Answer:
P [ Z < 66 ] = 35,15 %
Step-by-step explanation:
Normal Distribution
Population mean μ₀ = 75,4
Standard deviation σ = 5,2
Then:
P [ Z < 66 ] = ( 66 - 75,4 ) / 5,2
P [ Z < 66 ] = - 9,4 / 5,2
P [ Z < 66 ] = - 1,81
In z-table we look for the reciprocate area for that z score and find
P [ Z < 66 ] = 0,3515
P [ Z < 66 ] = 35,15 %
In the periodic compound interest formula Upper A equals Upper P (1 plus StartFraction r Over n EndFraction )Superscript nt , what does the variable n represent?
Answer:
The variable n represents the number of times in a year in which we compound the interest rate
Step-by-step explanation:
The periodic compound interest formula is given as;
A = P( 1 + r/n)^nt
The variable n represents the number of times in a year in which the interest rate is compounded
The perimeter of an equilateral triangle is 15 x + 30 units. Which expression can be used to show the side length of one side of the equilateral triangle? 15 (x + 2): Each side length is x + 2 units. 30 (one-half x + 1): Each side length is One-half x + 1 units. 5 (3 x + 6): Each side length is 3 x + 10 units. 3 (5 x + 10): Each side length is 5 x + 10 units.
Answer:
Each side length is 5x + 10 units.Step-by-step explanation:
An equilateral triangle is a triangle that has all of its sides equal. Let a, b and c be the sides of the equilateral triangle. Since all the sides are equal, then
a = b = c.
The perimeter of the triangle is the sum of all the sides of the triangle.
P = a + b+ c
GIVEN THE PERIMETER OF THE EQUILATERAL TRIANGLE AS P = 15 x + 30 units and a = b = c, then;
15 x + 30 = a + b + c
15 x + 30 = a + a + a (since all sides are equal)
15 x + 30 = 3a
3a = 15 x + 30
3a = 3(5x+10)
Dividing both sides by 3 will give;
3a/3 = 3(5x+10)/3
a = 5x+10
Hence, the length of one side of the equilateral triangle is 5x + 10 units.
Answer:
D.
Step-by-step explanation:
Edge 2020
There are three points on a line, A, B, and C, so that AB = 12 cm, BC = 13.5 cm. Find the length of the segment AC . Give all possible answers.
Answer:
AC = 25.5 or 1.5
Step-by-step explanation:
If they are on a line and they are in the order ABC
AB + BC = AC
12+13.5 = AC
25.5 = AC
If they are on a line and they are in the order CAB
CA + AB = BC
AC + 12 =13.5
AC = 13.5 -12
AC = 1.5
If they are on a line and they are in the order ACB
That would mean that AB is greater than BC and that is not the case
A small fruit basket with 6 apples and 6 oranges costs $7.50. A different fruit basket with 10 apples and 5 oranges costs $8.75. If x is the cost of one apple and y is the cost of one orange, the system of equations below can be used to determine the cost of one apple and one orange. 6x+6y=7.50 10x+5y=8.75 What is the cost of one apple?
Answer:
$0.50
Step-by-step explanation:
Let's remove common factors from the equations.
x + y = 1.25 . . . . divide the first equation by 62x +y = 1.75 . . . divide the second equation by 5Subtracting the first equation from the second, we find the cost of an apple:
(2x +y) -(x +y) = 1.75 -1.25
x = 0.50
The cost of one apple is $0.50.
Fifty students are enrolled in a Business Statistics class. After the first examination, a random sample of 5 papers was selected. The grades were 60, 75, 80, 70, and 90. a) Determine the standard error of the mean
Answer:
The standard error S.E of the mean is 5
Step-by-step explanation:
From the given data;
Fifty students are enrolled in a Business Statistics class.
After he first examination, a random sample of 5 papers was selected.
Now; let consider a random sample of 5 papers was selected. with the following grades : 60, 75, 80, 70, and 90
The objective of this question is to determine the standard error of the mean
In order to achieve this ; we need to find the mean and the standard deviation from the given data.
