The expression that means the same as “a number plus 14” is “14 more than a number”.
In mathematical terms, when we say “a number plus 14”, we are essentially talking about adding 14 to an unknown number.
The word “plus” is used to indicate the operation of addition.
Similarly, when we say “14 more than a number”, we are also talking about the same operation of addition. Here, we are adding 14 to an unknown number.
However,
The words used to describe the operation are different.
Both expressions essentially convey the same mathematical idea, which is adding 14 to an unknown quantity. Depending on the context and the problem at hand, either expression can be used interchangeably.
It is important to note that in mathematics, expressions can be written in different forms while still conveying the same meaning.
This flexibility in writing expressions allows for more efficient and effective communication in problem-solving.
The expression that means the same as "a number plus 14" can be written in algebraic form as x + 14, where x represents any number.
In this expression, the variable x can be replaced by any number, and when we add 14 to that number, we get the result of "a number plus 14".
For example,
If we substitute x with 7, we get 7 + 14 = 21, which means "a number plus 14" is equal to 21.
The algebraic expression x + 14 means the same as "a number plus 14".
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Samples of four people were asked whether gun laws should be more stringent. Respondents had a choice to answer "yes" or "no." The sampling distribution of the proportion of people who respond "yes" in the samples of 4 individuals is binomial because the number of people who respond "yes" has binomial distribution not possible to say because the sample size it too small not possible to say because population distribution is not known normal
According to the student question, the sampling distribution of the proportion of people who respond "yes" in the samples of 4 individuals is binomial because the number of people who respond "yes" has binomial distribution. The correct answer is A.
The sampling distribution of the proportion of people who respond "yes" in the samples of 4 individuals is binomial because the sample size is sufficiently small and each person's response is independent of the others.
Binomial distribution is used to model the number of successes in a fixed number of independent trials, where the probability of success is constant for each trial. In this case, the proportion of people who respond "yes" is the number of successes out of the total number of trials (i.e., 4 people).
Moreover, the responses of each individual are independent of each other, meaning that the probability of one person answering "yes" does not affect the probability of another person answering "yes." The correct answer is A.
Your question is incomplete but most probably your full question was
Samples of four people were asked whether gun laws should be more stringent. Respondents had a choice to answer "yes" or "no." The sampling distribution of the proportion of people who respond "yes" in the samples of 4 individuals is
a. Binomial because the number of people who respond "yes" has binomial distribution
b. Not possible to say because the sample size it too small
c. Not possible to say because population distribution is not known
d. Normal
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two step equation
find the value in the eqaution
4/q (q-10)=8
The solution q = -10 does not satisfy the original equation. Therefore, there is no solution to the equation.
What are equations?
A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13. 2x - 5 and 13 are expressions in this case. These two expressions are joined together by the sign "=".
To solve the equation [tex]\frac{4}{q}(q-10) = 8[/tex] we can begin by simplifying the left side of the equation:
[tex]\frac{4}{q}(q-10) = 8[/tex]
[tex]\Rightarrow \qquad 4(q-10) = 8q \text {multiply both sides by }q[/tex]
[tex]\Rightarrow \qquad 4q - 40 &= 8q && \text{distribute }4 \\\\\Rightarrow \qquad -40 &= 4q && \text{subtract }4q\text{ from both sides} \\\\\Rightarrow \qquad -10 &= q && \text{divide both sides by }-4.\\\end{align*}[/tex]
Therefore, the solution to the equation is q= -10. We can check our answer by plugging q= -10 back into the original equation:
[tex]\frac{4}{q}(q-10) &= 8 \\\\\\\Rightarrow \qquad \frac{4}{-10}(-10-10) &= 8 && \text{substitute }q=-10\\\\\\\Rightarrow \qquad -\frac{4}{5} \cdot (-20) &= 8 \\\\\\\Rightarrow \qquad 16 &= 8\end{align*}[/tex]
Since the last equation is false, the solution q = -10 does not satisfy the original equation. Therefore, there is no solution to the equation.
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Determine the value of k such that the points whose coordinates are given lie on the same line. (k, 2), (0, −2), (10, −7)
The value of k that makes the three points lie on the same line is -8.
To determine the value of k such that the given points lie on the same line, we can use the slope-intercept form of the equation of a line, which is:
y = mx + b
where m is the slope of the line, and b is the y-intercept.
