The perimeter of the rectangle is 16 feet.
The correct answer is an option (C)
In this question, the length of the rectangle is,
l = 1 yard 2 feet 1 inch
l = 3 feet + 2 feet + 0.0833 feet
l = 5.0833 feet
And the width of the rectangle is,
w = 2 feet 11 inches
w = 2 feet + 0.9167 feet
w = 2.9167 feet
So, the perimeter of the rectangle would be,
P = 2(l + w)
P = 2 * (5.0833 + 2.9167)
P = 16 feet
Therefore, the perimeter of the rectangle is 16 feet.
The correct answer is an option (C)
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Does anyone know how to solve this?
(2x^2)-6x+9 can be written in the form (a(x-b)^2)+c where a b c can be written as integers or fractions in their simplest form.
a) work out the values of a b c
b) using your answer to part a), solve (2x^2)-6x+9=12.5. give any fractions or surds in your answers in their simplest forms.
Answer:
it needs to be written step by step
Kegler bowling buys scorekeeping equipment with an invoice cost of $190,000. The electrical work required for the installation costs $20,000. Additional costs are $4,000 for delivery and $13,700 for sales tax. During the installation, the equipment was damaged and the cost of repair was $1,850. Required: indicate whether each cost should be included in the cost of the equipment or excluded and expensed as incurred.
The total Cost of the equipment is $2,27,700. In which the following included, excluded and expensed as incurred are
Invoicing costs - included in the price
Electrical work required for installation - Included in the price
Delivery costs - included in the price
Sales tax - included in the price
Repair costs - not included or excluded
A machine used by a company to produce products and services is known as a machine tool. It is a vital long-term asset as it speeds up the production process such as transportation, computers and other equipment. These costs will include the costs that were necessary to start opening the plant property. There are equipment costs.
We have given the following details ,
Total Cost DR Machinary DR Expense
Invoice cost $190,000 $190,000
electric work
and $20,000 $20,000
installation cost
delivery cost। $4,000 $4,000
sales tax $13,700 $13,700
repair cost $1,850 $1,850
total $22,9550 $22,7700 $ 1,850
Accordingly, all the mentioned costs except for the repair of the part will be included in the cost of the machinery.
Included in price Excluded
invoice repair cost
electric and installation
delivery
sales tax
Hence , the total equipment cost is $22,7700.
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149° + 13x + 5° = 180°
Answer:
Your answer should be x = 2
Step-by-step explanation:
149 + 13(2) + 5 = 180.
Hope this helps.
Answer:
x=2
Step-by-step explanation:
You add 149 and 5, which is 154. Then you take the total which is 180, and subtract it by 154. So 180-154=26 Then you take and do 26/13 which is 2.
149+13(2)+5=180
149+26+5=180
Definitely 2.
Hope this helps!!!
Which expression represents the product of 3 and 7? 7 ÷ 3 7 + 7 + 7 37 3 × 7
Answer:
3x7
Step-by-step explanation:
product is multiplication so 3x7 is only correct answer
Hopes this helps please mark brainliest
A cell phone company charges a flat rate of $3. 99 per month, with an additional charge of $0. 05 per minute. How many minutes did casey talk on her cell phone if her monthly bill was $38. 44?.
Answer:Total time minute Casey can talk= 689 Minute
Step-by-step explanation:Total charges of flat rate per month= $3. 99
Total Additional charge per minute = $0.05
Total monthly bill = $38. 44
Total additional charge=Total monthly bill - Total charge of flat rate
=$38.44-$3.99
=$34.45
Total time minute Casey cann talk=Total additional charge÷Total additional charge per minute
=$34.45÷$0.05
=689 Minute
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689 minutes long If Casey's monthly bill was $38.44, she would talk on her cell phone.
Given;
A cell phone provider charges a set monthly fee of $3. 99 plus an extra $0.05 per minute.
If Casey's monthly phone bill was $38.44, how many minutes did she use?
The total charges of the flat rate per month = $3.99
The total additional charge per minute = $0.05
Total monthly bill = $38.44
Total additional charge = Total monthly bill - Total charge of flat rate
= $38.44 - $3.99
= $34.45
Total time per minute Casey can talk = Total additional charge/Total additional charge per minute
= $34.45 / $0.05
= 689 Minutes
Therefore, for 689 minutes Casey talk on her cell phone if her monthly bill was $38.44
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what is the smallest positive integer a such that the intermediate value theorem guarantees a zero exists between 0 and a?
