A box with an open top is to be constructed from a 15 inch by 24 inch piece of cardboard by cutting squares of equal sides from the corners and folding up the sides. Find the dimensions of the box of the largest volume that can be constructed.

Answers

Answer 1

The dimensions of the box of the largest volume that can be constructed are

D=18,9,3

What are the dimensions?

Generally, the equation for the lenght is  mathematically given as

Lenght=(24-2x)

Widht= (15-2x)

Therefore

Volume =L*B*H

V=(24-2x)(15-2x)x

V=(360-48x-30x+4x)x

V=4x^3-78x^2+360x

Differnciating we have

dv/dx=12x^2-156x+360

put dv/dx=0

12(x^2-13x+30)=0

x^2-10x-3x+30=0

(x-10)(x-3)=0

root=10,3

Second diiferciation

d^v/dx^2=24x-156

[tex]lim _{x=3} =-84 < 0[/tex]

In conclusion,

L=24-2x

L=24-2x3

L=18in

w= 15-2x

w=15-2*3

w=9in

h=x

h=2in

Dimension=18,9,3

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Related Questions

Find the coefficient of determination, given that the value of the linear correlation coefficient, r, is –0.721.

Answers

The coefficient of determination is calculated as: 0.520.

How to Find the Coefficient of Determination?

The coefficient of determination = the square of the correlation coefficient.

Given the following:

Value of the linear correlation coefficient (r) = -0.721

Therefore, we would have:

The coefficient of determination = (-0.721)²

The coefficient of determination = 0.520

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Which diagram represents rx ◦ RO,180°?

Answers

Answer:

if this is for edge unity the answer is B

Will give brainliest

A radioactive element has a half-life of 55 days. what percentage of the original sample is left after 115 days? round to 4 decimals when necessary.

Answers

The percentage of the radioactive isotope left is 25.0000%.

What is the half life?

The half life of a radioactive isotope is the time that will elapse before only half of the number of original isotopes will remain.

Now;

We are told that;

Half life (t1/2) = 55 days

Time taken (t) =  115 days

Ratio of isotope remaining = N/No

Thus;

N/No = (1/2)^t/t1/2

N/No = (1/2)^115/55

N/No = (1/2)^2

N/No =1/4

Hence, the percentage = 1/4 * 100/1 = 25.0000%

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Solve the inequality and enter your solution as an inequality comparing the
variable to a number.
x+4>11

Answers

Answer:

⅝8⅝

Step-by-step explanation:

I made this with love and everything in the world of 9⁴⅝

Please help me with this on the picture

Answers

Answer:

5, 7

Step-by-step explanation:

The mode of the numbers is 5, which means that 5 should be the most common card (highest frequency). Therefore the cards should have at least one more 5 among them.

Considering that 5 is one of the hidden cards and x is the other,

• Using the equation for the mean:

[tex]mean = \frac{sum \space\ \space\ of \space\ \space\ numbers}{number \space\ \space\ of \space\ \space\ numbers}[/tex]

[tex]6 = \frac{4+5+ 9 + 5 + x}{5}[/tex]

⇒ [tex]30=23 + x[/tex]

⇒ [tex]x = 7[/tex]

This means 5 and 7 are the hidden cards.

From a group of 13 women and ​12 men, a researcher wants to randomly select 8 women and 8 men for a study. In how many ways can the study group be​ selected?

Answers

The total number of ways the study can be selected is: 637065

Given,

Total number of women in a group= 13

Total number of men in a group = 12

Number of women chosen = 8

Number of men chosen = 8

∴ the total number of ways the study group can be selected = 13C₈ and 12C₈.

This in the form of combination factor = nCr

                                                     ∴ nCr = n!/(n₋r)! r!

13C₈ = 13!/(13 ₋ 8)! 8!

        = 13!/5!.8!

        = 1287

12C₈ = 12!/(12₋8)! 8!

        = 12!/5! 8!