TO start with the mean;
Mean [tex]\overline X[/tex] = [tex]\dfrac{1}{n} \sum x_i[/tex]
Mean [tex]\overline X[/tex] = [tex]\dfrac{1}{5} (60+75+80+70+90)[/tex]
Mean [tex]\overline X[/tex] = 0.2(375)
Mean [tex]\overline X[/tex] = 75
On the other hand; the standard deviation is :
[tex]s = \sqrt{\dfrac{1}{n-1}\sum(x_i - \overline X)^2}[/tex]
[tex]s = \sqrt{\dfrac{1}{5-1}((60-75)^2+(75-75)^2+(80-75)^2+(70-75)^2+(90-75)^2 )}[/tex]
[tex]s = \sqrt{\dfrac{1}{4}(225+0+25+25+225 )}[/tex]
[tex]s = \sqrt{\dfrac{1}{4}(500 )}[/tex]
[tex]s = \sqrt{125}[/tex]
s = 11.18
Finally; the standard error S.E of the mean is:
[tex]S.E = \dfrac{s}{\sqrt{n}}[/tex]
[tex]S.E = \dfrac{11.18}{\sqrt{5}}[/tex]
[tex]S.E = \dfrac{11.18}{2.236}[/tex]
[tex]S.E = 5[/tex]
The standard error S.E of the mean is 5
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers. Factor completely and then place the factors in the proper location on the grid. 4y2 + 25y + 6
Answer:
(4y +1)(y +6)
Step-by-step explanation:
We can rewrite the middle term and factor by grouping.
4y^2 + 25y + 6 = (4y^2 +24y) +(y +6)
= 4y(y +6) +1(y +6)
= (4y +1)(y +6)
In a random sample of 40 refrigerators, the mean repair cost was $150. Assume the population standard deviation is $15.50. Construct a 99% confidence interval for the population mean repair cost. Then change the sample size to n = 60. Which confidence interval has the better estimate?
Answer: ($143.69, $156.31)
Step-by-step explanation:
Confidence interval to estimate population mean :
[tex]\overline{x}\ \pm z\dfrac{\sigma}{\sqrt{n}}[/tex]
, where [tex]\sigma[/tex] = population standard deviation
n= sample size
[tex]\overline{x}=[/tex] Sample mean
z= critical value.
As per given,
n= 40
[tex]\sigma[/tex] = $15.50
[tex]\overline{x}=[/tex] $150
Critical value for 99% confidence level = 2.576
Then, 99% confidence interval for the population mean:
[tex]150\pm(2.576)\dfrac{15.50}{\sqrt{40}}\\\\\Rightarrow\ 150\pm6.31 \ \ (approx)\\\\\Rightarrow(150-6.31,150+6.31)=(143.69,156.31)[/tex]
Hence, the required confidence interval : ($143.69, $156.31)
A graph shows an x- and y-axis. The data line is in the shape of a "vee." The begins above the x-axis and to the left of the y-axis, extends below the x-axis to a point on the y-axis, and ascends above the x-axis to the right of the y-axis. Which statement describes the relationship between x and y? As x increases, y decreases. As x increases, y increases. As x increases, y increases and then decreases. As x increases, y decreases and then increases.
Answer:
As x increases, y decreases and then increases
Step-by-step explanation:
You need only understand your own description of the graph:
begins above the x-axis, extends below the x-axis, and ascends above the x-axis
This is a description of decreasing, then increasing:
As x increases, y decreases and then increases
Answer:
C. As x increases, y increases and then decreases.
Step-by-step explanation:
Just took the Unit Test and got it correct on Edge.
(SAT Prep) Find the value of x.
Answer:
x = 65°
Step-by-step explanation:
Naming the sides of the parallelogram formed ABCD as shown in the attached image to this solution.
Angle A = 2x (vertically opposite angles are equal)
Angle A = Angle C (opposite angles of a parallelogram are equal)
Angle A = Angle C = 2x
(Angle C) + 50° = 180° (Sum of angles on a straight line is 180°)
2x + 50° = 180°
2x = 180° - 50° = 130°
x = (130°/2) = 65°
Hope this Helps!!!
Answer:
65 degrees
Step-by-step explanation:
An article reported on the results of an experiment in which half of the individuals in a group of 66 postmenopausal overweight women were randomly assigned to a particular vegan diet, and the other half received a diet based on National Cholesterol Education Program guidelines. The sample mean decrease in body weight for those on the vegan diet was 6 kg, and the sample SD was 3.2, whereas for those on the control diet, the sample mean weight loss and standard deviation were 3.8 and 2.4, respectively. Does it appear the true average weight loss for the vegan diet exceeds that for the control diet by more than 1 kg? Carry out an appropriate test of hypotheses at significance level .05 based on calculating a P-value.
Answer:
We conclude that the true average weight loss for the vegan diet exceeds that for the control diet by more than 1 kg.
