let h be the height of Asia. We get that
\(h=\frac{1}{3}\cdot(x+75)\)where x is the age in months
Ina certain year, the annual per capita of eggs was 496; that is, the average person ate 496 eggs per year. In a year many decades later, the annual per capita consumption had dropped to 255. Round each annual per capita consumption to the nearest ten. A) earlier year had (blank) eggsB) more recent year had (blank) eggsFill in the blank with a fraction. Use the rounded values. In the more recent year, the average person ate ( blank) as many eggs as the average person did in the earlier year.
Given:
Annual per capita consumption in earlier years = 496 eggs / year
Annual per capita consumption in recent years = 255 eggs/ year
Solution:
(A) Earlier year had 500 eggs (nearest ten)
(B) More recent years had 260 eggs (nearest ten)
(C) In more recent year, the average person ate :
\(\begin{gathered} =\frac{260}{500} \\ =\text{ }\frac{52}{100} \end{gathered}\)Hence, the average person in recent years ate 0.52 as many eggs as those consumed in earlier years
The manager of a medical center wants to schedule staff based on a pattern of 5 days working and 2 consecutive days off. Based on the history of their workload, below is their weekly staff requirement: Day Monday Tuesday Wednesday Thursday Friday Saturday Sunday Staff needed 6 5 4 4 6 5 3 a. Determine what days employee 3 does not need to work. multiple choice A) Sunday and Monday B) Monday and Friday C) Tuesday and Thursday D) Wednesday and Friday b. Determine the minimum number of full time staff. c. Determine the minimum number of part time staff.
The correct option A) Sunday and Monday, is the days employee 3 does not need to work.
Explain the term frequency table?A frequency table is a list of objects with the frequency of each item shown in the table.The distribution of sightings based on a variable's possible values is displayed in a frequency table. To understand which alternatives appear more or less frequently in the dataset, frequency tables are useful.This is useful for better understanding each variable and determining whether or not variables must be recoded.For the stated question-
A medical center's manager wants to schedule employees so that they work 5 days and take 2 days off in a row.
Thus, they are reportedly mandated to have consecutive days off on Saturday and Monday, and there is no better option than A.
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Which box-and-whisker plot represents this data: ?
A box-and-whisker plot is shown. The number line goes from 2 to 38. The whiskers range from 6 to 30, and the box ranges from 18 to between 24 and 26 with no median value.
A box-and-whisker plot is shown. The number line goes from 2 to 38. The whiskers range from 6 to 30, and the box ranges from between 12 and 14 and between 26 and 28 with a median of 22.
A box-and-whisker plot is shown. The number line goes from 2 to 38. The whiskers range from 6 to 30, and the box ranges from between 8 and 10 to 28 with a median between 20 and 22.
A box-and-whisker plot is shown. The number line goes from 2 to 38. The whiskers range from 6 to 30, and the box ranges from between 12 and 14 to between 26 and 28 with a median between 20 and 22.
A box-and-whisker plot which represents the given data is: B. A box-and-whisker plot is shown. The number line goes from 2 to 38. The whiskers range from 6 to 30, and the box ranges from between 12 and 14 and between 26 and 28 with a median of 22.
What is a box-and-whisker plot?In Mathematics, a boxplot is also referred to as box-and-whisker plot and it can be defined as a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.
By using an online box-and-whisker plot calculator, the five-number summary for the given data set include the following:
Minimum = 6.First quartile = 13.Median = 22.Third quartile = 27.5.Maximum = 30.By critically observing the box-and-whisker plots (see attachment), we can logically deduce that boxplot A correctly represents the given data set.
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Complete Question:
Which box-and-whisker plot represents this data: 6,9, 13, 13, 18, 20, 24, 25, 26, 28, 30, 30?
A boat is moored at a dock, as shown in the figure.
What is the length of rope A?
Note: The triangle formed is a right triangle.
8.3 ft
10.5 ft
12.3 ft
8.6 ft
Answer:
12.3
Step-by-step explanation:
i took the quiz
Gary's is a small publishing company that publishes math books.
the production costs include a one time cost for editing which is $1050 for the book the company is currently working on. once the book is in production, the only cost will be the variable cost, of printing which is $15 per book. the company will market the book at a price of $35.
if you were to plot a graph of the profit generated by the book, what would the slope and y intercept represent?
The slope of the graph is 20 and the y-intercept is -1050.
The slope of a linear graph is defined as the gradient of the graph .It is also defined by trigonometric properties as the tangent of the angle formed by the line with the positive y-axis.
The y-intercept is the point of intersection of the graph and the y-axis.
