Can somebody help me me with this math question?

Answer:

Base Side Length =1.59m

Height = 3.16 m

Step-by-step explanation:

Volume of the box = [tex]8$ m^3[/tex]

Let the base dimensions = x and y

Let the height of the box =h

However, for any optimal configuration, Width = Length as varying the length and width to be other than equal reduces the volume for the same total(w+l)

Volume, V=xyh=8

Since x=y

[tex]h=\dfrac{8}{x^2}[/tex]

Surface Area of the box

[tex]= 2(x^2+xh+xh)\\=2x^2+4xh[/tex]

The material for the top and bottom costs twice as much as the material for the sides.

Let the cost of the sides =$1 per square meter

Cost of the material for the sides = 4xh

Cost of the material for the top and bottom = [tex]=2*2x^2=4x^2[/tex]

Therefore:

Total Cost, [tex]C= 4xh+4x^2[/tex]

Substitution of  [tex]h=\frac{8}{x^2}[/tex]  into C

[tex]C= 4x(\frac{8}{x^2})+4x^2\\=\frac{32}{x}+4x^2\\C(x)=\dfrac{4x^3+32}{x}[/tex]

To minimize C(x), we find its derivative and solve for the critical points.

[tex]C'(x)=\dfrac{8x^3-32}{x^2}\\$Setting C'(x) to zero\\8x^3-32=0\\8x^3=32\\x^3=4\\x=\sqrt[3]{4}\\ x=1.59$ m[/tex]

To verify if it is a minimum, we use the second derivative test

[tex]C''(x)=8+\frac{64}{x^3}\\C''(1.59)=23.92[/tex]

Since C''(x) is greater than zero, it is a minimum point.

Recall:

[tex]h=\frac{8}{x^2}\\h=\frac{8}{1.59^2}=3.16$ m[/tex]

Therefore, the dimensions that minimizes the cost are:

Base Side Lengths of 1.59m; and

Height of 3.16 m

Answer:

speed of slower driver 30 mph

speed of faster driver = 55 mph

Step-by-step explanation:

let the speed of slower driver b x mph

given

One driver drives 25 mph faster than another driver does

Speed of faster driver = (x+25) mph

we know time = speed / distance

also in same time faster will travel more distance than the slower one.

thus

driver with speed  (x+25) mph would have traveled 165 miles

driver with speed  x mph would have traveled 90 miles

time for driver with speed  (x+25) mph = 165/(x+25)

time for driver with speed  x mph = 90/x

Given that

They start at the same time and after a certain amount of time, one driver has driven 90 miles, and the other driver has driven 165 miles.

\time for driver with speed  (x+25) mph =time for driver with speed  x mph

165/(x+25) = 90/x

165x = 90(x+25)

=> 165x = 90x + 2250

=> 165x -90x = 2250

=> 75x = 2250

=> x = 2250/75= 30

Thus, speed of slower driver 30 mph

speed of faster driver = 30+25 = 55 mph

Answer:

  x ≈ 8.37819064728

Step-by-step explanation:

Maybe you want to solve for x.

  [tex]\dfrac{x-4}{x-3}=\dfrac{2x^2-6}{x^2+2x-3}-\dfrac{x-1}{x+1}=\dfrac{2(x^2-3)}{(x-1)(x+3)}-\dfrac{x-1}{x+1}\\\\\dfrac{x-4}{x-3}=\dfrac{2(x^2-3)(x+1)}{(x-1)(x+3)(x+1)}-\dfrac{(x-1)(x-1)(x+3)}{(x+1)(x-1)(x+3)}\\\\\dfrac{x-4}{x-3}=\dfrac{(2x^3+2x^2-6x-6)-(x^3+x^2-5x+3)}{(x^2-1)(x+3)}\\\\\dfrac{(x^2-1)(x+3)(x-4)}{(x^2-1)(x+3)(x-3)}=\dfrac{(x^3+x^2-x-9)(x-3)}{(x^2-1)(x+3)(x-3)}\\\\\dfrac{x^4-x^3-13x^2+x+12}{(x^2-1)(x^2-9)}=\dfrac{x^4-2x^3-4x^2-6x+27}{(x^2-1)(x^2-9)}\\\\\dfrac{x^3-9x^2+7x-15}{(x^2-1)(x^2-9)}=0[/tex]

A graphing calculator shows the numerator cubic to have one real irrational zero near x ≈ 8.37819064728.

