:
A dog food company wishes to test a new high-protein formula for puppy food to determine whether it promotes faster weight gain than the existing formula for that puppy food. Puppies participating in an experiment will be weighed at weaning (when they begin to eat puppy food) and will be weighed at one-month intervals for one year. In designing this experiment, the investigators wish to reduce the variability due to natural differences in puppy growth rates. Which of the following strategies is most appropriate for accomplishing this?
A) Block on dog breed and randomly assign puppies to existing and new formula groups within each
breed.
B) Block on geographic location and randomly assign puppies to existing and new formula groups
within each geographic area.
C) Stratify on dog breed and randomly sample puppies within each breed. Then assign puppies by
breed to either the existing or the new formula.
D) Stratify on geographic location of the puppies and randomly sample puppies within each
geographic area. Then assign puppies by geographic area to either the existing or the new formula
E) Stratify on gender and randomly sample puppies within gender groups. Then assign puppies by
gender to either the existing or the new formula.
To reduce the variable of natural differences in puppy growth rates, the investigators should block on dog breed. Breed significantly impacts growth rates compared to geographic location or gender.
Explanation:In designing an experiment to test whether a new high-protein puppy food promotes faster weight gain than an existing formula, the strategy that would most effectively reduce variability due to natural differences in puppy growth rates would be option A- Block on dog breed and randomly assign puppies to existing and new formula groups within each breed.
Puppy growth rates can vary significantly by breed, with larger breeds often growing faster than smaller ones. By blocking on breed, the researchers can ensure that any differences in weight gain are due to the food, not differences in breed-specific growth rates.
The other strategies - blocking or stratifying on geographic location, or stratifying on gender - would not be as effective, because these factors have less influence on a puppy's growth rate compared to its breed.
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Last year, 31 2 acres of strawberry fields produced approximately 14,700 pounds of strawberries. This year the number of acres planted with strawberries increased to 5 acres. Use proportional reasoning to estimate the farm's income from the sale of strawberries this year.
So in 5 acres of land produces 21,000 pounds of strawberries.
Step-by-step explanation:
Step 1:
Last year, [tex]3\frac{1}{2}[/tex] acres i.e 3.5 acres produced 14,700 pounds of strawberries. So we need to determine how many strawberries were produced per acre.
To do this we divide the total number of strawberries produced by the number of acres it was produced in.
The number of strawberries produced per acre[tex]= \frac{14,700}{3.5} = 4,200[/tex] pounds.
Step 2:
To determine the number of strawberries in 5 acres of land, we multiply the number of strawberries per acre by the number of acres.
The number of strawberries produced in 5 acres[tex]= 5(4,200) = 21,000[/tex] pounds.
So in 5 acres of land produces 21,000 pounds of strawberries.
PLS HELP
f(x)=x^3−2x^2+12x−6
g(x)=4x^2−6x+4
What is (f−g)(x)?
Answer:
[tex](f - g)(x) = {x}^{3} - 6 {x}^{2} + 18x - 10[/tex]
Step-by-step explanation:
The given functions are:
[tex]f(x) = {x}^{3} - 2 {x}^{2} + 12x - 6[/tex]
and
[tex]g(x) = 4 {x}^{2} - 6x + 4[/tex]
We want to find
[tex](f - g)(x)[/tex]
Recall that:
[tex](f - g)(x) = f(x) - g(x)[/tex]
This implies that:
[tex](f - g)(x) = {x}^{3} - 2 {x}^{2} + 12x - 6 - (4 {x}^{2} - 6x + 4)[/tex]
[tex](f - g)(x) = {x}^{3} - 2 {x}^{2} + 12x - 6 - 4 {x}^{2} + 6x - 4[/tex]
We combine similar terms to get:
[tex](f - g)(x) = {x}^{3} - 6 {x}^{2} + 18x - 10[/tex]
Answer:
Solution given:
f(x)=x3−2x2+12x−6
g(x)=4x2−6x+4
now
(f-g)(x)=f(x)-f(g)=x3−2x2+12x−6-4x²+6x-4
=x³-6x²+18x-10
(3 plus 3 a )plus (1 plus 5 m )(3 plus 3 a )plus (1 plus 5 m )equals nothing (Simplify your answer.)
Answer:
[tex]7+6a+5m(4+3a)=0[/tex]
Step-by-step explanation:
We want to simplify the expression
[tex](3 + 3 a ) + (1 + 5 m )(3 + 3 a ) + (1 + 5 m )=0[/tex]
Expanding the expression in the middle
[tex](3 + 3 a ) + 1 (3 + 3 a )+ 5 m (3 + 3 a ) + (1 + 5 m )=0[/tex]
Eliminating all brackets
[tex]3 + 3 a + 3 + 3 a + 15m + 15m a + 1 + 5 m =0[/tex]
Next, we collect our like terms
[tex]3+3+1+3a+3a+15m+5m+15ma=0[/tex]
When you collect like terms, ensure the number of terms are still the same
[tex]7+6a+20m+15ma=0[/tex]
This simplified gives us:
[tex]7+6a+5m(4+3a)=0[/tex]
I caculated it all and it is the same as Newton9022
Hope this helps.