Step-by-step explanation:
We are given that an article reported on the results of an experiment in which half of the individuals in a group of 66 postmenopausal overweight women were randomly assigned to a particular vegan diet, and the other half received a diet based on National Cholesterol Education Program guidelines.
The sample mean decrease in body weight for those on the vegan diet was 6 kg, and the sample SD was 3.2, whereas, for those on the control diet, the sample mean weight loss and standard deviation were 3.8 and 2.4, respectively.
Let = true average weight loss for the vegan diet.
[tex]\mu_2[/tex] = true average weight loss for the control diet.
So, Null Hypothesis, : 1 kg {means that the true average weight loss for the vegan diet exceeds that for the control diet by less than or equal to 1 kg}
Alternate Hypothesis, : > 1 kg {means that the true average weight loss for the vegan diet exceeds that for the control diet by more than 1 kg}
The test statistics that will be used here is Two-sample t-test statistics because we don't know about population standard deviations;
T.S. = [tex]\frac{(\bar X_1-\barX_2)-(\mu_1-\mu_2)}{s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] ~ [tex]t__n_1_+_n_2_-_2[/tex]
where, = sample mean weight loss for the vegan diet = 6 kg
= sample mean weight loss for the control diet = 3.8 kg
= sample standard deviation weight loss for the vegan diet = 3.2 kg
= sample standard deviation weight loss for the control diet = 2.4 kg
[tex]n_1[/tex] = sample of vegan diet women = 33
[tex]n_2[/tex] = sample of control diet women = 33
Also, [tex]s_p=\sqrt{\frac{(n_1-1)\times s_1^{2}+(n_2-1)\times s_2^{2} }{n_1+n_2-2} }[/tex] = [tex]\sqrt{\frac{(33-1)\times 3.2^{2}+(33-1)\times 2.4^{2} }{33+33-2} }[/tex] = 2.83
So, the test statistics = [tex]\frac{(6-3.8)-(1)}{2.83 \times \sqrt{\frac{1}{33}+\frac{1}{33} } }[/tex] ~ [tex]t_6_4[/tex]
= 1.722
The value of t-test statistics is 1.722.
Also, the P-value of the test statistics is given by;
P-value = P([tex]t_6_4[/tex] > 1.722) = 0.0461 or 4.61%
Since the P-value of our test statistics is less than the level of significance as 0.0461 < 0.05, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.
Therefore, we conclude that the true average weight loss for the vegan diet exceeds that for the control diet by more than 1 kg.
The square below represents one whole.
Answer:
6 percent
Step-by-step explanation:
6/100 is shaded. This is the same thing as 0.06. Once I move the decimal two places to the right, I get 6. (I move the decimal place because percents are out of 100, so two decimal places.) This means 6 percent.
I can't solve this problem, can anyone help me?
Answer:
x < 5
Step-by-step explanation:
The total amount is 595$ and the amount Helena want to leave for equipement is 420$
595-420 = 175The amount helena can use is 175$
each ticket costs 35$
175/35 = 5so Helena can oly buy 5 tickets or less
x < 5 with x the number of tickets
2.4.6.8. 10.... geometrical,arithmetic or neither?
Answer:
This is an arithmetic sequence.
Step-by-step explanation:
The difference between the consecutive terms is constant => sequence is arithmetic.
4-2 = 2
6-4= 2
8-6 = 2
10-8 = 2
Step-by-step explanation:
It's an arithmetic sequences.
Formed by the n th term 2n.
As the difference is 2 between them.
let's find it, by formulae.
n th term = 2n
t1= 2×1=2t2 = 2×2=4t3=2×3=6t4=2×4=8and so on.....
Therefore, it's an arithmetic sequence.
Hope it helps..
Construct a quadrilateral ABCD in which AB = 4 cm, BC = 7 cm, angle A = angle C = 105 degree
and angle D = 60°
Answer: see attachment
Step-by-step explanation:
Since A = C = 105° and D = 60°,
then A + B + C + D = 360°
105° + B + 105° + 60° = 260°
B + 270° = 360°
B = 90°
A study of the annual population of butterflies in a county park shows the population, B(t), can be represented by the function B(t)=137(1.085)t, where the t represents the number of years since the study started. Based on the function, what is the growth rate?
Answer:
The growth rate is of 0.085 = 8.5% a year.