The general equation of a straight line in the cartesian plane is given by
y = m x + c where 'm' represents the slope and 'c' represents the y-intercept.
It is given that the one time editing cost is 1050 dollars.
Variable cost of printing each book = 15 dollars
Each book is sold at = 35 dollars
∴profit per book sold = 35 - 15 = 20 dollars
Let Gary sells x number of books . Profit from selling x books = 20 x
Let us consider the net profit of Gary after selling x books be represented by y.
∴ y = profit from x books - establishment cost
or, y = 20 x -1050
Now comparing the above equation with the general equation of a straight line( y = mx + c ) we can infer that:
slope(m) = 20
y-intercept (c) = -1050
Therefore the slope of the graph is 20 and the y-intercept is -1050.
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Emily buys a toaster during the sale off for 10% off if ellen pays 36$ what was the original price
Answer:
100%-10%=90%
90%=36$ what about 10%=4$
36$+4$=40$
What is 23/100 + 7/10
Answer:
93/100
Step-by-step explanation:
23/100 + 7/10
=> 23/100 + 70/100
=> 93/100
Answer and Step-by-step explanation:
First, before you add and solve, you need to make both denominators the same. So, multiply the numerator and denominator of 7/10 by 10 to get: 70/100. Now you should have:
23 + 70
100 100
Simply add the numerators to get 93/100. This cannot be simplified any further, so the final answer is:
93
100
I hope this helps.
500.00
-319.45 = m
Solve for m
Answer:
STo solve for m in the equation -319.45 = m, we can isolate the variable m by adding 319.45 to both sides of the equation:
-319.45 + 319.45 = m + 319.45
This simplifies to:
0 = m + 319.45
Finally, we can subtract 319.45 from both sides to solve for m:
0 - 319.45 = m + 319.45 - 319.45
-319.45 = m
Therefore, the value of m is -319.45.tep-by-step explanation:
How mant solutions are there for the equation? 12x+6=5x
Answer:
One solution
Step-by-step explanation:
12x+6=5x
7x+6=0
7x=-6
x=-6/7
Only one solution. Hope this helps!
i am confused on finding the answer i have tried a few times and i do not understand
Answer:
Volume = 7.912
Step-by-step explanation:
V = πr²h
V = 3.14 × 3/4 × 3/4 × 6 3/4 ( π = 22/7 or 3.14 )
V = 3.14 × 9/16 ×18/4
V = 3.14 × 0.56 × 4.5
V = 7.912
How many degrees is the measure of ∠4
?
Answer:
Below
Step-by-step explanation:
Angle 4 + 60 + 61 = straight line = 180 °
angle 4 = 180 - 60 - 61 = 59°
ASAPPPPPPPPPPPPPP!!!!!!!!!!!!!!!!!!!!!!!
Verify the identity.
sin (x + y) - sin (x - y) = 2 cos x sin y
Answer:
Step-by-step explanation:
Values of f(t) are given in the following table.
t 0 2 4 6 8 10
f(t) 132 129 120 109 94 77
a. Does this function appear to have a positive or negative first derivative? Second derivative?
The function appears to have a _____ first derivative, and a ____ second derivative.
b. Estimate f'(2) and f'(8) . Use difference quotients to the right.
f'(2) = ____
f'(8) = ____
The estimated values of f'(2) and f'(8) are -4.5 and -8.5, respectively.
What is function?In programming, a function is a self-contained block of code that performs a specific task or set of tasks. It is a reusable piece of code that can be called multiple times from different parts of a program. Functions typically take inputs, called arguments or parameters, and produce outputs, which can be returned to the calling code.
Given by the question.
a.
To determine whether the function has a positive or negative first derivative, we can examine the change in values of f(t) between adjacent values of t. Since the values of f(t) decrease as t increases, the function appears to have a negative first derivative.
To determine the second derivative, we can examine the change in the first derivative. Since the first derivative is negative, it is decreasing as t increases, suggesting a negative second derivative.
Therefore, the function appears to have a negative first derivative and a negative second derivative.
b.
To estimate f'(2) and f'(8) using difference quotients to the right, we can use the following formula:
f'(t) ≈ [f (t + h) - f(t)] / h
where h is a small positive value. To estimate f'(2), we can use h = 2:
f'(2) ≈ [f (4) - f (2)] / 2 = (120 - 129) / 2 = -4.5
To estimate f'(8), we can use h = 2:
f'(8) ≈ [f (10) - f (8)] / 2 = (77 - 94) / 2 = -8.5
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The radius of the base of a cylinder is expanding at a constant rate of 3 mm/min. If the height of
the cylinder is a constant 20 mm, find the rate at which the VOLUME of the cylinder is changing at the
moment when the radius of the base of the cylinder is 10 mm. Also find the rate at which the SURFACE
AREA of the cylinder is changing at this same moment.