Assume a round of golf requires four hours of leisure time, and attending a concert requires two hours. If the price of a round of golf is $40 and the price of a concert is $80, ceteris paribus, Joe will play
Answer:
Step-by-step explanation:
Relatively less golf and attend relatively more concerts whenever his leisure time becomes more scarce.
- This is called the marginal utility, that with every successive unit that utility decreases. With each passing hour while playing golf Joe is less inclined to play for an extra hour. When leisure time is less than 2 hrs he is equally likely to opt out of golf for concert.
nearest foot horizontal distance
The horizontal distance the plan has covered when it has flown 4,000 feet is 694 feet.
Step-by-step explanation:
Step 1:
For the given triangle, assume the opposite side has a length of x units, the hypotenuse of the triangle measures 4,000 feet. The given angle of the triangle is 10°. To calculate the opposite side's length of the triangle, we use the sine of the given angle.
[tex]sin A = \frac{oppositeside}{hypotenuse}[/tex]
Step 2:
The length of the opposite side = x feet.
The length of the hypotenuse side = 4,500 feet.
[tex]sin A = \frac{oppositeside}{hypotenuse}, sin 10 = \frac{x}{4000}.[/tex]
[tex]x = sin10 (4000), sin 10 = 0.1736, x = 0.1736(4000) = 694.4 feet[/tex].
So the horizontal distance is 694.4 feet, rounding this off to the nearest foot, we get the horizontal distance as 694 feet.
What do the graphs of sine and cosine have in common with the swinging you see?
Answer:
Period of 2π
Step-by-step explanation:
The graph of sine starts at zero on the y axis while that of cosine starts at the point 1 as sin 0=0 at t=0 and cos 0=1 at t=0. We say the cosine curve is a sine curve which is shifted to the left by [tex]\frac{\pi}{{2}}\[/tex]
The basic sine and cosine functions have a period of 2π (in radians). The period is the time it takes to go through one complete cycle. It means that after every complete cycle, the graph repeats itself over and over again..
Answer:
Check
Step-by-step explanation:
The high and low points repeat in a pattern.
The cycle repeats at equal time intervals.
The swinging motion is smooth, unabrupt.
Penelope goes to work after school for 4.5 hours on Mondays, Tuesdays, and Fridays. She doesn’t have classes on Wednesdays or Thursdays, so she works 8 hours each on those days. If she makes $413 each week, what’s her hourly rate? aner
Answer:
Her hourly rate is $14.
Step-by-step explanation:
Given:
Penelope goes to work after school for 4.5 hours on Mondays, Tuesdays, and Fridays.
She works 8 hours each on Wednesdays or Thursdays.
Now, to find her hourly rate.
So, total hours Penelope work on Mondays, Tuesdays, and Fridays:
[tex]4.5+4.5+4.5=13.5\ hours.[/tex]
And, total hours she work on Wednesdays and Thursdays:
[tex]8+8=16\ hours.[/tex]
Now, the total hours each week she work:
[tex]13.5+16=29.5\ hours.[/tex]
Total money she makes each week = $413.
Now, to get the hourly rate we divide the total hours each week she work by total money she makes each week:
[tex]413\div 29.5[/tex]
[tex]=\$14.[/tex]
Therefore, her hourly rate is $14.
Tim answered all the questions on his math test but got 101010 answers wrong. He received 444 points for every correct answer, and there was no penalty for wrong answers. His score was 767676 points. Write an equation to determine the total number of questions (q)(q)(, q, )on Tim's math test.
Answer:
q = 29
Step-by-step explanation:
4(q -10) = 76
Need help
The equation yˆ=2.391x+57.420 models the taste rating of a cereal, y, in a survey, where x is the number of grams of sugar per serving.
What does the y-intercept of the equation represent in context of the situation?
A cereal with 0 grams of sugar has a rating of about 2.391.
The average number of grams of sugar is 2.
A cereal with 0 grams of sugar has a rating of about 57.
The average number of grams of sugar is 57.
Answer: A cereal with 0 grams of sugar has a rating of about 57
Step-by-step explanation:
The equation modelling the taste rating of a cereal, y, in a survey, where x is the number of grams of sugar per serving is expressed as
yˆ=2.391x + 57.420
This is a straight line graph represented in the slope intercept form which is expressed as
y = mx + c
Where
m represents the slope of the straight line
c represents the y intercept. The y intercept is the point at which x = 0.
From the given equation, the y intercept is 57.420
It means that a cereal with 0 grams of sugar has a rating of about 57
A child, 1 m tall, is walking directly under a street lamp that is 6 m above the ground. If the child walks away from the light at the rate of 20 m/min, how fast is the child's shadow lengthening?
Final answer:
The child's shadow is lengthening at a rate of 6 m/min as they walk away from the street lamp.