First, we can find the slope of the line passing through the two points (0, -2) and (10, -7):
m = (y2 - y1) / (x2 - x1)
m = (-7 - (-2)) / (10 - 0)
m = -5 / 10
m = -1/2
Now, we can use the slope-intercept form with the point (0, -2) to find the value of b:
-2 = (-1/2)(0) + b
b = -2
So the equation of the line passing through the two points (0, -2) and (10, -7) is:
y = (-1/2)x - 2
To check if the point (k, 2) lies on this line, we can substitute k for x and 2 for y in the equation:
2 = (-1/2)k - 2
4 = (-1/2)k
k = -8
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Convert 2-³
=
into logarithmic form.
O log₂ (¹) = -3
O log₂ (-3) =
○ log(:) (−3) = 2
O log_3 (2) =
1/8
The expression 2⁻³ = 1/8 into logarithmic form is log₂(1/8) = -3
How to convert the expression into logarithmic form.In logarithmic form, the equation 2⁻³ = 1/8 can be written as log base 2 of 1/8 = -3.
Mathematically, we have
log₂(1/8) = -3
This means that the exponent that gives 2⁻³ is -3, and the logarithm base 2 of 1/8 is -3.
Logarithmic form is often used to solve exponential equations where the variable is in the exponent.
In logarithmic form, the variable is moved from the exponent to the logarithm, making it easier to solve for the unknown variable.
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a right conical tank with the point oriented down, a height of 14 feet, and a radius of 6 feet has sprung a leak. how fast does the depth of water change when the water is 2 feet high if the cone leaks water at a rate of 13 cubic feet per minute?
The depth of water changes at a rate of -13/72π feet per minute when the water is 2 feet high.
To begin, we must use the formula for the volume of a cone, which is given as:
V = 1/3πr2hwhere V represents the volume, π represents the constant pi, r represents the radius, and h represents the height.
Substituting the given values into the formula, we get:
V = 1/3π (6 ft)2(14 ft)V = 1/3π (36 ft2) (14 ft)V = 1/3π (504 ft3)V = 168π ft^3
Now, we must determine the rate at which water is leaking. It is given that the cone leaks water at a rate of 13 cubic feet per minute. This implies that the volume of the water reduces by 13 cubic feet every minute. Therefore, the rate of change of the volume of water is -13 cubic feet per minute. Here, the negative sign indicates a decrease in the volume of water.
Now, we must find how fast the depth of water changes when the water is 2 feet high. Let d represent the depth of water. Then, the volume of water is given as:
V = 1/3πr^2d
We know that when d = 2 ft, V = 1/3π(6 ft)2(2 ft)
V = 8π ft^3
Now, we must determine how fast the volume of water is changing with respect to time when d = 2 ft. We differentiate the expression for V with respect to time to get:
dV/dt = (d/dt)[1/3πr2d]
dV/dt = 1/3πr^2(d/dt)[d]
dV/dt = 1/3πr^2(d/dt)[2]
dV/dt = 2/3πr^2
The rate of change of the volume of water with respect to time is given as -13 cubic feet per minute. Therefore, substituting this into the expression above, we get:
-13 = 2/3π(6 ft)2(d/dt)
When we simplify the above equation, we get:
d/dt = -13/72π
Therefore, when the water is 2 feet high, the depth of the water changes at a rate of -13/72π feet per minute.
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the mean daily production of a herd of cows is assumed to be normally distributed with a mean of 37 liters, and standard deviation of 4 liters. a) what is the probability that daily production is less than 44.4 liters? use technology (not tables) to get your probability.
The probability that daily production is less than 44.4 liters is 96.71%
According to the given data, the mean daily production of a herd of cows is assumed to be normally distributed with a mean of 37 liters and a standard deviation of 4 liters.
We need to calculate the probability that daily production is less than 44.4 liters using technology, not tables.Using technology, we can use the standard normal distribution formula to get the required probability.
We can use the standard normal distribution to calculate the probability that the daily production is less than 44.4 liters. To do this, we first need to standardize the variable:
z = (x - μ) / σ
where x is the value we are interested in, μ is the mean, and σ is the standard deviation.