Step-by-step explanation:
General growth equation:
[tex]B(t) = B(0)(1+r)^{t}[/tex]
In which B(t) is the population of butterflies after t years, B(0) is the initial population and r is the growth rate, as a decimal.
We have:
[tex]B(t)=137(1.085)^{t}[/tex]
Comparing to the general equation, we have that:
[tex]B(0) = 137, 1 + r = 1.085[/tex]
Growh rate:
1 + r = 1.085
r = 1.085 - 1
r = 0.085
The growth rate is of 0.085 = 8.5% a year.
Suppose that any baseball that has a coefficient of restitution that exceeds 0.625 is considered too lively. Based on the available data, what proportion of the baseballs in the sampled population are too lively
Answer:
hello some parts of your question is missing attached below is the missing parts of the question
Answer : The proportion of the baseballs in the sampled population that are too lively
P = x / n = 18 / 40 = 0.450
Step-by-step explanation:
coefficient of restitution > 0.625
Based on available data the proportion of the baseballs that is in the sampled population that are too lively can be calculated using the values below
n = 40
x = n ( p > 0.625 ) = 18
The proportion of the baseballs in the sampled population that are too lively
P = x / n = 18 / 40 = 0.450
i neeed help thanksssss
Answer:
Volume: 366.6
Surface Area: 314.2
Explanation (look at below)
Step-by-step explanation:
Volume:
The radius of this sphere is 5 (half of 10). The equation will be [tex]\frac{4}{3} \pi[/tex]5^3
When you calculate that, it will become: 366.6<-- rounded to the nearest tenth.
Surface Area:
4[tex]\pi[/tex]5^2
=100Π
=314.2<-- rounded to the nearest tenth.
314.2 is the nearest tenth digit no.
I don’t know if this is right, I’m stuck. Help!
Answer:
C
Step-by-step explanation:
According to SohCahToa, cosine is adjacent over the hypotenuse.
The adjacent when looking from angle b, is 21.
The hypotenuse of this triangle is 29.
So Cos B=21/29
1. Manuel quiere fabricar banderitas chilenas para venderlas en los partidos de la selección nacional. Si se demora 1 hora en hacer 45 banderitas y trabaja 5 horas diarias. ¿Cuántos días se demorará en fabricar 1800 banderitas?
Answer:
[tex]\large \boxed{\text{Eight days}}[/tex]
Step-by-step explanation:
1. Calculate the hours
[tex]\text{Hours} = \text{1800 flags} \times \dfrac{\text{1 h}}{\text{45 flags}} = \textbf{40 h}[/tex]
2. Calculate the days
[tex]\text{Days} = \text{40 h} \times \dfrac{\text{1 da}}{\text{5 h}} = \text{8 da}\\\\\text{It will take $\large \boxed{\textbf{eight days}}$ to make 4500 flags.}[/tex]
PLEASE ANSWER FAST I WILL MARK BRAINLEIST AMD 20 POINTSBased on the figure below what is the value of X
Answer:
[tex]\boxed{9}[/tex]
Step-by-step explanation:
The two angles are complementary to each other.
That means they add up to 90 degrees.
[tex]5x+15+30=90[/tex]
[tex]5x+45=90[/tex]
[tex]5x=45[/tex]
[tex]x=9[/tex]
Answer:
x = 9
Step-by-step explanation:
So you know that the total is 90 degrees.
What you need to do is create an equation.
5x + 15 + 30 = 90
Then, solve the equation like this.
5x + 15 + 30 = 90
5x + 45 = 90
5x = 90 - 45
5x = 45
x = 45 ÷ 5
x = 9
Hope this helps! :)
find the slope of a line that is perpendicular to the line y= - 1/3x+7
the slope of the line is 3
Help thank you!!!!!!!
[tex] v = \sqrt{4900} + \sqrt{8100} = 70 + 90 = 160[/tex]
Answer: D. 160
The measure of minor arc JL is 60°. Circle M is shown. Line segments M J and M L are radii. Tangents J K and L K intersect at point K outside of the circle. Arc J L is 60 degrees. What is the measure of angle JKL? 110° 120° 130° 140°
Answer:
angle JKL = 120 degrees
Step-by-step explanation:
Since arc JL is 60 degrees, the central angle is also 60 degrees.
Point K is the intersection of tanges at J and L, therefore KJM and KLM are 90 degrees.
Consider quadrilateral JKLM whose sum of internal angles = 360.