(V = r²h, SA=2лrh+2rr²)
I’m getting 1800pi mm^3/min for volume and 360pi mm^2/min for surface area but I’m not sure if it’s correct
The rate at which the volume of the cylinder is changing is 600 mm^3/min, and the rate at which the surface area is changing is 240π mm^2/min.
To find the rate at which the volume and surface area of the cylinder are changing, we can use the given formulas for volume and surface area and differentiate them with respect to time. Let's calculate the rates at the moment when the radius of the base is 10 mm.
Given:
Radius rate of change: dr/dt = 3 mm/min
Height: h = 20 mm
Radius: r = 10 mm
Volume of the cylinder (V) = \(r^2h\)
Differentiating with respect to time (t), we have:
dV/dt = 2rh(dr/dt) + \(r^2\)(dh/dt)
Since the height of the cylinder is constant, dh/dt = 0.
Substituting the given values:
dV/dt = 2(10)(20)(3) + (10^2)(0)
dV/dt = 600 + 0
dV/dt = 600 mm^3/min
Therefore, the rate at which the volume of the cylinder is changing at the given moment is 600 mm^3/min.
Surface area of the cylinder (SA) = 2πrh + 2π\(r^2\)
Differentiating with respect to time (t), we have:
dSA/dt = 2πr(dh/dt) + 2πh(dr/dt) + 4πr(dr/dt)
Again, since the height of the cylinder is constant, dh/dt = 0.
Substituting the given values:
dSA/dt = 2π(10)(0) + 2π(20)(3) + 4π(10)(3)
dSA/dt = 0 + 120π + 120π
dSA/dt = 240π mm^2/min
Therefore, the rate at which the surface area of the cylinder is changing at the given moment is 240π mm^2/min.
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Need help with #2 and #3 all of the problem
Answer:
ang hirap wag nlang hahahahahahahaha
A rotating light is located 15 feet from a wall. The light completes one rotation every 4 seconds. Find the rate at which the light projected onto the wall is moving along the wall when the light's angle is 15 degrees from perpendicular to the wall.
To find the rate at which the light projected onto the wall is moving along the wall, we can use trigonometry and calculus. Let's denote the angle between the rotating light and the wall as θ.
Given:
Distance from the light to the wall, r = 15 feet
Rate of rotation, dθ/dt = 1 rotation every 4 seconds
We need to find the rate at which the light's projection moves along the wall, which is represented by dx/dt.
Using trigonometry, we know that the tangent of the angle θ is equal to the ratio of the distance along the wall (dx) to the distance from the light to the wall (r).
tan(θ) = dx / r
Differentiating both sides of the equation with respect to time t, we get:
sec^2(θ) * dθ/dt = dx/dt
Since we are given that the angle θ is 15 degrees, we can substitute the values and solve for dx/dt.
sec^2(15°) * (1 rotation / 4 seconds) = dx/dt
Simplify and calculate the value to find the rate at which the light's projection moves along the wall in feet per second.
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Another question (sorry)
Answer:
19.99
Step-by-step explanation:
First you would multiply .44 by 16 to get 7.04
then you would add 12.95 to get 19.99
What is the ratio of the number of 8 nickels to the number of 10 dimes?
Answer:
2/5
Step-by-step explanation:
start by 8*5 then 10 times 10 then simplify
Answer:
2/5
Step-by-step explanation:
A nickel is worth= 5 cents.
A dime is worth= 10 cents.
So ratio=8×5/10×10
=40/100
=2/5
So the ratio is 2/5
3. Adrian is 8 years older than his brother, Jose. In 3 years he will be twice as old as his brother. Find the present age of each.
Answer:
Age of Jose = 5 years
Age of Adrian = 13 years
Step-by-step explanation:
Let:
Age of Jose = x
Age of Adrian = x+8
After 3 years
Age of Jose = x+3
Age of Adrian = x+8+3 = x+11
Now, we are given, in 3 years he will be twice as old as his brother.
So, we can write
Age of Adrian = 2 (Age of Jose)
x+11 = 2(x+3)
x+11=2x+6
2x-x=11-6
x=5
So, we get value of x = 5
Now, the present ages will be:
Age of Jose = x = 5 years
Age of Adrian = x+8 = 5+8 = 13 years
Adrian is 8 years older than his brother, Jose. In 3 years, he will be twice as old as his brother. Find the present age of each.