The smallest positive integer that the intermediate value theorem guarantees a zero exists between 0 and a is 3.
What is the intermediate value theorem?
Intermediate value theorem is theorem about all possible y-value in between two known y-value.
x-intercepts
-x^2 + x + 2 = 0
x^2 - x - 2 = 0
(x + 1)(x - 2) = 0
x = -1, x = 2
y intercepts
f(0) = -x^2 + x + 2
f(0) = -0^2 + 0 + 2
f(0) = 2
(Graph attached)
From the graph we know the smallest positive integer value that the intermediate value theorem guarantees a zero exists between 0 and a is 3
For proof, the zero exists when x = 2 and f(3) = -4 < 0 and f(0) = 2 > 0.
Your question is not complete, but most probably your full questions was
Given the polynomial f(x)=− x 2 +x+2 , what is the smallest positive integer a such that the Intermediate Value Theorem guarantees a zero exists between 0 and a ?
Thus, the smallest positive integer that the intermediate value theorem guarantees a zero exists between 0 and a is 3.
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mating eagle pairs typically have two baby eagles (called eaglets). when there are two eaglets, the parents always feed the older eaglet until it has had its fill, and then they feed the younger eaglet. this results in an unequal chance of survival for the two eaglets. suppose that the older eaglet has a 50 percent chance of survival. if the older eaglet survives, the younger eaglet has a 10 percent chance of survival. if the older eaglet does not survive, the younger eaglet has a 30 percent chance of survival. let x be the number of eaglets that survive. which of the following tables shows the probability distribution of x ?
The set of probabilities for the number of eaglets is the
probabilities for how many eaglets will survive.
The table that shows the probability distribution is the option C;
X 0 1 2
p(x) 0.35 0.60 0.05
P(O) = 0.5 is the likelihood that the elder eaglet will live.
Therefore;
P(O') = 1 - 0.5 = 0.5 is the probability that the older eaglet won't survive.
The likelihood that the younger eaglet will survive if the older eaglet does not P(Y|O) = 10%
Therefore;
The likelihood that the elder eaglet will live while the younger eaglet does not survive is P(Y'|O) = 1 - 10% = 90%.
When the older eaglet does not survive, the younger eaglet has a 30% survival chance (P(Y|O')).
Therefore;
The likelihood that the younger eaglet will not survive, compared to the elder eaglet, is P(Y'|O') = 1 - 30% = 70%
The collection of potential probabilities for the number of eaglets that survive is expressed as the probability distribution, or P(X)
The range of potential results includes:
Never survives:
The likelihood that no eaglets survive is equal to P(O') × P(Y'|O') = 0.5 × 0.7 = 0.35.
The only survivor is:
The likelihood that only one eaglet survives is determined by P(O) = P(Y'|O) × P(O') = P(Y|O'), which results in P = 0.5 × 0.9 + 0.5 × 0.3 = 0.6 Both survive:
The odds of both eaglets surviving are P(O) ×P(Y|O) = 0.5 × 0.1 = 0.05.
The table of the probability distribution is therefore;
X 0 1 2
p(x) 0.35 0.60 0.05
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help please i will give you a snack
Answer:
26
Step-by-step explanation:
you are given 45° and 90° so you know the third angle will also be 45° because the sum of all angles always is 180°
with all 3 angles you apply the sine law
a / sin( α ) = b / sin( β ) = c / sin( γ )
then you'll see that a = 26
. If he is paid $15 per hour and $200 for each car that he sells, how many hours did he work if he sold 2 cars and made $520?
Answer:
8 hours
Step-by-step explanation:
2 cars will be $400 since 2x200=400
500-400=120
He made $120 from hours alone so now we divide by 15
120/15=8
He worked 8 hours
Hopes this helps please mark brainliest
The temperature today in Chicago is 50°E
Instead of using the standard conversion
formula °C = x(°F - 32), Tommaso uses his
9
grandmother's rule, which is easier but gives
an approximate value: "Subtract 32 from the
value in °F and multiply the result by 0.5."
Error = (10-9)°C & Error percentage = 10%.
Given that temperature today in Chicago is 50°F
Standard conversion formula
°C = [tex]\frac{5}{9} *(T^{0}F-32)[/tex] - 1
Given T = 50°F
Put the value in equation 1
[tex]^{0}C = \frac{5}{9} *(50-32) \\\\= \frac{5}{9}*18\\ \\= \frac{90}{9}[/tex]
= 10°C
Tommasa's grandmothers rule is to subtract 32 from the value in °F and multiply the result by 0.5
i.e. [tex]^{0}C = 0.5(T^{0} F-32)[/tex] - 2
Given temperature is T = 50°F
Put the value of T in equation 2
[tex]^{0}C = 0.5*(50-32)[/tex]
= 0.5 * 18
= 1/2 * 18
= 9°C
Temperature obtained by standard conversion Formula is 10°C and the temperature obtained by Tammaso's grandmother rule is 9°C.
So error = (10-9)°C
= 1°C
Error percentage = [tex]\frac{1}{10}*100[/tex]
= 10%
Hence the answer is Error = (10-9)°C & Error percentage = 10%.
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PLEASE HELP!!!!!!! i dont know how to solve this problem
Answer:
Step-by-step explanation:
3 because at the bottem it is 3 away and top three away.
the point p p is on the unit circle. if the x-coordinate of p p is 3 4 34 , and p p is in quadrant iv , then what is the value of y? evaluate by using the one of the pythagorean identities.
The value of y coordinate of the unit circle is given by [tex]\sqrt{7}/4[/tex]
Given that,
x - coordinate of p =-3/4 . Let the co-ordinate of point P = (-3/4 , y).
To find : The y coordinate in Quadrant IV
By using the formula for unit circle,
Unit circle means a circle whose radius is one or 1
x²+ y² = 1
y²+ (-3/4)² = 1
y²+ (9/16) = 1
y² = 1 -9/16
y² = 7/16
y= [tex]\sqrt{7/16}[/tex]
y = ± [tex]\sqrt{7}/4[/tex]
It is given that point P is in quadrant IV so in IV quadrant y is positive.
Therefore, y = [tex]\sqrt{7}/4[/tex]
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Determine the largest integer value of a in the solution of the following inequality.
4x+6 -13
The largest integer value of x in the solution of the following inequality is 7/4.
We have given equation is 4x+6 ≥13
In the question we have to determine the largest integer value of a in the solution of the following inequality.
So first we have to solve this inequality equation:
4x+6 ≥13
4x≥13-6
4x≥7
x≥7/4
So the largest value of x is 7/4
Hence, the largest integer value of a in the solution of the following inequality is 7/4.
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The right answer is
Determine the largest integer value of x in the solution of the following inequality.
4x+6≥13
Wich rule best represents the dilation that was applied to the quadrilateral ABCD to create quadrilateral A'B'C'D'?
Answer:
Step-by-step explanation:
It A (x,y) (0.4x,0.4y)
need answers for questions 23-26
The following are the answers:
23. The cost for 7 lessons is $82, and the cost of 11 lessons is $122, we have;
The total cost of lessons is; f(x) = y = 10·x + 12 and one lesson costs $22
24. The equation of population of Laredo, Texas is :
p = 92500t/17 + 123000
25. The linear equation to represent the temperature T at an elevation of x, where x is in thousands of feet is T = -(2000/3)x + (4228/3).
26. The equation to represent the amount 'R' Natalia and her friends raised after selling 'c' cakes will be;
⇒ R = 4c
Given:
23. Lydia wants to purchase guitar lessons.
7 lessons = $82
11 lessons = $122
we are asked to determine the linear equation which finds the total cost C for d lessons.
The general equation for the total cost of lessons is;
Let a represent the cost of 7 guitar lessons, and let b represent the cost of 9 guitar lessons, given that the cost increases linearly with the number of lessons, we have;
The cost increase per lesson = The slope of the linear function representing the total cost of a guitar lesson
Therefore,
slope = b-a/11-7 = b-a/4
Expressing the equation in slope and intercept form, we get:
(y-a) = b-a/4 . (x-7)
y = b-a/4 . x-7 × b-a/4 + a = b-a/4 . x + 11.a-7.b/4
y = b-a/4 . x + 11.a-7.b/4 = 1/4.((b-a).x+11.a-7.b
where a=$82 and b=$122 we ahve:
y = 1/4 . (122-82) . x+1/4 . (11×82-7×122) = 10x+12
The total cost of a lesson is:
y = 10×1+12
= 22
24. Given:
t = the number of years after 1990.
So, for 1990, t = 0. So the coordinate is (0, 123000).
For 2007, t = 17. So the coordinate is (17, 215500).
using point slope formula:
m = 215500-123000/17-0
m = 92500/17
⇒ p = 92500t/17 + 213000
25. The equation of a line in slope-intercept form is y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at
x = 0.
We know the slope is (y₂ - y₁)/(x₂ - x₁).
∴ Here the temperature is y and the height is x.
And the points are (6000, 76) and (12000, 49)
So, slope =(12000 - 6000)/(49 - 76).
Slope = (6000/-27).
Slope = -(2000/9).
Now we have to determine the y-intercept by putting any of the points in y = mx + b.
So, 76 = -(2000/9)×6000 + b.
76 = -(12000/9) + b.
76 = -(4000/3) + b.
b = 4000/3 + 76.
b = 4228/3.
∴ y = -(2000/3)x + (4228/3) or T = -(2000/3)x + (4228/3).
26. The equation of line passing through the points (x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
he friends sold 15 cakes on the first day and 22 cakes on the second day of the bake sale.
On first day, they collect = $60
On second day, they collect = $88
Now,
We have to find the equation as;
⇒ R = mc + b
We need to find the value of m and b.
Since, The first point = (15, 60)
The second point = (22, 88)
Hence, Slope (m) = (88 - 60) / (22 - 15)
m = 28 / 7
m = 4
And, To find b substitute R = 60 , c = 15 and m = 4 in above equation,
⇒ R = mc + b
⇒ 60 = 4 x 15 + b
⇒ b = 0
Thus, Substitute m = 4 and b = 0 in equation (i) we get;
⇒ R = mc + b
⇒ R = 4c + 0
⇒ R = 4c
Therefore, The equation to represent the amount 'R' Natalia and her friends raised after selling 'c' cakes will be;
⇒ R = 4c
Hence we get the required answers.
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whats eleven decreased by k ?
Answer:
11-k
Step-by-step explanation:
if you are asking what is as a equation its 11-7 because decreased means minus
The required mathematical expression for the given statement is 11-k.
What are expressions?A mathematical statement containing variables, numbers and related by at least one mathematical operator is considered as an expression.
Given that, a statement, what's eleven decreased by k,
Converting it into a mathematical expression,
Here, a value k is being extracted or subtracted by 11, that mean, the expression should be like k is being subtracted by 11.
That is = 11-k
Hence, the required mathematical expression for the given statement is 11-k.
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find the missing number so that the equation has no solution x+19=2x-4-7x
The missing number so that the equation has no solution is -3 5/6.
What is the missing number?A linear equation is an equation that has a single variable that is raised to the power of one. When shown on a graph, a linear equation is a straight line that slopes either upwards or downwards.
If the equation has no solution, it means that the value of the left hand equation and the value of the right hand equation are equal.
In order to determine the solution, take the following steps:
x + 19 = 2x - 4 - 7x
Combine similar terms together: 19 + 4 = 2x - 7x - x
Add similar terms together: 23 = -6x
Divide both sides of the equation by -6: x = 23 / - 6
x = -3 5/6
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In the next several games, the pitcher threw a total of 384 pitches and used a fastball 240 times. What decimal should Juanita use to update her report?
Juanita should use the decimal to update her report.
The decimal that Juanita can use to update her report is 1.6.
What is a decimal?A decimal is a number with a whole and a fractional part. Decimal numbers are between integers and represent numerical value for whole plus some fraction of a whole.
The decimal numeral system is the most widely used system for representing both integer and non-integer numbers. It is the Hindu-Arabic numeral system's extension to non-integer numbers. Decimal notation refers to the method of representing numbers in the decimal system.
In this case, the the pitcher threw a total of 384 pitches and used a fastball 240 times. The decimal will be:
= Number of throws / Fastball
= 384 / 240
= 1.6
The decimal is 1.6.
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Jackie travels 60 km to work. Since she began taking a new
route (still 60 km to work) she gets there 30 minutes sooner
because she can drive 10 km/hour faster. Which of the
following equations could you use to solve the problem?
According to the distance-speed-time formula, the equation that could be used to solve this formula is 60/x+10 - 60/x = 1/2
Distance-speed-time
Basically, the formula for speed is speed = distance ÷ time.
In order to work out what the units are for speed, you need to know the units for distance and time.
Given,
Jackie travels 60 km to work. Since she began taking a new route (still 60 km to work) she gets there 30 minutes sooner because she can drive 10 km/hour faster.
Here we need to find the equations could you use to solve the problem.
Let us consider x be the speed of Jackie.
Therefore, the time has been calculated as,
Time1 = 60/ x
Now, the speed is increased as 10, then it can be written as,
=> x + 10
Therefore, the new time Time2 is calculated as,
=> Time2 = 60 / x + 10
So, the equation is obtained by calculating the difference of the times,
So, the equation is,
=> Time 2 - Time1
=> 60/x+10 - 60/x
Now, we know in this one she gets there 30 minutes sooner,
So, it can be written as,
=> 60/x+10 - 60/x = 30/60
=> 60/x+10 - 60/x = 1/2
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In triangle EFG, m∠E = 84.3° and m∠F = 36.4°. Determine the measure of the exterior angle to ∠G.
47.9°
59.3°
121.1°
120.7°
By applying the exterior angle property, the measure of the exterior angle to ∠G in triangle EFG is 120.7°
What is the exterior angle property?In Mathematics, the exterior angle property can be defined as a theorem which states that the measure of an exterior angle in a triangle is equal in magnitude to the sum of the measures of the two remote or opposite interior angles of that triangle.
To determine the value of ∠G in triangle EFG (ΔEFG), we would have to apply exterior angle property.
Then, the exterior angle property can be used to model triangle EFG (ΔEFG) is given by:
∠G = m∠E +m∠F
Now Substituting the given parameters into the formula, we have
∠G = 84.3° + 36.4°.
∠G = 120.7°.
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As a fraction in simplest terms, what would you multiply the first number by to get
the second?
First number: 79
Second number: 65
First number 79 about friction is correct statement with initial velocity .
What is friction?
Friction is a force that opposes motion between any surfaces that are touching. Friction can work for us yet against of us .
It is the action of one surface or object rubbing against another .
According to the given question in this case force of friction has a tendency to rotate the cube in anticlock wise direction. So normal reaction will shift in forword direction to balance the force due to torque of friction.
Thus, During motion the normal reaction shift towards posetive x- axis from the centre of mass is correct.
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the international air transport association surveys business travelers to develop quality ratings for transatlantic gateway airports. the maximum possible rating is . suppose a simple random sample of business travelers is selected and each traveler is asked to provide a rating for the miami international airport. the file miami contains the ratings obtained from the sample of business travelers. develop a confidence interval estimate of the population mean rating for miami. round your answers to two decimal places.
The confidence interval estimate is (6.41, 7.11) of the population mean rating for Miami
The question includes a sample of the data.
The sample size, n = 50
The sample mean:
x= ∑X /n
= 6.76
The sample standard deviation;
s= √∑(X-x)²/(n-1)
=2.55
The confidence level =0.95
The significance level , α = 0.05
The sample mean, X
= 6.76
The sample standard deviation, s = 2.55
The sample size , n= 50
Degree of freedoms :
Df = n-1
=49
Using the t-distribution table, the critical value of t is:
t critical = t α/2, df
= t 0.025,49
= 0.098
95% confidence interval :
μ = X ± t.s/√n
t.s /
= 6.76 2.01 2.55 / √50
= 6.76 0.7249
Therefore, The confidence interval is ( 6.41, 7.11)
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What is the coefficient of this number written in scientific notation?
(3.6 x 10^5)
Enter the coefficient only. Don't change to standard form!
The coefficient would be 3.6
How to find a percent change. (Decrease and Increase). Please use simple terms and include a formula. (Also please use a visual demonstration) Thank you!
Percentage change expresses the ratio of the change in the amount of an initial quantity to the initial quantity as a percentage.
What is the mathematical formula for percentage change?Mathematically, the formula for percentage change, C, can be presented as follows;
[tex]C = \dfrac{x_{2} - x_{1} }{ x_{1} } \times 100[/tex]
Where:C = The percentage change
[tex]x_{1} [/tex] = The original value
[tex]x_{2} [/tex] =The new value
Graphically, percentage change can be presented as follows;
When the number of fruits that drops from a three each month, changes from 10 to 8, the percentage change is therefore;
[tex] C = \dfrac{10-8}{10} = 20\% [/tex]The percentage change is 20%
Initial number of fruits that drops monthly from the tree;
##########
The new number of fruits that drops from the tree on the specified month;
########
The difference in the number of fruits that drops from the tree is 2, which corresponds to the 20 % calculated for the percentage change.
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find the following percentiles for the standard normal distribution. interpolate where appropriate. (round your answers to two decimal places.)
The interpolations;
(a) 81st
= NORM.INV(0.81;0;1)
0.878
(b) 19th
=NORM.INV(0.19;0;1)
-0.878
(c) 76th
=NORM.INV(0.76;0;1)
0.706
(d) 24th
=NORM.INV(0.24;0;1)
-0.706
(e) 11th
=NORM.INV(0.11;0;1)
-1.227
Given,
Data near the mean are more likely to occur than data distant from the mean, according to the normal distribution, which is a probability distribution that is symmetric around the mean.
