Using the given data, the equation of the regression line is y=7.033+0.683x.
What is equation?An equation is a mathematical statement that two expressions are equal. It is composed of two expressions, one on either side of an "equals" sign. Equations can be used to solve problems and express relationships between different quantities. Equations can also provide insights into the behavior of a system. Equations are an essential part of mathematics and are used in almost all areas of science.
To determine if the regression equation is appropriate for making predictions at the 0.05 level of significance, a t-test must be performed. The t-statistic associated with the slope is 3.521 and is significant at the 0.01 level of significance (p-value < 0.01). Therefore, the regression equation is appropriate for making predictions at the 0.05 level of significance.
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The regression line's equation for the provided data is y=7.033+0.683x.
What is equation?
A mathematical equation is a declaration that two expressions are equal. Two expressions make up this phrase, one on either side of the equals sign. Equations are a useful tool for problem-solving and expressing relationships between various quantities.
A t-test must be carried out to see if the regression equation is suitable for making predictions at the 0.05 level of significance. At the 0.01 level of significance, the slope's t-statistic of 3.521 is significant (p-value < 0.01). Hence, at the 0.05 level of significance, predictions can be made using the regression equation.
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Select the correct answer. What is this expression in simplified form? √32 . 5√2
Answer: The answer is 40
Explanation: The picture
Nancy has twice as many apples as jay. Jay has 3 more apples than Ava. Nancy has 22 apples. How many apples dose Ava have?
Answer:
Step-by-step explanation:
nancy: 22
jay: 11 cause nancy has twice as many apples as jay.
ava has 8 apples cause jay has 3 more apples than ava :)
6(t+2) I need work to be shown
Answer:
6t + 12
Step-by-step explanation:
6(t+2)
= 6t + 12
So, the answer is 6t + 12
(write the slope-intercept form of the equation of each line) helllpppppp- pls-
Answer:
(-1,0) and (0, 4)
Step-by-step explanation:
The x and y intercept of a function (say the x intercept), is when y = 0 and vice versa.
The x intercept in this function is when y = 0
Thus,
4x-0=-4
4x = -4
x = -1.
So the x- intercept point = (-1, 0)
Similarly,
4(0)-y= -4
(x is equated to 0 to find the y - intercept)
-y = -4
∴ y = 4
y- intercept point = (0, 4)
Hope this helps! :)
6. andrew is flipping over the cards in a standard 52-card deck. he continues until he has revealed an ace. what is the probability that no face card has been revealed? what is the expected number of face cards he has revealed?
The probability that no face card has been revealed is 1/3.
The expected number of face cards he has revealed is 12.
Probability is the branch of mathematics that deals with uncertainty. When a fair die is rolled, there are 6 possible outcomes. A deck of 52 cards has 13 ranks of four suits each. These suits are spades, clubs, hearts, and diamonds. A standard deck of cards contains 26 red cards and 26 black cards.
There are four aces in a deck of 52 cards. The probability of obtaining an ace on the first attempt is
4/52 ⇒ 1/13 ⇒ 0.0769.
The probability of not getting an ace on the first try is
48/52 ⇒ 12/13 ⇒ 0.9231.
The second attempt at drawing an ace is conditional on the first attempt.
If the first attempt results in not getting an ace, the probability of getting an ace on the second attempt are 4/51.
If the first attempt is unsuccessful, the probability of not getting an ace on the second attempt is 47/51.
The probability of getting an ace on the third attempt, after the first two attempts have failed, is 4/50.
The probability of not getting an ace on the third attempt is 46/50. And so on...
The probability of not revealing any face card is 16/48 = 1/3 because there are 16 non-face cards in the deck.
The expected number of face cards he has revealed is 12, and the expected number of non-face cards he has revealed is 40.
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A carpenter has a piece of plywood whose area is 20ft2. He cuts out a 0.75ft2 notch and a 3.25ft2 hole in the plywood.
What is the sum?
13.5
15.0
16.0
The tοtal area οf the plywοοd after cutting οut the nοtch and hοle is 16ft²
Define the term area?Area is the measure οf a regiοn's size οn a surface. The area οf a plane regiοn οr plane area refers tο the area οf a shape οr planar lamina, while surface area refers tο the area οf an οpen surface οr the bοundary οf a three-dimensiοnal οbject.