        = 495

Now multiply both the combinations of men and women

= 1287 × 495

= 637065

Hence the total number of ways the study group is selected is 637065

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Identify the segments that are parallel, if any angle ABC equals angle HCB

Answers

Answer: A. DC||AB

Step-by-step explanation:

Line DC is parallel to AB so the correct answer is option B.

What is the similarity?

If two objects are having the same shape then they will be termed as similar. So in mathematics, if two figures have the same shapes, lines or angles then they are called similar.

In the given image we can see that the two angles ABC and HCB are congruent to each other. So the line DC is parallel to AB.

Therefore Line DC is parallel to AB so the correct answer is option B.

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Peter analyzed a set of data with explanatory and response variables x and y. He concluded the mean and standard deviation for x as 7.8 and 3.70, respectively. He also concluded the mean and standard deviation for y as 12.2 and 4.15, respectively. The correlation was found to be 0.964. Select the correct slope and y-intercept for the least-squares line. Answer choices are rounded to the hundredths place.

Answers

The y-intercept is 3.78.

We have given that,

[tex]\overline{x}=7.8 ,S_x=3.70,\\\overline{y}= 12.2,S_y=4.15\\r=0.964[/tex]

What is the formula of the slope?

[tex]Slope=r \times\frac{S_y}{S_x} \\\\Slope=0.964\times \frac{4.15}{3.70}\\ Slope=1.08=\overline{y}-slope\:\times \overline{x}\ intercept\\=\overline{y}-slope\:\times \overline{x}\\=12.2-1.08(7.8)\\=3.78[/tex]

Therefore the y-intercept is 3.78.

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Melissa's mother asked her to buy a gallon of milk at the store. The store only had quarts of milk. How many quarts of milk does Melissa need to buy?

Answers

Answer:

4 quarts of milk

Step-by-step explanation:

4 quarts = 1 gallon

so, melissa needs to buy 4 quarts

can someone please help with part III?? don’t use my work it’s prob wrong lol :)

Answers

Answer: formula

AB= (-1- -3)+((3-1)

(-1+3 )^2+(3-1)^2

2^2+2^2

Sq rt of 8 is 2.83

length of AB is 2

BC= (-3- -1)^2 + (5-3)^2

-3+1 =-2^2+2^2=4+4=8

Sq rt of 8 is 2.828= 2.83

Step-by-step explanation:

In isosceles ∆ABC, points M and N belong to base
BC
so that BM = CN. Prove:

∆BAM ≅ ∆CAN
∆AMN is an isosceles triangle.

Answers

From the statements and reasons given below as regards the Isosceles Triangle, we have been able to prove that; ∆BAM ≅ ∆CAN

How to prove an Isosceles Triangle?

Isosceles Triangle means that two sides of the triangle are equal and also 2 angles are equal.

Now, we are told that triangle ABC is an Isosceles and as such, AB and AC are congruent.

We are given that BM and NC are congruent. Now, due to the fact that Triangle AMN is an isosceles triangle, it means that the sides AM and AN are congruent to each other.

Thus, from the proofs above and from the definition of the isosceles Triangle, we can say that triangles BAM and CAN are congruent.

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Answer & Step-by-step explanation:

To prove ∆BAM ≅ ∆CAN:

1. Given that ∆ABC is an isosceles triangle with base BC, and BM = CN, we know that AB = AC.

2. Using the Side-Angle-Side (SAS) congruence criterion, we can show that ∆ABM and ∆ACN are congruent.

3. Therefore, corresponding angles ∠BAM and ∠CAN are congruent.

4. Similarly, ∠BMA and ∠CNA are congruent.

5. By showing that corresponding angles in ∆ABM and ∆ACN are congruent, we can conclude that ∆BAM ≅ ∆CAN.

To prove ∆AMN is an isosceles triangle:

1. From the given information, we know that BM = CN.

2. By proving ∆BAM ≅ ∆CAN, we have shown that ∠BAM ≅ ∠CAN.

3. Since ∠BAM and ∠CAN are congruent, we can conclude that ∠BAN ≅ ∠CAM using the Transitive Property of Congruence.

4. By establishing that ∠BAN ≅ ∠CAM, we can conclude that ∆AMN is an isosceles triangle because it has two congruent angles.