Answer:

Only 1 because you can only have 3 favourite desserts.

Answer:

Only 1 desert :)

Step-by-step explanation:

Answer:

True.

Step-by-step explanation:

If we have for a sample of size n=25 a sample variance of 400, the standard error can be written as:

[tex]\sigma_s=\dfrac{\sigma}{\sqrt{n}}=\dfrac{\sqrt{400}}{\sqrt{25}}=\dfrac{20}{5}=4[/tex]

This way of calculating the standard error is the same used for estimating the standard deviation of the sample means for samples of size n=25.

Answer:

4x + 6

Step-by-step explanation:

[tex] \frac{x}{x² + 3x + 2} + \frac{3}{x + 1} [/tex]

To determine what the numerator would be, after simplifying both fractions, take the following steps:

Step 1: Factorise the denominator of the first fraction, x² + 3x + 2.

Thus,

x² + 2x + x + 2

(x² + 2x) + (x + 2)

x(x + 2) +1(x + 2)

(x + 1)(x + 2)

We would now have the following as our new fractions to add together and simplify:

[tex] \frac{x}{(x + 1)(x + 2)} + \frac{3}{x + 1} [/tex]

Step 2: find the highest common factor of the denominator of both fractions.

Highest common factor of (x + 1)(x + 2) and (x + 1) = (x + 1)(x + 2)

Step 3: To add both fractions, divide the highest common factor gotten in step 2 by each denominator, and then multiply the result by the numerator of each fraction.

Thus,

[tex] \frac{x}{(x + 1)(x + 2)} + \frac{3}{x + 1} [/tex]

[tex] \frac{x + 3(x + 2)}{(x + 1)(x + 2)} [/tex]

[tex] \frac{x + 3x + 6)}{(x + 1)(x + 2)} [/tex]

[tex] \frac{4x + 6)}{(x + 1)(x + 2)} [/tex]

Therefore, the numerator of the simplified form sum of both fractions = 4x + 6

Answer:

C - 4x+6

Explanation:

Edg2020

Answer:

Explanation:

F(2) means, value of function at x=2.

Here,you can see from the graph,from 0 to 4, it's a straight line and value of y is 2.

Hope this helps...

Good luck on your assignment....

Answer:

The y-intercept is -1

The x-intercept is 4.5

Step-by-step explanation:

We have the following equation:

f(x) = log(2x+1) - 1

The y intercept is the value of f(x) when x is equal to 0, so replacing x by 0 and solving for f(x), we get:

f(0) = log(2*0 + 1 ) -1

f(0) = log(1) - 1

f(0) = 0 - 1 = -1

Additionally, the x-intercept is the value of x when f(x) is equal to 0. So, replacing f(x) by 0 and solving for x, we get:

[tex]0 = log(2x + 1) - 1\\1 = log(2x + 1)\\10^1=10^{log(2x + 1)}\\10 = 2x + 1\\10 - 1 = 2x\\4.5 = x[/tex]

Answer: -64

Step-by-step explanation: Since we know that -4 x -4 is a positive, it equals 16, then a positive plus a negative equals a negative, so 16 x -4 equals -64

Answer:

-64

Step-by-step explanation:

-4 • -4 • -4

-4*-4 = 16

16*-4

-64

Answer:

a

The  estimate for the percentage of yellow peas lie within the confidence interval  23.66%  and  30.83 %

b

Since the expected value for the estimate of the yellow peas lies between  the confidence interval it means that the given estimate  of yellow peas does not contradict the expectation

Step-by-step explanation:

From the question we are told that

       The number of green peas is  [tex]g = 453[/tex]

        The number of  yellow peas is  [tex]y = 163[/tex]