Substituting the given values, we have:
z = (44.4 - 37) / 4 = 1.85
Using a standard normal distribution table or a calculator with a normal distribution function, we can find that the probability of a standard normal random variable being less than 1.85 is approximately 0.9671.
Different calculators may have slightly different ways to calculate normal probabilities. Here is an example using a TI-84 calculator:
Press the "2nd" key, then "Vars" to access the "Distr" menu.Select "normalcdf" from the menu.Enter the lower bound (-1E99 if it's negative infinity), the upper bound (44.4), the mean (37), and the standard deviation (4) in the appropriate fields. For this problem, you would enter normalcdf(-1E99, 44.4, 37, 4).Press "Enter" to calculate the probability. The answer should be approximately 0. 9671.Therefore, the probability that the daily production is less than 44.4 liters is approximately 0.9671, or 96.71% (rounded to two decimal places).
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find the area of the circle shown. the diameter is given.
Answer:
624.26 m²Step-by-step explanation:
We are given with a circle whose diameter is 28.2 m
Then, Radius will be diameter/2
=> 28.2 /2
=> 14.1 m
Area of circle = πr²
=> 31.4 × (14.1)²
=> 31.4 × 198.81
=> 624.26 m²
Therefore, the area of the given circle is 624.26 m²
The hire purchase for motor bike is GHC 540.00, if this is to be paid in twenty equal monthly installments, what amount is paid each monthly installments
Answer:
The monthly installment for the hire purchase of the motorbike is GHC 27.00
Step-by-step explanation:
To calculate the monthly installment for the hire purchase, we can divide the total cost by the number of months:
Monthly installment = Total cost / Number of months
In this case, the total cost is GHC 540.00 and the number of months is 20:
Monthly installment = GHC 540.00 / 20
Monthly installment = GHC 27.00
Therefore, the monthly installment for the hire purchase of the motorbike is GHC 27.00
can you do a step by step explanation please and thank you!!!
The total area of the shaded region is 67.92 sq. in.
What is sector of a circle?A sector is a section of a circle that may be described using the following four criteria:
Two radii and an arc surround a section of a circle. The two sectors that make up a circle are referred to as the minor and major sectors. The main sector of the circle is the larger area, while the minor sector is the smaller area. The circle is split into two equally sized sections in the case of semicircles.
Let us suppose the central angle of the shaded portion = x.
From the given figure we observe that angle DEC = 143 degrees, and angle AEB are equal as they are vertically opposite angles.
The angle formed by the shaded regions are same as they are vertically opposite angles.
Thus,
143 + 143 + x + x = 360
286 + 2x = 360
2x = 74
x = 37
Now, the area of the sector is given as:
A = α/360 πr²
Here, r = 10.4 in.
Substituting the values:
A = (37/360)π(10.4)²
A = (0.10)(3.14)(10.4)²
A = 33.96 sq in.
There are two shaded portions thus:
Total area = 2(33.96)
Total area = 67.92 sq. in.
Hence, the total area of the shaded region is 67.92 sq. in.
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a colony of bacteria starts at 10,000 and the number doubles every 40 minutes. find the formula for the number of bacteria at time t.
The formula for the number of bacteria at time t is given by N = 10,000e^(0.0173t).
The formula for the number of bacteria at time t can be found using the exponential growth formula. The formula for exponential growth is given by;N = N0ertWhere;N is the number of bacteria after t minutes.N0 is the initial number of bacteria.r is the growth rate.t is the time interval.
To find the formula for the number of bacteria at time t, substitute the given values into the exponential growth formula.N0 = 10,000r = ln2/40 = 0.0173 (since the number of bacteria doubles every 40 minutes, the growth rate is equal to the natural log of 2 divided by 40.)t = t minutesN = 10,000e^(0.0173t)
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what if circumference of circular table having diameter 'd 'mater? find it
3.What is the measure of angle d₁º?
4.What is the tangent ratio of angle c₂?
Step-by-step explanation:
remember answer 2.
3. I answered already in my other answer.
remember, the diagonals split the angles in half.
so,
d1 = 50°
4. the tangent ratio is sine/cosine (that is the definition of tangent).
c2 = 40°
sin(40) × 5 = OD (half of BD)
cos(40) × 5 = OC
the tangent ratio is
(sin(40) × 5) / (cos(40) × 5) = sin(40)/cos(40) = OD/OC =
≈ 3.2 / 3.8 = 1.6/1.9 =
= 0.842105263...
control : tan(40) = 0.839099631... close enough (we used round numbers with 3 2 and 3.8 - see again 1. and 2.).
consider the sample of 1,400 past negligence cases. suppose you are willing to let the 67% estimate be within .025 (2.5%) of the true proportion. you are willing to assume 95% confidence. is 1,400 an adequate sample size for the estimate of 67%? show why or why not
We can be reasonably confident that our estimate of 67% is within 2.5% of the true proportion.
What is percentage?
A percentage is a way to describe a part of a whole. such as the fraction 1/4 can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
To determine if a sample size of 1,400 is adequate for estimating a proportion of 67%, we need to calculate the margin of error and compare it to the given tolerance level of 0.025.
We can use the following formula to calculate the margin of error:
E = z x √(p x (1-p)/n)
where:
E is the margin of errorz is the z-score corresponding to the desired confidence level (95% corresponds to a z-score of 1.96)p is the estimated proportion (67% or 0.67 as a decimal)n is the sample size (1,400)Plugging in the values, we get:
E = 1.96 x √(0.67 x (1-0.67)/1400) ≈ 0.025
So, the margin of error is approximately 0.025. This means that we can expect the true proportion to be within 0.025 of the estimated proportion with 95% confidence.
Since the calculated margin of error is equal to the desired tolerance level, we can conclude that a sample size of 1,400 is adequate for estimating a proportion of 67% with the given level of confidence and tolerance. Therefore, we can be reasonably confident that our estimate of 67% is within 2.5% of the true proportion.
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4 3/4 plus 1/3 what does it equal
One pump can fill a swimming pool in 4 hours. A second pump can fill the pool in 6 hours. If the pool starts empty, what part of the pool will be filled in each situation? The first pump works for 5 hours and the second pump works for 6 hours.
According to the solving this word problem It will take the slowest pump [tex]\frac{7}{2}[/tex] hours to complete filling the pool.
What does a math word puzzle entail?A math word problem is a question that is written as one or more sentences and asks students to use their mathematical understanding to solve a problem from "real life." In order for kids to understand the word problem, they must be acquainted with the vocabulary that goes along with the mathematical symbols that they are used to.
According to the given information,
The first pump can fill the pool in 4 hours, so its rate is 1/4 of the pool per hour.
The second pump can fill the pool in 6 hours, so its rate is 1/6 of the pool per hour.
The total work done in fraction by both pumps in an hour is:
[tex]\frac{1}{4} + \frac{1}{6} = \frac{5}{12}[/tex]
The remaining work to be completed by the slowest pump is:
[tex]1 - \frac{5}{12} = \frac{7}{12}[/tex]
The ratio of the amount of work left to be done by the weakest pump's work rate determines how long it will take to fill the pool:
[tex]\frac{7}{12} \frac{1}{6} = \frac{7}{12} * 6 = \frac{7}{2}[/tex]
According to the solving It will take the slowest pump [tex]\frac{7}{2}[/tex] hours to complete filling the pool.
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Find the probability of rolling a 6-sided dice and getting a number that is a divisor of 20.
Answer:
The divisors of 20 are 1, 2, 4, 5, 10, and 20. A 6-sided dice has the numbers 1 to 6 on its faces. The probability of rolling a number that is a divisor of 20 is the number of favorable outcomes divided by the number of possible outcomes. There are four favorable outcomes (1, 2, 4, and 5) and six possible outcomes (1 to 6). Therefore, the probability is 4/6 or 2/3 or about 0.67.
The number of minutes, m, that it takes to
print a batch of newspapers is inversely
proportional to the number of printers used,
n.
The equation of proportionality is m =
100
n
Calculate how long it will take to print a
batch of newspapers if 20 printers are
used.
If your answer is a decimal, give it to 1 d. p.
It will take 5 minutes to print a batch of newspapers if 20 printers are used.
What is proportionality?
Proportionality is a mathematical relationship between two variables, where one variable is a constant multiple of the other. In other words, two quantities are proportional if they maintain a constant ratio to each other, meaning that as one quantity increases or decreases, the other quantity changes in the same proportion.
We are given that the time it takes to print a batch of newspapers, m, is inversely proportional to the number of printers used, n, and the equation of proportionality is:
m = k/n
where k is a constant of proportionality. We are also given that when k = 100, the equation is satisfied. So we can substitute k = 100 into the equation to get:
m = 100/n
To find the time it will take to print a batch of newspapers if 20 printers are used, we can substitute n = 20 into the equation:
m = 100/20 = 5
So it will take 5 minutes to print a batch of newspapers if 20 printers are used. Rounded to 1 decimal place, the answer is 5.0 minutes.
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Pls help due tomorrow!!!
Answer:
C = 11,21 cm
using the formulas :
A (area) = 10 [tex]cm^{2}[/tex]
A = π [tex]r^{2}[/tex]
C = 2 π r
colving for C :
C = 2 *√(π*Α) = 2 *√(π * 10) = 11,20998 cm
Select the expression that represents this real-world situation.
A roll of ribbon is r inches long. There are 4 colors of ribbons. If Ava used 4 inches from each roll, what is the expression for the total length of ribbons left?
4 x (r − 4)
(4 x r) − 4
4 ÷ r − 4
4 ÷ 4 + r
The expression for the total length of ribbons left is: r - 16 . But we can also write this expression as: 4 x (r - 4) because 4 x (r - 4) = 4r - 16, which is equivalent to r - 16.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
The expression that represents the total length of ribbons left is:
4 x (r - 4)
This is because Ava uses 4 inches from each roll of ribbon, and there are 4 rolls of ribbon in total. So the total length of ribbon used is 4 x 4 = 16 inches.
To find the total length of ribbon left, we need to subtract the length of ribbon used from the original length of ribbon, which is r inches.
Therefore, the expression for the total length of ribbons left is: r - 16
But we can also write this expression as: 4 x (r - 4) because 4 x (r - 4) = 4r - 16, which is equivalent to r - 16.
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Math help . Find x in the picture please
Answer:
x = 7 ft
Step-by-step explanation:
[tex]tan 55=\frac{10}{x}\\x=\frac{10}{tan 55}\\x=7.0020\\x=7[/tex]
13) Ellen wanted to buy the following items: A DVD holder for $19.95, headphones for $41.25, and a personal stereo for $30.65. How much money does Ellen need?
Answer: $91.85
Step-by-step explanation:
19.95 + 41.25 + 30.65
= 91.85
And bro, its not that hard to simply calculate it in your head, or even on a paper. Like literally, there's calculators too
what fraction of the numbers from 1 to 20 contain digit 1
Answer:
11/20
Step-by-step explanation:
1,10,11,12,13,14,15,16,17,18,19 All have the number "1"
there are 11 of them so 11/20 have the digit 1.
:)
Answer:
To find the fraction of the numbers from 1 to 20 that contain the digit 1, we can count the number of such numbers and divide by the total number of numbers from 1 to 20.
The numbers from 1 to 20 are: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20.
The numbers that contain the digit 1 are: 1, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19.
Therefore, there are 11 numbers from 1 to 20 that contain the digit 1.
The fraction of the numbers from 1 to 20 that contain the digit 1 is:
fraction = number of numbers containing 1 / total number of numbers
fraction = 11 / 20
So, the fraction of the numbers from 1 to 20 that contain the digit 1 is 11/20 or 0.55.
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er
A keyboarding instructor at a community
college collected data comparing a
student's age and their typing speed.
The equation for the line of best fit is
given as y=-1.4x + 117.8, where x is the
"age in years" and y is the "typing speed.
If you are 25 years of age, what is your
typing speed?
If you are 25 years of age, your typing speed is equal to 82.8 units.
What is a line of best fit?In Mathematics, a line of best fit is sometimes referred to as a trend line and it can be defined as a statistical or analytical tool that is typically used by researchers and mathematicians in conjunction with a scatter plot, in order to determine whether or not there is any form of association and correlation between a data set.
Based on the scatter plot, we can logically deduce that an equation which represents the line of best fit include the following:
y = -1.4x + 117.8
When you are 25 years of age, your typing speed can be calculated as follows;
y = -1.4x + 117.8
y = -1.4(25) + 117.8
y = -35 + 117.8
y = 82.8 units.
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PLEASE ANSWER USE PEMDAS
What is the correct mathematical description of the expression (14.8 ÷ 2) + 6 x 3 − 12?
14 and 8 tenths divided by 2 plus 6 times 3 minus 12
14 and 8 tenths divided by 2 plus 6 times the difference of 3 minus 12
The quotient of 14 and 8 tenths divided by 2 plus six times 3 minus 12
The quotient of 14 and 8 tenths divided by 2 plus the product of 6 and 3 minus 12
Answer: D or the Fourth Choice-The quotient of 14 and 8 tenths divided by 2 plus the product of 6 and 3 minus 12
PEDMAS means Parentheses, Exponents, Divide, Multiply,Add,Subtract. The first thing we must solve is what is in the parentheses, that is 14.8 divided by 2. We don't have any exponents, so we move to divide. We have already solved the division sentence that was in the parentheses, so we have to multiply 6x3 next. 6x3 will then be added to the answer that was divided by 14.2 and 2, and lastly we will subtract 12. The only answer choice that follows that pattern is D or The quotient of 14 and 8 tenths divided by 2 plus the product of 6 and 3 minus 12.
I hope this helped & Good Luck <3!!!!
what is the value of the expression
v/2 +(3/4 +w)
when v=1 and w= 5/8
a 1/8
b 3/8
c 5/8
d 1
The value of v/2 +(3/4 +w) when v = 1 and w = 5/8 is 1 7/8
What is substitution of variables?substitution of variables is a basic technique used to simplify problems in which the original variables are replaced with functions of other variables.
Since V = 1 and W = 5/8, by substituting 1 for V and 5/8 for w in the expression
v/2 +(3/4 +w) = 1/2+ ( 3/4 + 5/8)
= 1/2 + (6+5)/8
= 1/2 + 11/8
= (4+11)/8
= 15/8
= 1 7/8
Therefore the value of v/2 +(3/4 +w) when v is 1 , and w is 5/8 is 1 7/8
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Use the figure below to answer the following questions. NOT TO SCALE!
10
2
12
6
6
a. Give the perimeter of the figure.
b. Give the area of the figure.
Junits2
c. If the figure above was a yard measured in feet, and sod cost $2.99 per square foot, how much would it cost to sod the yard.
units
d. If the figure above was a garden measured in feet, and you wanted to put up edging that cost $8.87 per 6 foot piece, how much would it cost to
edge the garden? (you cannot by part of a piece) S
Perimeter of the figure is 56 units.
Area of figure is 100sq. units²
Cost to sold the yard is $299
For edging, total cost is $82.8
Define perimeter and areaPerimeter and area are two important measurements used in geometry to describe the size and shape of two-dimensional figures.
Perimeter is the measurement of the distance around the outside of a two-dimensional shape. It is the sum of the lengths of all the sides of the shape.
Area is the measurement of the space inside a two-dimensional shape. It is the amount of surface that the shape covers. For example, the area of a rectangle can be calculated by multiplying the length of the rectangle by its width.
Perimeter of the figure=sum of all sides of the figure
=10+4+2+12+6+6+2+4+6+4=56 units.
Area of figure=10×4+6×6+4×6
=40+36+24
=100sq. units²
Cost to sold the yard=area× cost per square foot
=100×2.99
=$299
Given: edging costs $8.87 per 6 foot piece
For edging, total cost =total perimeter/no.of foot piece×$8.87
=(56/6)×8.87
=496.72/6
=$82.78≈$82.8
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john is looking for an existing multi-story building zoned for mixed-use. he wants to open a small, by-reservation-only restaurant on the lowest floor. local code requires 15 square feet per person in a commercial setting with non-concentrated seating. what is the minimum square footage he needs to serve 50 people?
To serve 50 people, the minimum square footage needed would be 750 square feet.
Let us analyze the given question and solve the problem given. The problem is asking about the minimum square footage of the multi-story building that is required to open a small restaurant on the lowest floor. The building is already zoned for mixed use.
John wants to open a small, by-reservation-only restaurant on the lowest floor. He needs to calculate the minimum square footage he needs to serve 50 people. Let's calculate the minimum square footage that John needs to open the restaurant. If local code requires 15 square feet per person, then 15 x 50 = 750 square feet are needed for 50 people. In other words, John needs at least 750 square feet of space to serve 50 people at his restaurant.
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Pls help right away asap 20 point question!!
The answer of the given question is , the predicted average retail price of a car in 2003 is $9860.40.and the car will be worth $814 in the year 2010.
What is Regression Equation?A regression equation is a mathematical formula that is used to describe the relationship between two or more variables. It is typically used in statistical analysis to model the relationship between a dependent variable and one or more independent variables.In simple linear regression, there is only one independent variable, and the regression equation takes the form of a straight line. In multiple regression, there are two or more independent variables, and the regression equation takes the form of a more complex mathematical function.
Using a calculator, we can input the data points into a regression equation to find the line of best fit. Using the given data, we get the regression equation:
y = -1357.4x + 18003.8
where y represents the retail price of a car and x corresponds to the year, with x = 1 representing 1998.
To predict the average retail price of a car in 2003, we need to substitute x = 6 (since 2003 corresponds to x = 6) into the regression equation:
y = -1357.4(6) + 18003.8
y = -8144.4 + 18003.8
y = 9860.4
So, the predicted average retail price of a car in 2003 is $9860.40.
To determine the year when the car will be worth $814, we need to substitute y = 814 into the regression equation and solve for x:
814 = -1357.4x + 18003.8
Simplifying, we get:
-1357.4x = -17189.8
x = 12.65
Rounding up to the nearest whole number, we get x = 13, which corresponds to the year 2010. Therefore, the car will be worth $814 in the year 2010.
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On a certain route, an airline carries 9000 passengers per month, each paying $30 . A market survey indicates that for each $1 increase in the ticket price, the airline will lose 50 passengers. Find the ticket price that will maximize the airline's monthly revenue for the route. What is the maximum monthly revenue?
Let's start by finding the current monthly revenue of the airline for the given number of passengers and ticket price:
Monthly revenue = number of passengers x ticket price
Monthly revenue = 9000 x $30
Monthly revenue = $270,000
Now, let's find the number of passengers for each $1 increase in the ticket price:
Number of passengers lost = 50
So, for a ticket price increase of $x, the number of passengers will be:
Number of passengers = 9000 - 50x
The ticket price will then be $30 + $x, and the revenue will be:
Revenue = (9000 - 50x) x ($30 + $x)
Revenue = 270,000 - 1500x + 30x + x^2
Revenue = x^2 - 1470x + 270,000
To find the ticket price that will maximize the revenue, we need to find the vertex of the parabola given by the revenue equation. The x-coordinate of the vertex is:
x = -b/2a
Where a = 1, b = -1470, and c = 270,000.
x = -(-1470)/2(1)
x = 1470/2
x = 735
So, the ticket price that will maximize the revenue is $30 + $735 = $765. The maximum monthly revenue is then:
Revenue = (9000 - 50(735)) x ($30 + $735)
Revenue = 105 x $765
Revenue = $80,325
Therefore, the ticket price that will maximize the airline's monthly revenue for the route is $765, and the maximum monthly revenue is $80,325.
Solve the separable differential equation, showing working out:
[tex]\frac{dy}{dx}=\frac{2y+4}{x}[/tex]
The solution of the given differential equation by using variable separable is [tex]y=\frac{x^2c}{2}-2[/tex]
An equation involving one or more functions and their derivatives is referred to as a differential equation in mathematics. The rate of change of a function at a particular moment is determined by the function's derivatives. It is mostly employed in disciplines like biology, engineering, and physics. The study of solutions that satisfy the equations and the characteristics of the solutions is the main goal of the differential equation.
The rules to solve differential equations using variables separable,
1) [tex]\frac{dy}{dx}=f(x)/f(y)[/tex]
2) separate terms with the same variable
f(y)dy=f(x)dx
3) Take integration on both sides
4) solve integration by using a suitable method
5) Then get the Solution of the differential equation.
The given differential equation is-
[tex]\frac{dy}{dx}=\frac{2y+4}{x}\\\\\frac{dy}{2y+4}=\frac{dx}{x}\\\\\int\frac{dy}{2y+4}=\int\frac{dx}{x}\\\\\frac{log(2y+4)}{2}=logx+logc\\log(2y+4)=2logxc\\2y+4=x^2c\\2y=x^2c-4\\y=\frac{x^2c}{2}-2[/tex]
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