"A numerical measurement used in statistics of a value's relationship to the mean (average) of a set of values, assessed in terms of standard deviations from the mean," according to Wikipedia, is the Z-score.
For this case we can find the percentiles with the Norm.inv function in Excel and we got:
(a) 81st
= NORM.INV(0.81;0;1)
0.878
(b) 19th
=NORM.INV(0.19;0;1)
-0.878
(c) 76th
=NORM.INV(0.76;0;1)
0.706
(d) 24th
=NORM.INV(0.24;0;1)
-0.706
(e) 11th
=NORM.INV(0.11;0;1)
-1.227
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PLS HELPPPP THIS IS URGENT
There were 20 illustrations in Julio's sketch pad. While at a museum, he drew x more illustrations in the sketch pad. Which expression represents the total number of illustrations in Julio's sketch pad after his museum visit?
The expression that represents the total number of illustrations in Julio's sketch pad after his museum visit is given as follows:
Total number = 20 + x.
How to obtain the expression for the total number of illustrations?The expression that represents the total number of illustrations in Julio's sketch pad after his museum visit is obtained adding the previous amount of illustrations to the number of illustrations that were added during the visit to the museum, hence:
Total number of illustrations = Previous number of illustrations + number of illustrations added during the visit.
In the context of this problem, the values of these parameters are given as follows:
Previous number of illustrations = 20 -> as stated in the problem.Number of illustrations added during the visit = x.Hence the expression is defined as follows:
Total = 20 + x.
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Using the graph below:
Find the values of x and y that maximize the objective function C=3x+4y for the graph.
What is the minimum value? Show why.
What is the maximum value? Show why.
Regarding the objective function C = 3x + 4y, the minimum and the maximum value are given as follows:
Minimum value: C = 0 at (0,0).Maximum value: C = 16 at (0,4).How to find the extrema values of the objective function?The objective function is defined as follows:
C = 3x + 4y.
The extremas of the function, that is, the minimum and the maximum values, can be obtained at either of these following points:
Intercepts = vertices of the curve.Intersection point between two curves.These extreme values are the numeric values at these points.
In this problem, there is only a single curve, hence the vertices are given as follows:
(0,0), (0,4) and (4,0).
Then the numeric values of the objective function are these points are given as follows:
(0,0): C = 3(0) + 4(0) = 0 -> minimum value.(0,4): C = 3(0) + 4(4) = 16 -> maximum value.(4,0): C = 3(4) + 4(0) = 12.More can be learned about maximizing functions at https://brainly.com/question/28788613
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What is the value sinθ?
question options:
A. 5/13
B. 13/5
C. 12/13
D.5/12
The value of sin θ of the given right angle triangle using trigonometric ratios is; A: 5/13
How to solve Trigonometric ratios?The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec). They are based on the angles formed from the ratio of sides of a right angle triangle. Thus;
sin θ = opposite/hypotenuse
cos θ = adjacent/hypotenuse
tan θ = opposite/adjacent
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
From the given image, we see that;
Hypotenuse = 13
Adjacent = 12
Opposite = 5
Thus;
tan θ = 5/12
θ = tan⁻¹(5/12)
sin θ = 5/13
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Would 8.1^4 x 8.1^8 be equal to 8.1^12? If so, would 8.1^12 = 8.1^6?
8.1^4 x 8.1^8 will be equal to 8.1^12. But, 8.1^12 will not be equal to 8.1^6.
Some laws of exponents are:
(a²) · (a³) = a²⁺³ = a⁵(a²)³ = a²ˣ³ = a⁶(a²) ÷ (a³) = a²⁻³ = a⁻¹We are given:
8.1^4 x 8.1^8
We need to check if 8.1^4 x 8.1^8 be equal to 8.1^12 and if 8.1^12 be equal to 8.1^6.
We will use laws of exponents to solve the given expression:
8.1^4 x 8.1^8 = 8.1^(4 + 8) = 8.1^12
So, 8.1^4 x 8.1^8 = 8.1^12
Also,
8.1^12 = 8.1^(2 * 6) = (8.1^2)^6
So, 8.1^12 ≠ 8.1^6.
Thus, 8.1^4 x 8.1^8 will be equal to 8.1^12. But, 8.1^12 will not be equal to 8.1^6.
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