       The sample size is  [tex]n = y + g = 435 + 163 = 598[/tex]

 The  sample proportion of the yellow peas is  [tex]\r p_y = \frac{y}{n}[/tex]

substituting values  

               [tex]\r p_y = \frac{163}{598}[/tex]

               [tex]\r p_y = 0.2726[/tex]

Given that the confidence level is  [tex]c = 95[/tex]%

The level of significance is  [tex]\alpha = 100 - 95 = 5[/tex]%

    The critical values at this  level of significance is  obtained from the table of critical values as

         [tex]t_{\alpha } = 1.960[/tex]

Now the confidence interval is  mathematically evaluated as

       [tex]k = \r p _y \pm t_{\alpha } \sqrt{\frac{\r p (1 - \r p) }{n} }[/tex]

substituting values  

      [tex]k =0.2726 \pm 1.96 \sqrt{\frac{0.2726 (1 - 0.2726) }{598} }[/tex]

       [tex]k =0.2726 \pm 0.036[/tex]

So the 95%  confidence interval is  

      k = (  0.2366, 0.3083)

This mean that the estimate of the yellow peas(25%) lies between

             23.66%  and  30.83 %

Given that the expected value for the estimate of the yellow peas lies between  the confidence interval it means that the given estimate  of yellow peas does not contradict the expectation

Using the percentage concept, it is found that 51% of 10th graders surveyed preferred robotics, hence option B is correct.

The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:

[tex]P = \frac{a}{b} \times 100\%[/tex]

In this problem, we have that 33% out of 65% of the students are 7th graders who preferred robotics, hence the percentage is given by:

[tex]P = \frac{33}{65} \times 100\% = 51%[/tex]

Which means that option B is correct.

More can be learned about percentages at https://brainly.com/question/14398287

#SPJ1

Answer:

It's A. 61% The dude above me is wrong.

Step-by-step explanation:

I just took the test

Answer:

a^x/y=1              x: 0

Step-by-step explanation: w.k.t,        a^0=1( any variable raised to 0 is 1)

                                    so, here the exponent is x/y which should have been 0 so that answer was 1.

Answer:

x=-2

Step-by-step explanation:

2 times -2=-4+3=-1

Answer:

The required matrix is[tex]A = \left[\begin{array}{ccc}1.07&-0.21\\-0.86&1.35\end{array}\right][/tex]

Step-by-step explanation:

Matrix of rotation:

[tex]P = \left[\begin{array}{ccc}cos\pi/4&-sin\pi/4\\sin\pi/4&cos\pi/4\end{array}\right][/tex]

[tex]P = \left[\begin{array}{ccc}1/\sqrt{2} &-1/\sqrt{2} \\1/\sqrt{2} &1/\sqrt{2}\end{array}\right][/tex]

x' + iy' = (x + iy)(cosθ + isinθ)

x' = x cosθ - ysinθ

y' = x sinθ + ycosθ

In matrix form:

[tex]\left[\begin{array}{ccc}x'\\y'\end{array}\right] = \left[\begin{array}{ccc}cos\theta&-sin\theta\\sin \theta&cos\theta\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right][/tex]

The matrix stretches by 1.8 on the x axis and 0.7 on the y axis

i.e. x' = 1.8x

y' = 0.7y

[tex]\left[\begin{array}{ccc}x'\\y'\end{array}\right] = \left[\begin{array}{ccc}1.8&0\\0&0.7\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right][/tex]

[tex]Q = \left[\begin{array}{ccc}1.8&0\\0&0.7\end{array}\right][/tex]

According to the question, the result is rotated by pi/3 clockwise radians

[tex]R = \left[\begin{array}{ccc}cos(-\pi/3)& -sin(-\pi/3)\\-sin(\pi/3)&cos(\pi/3)\end{array}\right][/tex]

[tex]R = \left[\begin{array}{ccc}1/2&\sqrt{3}/2 \\-\sqrt{3}/2 &1/2\end{array}\right][/tex]

To get the matrix A, we would multiply matrices R, Q and P together.

[tex]A = RQP = \left[\begin{array}{ccc}1/2&\sqrt{3}/2 \\-\sqrt{3}/2 &1/2\end{array}\right] \left[\begin{array}{ccc}1.8&0\\0&0.7\end{array}\right] \left[\begin{array}{ccc}1/\sqrt{2} &-1/\sqrt{2} \\1/\sqrt{2} &1/\sqrt{2}\end{array}\right][/tex]

[tex]A = \left[\begin{array}{ccc}1.07&-0.21\\-0.86&1.35\end{array}\right][/tex]

Answer:

Step-by-step explanation:

A standard normal probability distribution is a normal distribution that has a mean of zero and a standard deviation of 1.

Answer:

3 is the answer

Step-by-step explanation:

They are 8 blocks the ones shaded is the  denominator and the amount un-shaded are the numerator.

Answer:

In that year approximately 2114 thousand people visited the park.

Step-by-step explanation:

Since the expression [tex]y(x) = -7.5*x^2 + 103*x + 2142[/tex] models the number of visitors in the park, where x represents the number of years after 2007 and 2021 is 14 years after that, then we need to find "y" for that as shown below.

[tex]y(14) = -7.5*(14)^2 + 103*14 + 2142\\y(14) = -7.5*196 + 1442 + 2142\\y(14) = -1470 + 3584\\y(14) = 2114[/tex]

In that year approximately 2114 thousand people visited the park.

Answer:

-2√2.

Step-by-step explanation:

Treat the radical as if it were a variable.

3x  -    5x   = -2x

3√2 - 5√2 = -2√2.

Answer:

The guy above me is right, it is A

Step-by-step explanation:

I got that answer right on the Quiz... In total I got an 80% But this was one of the right answers.

Answer

3 5/6   or   3.83

Step-by-step explanation:

Answer:

There are a total of 840 possible different teams

Step-by-step explanation:

Given

Number of boys = 6

Number of girls = 8

Required

How many ways can 4 boys and 5 girls be chosen

The keyword in the question is chosen;

This implies that, we're dealing with combination

And since there's no condition attached to the selection;

The boys can be chosen in [tex]^6C_4[/tex] ways

The girls can be chosen in [tex]^8C_5[/tex] ways

Hence;

[tex]Total\ Selection = ^6C_4 * ^8C_5[/tex]

Using the combination formula;

[tex]^nCr = \frac{n!}{(n-r)!r!}[/tex]

The expression becomes

[tex]Total\ Selection = \frac{6!}{(6-4)!4!} * \frac{8!}{(8-5)!5!}[/tex]

[tex]Total\ Selection = \frac{6!}{2!4!} * \frac{8!}{3!5!}[/tex]

[tex]Total\ Selection = \frac{6 * 5* 4!}{2!4!} * \frac{8 * 7 * 6 * 5!}{3!5!}[/tex]

[tex]Total\ Selection = \frac{6 * 5}{2!} * \frac{8 * 7 * 6}{3!}[/tex]

[tex]Total\ Selection = \frac{6 * 5}{2*1} * \frac{8 * 7 * 6}{3*2*1}[/tex]

[tex]Total\ Selection = \frac{30}{2} * \frac{336}{6}[/tex]

[tex]Total\ Selection =15 * 56[/tex]

[tex]Total\ Selection =840[/tex]

Hence, there are a total of 840 possible different teams

Answer:

14    -50    -29    -541

Step-by-step explanation:

8-3=5-1=4+5=9-8=1+13=14-64=-50+21=-29-512=-541  

i got this by looking up sequence pattern finder in google and clicking on the second option then inserting the numbers you gave hope this helps

Answer:

Step-by-step explanation:

The question is incomplete. The complete question is:

A production line operation is designed to fill cartons with laundry detergent to a mean weight of 32 ounces. A sample of cartons is periodically selected and weighed to determine whether under filling or overfilling is occurring. If the sample data lead to a conclusion of under filling or overfilling, the production line will be shut down and adjusted to obtain proper filling.

A. Formulate the null and alternative hypotheses that will help in deciding whether to shut down and adjust the production line.

B. Comment on the conclusion and the decision when H0 cannot be rejected.

C. Comment on the conclusion and the decision when H0 can be rejected.

Solution:

A) We would set up the hypothesis. Under filling or over filling means two ways. Thus, it is a two tailed test

For null hypothesis,

H0: μ = 32

For alternative hypothesis,

H1: μ ≠ 32

B) if H0 cannot be rejected, it means that there was insufficient evidence to reject it. Thus, it would be concluded that the production line operation filled the cartons with laundry detergent to a mean weight of 32 ounces.

C) There was sufficient evidence to reject the null hypothesis. Thus, it can be concluded that there was under filling or over filling.

Answer:

h < 2

Step-by-step explanation:

Step 1: Distribute

10h + 40 < 60

Step 2: Subtract 40 on both sides

10h < 20

Step 3: Divide both sides by 10

h < 2

Answer:

Therefore, the perimeter of the triangle is 26.7 units and the area is 22 square units.

Step-by-step explanation:

Given the vertices of a triangle as: A(3, 5), B(− 1, 5), and C(3,− 6)

Since A and B are on the same y-coordinate, we have that:

AB = 3-(-1)=4 Units

Since A and C are on the same x-coordinate, we have that:

AC=5-(-6)=11 Units

Next, we determine the distance BC using the distance formula.

Given: B(− 1, 5), and C(3,− 6)

[tex]BC=\sqrt{(3-(-1))^2+(-6-5)^2}\\= \sqrt{(4)^2+(-11)^2}=\sqrt{137}$ Units[/tex]

Therefore:

Perimeter of the Triangle

[tex]= 4+11+\sqrt{137}\\ =15+\sqrt{137}$ Units\\=26.7 Units[/tex]

On plotting the triangle, it forms a right triangle such that the:

Base = 4 Units

Height = 11 Units

Therefore:

Area of a triangle [tex]=\dfrac12 *Base*Height[/tex]

Therefore:

Area of the Triangle = 0.5 X 4 X 11

=22 Square Units.

Therefore, the perimeter of the triangle is 26.7 units and the area is 22 square units.

Answer:

A type II error is failing to reject the hypothesis that μ is equal to 2800 when in fact, μ is less than 2800.

Step-by-step explanation:

A Type II error happens when a false null hypothesis is failed to be rejected.

The outcome (the sample) probability is still above the level of significance, so it is consider that the result can be due to chance (given that the null hypothesis is true) and there is no enough evidence to claim that the null hypothesis is false.

In this contest, a Type II error would be not rejecting the hypothesis that the mean lifetime of the light bulbs is 2800 hours, when in fact this is false: the mean lifetime is significantly lower than 2800 hours.

Answer:

The answer is only c) x=5

Step-by-step explanation:

|x| means that this is an absolute value. If the number is a negative, removing the value bars will make it a positive again. Positives stay positives. So the only answer greater than value of 2 is 5.

Answer:

  (1, 2), (-2, -1)

Step-by-step explanation:

We can choose x = 1 and find y:

  y = 2/1 = 2

  (x, y) = (1, 2)

We can choose x = -2 and find y:

  y = 2/(-2) = -1

  (x, y) = (-2, -1)

Answer:

1 2/1 ÷1 1/2  = 2

Step-by-step explanation:

dividend ÷ divisor = quotient

1 2/1 ÷1 1/2  = 2

In order to solve this you need to make the mixed numbers into an improper fraction:

3/1 ÷ 3/2

use the KFC method (Keep Change Flip)

When you got to fractions you wanna divide flip the right and multiply

3/1 (2/3)= 2

Answer:

40 ml of 73% solution required and 80 ml of 13% solution

Step-by-step explanation:

Let x = amt of 58% solution

It say's the amt of the resulting mixture is to be 120 ml, therefore

(120-x) = amt of 13% solution

A typical mixture equation

0.73x + 0.13(120-x) = 0.33(120)

0.73x + 15.6 - 0.13x = 39.6

0.6x=24

x=40 ml of 73% solution required

and

120 - 40 =80 ml of 13% solution