Therefore
angle JKL + angle KLM + angle LMJ + angle MJK = 360 degrees
angle JKL + 90 + 60 + 90 = 360
angle JKL = 360 - 90 - 60 -90 = 120 degrees
Answer:
120 degrees
Step-by-step explanation:
Since arc JL is 60 degrees, the central angle is also 60 degrees.
Point K is the intersection of tanges at J and L, therefore KJM and KLM are complementary or equal 90 degrees.
look at quadrilateral JKLM whose sum of internal angles = 360.
Therefore
angle JKL plus angle KLM plus angle LMJ plus angle MJK = 360 degrees
angle JKL + 90 + 60 + 90 = 360
Find the value of the chi-square test statistic for the goodness-of-fit test. You wish to test the claim that a die is fair. You roll it 48 times with the following results. Number 1 2 3 4 5 6Frequency 5 10 12 9 4 8Observed frequency (O) 5,10,12,9,4,8Expected frequency (E) 8,8,8,8,8,8What is the value of the 2 test statistic?a. X2 = 3.538b. X2 = 4.182c. X2 = 5.75d. X2 = 7.667
Answer:
The value of Chi-square test statistic is χ² = 5.75.
Step-by-step explanation:
The Chi-square Goodness of fit test will be used to determine whether the die is fair or not.
The hypothesis can be defined as follows:
H₀: The die is fair.
Hₐ: The die is not fair.
The Chi-square test statistic is given by:
[tex]\chi^{2}=\sum\limits^{n}_{i=1}{\frac{(O_{i}-E_{i})^{2}}{E_{i}}}[/tex]
Consider the table attached below.
The value of Chi-square test statistic is χ² = 5.75.
Professor Easy's final examination has 9 true-false questions followed by 3 multiple-choice questions. In each of the multiple-choice questions, you must select the correct answer from a list of five. How many answer sheets are possible? choices
Answer: 2⁹5³ = 64,000
Step-by-step explanation:
There are 9 questions with 2 options (true or false) = 2⁹
There are 3 multiple questions with 5 options = 5³
true/false questions AND multiple choice questions
2⁹ x 5³ = 2⁹5³
Safegate Foods, Inc., is redesigning the checkout lanes in its supermarkets throughout the country and is considering two designs. Tests on customer checkout times conducted in two stores where the two new systems have been installed result in the following summary of the data: System A System B Size 120 100 mean 4.1 minutes 3.4 minutes Standard Deviation 2.2 minutes 1.5 minutes Test at the 0.05 level of significance to determine whether the population mean checkout times of the two systems differ. Which system is preferred?
Use both the critical and p-value approach.
Hypotheses:
Decision rule:
Calculations:
Conclusions:
Answer:
the answer would be calculations
Step-by-step explanation:
because they have do determine if the check out times differ between the two systems so they need to calculate the difference between the two
Find the slope of the line passing through the points (8,-4) and (4, -8).
Answer:
1
Step-by-step explanation:
We can find the slope using
m= ( y2-y1)/(x2-x1)
= ( -8 - -4)/( 4 - 8)
= ( -8 +4)/( 4 - 8)
= -4 / -4
= 1
Answer:
slope equals 1
Step-by-step explanation:
To do this you would need to do an equation that is [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex] so in this case -8 would be y2 and -4 would be y1 and 4 would be x2 and 8 would b e x1 so if you plug it into the equation we would get [tex]\frac{-8-(-4)}{4-8}[/tex] and if we simplify we get [tex]\frac{-4}{-4}[/tex] which simplifies to 1 so the slope would equal 1
Which is the simplified form of m Superscript negative 8 p Superscript 0? StartFraction 1 Over m Superscript 8 Baseline p EndFraction StartFraction 1 Over m Superscript 8 EndFraction StartFraction p over m Superscript 8 EndFraction m Superscript 8 PLS HELPP
Answer:
Correct Option is : StartFraction 1 Over m Superscript 8 EndFraction
Step-by-step explanation:
=> [tex]m^{-8} p^0[/tex]
According to law of exponents [tex]a^0 = 1[/tex]
=> [tex]m^{-8} (1)[/tex]
Using Law of exponents [tex]a^{-m} = \frac{1}{a^m}[/tex]
=> [tex]\frac{1}{m^8}[/tex]
The simplified form of [tex]m^{-8}p^0[/tex] is [tex]\frac{1}{m^8}[/tex].
The question is not well formatted the question might be as follows:
Which is the simplified form of [tex]m^{-8}p^0[/tex]?