Explanation:
The child's shadow lengthens as they walk away from the street lamp because the angle between the child and the light source increases. To find the rate at which the shadow lengthens, we can use similar triangles. The ratio of the length of the shadow to the height of the child remains constant. So, if the child's height increases by 1 meter, the shadow length increases by 6 meters. Therefore, the child's shadow is lengthening at a rate of 6 m/min.
The rate of lengthening of the child's shadow is 4 meters per minute.
Step 1: Defining the variables.
Let:
h = height of the street lamp = 6 my = height of the child = 1 mx = distance of the child from the lamp posts = length of the child's shadowIt is given that the child walks away from the light at a rate of 20 m/min. This is:
[tex]\frac{dx}{dt} = 20\ meters\ per\ min[/tex]
Step 2: Relating the variables using similar triangles.
The two triangles formed (one by the lamp post and its shadow, and the other by the child and the child's shadow) are similar. Therefore, the following proportion:
[tex]\frac{x+s}{h} = \frac{s}{y}[/tex]
Substituting the known values (h = 6 m and y = 1 m), we get:
[tex]\frac{x+s}{6} = \frac{s}{1}[/tex]
Step 3: Solving for s.
Cross-multiplying gives:
[tex]6s=x+s[/tex]
Rearranging terms:
[tex]5s=x[/tex]
So the length of the shadow, s, in terms of the child's distance from the lamp, x, is:
[tex]s = \frac{x}{5}[/tex]
Step 4: Differentiate with respect to time.
Differentiating both sides with respect to t:
[tex]\frac{ds}{dt} = \frac{1}{5}\frac{dx}{dt}[/tex]
Substituting the known rate of change [tex]\frac{dx}{dt} = 20\ meters\ per\ min[/tex]:
[tex]\frac{ds}{dt} = \frac{1}{5}*20 = 4\ meters\ per\ min[/tex]
Therefore, the child's shadow is lengthening at a rate of 4 meters per min.
You buy a new stereo for $1300 and are able to sell it 4 years later for $275. Assume that the resale value of the stereo decays exponentially with time. Write an equation giving the resale value $V$ (in dollars) of the stereo as a function of the time $t$ (in years) since your bought it. Round all decimals to four decimal places.
The equation for the resale value of the stereo is V = V0 * e^(-kt), where V0 is the initial value, V is the resale value at time t, and k is the decay constant. Using the given resale value after 4 years, we can solve for k and substitute it back into the equation to find the resale value of the stereo as a function of time.
Explanation:To find an equation giving the resale value of the stereo as a function of time, we can use the formula for exponential decay: V = V0 * e^(-kt). V0 represents the initial value, V represents the resale value at time t, and k is the decay constant. The given resale value after 4 years is $275, so we can substitute these values into the equation: 275 = 1300 * e^(-4k). To solve for k, divide both sides by 1300 and take the natural logarithm of both sides: ln(275/1300) = -4k. Calculate the logarithm and solve for k to get the decay constant. Finally, substitute the value of k into the equation to get the complete equation for the resale value of the stereo.
HELP PLS A medical team has found that the blood concentration of a particular medicine has a decay rate of 40% in 24 hours. How much of an initial dose of 1,000 mg of the medicine will be detected after 48 hours? Round to the nearest mg
Answer: 360 mg of the medicine will be detected after 48 hours
Step-by-step explanation:
We would apply the formula for exponential decay which is expressed as
A = P(1 - r)^t
Where
P represents the initial dosage of the medicine.
A represents the final dosage of the medicine after t hours.
t represents the number of hours.
r represents the rate of decay
From the information given
P = 1000 mg
r = 40% = 40/100 = 0.4
The expression becomes
A = 1000(1 - 0.4)^t
A = 1000(0.6)^t
In 48 hours, t = 2
Therefore,
A = 1000(0.6)^2
A = 360
At a refinery 144,000 tons of sand are required to produce each 125,000 barrels of a tarry material. How many tons of sand are required to produce 2,500 barrels of this tarry material?
Answer:
2,880 tons of sand
Step-by-step explanation:
In this question, we are asked to calculate the amount of tons of sand required to produce a certain amount of tarry materials if a certain amount of sand had produce an amount of tarry materials.
We work as follows:
First, we write the relation that 144,000 tons of sand produces 125,000 barrels of tarry material, then x of tons would produce 2,500 barrels of tarry materials
To find c, we cross multiply:
x * 125,000 = 2,500 * 144,000
x = (2,500 * 144,000)/125,000
x = 2,880
The final cost of a bookstore purchase with a $5 coupon in a state that chargers 8% sales tax is given by the expression. The variable x represents the amount of the purchase before the sales tax and the coupon is applied. 1.08 ( x-5) What does ( x-5) represent ? The cost before applying the coupon The total charge before applying sales tax The rate at which the total cost increases The total charge after tax
Answer: 5.37.
Step-by-step explanation:8 percent markup which in this case is 8 cents per dollar and s in nice its 5 multiply 5 by 8 and that gives you the cents part.