If f(x) = 8- 10x and g(x) = 5x + 4, what is the value of (fg) (-2)?
O -196
O -168
O 22
O 78

Answers

F(g(x)) = 8-10(5x+4)
= 8-50x-40
= -50x-32
So F(g(-2)) = -50(-2)-32
= 100-32
= 68
I think the choices are wrong.

Select the expression that is modeled on the number line. A number line from zero to one partitioned into sixths. There are four hops beginning at one sixth and ending at five sixths.

Answers

The answer to the question that is modeled here is one sixth plus four sixths.

How to solve for the expression

We have the following fractions

1/6 and 5/6

We are to find the fraction which when added to 1/6 would give us 5/6. Hence we have

1/6 + 4/6 = 5/6

Hence the correct answer to the question here is option a.

complete question

PLS HELP 1HOUR LEFT Select the expression that is modeled on the number line. A number line from zero to one partitioned into sixths. There are four hops beginning at one sixth and ending at five sixths one sixth plus five sixths

one sixth plus four sixths

five sixths minus one sixth

five sixths minus four sixths

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Which expression is a non-real complex number?
-4 +√7
3
1 + √²
5-√15
27
28

Answers

The expression that represents a complex number is the one in the second option.

[tex]\frac{2}{3} + \sqrt{-\frac{27}{28} }= \frac{2}{3} + \sqrt{\frac{27}{28} } i\\[/tex]

Which expression is a non-real complex number?

Remember that the complex number i is given by:

[tex]i = \sqrt{-1}[/tex]

So we have complex numbers when we have negative arguments inside of square roots.

In this particular case, the only option with a negative argument on a square root is on the second option:

[tex]\frac{2}{3} + \sqrt{-\frac{27}{28} } \\\\\frac{2}{3} + \sqrt{-1} *\sqrt{\frac{27}{28} } \\\\\frac{2}{3} + \sqrt{\frac{27}{28} } i\\[/tex]

We conclude that the correct option is the second one.

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Answer:

(2)/(3)+\sqrt(-(27)/(28))

Step-by-step explanation:

Plato/Edmentum

A​ student's grade on the Fundamentals of Engineering exam has a​ z-score of 0.5. Make an observation about the​ student's grade.

Answers

The observation about the student's grade with the z score illustrated is that it's a half standard deviation above the mean of the total test score.

What is z score?

It should be noted that the z score is a numerical measurement which describes the relationship of a value to the mean value of the group.

In this case, the observation about the student's grade with the z score illustrated is that it's a half standard deviation above the mean of the total test score.

This is illustrated as the z score is 0.5.

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Find the value of x and y using the diagram below.​

Answers

[tex]\huge\underline{\red{A}\green{n}\blue{s}\purple{w}\pink{e}\orange{r} →}[/tex]

x = 2 , y = 3

Step-by-step explanation:

As the given figure is a rectangle, therefore the opposite sides should be equal. So -

3x + y = 12 – y...(eqn (i) )

and

y – x = x – 1...(eqn (ii) )

Solving eqn (ii) we get -

→ y – x = x – 1

→ y = x + x – 1

→ y = 2x – 1...eqn(iii)

Solving eqn (i) we get -

→ 3x + y = 12 – y

→ 3x = 12 – y – y

→ 3x = 12 – 2y

Substituting the value of eqn (iii)

→ 3x = 12 – 2(2x– 1)

→ 3x = 12 – 4x + 2

→ 3x + 4x = 14

→ 7x = 14

→ x = 14/7

→ x = 2

Hope it helps you!!

Answer:

x = 2; y = 3

Step-by-step explanation:

Since the quadrilateral has 4 right angles, it is a rectangle.

In a rectangle, opposite sides are congruent.

3x + y = 12 - y

x - 1 = y - x

We have a system of two equation is 2 variables.

Let's simplify both equations.

3x + 2y = 12

2x - y = 1

Rewrite the first equation. Multiply both sides of the second equation by 2. Add the equations.

      3x + 2y = 12

(+)   4x - 2y = 2

-------------------------

      7x        = 14

Divide both sides by 2.

x = 2

Substitute 2 for x in the second original equation and solve for y.

x - 1 = y - x

2 - 1 = y - 2

1 = y - 2

y = 3

Answer: x = 2; y = 3

Please solve this question

Answers

Answer:

a) 0.2098

b) 0.036

c) 0.1866

d) 0.9849

Step-by-step explanation:

Image is color coordinated for each part below,

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The surface area of an open-top box with length
L
, width
W
, and height
H
can be found using the formula:

A
=
2
L
H
+
2
W
H
+
L
W


Find the surface area of an open-top box with length 4 cm, width 8 cm, and height 5 cm.

Answers

Answer:

Surface Area is equal to 160 cm²

here is your answer

Solve the following equation for m.
F=mv^2 / r

Answers

Answer:

Step-by-step explanation:

F = [tex]\frac{mv^2}{r}[/tex]

mv² = Fr

m = [tex]\frac{Fr}{v^2}[/tex]

find the quotient: -10/9 divided by -5/7

Answers

Answer:

70/45

Step-by-step explanation:

(-10/9) divided by (-5/7)  = (-10/9) / (-5/7)

dividing two fractions is the same as multiplying the top fraction by the reciprocal of the bottom one

top fraction = -10/9

bottom fraction = -5/7

reciprocal just means switching the numerator and denominator

reciprocal of bottom fraction = 7 / -5 = -7/5

thus,

(-10/9) / (-5/7) = (-10/9) * reciprocal of (-5/7) = (-10/9) * (-7/5) = 70/45

note that to multiply two fractions, you just multiply the numerators to get your new numerator and do the same thing with the denominators

The equation of the line of best fit of a scatter plot is y = 6x − 9. What is the slope of the equation?

Answers

Answer:

  6

Step-by-step explanation:

The equation of the line is written in the slope-intercept form:

  y = mx +b

where m is the slope and b is the y-intercept.

Matching patterns

The given equation is ...

  y = 6x -9

Comparing this to the slope-intercept form, we see that ...

  m = 6

  b = -9

The slope of the line is m = 6.

2. For the following data, calculate the z-score. (5 points)
a. Sierra wishes to enroll her son in an exclusive academy. Her son must
score an 107 on their aptitude test in order to be accept. Calculate the z-
score for a score of 107 based on the data provided.
Score (Y) = 107
Mean = 95
Standard Deviation = 7.5
hint: Use the z-score formula to convert 107 into a z-score

Answers

The z-score for a score of 107 is 1.6

How to determine the z-score?

The given parameters are:

Score (Y) = 107Mean = 95Standard Deviation = 7.5

The z-score is calculated using:

[tex]z = \frac{x -\bar x}{\sigma}[/tex]

So, we have:

[tex]z = \frac{107 -95}{7.5}[/tex]

Evaluate the difference

[tex]z = \frac{12}{7.5}[/tex]

Divide

z = 1.6

Hence, the z-score is 1.6

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how do i find x?? whats the answer?

Answers

Through proportionality theorem.

Therfore [tex] \frac{ 11}{121} = \frac{10}{5x + 10} \\ \\ 11(5x + 10) = 121(10) \\ (5x + 10) = \frac{121(10)}{11} \\ 5x + 10 = 110 \\ 5x = 110 - 10 \\ 5x = 100 \\ \frac{5x}{5} = \frac{100}{5 } \\ x = 20cm[/tex]HOPE THIS HELPS!

Desperately need help. pls

Answers

By applying the concept of composition between two functions and utilizing the information given in the two tables, we find the following results: f ° g (0) = - 2, f ° g (x) = 1.

How to find the value of composition between two functions

Compositions are binary operators between two functions: f - Former function, g - Latter function.

f ° g (x)

Where the input of the former function is the output of the latter function. By a brief observation, we find the following relationships in accordance with the two tables:

Case I

f(x):

0 → 1

g(x):

1 → - 2

Case II

f(x):

1 → 0

g(x):

0 → 1

By applying the concept of composition between two functions and utilizing the information given in the two tables, we find the following results: f ° g (0) = - 2, f ° g (x) = 1.

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The cost of 25 apples is $18.50. What is the cost of one apple

Answers

Answer:

0. 74$

Step-by-step explanation:

$18. 50÷25=0. 74$

6) Simplify the following:
axaxbxb

Answers

The simplified expression of axaxbxb is a^2b^2

How to simplify the expression?

The expression is given as;

axaxbxb

Rewrite properly as:

a * a * b * b

Evaluate the product

a^2b^2

Hence, the simplified expression of axaxbxb is a^2b^2

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Find the value of x.

x = 2
x = 3
x = 33
x = 52

Answers

The answer is B.

x=3
yeah its i got it right x=3

While researching different companies, she discovers the following standard deviations of one year of daily stock closing prices.

Masterful Pocket Watches: Standard deviation of stock prices =$9.83
Eye Remember Enterprises: Standard deviation of stock prices =$1.15

Based on the data and assuming these trends continue, which company would give Donna a stable long-term investment?

a} eye remember enterprises; the smaller deviation indicates that eye enterprises have less variability in its closing prices than masterful pocket watches.

b}masterful pocket watches; the larger standard deviation indicates that masterful pocket watches have less variability in its closing prices than eye remember enterprises.

c} eye remember the enterprises; the smaller standard deviation indicates that eye remember enterprises has a greater mean closing price than masterful pocket watches.

d}masterful pocket watches; the larger standard deviation indicates that masterful pocket watches have a greater mean closing price than eye remember enterprises.

Answers

The data and assuming shows that the company that would give Donna a stable long-term investment is A. eye remember enterprises; the smaller deviation indicates that eye enterprises have less variability in its closing prices than masterful pocket watches.

How to illustrate the information?

It should be noted that the information given implies that Donna needs a stable long term investment.

In this case, it's appropriate that the company that has the less standard deviation should be chosen.

This illustrates that Perfect Plungers has less variability.

In conclusion, the correct option is A.

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Question 5 3 pts A corral for cattle is in the shape of a circle with a radius of 17.8 m; find the total area of the corral. Round your answer to the nearest whole number. Do not type the units in the space below.

Answers

Step-by-step explanation:

the area of s circle is

pi×r²

r being the radius.

so, in our case

pi×17.8² = pi×316.84 = 995.3822164... ≈ 995 m²

One of the tables shows a proportional relationship.
Use the points from this table to graph the line representing the proportional
relationship.
Line
10-
9
8-
7
5
4
3
2
-2-
3 7 4
-3-
Undo
1 2
3
4
Redo
$
6
x Reset
7 8 9 10
X
y
x
y
X
y
X
y
2
1
2
1
0
2
1
3
2
4
3
2
2
2
4
5
6
3
4
6
4
5
3
7
27
6
4
8
4
5
8
9
6

Answers

Answer:

See attached

Step-by-step explanation:

The graph of a proportional linear relationship is a line that passes through the origin (0, 0).

From inspection of the given tables, the linear equations for each table of points is:

Table 1:  y = x + 1Table 2:  y = x/2Table 3:  y = x + 2Table 4:  y = 2x + 1

The only equation for which y = 0 when x = 0 is y = x/2  →  Table 2.

Given points from Table 2:

(2, 1)(4, 2)(6, 3)(8, 4)

To graph the line, plot the given points and draw a line through them (see attached).

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