[tex]\frac{1}{m^8p}[/tex][tex]\frac{1}{m^8}[/tex][tex]\frac{p}{m^8}[/tex]m⁸What are exponents?Exponents are numbers that say how many times a number is to be multiplied. For example, 2⁸ means 2 is multiplied 8 times.
How to solve the problem?[tex]m^{-8}p^0[/tex] = [tex]m^{-8}[/tex] since, p⁰=1.
⇒[tex]m^{-8}[/tex] = [tex]\frac{1}{m^8}[/tex] .
Hence, the simplified form of [tex]m^{-8}p^0[/tex] is [tex]\frac{1}{m^8}[/tex].
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The top and bottom margins of a poster are each 9 cm and the side margins are each 6 cm. If the area of the printed material on the poster is fixed at 864 cm2, find the dimensions of the poster with the smallest area.
Answer:
the dimensions of the poster with the smallest area is 36cm by 54cm
Step-by-step explanation:
✓Let us represent the WIDTH of the printed material on the poster as "x"
✓Let us represent the HEIGHT of the printed material on the poster as "y"
✓ The given AREA is given as 864 cm2
Then we have
864 cm2= xy ...................eqn(1)
We can make "y" subject of the formula.
y= 864/x .......................eqn(2)
✓The total height the big poster which includes the 9cm margin that is at the bottom as well as the top is
(y+18)
✓The total width of the poster which includes the 6cm margin that is at the bottom as well as the top is
(x+12)
✓Then AREA OF THE TOTAL poster
A= (y+18)(x+12) ...................eqn(3)
Substitute eqn (2) into eqn(3)
A= ( 18+ 864/x)(x+12)
We can now simplify by opening the bracket, as
A=18x +1080 +10368/x
A= 18x +10368/x +1080
Let us find the first derivative of A which is A'
A'= 18-(10368/x²)
If we set A' =0
Then
0= 18- (10368/x²)
18= (10368/x²)
x²= 10368/18
x²= 576
x=√576
x=24
The second derivatives will be A"= 2(10368)/x³ and this will be positive for x> 0, and here A is concave up and x=24 is can be regarded as a minimum
The value of "y" when x=24 can now be be calculated using eqn(2)
y= 864/x
y= 864/24
y=36cm
✓The total width of the poster= (x+12)
= 24+12=36cm
✓The total height big the poster= (y+18)=36+18=54cm
the dimensions of the poster with the smallest area is 36cm by 54cm
Answer:
The total width of the paper [tex]=36 cm.[/tex]
The total height of the paper [tex]=54cm[/tex]
Step-by-step explanation:
Given information:
Top margin of the paper = 9 [tex]cm\\[/tex]
Bottom margin of the paper = 6 [tex]cm\\[/tex]
Area of the printed material = [tex]864[/tex] [tex]cm^2[/tex]
Let, the width of the printed material = [tex]x[/tex]
And the height of the printed material = [tex]y[/tex]
So, Area [tex]x \times y=864[/tex] [tex]cm^2[/tex]
After including margins;
Width of the paper [tex]= (x+12)[/tex]
Height of the paper [tex]= (y+18)[/tex]
Area [tex](A) = (y+18) (x+12)[/tex]
[tex]A=18x+(10368/x)+1080\\[/tex]
Take first derivative:
[tex]A'= 18- (10368/x^2)[/tex]
When [tex]A'=0[/tex]
Then,
[tex]18-(10368/x^2)=0\\x^2=576\\x=24[/tex]
Now ,when we take second derivative and check if it is positive or not ,
We find that it is grater than zero so the obtained value can be consider as minimum and can be proceed for further solution.
Hence ,
[tex]x \times y=864\\y=864/24\\y=36\\[/tex]
Now ,
The total width of the paper
[tex]= 24+12\\=36 cm.[/tex]
And , total height of the paper
[tex]=36+18\\=54 cm.[/tex]
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Select the type of equations. Consistent. Equivalent. Inconsistent
Answer:
Consistent.
Step-by-step explanation:
Since there is one solution ( the lines intersect), the equations are consistent
They would be inconsistent if the lines do not intersect
The would be equivalent if they are the same line
The answer would be consistent.
Step-by-step explanation:
In the graph shown here, there is only one solution
because the lines intersect at the point (5, 3).
In order for the lines to be inconsistent, the lines would have to not
meet or intersect each other but notice that this is not the case here.
The would be equivalent if they are the same exact line
so it would look like there would just be one line.