Answer:Jose is currently 5 years old.Adrian is currently 13 years old.Solution and Explanation:Let's represent the age of Jose as \(\large\rm x\)
According to the problem, Adrian is 8 years older than Jose, so Adrian's age can be represented as \(\large\rm x + 8\).
In 3 years, Adrian's age will be \(\large\rm (x + 8) + 3\) and Jose's age will be \(\large\rm (x + 3)\).
The problem also tells us that in 3 years, Adrian will be twice as old as Jose:
\(\Large\begin{aligned}\rm{(x + 8) + 3}& =\rm{2(x + 3)}\\\rm{x + 11}&=\rm{2x +6}\\\rm{\cancel{x\red{-x}} + 11}&=\rm{2x \red{-x} + 6}\\\rm{11}&=\rm{x + 6}\\\rm{11\red{-6}}&=\rm{x + \cancel{6\red{-6}}}\\\bold{5}&=\rm{x}\end{aligned}\)
So Jose is currently 5 years old.
To find Adrian's age, we can use the fact that Adrian is 8 years older than Jose:
\(\Large\begin{aligned}\rm{Adrian's\: age}& =\rm{x + 8}\\\rm{Adrian's\: age}&=\rm{\red{5} + 8}\\\rm{Adrian's\: age}&=\bold{13}\end{aligned}\)
Therefore:
Jose is currently 5 years old.Adrian is currently 13 years old.\(\\\\\)
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Note: Enter your answer and show all the steps that you use to
solve this problem in the space provided.
You have a credit card with a balance of $1,367.90 at a 9.5%
APR. You pay $400.00 each month on the due date until the
card is paid off. How many months does it take to pay off the
card, and what is the total amount paid including interest?
Be sure to include in your response:
• the answer to the original question
. the mathematical steps for solving the problem
demonstrating mathematical reasoning
Given statement solution is :- It takes 4 months to pay off the card, and the total amount paid, including interest, is $1600.
To determine the number of months it takes to pay off the credit card and the total amount paid, including interest, we can follow these steps:
Step 1: Calculate the monthly interest rate.
The APR (Annual Percentage Rate) is given as 9.5%. To find the monthly interest rate, we divide this by 12 (the number of months in a year):
Monthly interest rate = 9.5% / 12 = 0.0079167
Step 2: Determine the monthly payment.
The monthly payment is given as $400.
Step 3: Calculate the interest and principal paid each month.
The interest paid each month can be calculated by multiplying the monthly interest rate by the current balance.
Principal paid = Monthly payment - Interest paid
Step 4: Track the remaining balance each month.
Starting with the initial balance of $1,367.90, subtract the principal paid each month to determine the new balance.
Step 5: Repeat Steps 3 and 4 until the balance reaches zero.
Continue calculating the interest and principal paid each month, updating the balance, until the remaining balance becomes zero.
Step 6: Determine the total number of months and the total amount paid.
Count the number of months it takes to reach a balance of zero. Multiply the number of months by the monthly payment ($400) to find the total amount paid.
Let's calculate the number of months and the total amount paid, including interest:
Month 1:
Interest paid = 0.0079167 * $1,367.90 = $10.84
Principal paid = $400 - $10.84 = $389.16
New balance = $1,367.90 - $389.16 = $978.74
Month 2:
Interest paid = 0.0079167 * $978.74 = $7.75
Principal paid = $400 - $7.75 = $392.25
New balance = $978.74 - $392.25 = $586.49
Month 3:
Interest paid = 0.0079167 * $586.49 = $4.64
Principal paid = $400 - $4.64 = $395.36
New balance = $586.49 - $395.36 = $191.13
Month 4:
Interest paid = 0.0079167 * $191.13 = $1.51
Principal paid = $400 - $1.51 = $398.49
New balance = $191.13 - $398.49 = -$207.36 (Paid off)
It takes 4 months to pay off the credit card. Now, let's calculate the total amount paid, including interest:
Total amount paid = 4 * $400 = $1600
Therefore, it takes 4 months to pay off the card, and the total amount paid, including interest, is $1600.
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Construct the 99% confidence interval estimate of the mean wake time for a population with the treatment
m
(Round to one decimal place as needed)
ample Get more help-
HW Score: 39.53%, 17 of 43 points
O Points: 0 of 6
A clinical trial was conducted to test the effectiveness of a drug for treating insomnia in older subjects. Before treatment, 14 subjects had a mean wake time of 105 0 min After treatment, the 14 subjects had a
mean wake time of 782 min and a standard deviation of 24 1 min Assume that the 14 sample values appear to be from a normally distributed population and construct a 99% confidence interval estimate of the
mean wake time for a population with drug treatments What does the result suggest about the mean wake time of 105 0 min before the treatment? Does the drug appear to be effective?