Area can be understοοd as the amοunt οf material with a given thickness that wοuld be necessary tο fashiοn a mοdel οf the shape, οr the amοunt οf paint necessary tο cοver the surface with a single cοat
Area is a measure οf the amοunt οf space inside a 2-dimensiοnal shape οr regiοn, typically expressed in square units such as square inches, square feet, οr square meters.
Tο find the tοtal area οf the plywοοd after cutting οut the nοtch and hοle, we need tο subtract their areas frοm the οriginal area:
Tοtal area = 20ft² - 0.75ft² + 3.25ft²
Tοtal area = 16ft²
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an urn consists of 20 red balls and 30 green balls. we choose 10 balls at random from the urn (without replacement). what is the probability that there will be exactly 4 red balls among the chosen balls?
The probability of selecting exactly 4 red balls from an urn with 20 red balls and 30 green balls is given by the formula P(X=4) = (20C4)(30C6) / (50C10) where X is the number of red balls chosen. This simplifies to P(X=4) = 0.2032.
One day, David hands out flyers to 7 people. The next day, each person copies the flyer and hands them out to 7 people. The following day, these people copy their flyer and hand them out to 7 people.
How many people now have flyers?
THE ANSWER IS 343
The total number of people with flyers after 3 days of copying and distributing them is 343, which can be calculated using the formula P = 7^n, where P is the total number of people with flyers and n is the number of times the flyers are copied and distributed.
The formula for this problem is P = 7^n where P is the total number of people with flyers and n is the number of times the flyers are copied and distributed.
In this problem, n = 3 as the flyers were distributed on three separate days.
Therefore, P = 7^3 = 343
The calculation can be shown as follows:
1st day: 7 people receive the flyer
2nd day: 7 x 7 = 49 people receive the flyer
3rd day: 49 x 7 = 343 people receive the flyer
Therefore, the total number of people with flyers after 3 days is 343.
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What is a counter example to the conditional statement? If an odd number is greater than 1 and less than 10, then it has no other factors than 1 and its self
The factors of 9 are 1 and 9.. To determine this, one can use the formula to find the factors of a number, which is n = a × b.
A counter example to the conditional statement "If an odd number is greater than 1 and less than 10, then it has no other factors than 1 and its self" would be the number 9. 9 is an odd number that is greater than 1 and less than 10, but it has other factors than 1 and itself. The factors of 9 are 1, 3, and 9. To determine this, one can use the formula to find the factors of a number, which is n = a × b, where n is the number, a is the first factor, and b is the second factor. In this case, n = 9, a = 1, and b = 9. Therefore, the factors of 9 are 1 and 9.
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Please ASAP Help
Will mark brainlest due at 12:00
Answer:
(0,-2)
Step-by-step explanation:
Which segment is perpendicular to DE?
C. DF
a. AB
d. EF
b. CF
The required perpendicular segment to DE is EF.
What is perpendicular?In simple geometry, two geometric objects are perpendicular if the intersection at the place of intersection known as a foot results in right angles. The perpendicular symbol can be used to graphically depict the condition of perpendicularity.
According to question:In the given diagram we can see that segment DE and EF.
So, we can say that,
Segment DE is perpendicular to segment EF.
Thus, required perpendicular segment to DE is EF.
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Complete question:
Put the function y=-8x(x+6) in factored form f(x)=
a(x-r)(x-s) and state the values of a,r, and s. Assume
r_
The factored form of the function y = -8x(x + 6) is f(x) = -8(x + 3)(x - 3). The values of a, r, and s are -8, -3, and 3, respectively.
To put the function y = -8x(x + 6) in factored form f(x) = a(x - r)(x - s), the values of a, r, and s have to be identified. The step-by-step explanation is given below.Step 1: The given function is y = -8x(x + 6).Step 2: To write it in the factored form f(x) = a(x - r)(x - s), let us first multiply -8 by 6, which gives -48.Step 3: We now have y = -8x(x + 6) = -8x² - 48x.Step 4: Rearranging it, we get y = -8x² - 48x.Step 5: Factoring out -8 from both the terms, we get y = -8(x² + 6x).Step 6: Next, add (6/2)² = 9 to both the sides to make the expression a perfect square. y + 72 = -8(x² + 6x + 9).Step 7: The right side of the equation is now a perfect square. It can be written as y + 72 = -8(x + 3)². (x + 3)² = x² + 6x + 9Step 8: Simplifying, we get y = -8(x + 3)² - 72.Step 9: The function y in factored form is f(x) = -8(x + 3)² - 72. Here, a = -8 and r = -3. Since the function is in the form f(x) = a(x - r)(x - s), we can find s by dividing -72 by -8 and adding r to the quotient. That is, s = (-72/-8) - 3 = 6 - 3 = 3. Therefore, the factored form of the function y = -8x(x + 6) is f(x) = -8(x + 3)(x - 3). The values of a, r, and s are -8, -3, and 3, respectively.
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Create a rational expression that simplifies to 2x/(x+1)
and that has the following restrictions on x:
x ≠ −1, 0, 2, 3. Write your expression here.
-Contains multiplication of two rational
expressions
-Contains division of two rational expressions
Answer:
One possible expression that meets the given requirements is:
(2x)/(x+1) = (2x/[(x-2)(x-3)]) / ([(x+1)/(x-2)(x-3)])
This expression simplifies to 2x/(x+1) when x is not equal to -1, 0, 2, or 3, as required.
Explanation: We can rewrite 2x/(x+1) as (2x/(x-2)(x-3)) * ((x-2)(x-3)/(x+1)). The first term in this expression is a division of two rational expressions, while the second term is a multiplication of two rational expressions. Then, we can simplify the first term by cancelling the (x-2)(x-3) terms in the numerator and denominator, which gives 2x/[(x-2)(x-3)]. We can also simplify the second term by expanding the denominator, which gives (x-2)(x-3)/(x-2)(x-3)(x+1) = 1/[(x-2)(x-3)] * 1/(x+1). Then, we can combine the two simplified terms to get the expression given above.
Step-by-step explanation:
Rebecca buys some scarves that cost $5 each and 2 purses that cost $12 each. The cost of Rebecca’s total purchase is $39. What equation can be used to find n, the number of scarves that Rebecca buys?
1.5 + 24n = 39
2.5n + 24 = 39
3.(24 + 5) n = 39
4.24 + n = 39
The equation [tex]24 + n = 39[/tex] may be used to get n, the quantity of scarves Rebecca purchases.
What sort of equation would that be?The concept of an equation in algebra is a logical statement that demonstrates the equality of two mathematical equations. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
What does a basic equation mean?A formula that describes how contain a copy on either sides of a symbol are connected. It typically has an equal sign and one variable. The variable x is included in the preceding example.
The cost of one scarf is $[tex]5[/tex]
The cost of one purse is $[tex]12[/tex]
Rebecca buys 2 purses, so the cost of the purses is [tex]2*12=24[/tex]
The total cost of the purchase is $[tex]39[/tex]
[tex]Total cost = Cost of scarves + Cost of purses[/tex]
[tex]39 = 5n + 24[/tex]
Now we can solve n,
[tex]39 - 24 = 5n[/tex]
[tex]15 = 5n[/tex]
[tex]n = \frac{15}{5}[/tex]
[tex]n=3[/tex]
Therefore, Rebecca buys [tex]3[/tex] scarves.
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What is the best prediction for the number of times the spinner will not land on an elephant?
We might estimate that 0.8n is the approximate prediction number of times it won't land on the elephant.
We need to know the likelihood that the spinner will land on an elephant as well as the total number of spins in order to anticipate the number of times it won't.
Assume the spinner contains five equal parts, one of which is decorated with an elephant. The likelihood of the spinner touching the elephant is then 1/5, or 0.2.
If we know the total number of spins, we can use the likelihood that the spinner will fall on an elephant to calculate the likelihood that it won't. 1 - 0.2 = 0.8 is the probability that the spinner will miss the elephant.
Hence, if we suppose that the spinner is spun n times, we may estimate that 0.8n is the approximate number of times it won't land on the elephant. The prediction of probability of the spinner landing on the elephant is assumed to be constant for each spin and that each spin is independent of the others.
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select all statements that are true. assume that is smooth function in a neighborhood around and that all the difference points are contained in that neighborhood. and are the forward and backward finite differences, respectively.
There are several statements that are true when it comes to a smooth function in a neighborhood around a point and the forward and backward finite differences.
The true statements are:
1) The forward finite difference is the difference between the function value at a point and the function value at the next point.
2) The backward finite difference is the difference between the function value at a point and the function value at the previous point.
3) The forward and backward finite differences can be used to approximate the derivative of a function at a point.
4) The forward and backward finite differences are both equal to the slope of the tangent line to the function at the point.
5) The forward and backward finite differences are both equal to the derivative of the function at the point.
Therefore, the true statements are "The forward finite difference is the difference between the function value at a point and the function value at the next point.", "The backward finite difference is the difference between the function value at a point and the function value at the previous point.",
"The forward and backward finite differences can be used to approximate the derivative of a function at a point.", "The forward and backward finite differences are both equal to the slope of the tangent line to the function at the point.", and "The forward and backward finite differences are both equal to the derivative of the function at the point."
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HEEEELLLLLLLPPPPPP MEEEEEEEEEEEE PLS
1. 10-7 13. -4+(-7)
2. 5-(-9) 14. -5+5
3. -14-9 15. 13+(-1)
4. -2+(-1) 16. 14+(-1)
5. 12-(-12) 17. 9+(-5)
6. 9+(-3) 18. -3+4
7. 7-5 19. 7+(+2)
8. 9-(-7) 20. 15+(-7)
9. -16-(-8) 21. -5+(-5)
10. 3-5 22. -11. 4
11. -6+13 23. 26-(-1)
12. 8+(-3) 24. 7-(-4)
Answer:
Step-by-step explanation:
Simplify 10−7 to 3
3,13.−4−7
simplify 13.- 4 13. - 4
3,13.−11
What is the minimum number of rows of bricks needed to build a wall that is at least 4 feet tall if each brick is 2.25 inches tall?
Answer:
22 rows
Step-by-step explanation:
Divide 48 by 2.25 and round up
(09.01 LC)
The circle shown below has AB and BC as its tangents:
AB and BC are two tangents to a circle which intersect outside the circle at a point B.
If the measure of arc AC is 140°, what is the measure of angle ABC? (1 point)
The measure of angle ABC is: 20°
How to find the measure of the angle in the circle?Consider quadrilateral ABCO. The sum of all of the measures of all interior angles in the quadrilateral ABCO is equal to 360°.
The Lines given as BA and BC are seen to be tangent to the circle, and then this means that the radii OC and OA are perpendicular to the tangent lines BC and BA. Therefore,
m∠BCO=90°;
m∠BAO=90°.
The measure of the angle AOC is 160° (because the measure of arc AC is 140°). So,
m∠ABC + m∠BCO + m∠BAO + m∠AOC = 360°,
m∠ABC = 360° - (m∠BCO + m∠BAO + m∠AOC)
= 360° - (90° + 90° + 160°)
= 20°
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In a race, 29 out of the 50 swimmers finished in less than 39 minutes. What percent of swimmers finished the race in less than 39 minutes? Write an equivalent fraction to find the percent.
Answer:
percentage = (part/whole) x 100
where the "part" is the number of swimmers who finished in less than 39 minutes, and the "whole" is the total number of swimmers.
So, if 29 out of 50 swimmers finished in less than 39 minutes:
percentage = (29/50) x 100
percentage = 58
Therefore, 58% of swimmers finished the race in less than 39 minutes.
An equivalent fraction to represent 58% is 29/50.
Step-by-step explanation:
The function h is defined by the following rule.
h(x) = 4x+5
Complete the function table.
X
-5
0
3
4
5
X
0
0
0
0
5
Answer:
-15, 5, 17, 21, 25
Step-by-step explanation:
See attached worksheet.
Calculate each of the values of x on the table by using the number in place of the x in the equation.
h(x) = 4x + 5
h(-5) = 4*(-5) + 5
h(-5) = -15
===
h(3) = 4*(3)+5
h(3) = 12 + 5 or 17
==
Do the other values of x in the same manner to produce the attached table.
The volume of the cylinder?
Step-by-step explanation:
Volume of a cylinder = πr²h
[tex]\pi = 3.14[/tex]
[tex]r = \frac{d}{2} [/tex]
[tex]d = 14[/tex]
[tex]r = \frac{14}{2} [/tex]
[tex]r = 7[/tex]
[tex] {r}^{2} = 49[/tex]
[tex]h = 12[/tex]
substitute the formular with the values above
[tex]3.14 \times 7 \times7 \times 12 = 1846.32[/tex]
To one decimal place
[tex] = 1846.3[/tex]
Answer[tex]1846.3[/tex]
3. A yard plan includes a rectangular garden that is surrounded by bricks. In the drawing, the garden is 7 inches
by 4 inches. The length and width of the actual garden will be 35 times larger than the length and width in the
drawing.
(a) What is the perimeter of the drawing? Show your work.
(b) What is the perimeter of the actual garden? Show your work.
(c) What is the effect on the perimeter of the garden with the dimensions are multiplied by 35? Show
your work.
For the rectangle, the answers will be a. Perimeter=52 inches, b. Perimeter=770 inches and c. Perimeter will be multiplied by 35 also.
What exactly is a rectangle?
A rectangle is a four-sided flat shape with opposite sides that are parallel and equal in length. It is a type of quadrilateral, a polygon with four sides.
Now,
(a) The perimeter of the drawing is the sum of the lengths of all sides of the rectangular garden plus the lengths of the two bricks on the top and bottom and the lengths of the two bricks on the left and right.
The length of the garden in the drawing is 7 inches, and the width is 4 inches. Thus, the perimeter of the garden in the drawing is:
P = 2(7 inches) + 2(4 inches) = 14 inches + 8 inches = 22 inches
Since the garden is surrounded by bricks, we need to add the lengths of the two bricks on the top and bottom and the lengths of the two bricks on the left and right. Each brick has a length of 1 inch, so the total length of the bricks is:
2(1 inch + 7 inches + 1 inch) + 2(1 inch + 4 inches + 1 inch) = 2(9 inches) + 2(6 inches) = 18 inches + 12 inches = 30 inches
Therefore, the perimeter of the drawing is:
22 inches + 30 inches = 52 inches
(b) The actual garden is 35 times larger than the drawing, so its length is 35 × 7 inches = 245 inches, and its width is 35 × 4 inches = 140 inches. Thus, the perimeter of the actual garden is:
P = 2(245 inches) + 2(140 inches) = 490 inches + 280 inches = 770 inches
(c) When the dimensions of the garden are multiplied by 35, the perimeter of the garden is also multiplied by 35. This is because the perimeter is a linear function of the length and width of the garden. Therefore, the effect on the perimeter of the garden is to increase it by a factor of 35.
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If a vendor sells single roses for R1,20 each, he can sell 350 roses. However, he will sell three fewer roses for each 20c increase in the price. If the price is increased to R1,80 per rose, then the vendor's revenue (to the nearest cent) will be equal to
The vendor's revenue at a price of R1.80 per rose is R9.72
Let's assume that the vendor sells x roses at a price of p per rose.
According to the given condition, if he sells roses at R1.20 per rose, he can sell 350 roses. Hence, we can write:
350 = x - 3((p - 1.20)/0.20)
Simplifying the above equation, we get:
x = 3(p - 0.60) + 350
Now, if the price is increased to R1.80 per rose, the vendor's revenue will be:
Revenue = number of roses sold * price per rose
= (x - 3((1.80 - 1.20)/0.20)) * 1.80
= (x - 15) * 1.80
Substituting the value of x from the first equation, we get:
Revenue = (3(p - 0.60) + 350 - 15) * 1.80
= (3p - 0.30) * 1.80
Simplifying the above equation, we get:
Revenue = 5.4p - 0.54
Therefore, the vendor's revenue at a price of R1.80 per rose is given by the equation 5.4p - 0.54, where p is the price per rose in rands.
To find the vendor's revenue to the nearest cent, we need to substitute p = 1.80 in the above equation:
Revenue = 5.4(1.80) - 0.54
= R9.72 (approx.)
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Many students from Europe come to the United States for their college education.
From 1980 through 1990, the number S(in thousands), of European students
attending a college or university in the U. S. Can be modeled by
S=0. 05(t3 - 11ť + 45t +277), where t = Ocorresponds to 1980.
In what year were there 31. 35 thousand European students attended a U. S. College
or university?
we can use the cubic equation formula to solve for t. The answer is t=1988, which means that there were 31.35 thousand European students in 1988.
To solve this problem, we need to find the value of t that corresponds to 31.35 thousand European students. We can use the given equation S=0.05(t3-11t+45t+277) and solve it for t. To do this, we can first subtract 277 from both sides to get S-277=0.05(t3-11t+45t). Then, we can divide both sides by 0.05 to get (S-277)/0.05=t3-11t+45t. Finally, we can use the cubic equation formula to solve for t. The answer is t=1988, which means that there were 31.35 thousand European students in 1988.
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Slope models the direction and steepness of a line, while the y-intercept defines the starting point. Explain what following equation of a line represents y= -2/3x + 6.
can someone please answer and explain this problem to me?
The equation y = (-2/3)x + 6 represents a line that starts at the point (0, 6) on the y-axis and slopes downwards from left to right at a rate of 2 units down for every 3 units to the right.
What is co-ordinate geometry ?Coordinate geometry is a branch of mathematics that deals with the study of geometry using the principles of algebra. It involves using algebraic equations and geometric concepts to analyze shapes and figures in a plane or in higher dimensions.
According to given information:In this equation, -2/3 is the slope of the line, which tells us how steep the line is and in what direction it's heading. Specifically, a slope of -2/3 means that for every increase of 3 units in the x-direction, the y-value decreases by 2 units. So the line slopes downwards from left to right.
The 6 in the equation is the y-intercept of the line, which tells us where the line intersects the y-axis. Specifically, the y-intercept is the point (0, 6) on the line. This means that when x = 0, y = 6, so the line starts at the point (0, 6) on the y-axis.
Therefore, the equation y = (-2/3)x + 6 represents a line that starts at the point (0, 6) on the y-axis and slopes downwards from left to right at a rate of 2 units down for every 3 units to the right.
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The design of a digital box camera maximizes the volume while keeping the sum of the dimensions at 7 inches. If the length must be 1.1 times the height, what should each dimension be?
To optimise the volume while maintaining the total dimensions at 7 inches, the camera's dimensions should be roughly 3.01 inches besides 3.311 inches besides 0.679 inches.
What 3 dimensions do we have?
The homes we reside in and the items we use on a daily basis all have three dimensions: length, weigth, and breadth.
Let's start by assigning variables to the dimensions. Let x be the height of the camera, then the length must be 1.1 times the height, which gives us a length of 1.1x.
The width is not explicitly given, but we can express it in terms of x and 1.1x. Since the sum of the dimensions is 7 inches, we have:
x + 1.1x + w = 7
where w is the width of the camera. Simplifying this equation, we get:
2.1x + w = 7
w = 7 - 2.1x
Now we can express the volume of the camera in terms of x:
V = x(1.1x)(7 - 2.1x)
Simplifying this expression, we get:
V = 8.235x³ - 15.365x² + 7x
To find the maximum volume, we need to find the value of x that maximizes V. We can do this by taking the derivative of V with respect to x, and setting it equal to zero:
dV/dx = 24.705x² - 30.73x + 7 = 0
Using the quadratic formula, we can answer this quadratic equation:
x = (-b ± √(b² - 4ac)) / 2a
where a = 24.705, b = -30.73, and c = 7. Plugging in these values, we get:
x = 0.735 inches or x = 3.01 inches
Since x represents the height of the camera, we discard the smaller root and take x = 3.01 inches.
Then the length is 1.1 times the height, which gives us a length of 3.311 inches.
The width can be found using the equation w = 7 - 2.1x, which gives us w = 0.679 inches.
Therefore, the dimensions of the camera should be approximately 3.01 inches by 3.311 inches by 0.679 inches to maximize the volume while keeping the sum of the dimensions at 7 inches.
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Sid mows two laws the first one is 60 feet long and 59 feet wide the area of the second lawn is 3 times as big but has the same width as the first want is the length of the second lawn
The length of the second lawn that Sid mows is 60 feet. We simply calculated the area of lawn here.
The area of the first lawn is given by:
A1 = 60 x 50 = 3000 square feet
Let L2 be the length of the second lawn. Since the width of the second lawn is the same as the first lawn, the area of the second lawn can be expressed as:
A2 = L2 x 150
Since the area of the second lawn is 3 times as big as the first lawn, we have:
A2 = 3A1
Substituting A1 and simplifying, we get:
L2 x 150 = 3 x 3000
L2 x 150 = 9000
L2 = 60 feet
Therefore, the length of the second lawn is 60 feet.
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You drive 180 miles and your friend drives 150 miles in the same amount of time. Your
average speed is 10 miles per hour faster than your friend's speed. Write and use a
rational model to find each speed
Your speed is 60 miles per hour, when your friends average speed is 50 miles.
A reasonable model is what?A rational function, which is a function that can be represented as the ratio of two polynomials, is a function that may be used in a rational model, which is a mathematical model. Rates of change, growth or decay, and proportions are only a few examples of the many various kinds of real-world events that may be represented using rational models. In order to describe complicated systems or processes, they are frequently employed in disciplines like economics, physics, and engineering. To determine the values of the variables that make the equation true, rational models can be solved using algebraic techniques including factoring, simplification, and cross-multiplication.
Given that, average speed is 10 miles per hour faster than other person.
Then, your speed is = s + 10.
For 180 miles, and 150 miles for friend the equation can be set as:
180/(s+10) = 150/s
We can cross-multiply to simplify:
180s = 150(s+10)
180s = 150s + 1500
30s = 1500
s = 50
Substituting the value in s + 10 = 50 + 10 = 60.
Hence. your speed is 60 miles per hour.
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Alex wants to fence in an area for a dog park. he has plotted three sides of the fenced area at the points e (3, 5), f (6, 5), and g (9, 1). he has 22 units of fencing. where could alex place point h so that he does not have to buy more fencing? (0, 0) (−1, 0) (0, −3) (0, 3)
We found that he can only use approximately 7.39 units of fencing for the fourth side. The possible locations for point H are (4.5, 12.39) and (4.5, -2.39).
To determine where Alex could place point H, we need to first calculate the length of the three sides of the fenced area that he has already plotted. We can do this using the distance formula:
Distance [tex]= \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
From point E to point F:
Distance = [tex]\sqrt{(6-3)^2 + (5-5)^2}[/tex]
= 3 units
From point F to point G:
distance = [tex]\sqrt{(9-6)^2 + (1-5)^2)}[/tex]
= [tex]\sqrt{(9 + 16)}[/tex]
= 5 units
From point G to point E:
Distance = [tex]\sqrt{(3-9)^2 + (5-1)^2}[/tex]
= [tex]\sqrt{(36 + 16)}[/tex]
= [tex]\sqrt{(52)[/tex]
= [tex]2 \sqrt{(13)}[/tex] units
Therefore, the total length of fencing that Alex has already plotted is 3 + 5 + 2√13 = approximately 14.61 units.
To find the possible x-coordinate(s) of point H, we can use the formula for the distance between two points on the coordinate plane:
distance = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
For point H to be 7.39 units away from the midpoint of side EF (4.5, 5), we have:
[tex]\sqrt{(x - 4.5)^2 + (y - 5)^2}[/tex]
= 7.39
Squaring both sides and simplifying gives:
(x - 4.5)² + (y - 5)²= 7.39²
Since we know that x=4.5, we can substitute this value into the equation and solve for y:
(4.5 - 4.5)²+ (y - 5)² = 7.39²
(y - 5)² = 7.39²
y - 5 = ±7.39
y = 5 ± 7.39
So the possible locations for point H are (4.5, 5+7.39) and (4.5, 5-7.39), which correspond to the points (4.5, 12.39)
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