A clothing designer is selecting models to walk the runway for her fashion show. The clothes she designed require each model’s height to be no more than y inches from 5 feet 10 inches, or 70 inches. Which graph could be used to determine the possible variance levels that would result in an acceptable height, x?
Answers
The graph that could be used to determine the possible variance levels that would result in an acceptable height is the third graph.
How can one depict the graph?Fron the information, the required model height for the designed clothes should be less than or equal to 5 feet 10 inches. In this case, the equation for the variance in height is of the straight line form;
y = m·x + c
Where x is the height in inches
Given that the maximum height allowable is 70 inches, when x = 0 we have;
y = m·0 + c = 70
Therefore, c = 70
Also when the variance = 0 the maximum height should be 70 which gives the x and y-intercepts as 70 and 70 respectively such that m = 1
The equation becomes;
y ≤ x + 70
Also when x > 70, we have y ≤ -x + 70 with a slope of -1
In this case, to graph an inequality, we will need to shade the area of interest which in this case of ≤ is on the lower side of the solid line.
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Related Questions
use an appropriate taylor series to find the first four nonzero terms of an infinite series that is equal to ln(5/3).
Answers
The appropriate Taylor series for an infinite series with the first four nonzero terms equal to ln(5/3) is 0/1!, 0/2!, 0/3!, and 0/4! .......
What is taylor series?An infinite sum of words that are expressed in terms of a function's derivatives at a single point is known as the Taylor series or Taylor expansion of a function in mathematics. Near this point, the function and the sum of its Taylor series are equivalent for the majority of common functions. The polynomial or function of an infinite sum of terms is the Taylor series. The exponent or degree of each succeeding term will be greater than the exponent or degree of the one before it.
The formula is:
∑n=0 to ∞(fⁿ(a)(x-a)ⁿ)/n!
Here,
∑n=0 to ∞(fⁿ(a)(x-a)ⁿ)/n!
at n=1,
=0/1!
at n=2,
=0/2!
at n=3,
=0/3!
at n=4,
=0/4!
Appropriate taylor series for first four nonzero terms of an infinite series that is equal to ln(5/3) is 0/1!, 0/2!, 0/3!, 0/4!.......
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Determine whether the equation is true or false. Where possible, show work to support your conclusion. If the statement is false, make the necessary change(s) to produce a true statement.
log(x+3)-log(8x)=log(x+3)/log(8x)
if false make necessary changes to produce a true statement
Answers
So the RHS of the given equation is incorrect.
Which inequality does the graph represent?
A two-dimensional graph with an x-axis and a y-axis is given. A dotted line is passing through the co-ordinates (1,0), and (-1,2). The region below the dotted line is shaded in grey.
A. y < –x – 1
B. y < –x + 1
C. y < x – 1
D. y < x + 1
Answers
The inequality that the graph represent is y < -x + 1. The correct option is B. y < –x + 1
Determining the inequality that represents a graphFrom the question, we are to determine the inequality that represents the given graph.
From the given information,
The line is passing through the coordinates (1, 0) and (-1, 2).
Using the formula for the equation of a line,
Using the formula,
(y - y₁)/(x - x₁) = (y₂ - y₁)/(x₂ - x₁)
Then,
(y - 0)/(x - 1) = (2 - 0)/(-1 - 1)
y/(x-1) = 2/-2
y/(x -1) = -1
y = -1(x -1)
y = -x + 1
Since the line is dotted and the shaded region is below the line, the inequality becomes
y < -x + 1
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Whenever he is injured and unable to play, Patrice Bergeron likes to earn a little extra cash by doing some tutoring. He currently charges $50/hr and has 20 students that he works with. He has discovered that for every $5/hr he increases the price, he loses one student.
Answers
The revenue function of Patrice Bergeron earnings is R(x) = (50 + 5x)(20 -x)
How to determine the revenue function?From the question, we have the following parameters that can be used in our computation:
Charges = $50
Students = 20
Also, we have:
For every $5/hr he increases the price, he loses one student.
This means that
Charges = 50 + 5x
Students = 20 - x
So, the revenue equation is
R(x) = Charges * Students
Substitute the known values in the above equation, so, we have the following representation
R(x) = (50 + 5x)(20 -x)
Hence, the function is R(x) = (50 + 5x)(20 -x)
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Complete question
Whenever he is injured and unable to play, Patrice Bergeron likes to earn a little extra cash by doing some tutoring. He currently charges $50/hr and has 20 students that he works with. He has discovered that for every $5/hr he increases the price, he loses one student.
What is the revenue function
Departments D1 and D2. Each unit of product1 requires processing for 1 minute at D1 and 3 minutes at D2; each unit of product 2 requires processing for 2 minutes at D1 and 2 minutes at D2. Machine time available per day is 860 minutes at D1 and 1200 minutes at D2. How much of product 1 and 2 should be produced every day so that total profit is maximum. Make the mathematical model for the given problem
Answers
Answer:
510
Step-by-step explanation:
1200-860x3 /2 = 510
A fair die with its faces numbered from 1 to 6 will be rolled. Which of the following is the best interpretation of the probability that the number landing face up will be less than three?
For many rolls of the die, the long- run relative frequency of a number less than three landing face app is 1/3.
Answers
For many of the rolls die, the long run relative frequency of a number less than 3 landing face up is 1/3.
What is relative frequency?
The proportion of outcomes where a specific event occurs to all trials, not in a hypothetical sample space but in a real experiment, is known as the empirical probability, relative frequency, or experimental probability of an event.
Given that, Only two integers (1 and 2) are smaller than 3, hence their relative frequency will be 2/6=1/3.
The best way to interpret the data is thus,
For many rolls of the die, the long- run relative frequency of a number less than three landing face up is1/3.
Hence option A is correct which is for many of the rolls die, the long run relative frequency of a number less than 3 landing face up is 1/3.
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A local movie theater has a movie lovers club. After paying a membership fee,
all ticket purchases are discounted. The cost after buying 5 movie tickets is $48.75. The
cost after buying 7 movie tickets is $58.25. Write an equation in slope-intercept form to
represent the data. Describe what the slope and intercept mean. Use the equation to
find the total cost after buying 12 tickets.
Answers
Answer: 57 dollars, hope this helps!
Write the systems of equations from the table below and find the solution?
Answers
The system of equations is y = 4x - 3 and y = -1/3x + 4 and the solution is (21/13, 45/13)
How to determine the system of equations?From the question, we have the table of values as the parameters that can be used in our computation:
From the table, we have
Table 1
(x, y) = (0, -3) and (4, 13)
A linear equation is represented as
y = mx + c
Where
Slope = m
c = y when x = 0
This means that
c = -3
So, we have
y = mx - 3
The point (4, 13) implies that
13 = m * 4 - 3
So, we have
4m = 16
m = 4
So, the equation is
y = 4x - 3
Table 2
(x, y) = (0, 4) and (4, 6)
A linear equation is represented as
y = mx + c
This means that
c = 4
So, we have
y = mx + 4
The point (4, 6) implies that
6 = m * 4 + 4
So, we have
4m = -2
m = -1/3
So, the equation is
y = -1/3x + 4
Substitute y = -1/3x + 4 in y = 4x - 3
-1/3x + 4 = 4x - 3
So, we have
-x + 12 = 12x - 9
Evaluate the like terms
13x = 21
Divide
x = 21/13
y = -1/3x + 4 implies that
y = -1/3 x 21/13 + 4
So, we have
y = -7/13 + 4
Evaluate
y = 45/13
So, the solution is (21/13, 45/13)
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In a random sample of 125 people, 42 of them owned two vehicles. The sample proportion of people who own two vehicles is
Answers
In a random sample of 125 people, 42 of them owned two vehicles. The sample proportion of people who own two vehicles is 0.336
The percentage of people in a sample that exhibit a particular attribute or trait is expressed by the sample proportion (p).
Divide the total number of individuals (or things) in the sample by the number of individuals (or items) who share the characteristic of interest to obtain the sample proportion.
p = x/n, where x stands for the sample's success rate and n for sample size, gives the sample proportion p.
According to the question,
Sample size = 125
Number of people owned two vehicles = 42
Sample Proportion (p) = x/n
=> p = 42 / 125
=> p = 0.336
Therefore , The sample proportion of people who own two vehicles is 0.336
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In 2010, a total of 2187 of the employees at Zoe's company owned a petrol
car.
In 2013, there were 1029 employees with petrol cars.
Assuming this number decreases exponentially, work out how many
employees owned a petrol car in 2017.
Give your answer to the nearest integer.
Answers
The number of employees with petrol cars is 423
Exponential Decay:In exponential decay, a quantity initially drops gradually before decreasing quickly. Finding the exponential drop of a fast reduction over time is made easier by the exponential decay formula.
The exponentially decreasing formula is used to calculate the radioactivity decay, population decay, and half-life.
The formula for Exponential Decay is given by
f(x) = a (1 - r)ˣHere we have
In 2010, a total of 2187 of the employees at Zoe's company owned a petrol car.
In 2013, there were 1029 employees with petrol cars.
The number of cars decreases exponentially,
As we know the formula for Exponential Decay, A = P (1 - r)^t
From the given data, a = 2187 and t = 3
The number of cars decreased = 2187 (1 - r)³
=> 2187 (1 - r)³ = 1029
=> (1 - r)³ = 1029/2187
=> (1 - r)³ = 343/729
=> (1 - r)³ = 7³/ 9³
=> 1 - r = 7/9
=> r = 1 - 7/9
=> r = 2/9
=> r = 0.2222
The Number of cars in 2017 i.e after 4 years from 2013
=> (1029)(1 - 0.2222)⁴
=> 423.0721516 ≅ 423
Therefore,
The number of employees with petrol cars is 423
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[tex]\lim_{n \to \pi/2} (tanx)^{2cosx}[/tex]
Answers
Let a dilation be defined by a scale factor s and center of dilation (x,y). Each of the options below represents a dilation of a polygon according to the given values of s,x and y. Which of the following dilations produce an image congruent to its pre-image. Select all that apply.
Answers
s = 1, x = 0, y = 3 and s = 1, x = 2, y = 0 produce an image congruent to its pre-image so option C and D are correct
What is dilation?
Dilation is the increase or decrease in the size of a figure by a scale factor. Rigid transformations preserve the shape of a figure. Examples of rigid transformation are reflection, rotation and translation.
Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is a picture with the same shape as the original. However, there is a variation in the shape's size. The initial form should be stretched or contracted during a dilatation. The phrase "scale factor" describes this transition.
Enlargement is the term used when a dilatation results in a bigger picture.Reduction occurs when a dilatation results in a smaller picture.Dilation is said to be a rigid transformation if the scale factor is equal to one.
Therefore the dilation by a scale factor of one produce an image congruent to its pre-image.
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Gina changes the amount of milk she purchases depending on whether it costs $1,$1.50, or $1.75 a pound. What other information do we need to come up with her demand curve for milk?
Select the correct answer below:
whether her milk consumption goes up or down with price
how much milk she buys in total
whether or not she switches to a substitute when the price is high
how much milk she buys at each price point
Answers
The information that we need to come up with her demand curve for milk is D how much milk she buys at each price point
What is a demand curve?A demand curve is a graph that shows the relationship between a commodity's price and the amount that is desired at that price. Demand curves can be applied to the price-quantity relationship for either a specific consumer or for every consumer in a given market.
Individual demand curves and market demand curves are the two types of demand curves. It shows a graphic depiction of the demand schedule. It should be noted that based on the information, the quantity is needed. The correct option is D.
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Given the equation v over 9.4 equals 13.7, solve for v.
4.3
23.1
128.87
128.78
Answers
Therefore the solution to the given question is option d)128.78 for this particular equation.
What is Equation?Many different definitions exist for a mathematical equation. In algebra, a statement that mathematically establishes the equality of two mathematical expressions is known as an equation.. Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal." Mathematical variables are used in even the most fundamental and straightforward algebraic equations.
Here,
=> v/9.4 = 13.7
=> v = 13.7*9.4
=> v= 128.78
Therefore the solution to the given question is option d)128.78 for this particular equation
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rectangle abcd is similar to rectangle wxyz what is the value of ab if wx is 8 feet ad is 12 feet and wz is 16feet
Answers
The value of AB is 6 units.
What are Similar Rectangles ?
Similar rectangles states that the corresponding sides are in proportion.Two rectangles are similar when the corresponding adjacent sides have the same ratio. We do not need to check the angles as all angles in a rectangle are 90 degrees.
As per the statement:
Rectangle ABCD is similar to rectangle WXYZ.
WX = 8 feet, AD = 12 feet and WZ = 16 feet.
Since. Rectangle ABCD and rectangle WXYZ are similar
then;
their corresponding sides are in proportion:
[tex]\frac{AB}{WX} =\frac{BC}{XY} = \frac{CD}{YZ} =\frac{AD}{ZW}[/tex]
To find the value of AB:
[tex]\frac{AB}{WX} =\frac{AD}{ZW}[/tex]
Substitute the given values we have;
[tex]\frac{AB}{8} =\frac{12}{16}[/tex]
Multiply both sides by 8 we have;
[tex]AB = \frac{12}{16} * 8 = 6[/tex]
Therefore, the value of AB is 6 units.
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Question 21 Suppose that 12 inches of wire costs 36 cents. At the same rate, how much (in cents) will 5 inches of wire cost?
Answers
Answer: To determine how much 5 inches of wire would cost at the same rate as 12 inches of wire, we can first determine the rate at which the wire is being sold by dividing the cost of the wire by the length of the wire:
36 cents / 12 inches = 3 cents/inch
We can then use this rate to determine the cost of 5 inches of wire by multiplying the rate by the length of the wire:
3 cents/inch * 5 inches = 15 cents
Therefore, 5 inches of wire would cost 15 cents at the same rate as 12 inches of wire.
Need help, please!
Suppose you will perform a test to determine whether there is sufficient evidence to support a claim of a linear correlation between two variables. Find the critical values of r given the number of
pairs of data in and the significance level a
n=14,a=0.01
A: r=0.661
B: r= +- 0.532
C: r= 0.684
D: r= +- 0.661
Answers
Answer:
c or b
Step-by-step explanation:
What is the probability of flipping a coin 50 times and getting tails 22 times or fewer? Round your answer to the nearest tenth of a percent.
Answers
The probability of flipping a coin 50 times and getting tails 22 times or fewer is given as follows:
A. 24%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution of the data-set, depending if the obtained z-score is positive(above the mean) or negative(below the mean).The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure X in the distribution.The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with [tex]\mu = np, \sigma = \sqrt{np(1-p)}[/tex].The parameters for the binomial distribution are given as follows:
n = 50, p = 0.5.
Hence the mean and the standard deviation are obtained as follows:
[tex]\mu = 50 \times 0.5 = 25[/tex][tex]\sigma = \sqrt{50 \times 0.5 \times 0.5} = 3.54[/tex]Using continuity correction, the probability of 22 or fewer tails is the p-value of Z when X = 22.5, hence:
Z = (22.5 - 25)/3.54
Z = -0.71
Z = -0.71 has a p-value of 0.2709.
Which is closest to 24%.
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Aunt Georgia agreed to pay 40% of the cost of the new UMSHQYGT 2000, which costs $649.99. Does Kayan have enough money in the bank to get the phone?
Answers
Kayan will have enough money in the bank to get the phone.
Will Kayan have enough money?It is important to note that percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
Since Aunt Georgia has $1000 and bought a gadget for $300, the remaining amount will be:
= $1000 - $300
= $700
Therefore, since also agreed to pay 40% of the cost of the new UMSHQYGT 2000, which costs $649.99, she will have money left. This will be:
= $700 - $649.99
= $50.01
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Complete question
Aunt Georgia has $1000 and bought a gadget for $300 She also agreed to pay 40% of the cost of the new UMSHQYGT 2000, which costs $649.99. Does Kayan have enough money in the bank to get the phone?
An art class is making a mural for their school which has a triangle drawn in the middle. The length of the bottom of the triangle is . Another side is 8 more than times the length of the bottom of the triangle. The last side is more than the bottom of the triangle. Write and simplify an expression for the perimeter of the triangle.
Answers
Let's call the length of the bottom of the triangle x. The length of another side of the triangle is 8 more than 3 times the length of the bottom of the triangle, or 3x + 8. The last side of the triangle is y, where y is more than x.
The perimeter of the triangle can be expressed as:
x + (3x + 8) + y
Simplifying this expression gives:
4x + 8 + y
Therefore, the perimeter of the triangle can be expressed as the sum of 4 times the length of the bottom of the triangle, 8, and the length of the last side of the triangle, y.
PLS HELP 10 POINTS!!
Perpendicular to the y-axis and has the point of (-4,5)
Answer choices
Y=5
Y=-4
X=5
X=-4
Answers
The line passes through Y=5. Correct option is A.
What is a perpendicular line?Two lines are perpendicular to each other if they are at right angle
to each other.
Given, line is perpendicular to Y-axis and passes through (-4,5).
Therefore, the given line is parallel to X-axis and passes Y-axis at y=5.
Hence, the given line passes through Y=5.
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To multiply a decimal number by 10,
O move the decimal point one place to the right.
move the decimal point two places to the right.
O move the decimal point one place to the left.
O move the decimal point two places to the left.
Answers
Answer:
[tex]\huge{\boxed{\text{A) move the decimal point one place to the right}}}}[/tex]
Step-by-step explanation:
Think about the following scenarios
4.00 * 10
529.00 * 10
4 * 10 = 40 (4.00 * 10 = 40.0)
529 * 10 = 5290 (5290.00 * 10 = 5290.0)
As you can see, the decimal point is moving one space to the right when multiplying by ten.
In the decimal system, moving the decimal point one place to the right multiplies by ten, while moving the decimal point one place to the left multiplies by 1/10.
Hope it helps :) and let me know if you want me to elaborate.
Explanation is edge
Graph the line with y-intercept.....
Can you also mark the two points on the graph.
Answers
Two points would be (0,7) and (5,8)
pat radigan wants to purchase a new home for $312,500. pat puts 20% down and will finance the remainder of the purchase. compare the following two mortgage options he has: 20 years at 6.5% or 25 years at 7.0%.
Answers
Difference in interest paid = $82,740.52
Total interest paid for 25 year loan interest - Total interest paid for 20 year loan interest
According to the given information
A.
Monthly payment for 20 year mortgage [tex]& $=$ PMT $\left(6.5 \% / 12,20^* 12,-312500^* 0.8\right)$ & $=$ PMT $($ rate, nper, $-$ pv $)$ \[/tex]\
Monthly payment for 25 year mortgage [tex]& $=$ PMT $\left(7 \% / 12,25^* 12,-312500^* 0.8\right)$ & $=$ PMT(rate,nper,-pv) \\[/tex]
B
Total cost of interest for 20 year mortgage [tex]& $=(\mathrm{B} 2 * 20 * 12)-(312500 * 0.8)$ \\[/tex]
Total cost of interest for 25 year mortgage [tex]$=(\mathrm{B} 3 * 25 * 12)-(312500 * 0.8)$ &[/tex]
C.
Difference in interest paid [tex]& $=\mathrm{B} 7-\mathrm{B} 6$ &[/tex] = Total interest for 25 year loan-total interest for 20 years
A.
Monthly payment for 20 year mortgage [tex]& $\$ 1,863.93$ & $=$ PMT(rate,nper,-pv) \\[/tex]
Monthly payment for 25 year mortgage [tex]& $\$ 1,766.95$ & $=$ PMT(rate,nper,-pv) \\[/tex]
B.
Total cost of interest for 20 year mortgage = [tex]& $\$ 197,343.88$ & $=$[/tex] total monthly payments-loan taken
Total cost of interest for 25 year mortgage = [tex]& $\$ 280,084.40$ & $[/tex] = total monthly payments-loan taken
C.
Difference in interest paid = $82,740.52
Total interest paid for 25 year loan interest - Total interest paid for 20 year loan interest
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a sample of 79 eggs yields a sample mean weight of 1.00 ounces. assuming that the population standard deviation
Answers
The margin of error for 16 eggs with sample means 2 ounce and standard deviation as 42 ounces is 18.407 .
In the question ,
it is given that ,
the number of eggs = 16
the sample means weight is = 2 ounce .
the standard deviation is = 42 ounces .
we have to find the margin of error .
degree of freedom is 16 - 1 = 15 .
and the t score for the 90% confidence interval is
t₁₅,₀.₀₅ = 1.753
So , the margin of error is = t₁₅,₀.₀₅×(standard deviation/√n)
Substituting the values ,
we get ,
= 1.753×(42/√16)
On simplifying further ,
we get ,
= 18.407
Therefore , the margin of error is = 18.407 .
The given question is incomplete , the complete question is
A sample of 16 eggs yields a sample mean weight of 2.00 ounces and a sample standard deviation = 42.0 ounces, find the margin of error in estimating a confidence interval estimate at the 90% level of confidence. Round your answer to three decimal places. You may assume that egg weights are normally distributed .
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Of the 20 students in Mr . Evans class , 45% of them brought their lunches. Which of the following is the number of students who brought their lunches ?
Answers
Answer: 9 because 45% of 20 is 9
Dhara will be 26 years old when she graduates. If her mean bi-weekly wage over her career is $1,875.00, what will her lifetime earnings be when she retires at the age of 65?
Answers
Dhara's Lifetime earnings when she retires at the age of 65 is; $1,901,250
How to find the lifetime earnings?The first thing we will do here is to find the difference between Dhara's current age and the age he will be when he retires. Thus;
Difference in age = 65 - 26
Difference in age = 39 years old
Bi- weekly wage = 52 weeks/2
Bi- weekly wage = 26 paychecks per annum
Thus;
Lifetime earnings = $1875.00 × 26 paychecks per annum × 39
Lifetime earnings = $1,901,250
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Solve equation with rational exponents. Check all proposed solutions.
8x^3/2-56=0
Answers
Answer: x=3√14
Step-by-step explanation:
6. Jesse roasted 12 marshmallows in 4 minutes. How many marshmallows could she roast in 7 minutes?
Answers
Answer: 21
Step-by-step explanation: 12 in 4 minutes means every minute 3 marshmallows are roasted, 4x3=12, so add three more minutes and you get 21. 7x3=21
Answer: 21 marshmallows
Step-by-step explanation:
4 minutes x 1.75 = 7 minutes
multiply marshmallows by 1.75 as well.
12 marshmallows x 1.75 = 21 marshmallows
Carmen made $209 for 11 hours of work.
At the same rate, how much would she make for 8 hours of work?
Answers
Answer:
Step-by-step explanation:
First find the hourly rate Carmen makes. You can find it by dividing the amount she made by the number of hours she worked
209 / 11 = 19
Now multiply that rate by the amount of hours you want to figure out.
19 * 8 = 152
Answer: $152
Step-by-step explanation:
Divide 209 by 11 to find how much money she gets for 1 hour of work ($19) then multiply that value by 8.