The result suggests that the mean wake time might have really reduced since the values barely fall above 100 min as in before treatment with a high degree of confidence. thus , the drug is effective.
Confidence interval is written in the form as;
(Sample mean - margin of error, sample mean + margin of error)
The sample mean represent x , it is the point estimate for the population mean.
Margin of error = z × s/√n
Where s = sample standard deviation = 21.8
n = number of samples = 17
Now the population standard deviation is unknown and the sample size is small, hence, we would use the t distribution to find the z score
then the degree of freedom, df for the sample.
df = n - 1 = 17 - 1 = 16
Since confidence level = 99% = 0.99, α = 1 - CL = 1 – 0.99 = 0.01
α/2 = 0.01/2 = 0.005
Therefore the area to the right of z0.005 is 0.005 and the area to the left of z0.005 is 1 - 0.005 = 0.995
the t distribution table, z = 2.921
Margin of error = 2.921 × 21.8/√17
= 15.44
The confidence interval for the mean wake time for a population with drug treatments will be; 90.3 ± 15.44
The upper limit is 90.3 + 15.44 = 105.74 mins
The lower limit is 90.3 - 15.44 = 74.86 mins
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A car’s gas tank will hold 24 gallons when full. The car’s tank is presently 1/3 full. How much more gas will it take to fill the tank?
The additional gas it will take to fill the tank is 16 gallons
How much more gas will it take to fill the tank?From the question, we have the following parameters that can be used in our computation:
Capacity = 24 gallons
Current volume = 1/3 full
This means that
Remaning volume = 1 - 1/3
Evaluate
Remaning volume = 2/3
The additional gas it will take to fill the tank is
Additional = 2/3 * 24
Evaluate
Additional = 16
Hence, the additional gas it will take to fill the tank is 16 gallons
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please please solve for x
Answer:
Step-by-step explanation:
You pick a card at random. 5 6 7 What is P(odd or greater than 6)?
The answer to the question is 1/3.
There are three possible outcomes: 5, 6, or 7.
Out of these three outcomes, only two satisfy the condition of being odd or greater than 6: 7.
Therefore, the probability of picking a card that is odd or greater than 6 is 1/3, or approximately 0.333 or 33.3%.
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If we set α=0.01, what is the probability that we reject the null hypothesis when it was in fact true?
The probability is  _____
The probability by the given data is 1%.
We are given that;
set α=0.01
Now,
The probability of making a type I error is the significance level, or alpha (α), which is the threshold we set for rejecting the null hypothesis124. It is also known as the false positive rate3.
If we set α=0.01, it means that we are willing to accept a 1% chance of making a type I error. Hence, the probability that we reject the null hypothesis when it was in fact true is 0.01 or 1%.
Therefore, by probability the answer will be 1%.
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GET 5 STARS, THANKS, AND BRAILIEST!!!
Solve by elimination:
-3x + 3y = 3
-5x + y = 13
Group of answer choices
(3 , 2)
(2 , 3)
(-3 , -2)
(3 , -2)
Answer:
C. (-3 , -2)
Step-by-step explanation:I double checked on math.way
Hope this helps
which expression is equivalent to n+n-0.18n
a. 1.18n
b. 1.82n
c. n- 0.18
d. 2n - 0.82
Answer:
Simplifying the expression `n + n - 0.18n`, we get:
n + n - 0.18n = 2n - 0.18n
Therefore, the expression `n + n - 0.18n` is equivalent to `2n - 0.18n`.
Looking at the answer choices:
a. 1.18n
b. 1.82n
c. n- 0.18
d. 2n - 0.82
We can see that choice d is equivalent to the simplified expression `2n - 0.18n`.
Therefore, the answer is d. 2n - 0.82.
Step-by-step explanation:
rearranging formulae make x the subject y=x+2
The rearranged formulae with x as the subject is x=y-2
What are linear equations?Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.
Given here:
y=x+2
rearranging we get
x=y-2
Hence, The rearranged formulae with x as the subject is x=y-2
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Which of the following situations does NOT represent a linear function?
A. Jasmine's mother gives her an allowance of $20 each week.
B. Over the past few months, Cesar's cell phone bill has doubled from the previous month.
Blair is going to earn $7.00 per hour working at a concession stand at a football gamo.
D. The Landscaping company charges the Anderson's $15 for the first hour and $10 for each additional hour to mow the lawn.
C
Answer:
B. Over the past few months, Cesar's cell phone bill has doubled from the previous month.
Step-by-step explanation: