I need help with this asap

Answer:

x=15.08 cm

y=7.54 cm

Step-by-step explanation:

We are given that

Volume of box=1715 cubic cm

Side length of base=x

l=b=x

Height of box=h=y

Volume of box=lbh=x^2y

[tex]1715=x^2y[/tex]

[tex]y=\frac{1715}{x^2}[/tex]

Surface area of box=Area of bottom+area of four faces=[tex]x^2+4xy[/tex]

[tex]S=x^2+4x(\frac{1715}{x^2}=x^2+\frac{6860}{x}[/tex]

Differentiate w.r.t x

[tex]S'(x)=2x-\frac{6860}{x^2}[/tex]

[tex]S'(x)=0[/tex]

[tex]2x-\frac{6860}{x^2}=0[/tex]

[tex]2x=\frac{6860}{x^2}[/tex]

[tex]x^3=\frac{6860}{2}=3430[/tex]

[tex]x=(3430)^{\frac{1}{3})=15.08[/tex]

Again differentiate w.r.t x

[tex]S''(x)=2+\frac{13720}{x^3}[/tex]

Substitute x=15.08

[tex]S''(x)=2+\frac{13720}{(15.08)^3}>0[/tex]

Hence, the surface area is minimum at x=15.08 cm

[tex]y=\frac{1715}{(15.08)^2}=7.54 cm[/tex]

The dimensions of the bin that will minimize the surface area are:

Base side (x): 7.5cm

Height (y): 36.13cm

Let's express the surface area and volume of the box in terms of x and y:

Surface area (A):

A = 2x^2 + 4xy

Volume (V)V = x^2y

We are given that the volume of the box must be 1715cm3:

1715cm3 = x^2y

Solving for y, we get:

y = 1715/x^2

Now, we want to minimize the surface area (A) subject to the constraint that the volume (V) is 1715cm3. We can use Lagrange multipliers to solve this optimization problem.

L(x, y, λ) = A - λ(V - 1715)

L(x, y, λ) = 2x^2 + 4xy - λ(x^2y - 1715)

Taking partial derivatives of L with respect to x, y, and λ, we get:

∂L/∂x = 4x + 4y - 2λxy = 0

∂L/∂y = 4x - λx^2 = 0

∂L/∂λ = -x^2y + 1715 = 0

Substituting V = x^2y into the third partial derivative, we get:

∂L/∂λ = -V + 1715 = 0

Solving these equations simultaneously, we get:

x = 7.5

y = 36.13

Answer:

50

Step-by-step explanation:

An angle that measures 50° Turns through 50 1° angles because 50 *1 = 50

1 degree * 50 turns = 50 degrees

Answer:

Step-by-step explanation:

%17 because you take %78 of %22

(the second part is more tricky...

17% were first time takers who past.

%60  of %78 = %46.8 = percentage of people who were first time takers who failed.

so total percentage of first time takers = 46.8 +17 = %63.8.

Then 17/63.8 X %100 = percent of first time takers who passed.

=26.6 percent therefore %27 is correct.

The dimensions of the tank that minimize the surface area are a square base of 24 ft × 24 ft and a height of 12 ft.

To minimize the surface area, we need to minimize the sum of the areas of the five sides of the tank. Let's denote the side length of the square base as x and the height of the tank as h.

Given that the volume V = 6912 ft³, and for a rectangular tank, the volume is V = base area × height = x² × h.

So, we have x² × h = 6912.

To minimize the surface area, we differentiate the surface area formula with respect to x, set it equal to zero, and solve for x.

The surface area A = x² + 4xh.

Differentiating A with respect to x, we get [tex]\frac{dA}{dx}[/tex] = 2x + 4h.

Setting [tex]\frac{dA}{dx}[/tex] = 0 gives us 2x + 4h = 0, so x = -2h.

Since x cannot be negative, we ignore this solution.

Now, using x² × h = 6912, we can solve for h:

h = [tex]\frac{6912}{x^{2} }[/tex]

Substituting x = -2h:

[tex]\[ h = \frac{6912}{(-2h)^2} = \frac{6912}{4h^2} = \frac{1728}{h^2} \][/tex]

Solving for h:

[tex]h^3 = \frac{1728}{h^2}\\h^5 = 1728\\h = \sqrt[5]{1728} = 12[/tex]

Now, substituting h = 12 back into x² × h = 6912:

[tex]x^2 \times 12 = 6912\\x^2 = \frac{6912}{12} = 576\\x = \sqrt{576} = 24[/tex]

Answer:

The answer is $206,451

Step-by-step explanation

This scenario is asking to subtract 19 percent away from 229,390 .

Step one :  Divide 229,390 by 10 ( take away the zero behind the 9 )

Step 2 : Subtract 22,939 from 229,390 since we know ten percent of 229,390 is 22,939 = 206451

Answer:

Joe makes $206,451 annually

Step-by-step explanation:

 229,390 divided by 10 = 22,939

Then Subtract 22,939 from 229,390 = 206,451

The function [tex]k(x) = 2x^2[/tex] is which the average rate of change over the interval 1 < x < 5 greater than the average rate of change of g(x).

Given data:

The function is represented as [tex]g(x)=1.8x^2[/tex].

Now, the average rate of change of the function is S.

The value of [tex]S=\frac{f(x_{2})-f(x_{1})}{x_{2}-x_{1}}[/tex].

The interval of the function is from 1 < x < 5.

So, for g(x), [tex]S=\frac{f(5)-f(1)}{5-1}[/tex].

The value of S = 10.8

For the function [tex]k(x) = 2x^2[/tex], the rate of change is:

[tex]S=\frac{k(5)-k(1)}{4}[/tex]

[tex]S=\frac{50-2}{4}[/tex]

So, the value of S = 12 and is greater than 10.8

Hence, the function is [tex]k(x) = 2x^2[/tex].

To learn more about rate of change of function, refer:

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The complete question is attached below:

For which function is the average rate of change over the interval 1 < x < 5 greater than the average rate of change over the same interval for the function g(x) = 1.8x^2?
A.=f(x) = x^2

B.=g(x) = 1.2x^2

C.=h(x) = 1.5x^2

D.=k(x) = 2x^2

Answer:

The answer is A.

Step-by-step explanation:

(Only if your question "Amos’s solution is (2, –14). What did he do wrong? ")

Trust me, I got it right

Given Information:  

standard deviation = σ = 15 ft²

Confidence interval = 95%

Margin of error = 2.5 ft²

Required Information:  

Sample size = n = ?

Answer:

Sample size = n ≈ 139

Step-by-step explanation:  

The required number of observations can be found using ,

Me = z(σ/√n)

Where Me is the margin of error, z is the corresponding z-score of 95% confidence interval, σ is the standard deviation and n is the required sample size.

Rearrange the above equation to find the required number of sample size

√n = σz/Me

n = (σz/Me)²

For 95% confidence level, z-score = 1.96

n = (15*1.96/2.5)²

n = 138.29

since the sample size can't be in fraction so,

n ≈ 139

Therefore, a sample size of 139 would be needed.

Answer:

0.28142

Explanation

First change 0.792 into standard form

To evaluate the square root of 0.792 using tables, you would typically refer to a set of pre-calculated square root values in the form of a table. These tables were commonly used before calculators and computers became widely available.

To begin the evaluation process, you would follow these steps:
**Step 1: Locate the closest square values**
First locate the two perfect square values that surround 0.792. If you have a comprehensive table, you may find an exact value, but often you'll need to interpolate between two values.
**Step 2: Interpolation**
If 0.792 is not a value directly found in the table, you use interpolation. Let's assume that your table shows that the square root of 0.784 (which is \( 0.28²  \)) is 0.28, and the square root of 0.81 (which is \( 0.9²  \)) is 0.9. Your value, 0.792, lies between these two.
**Step 3: Estimation**
Since \( 0.28² \) is 0.784 and \( 0.9² \) is 0.81, 0.792 is closer to 0.784 than 0.81. You would then estimate it to be closer to 0.28 than 0.9.
**Step 4: Fine-tuning**
Now, find the difference between the square roots and the differences between the squares:
- The difference between 0.28 and 0.9 is 0.62.
- The difference between 0.784 and 0.81 is 0.026.
Next, find out where 0.792 falls between 0.784 and 0.81 in proportion to the difference between the square roots.
- The difference between 0.792 and 0.784 is 0.008.
- To find the proportion of 0.008 to the total difference 0.026, you divide 0.008 by 0.026 to get approximately 0.308.
- Now, multiply this proportion by the difference between the square roots to refine your estimate: 0.62 * 0.308 ≈ 0.191.
**Step 5: Calculate your estimate**
Add this value to the lower square root to get an approximation of the square root of 0.792:
0.28 + 0.191 ≈ 0.471.
**Final Answer**
The square root of 0.792 is approximately 0.471 using interpolation with table values.

Answer:

Ann=£38

Bill=£171

Chloe=£95

Dave=£95

Step-by-step explanation:

By the information provided we can create an equation:

[tex]2x+9x+2*5x=399\\11x+10x=399\\21x=399\\x=19[/tex]

Now that we know x, we multiply it correspondingly.

For Ann -> 2*19=38

Bill -> 9*19= 171

Chloe and Dave have the exact same amount each (because they both have 2.5 times the amount Ann's money)

Chloe/ Dave -> 5*19=95 each.

Answer:

73.8 degrees because 96.5-22.7=73.8

Step-by-step explanation:

The number of  liters of solution in all is there in the test tubes is 2.25L, the correct option is A.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Given;

Edwin fills 15 test tubes with a solution.

Each test tube contains 150 milliliters of solution.

Now,

The solution in all the tubes=150ml x 15

=2250ml

To convert it in liters

=2250/1000

=2.250L

Therefore, by algebra the answer will be 2.250L.

More about the Algebra link is given below.

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Answer:

Yes

Step-by-step explanation:

For the equation to be equivalence then it must be

Reflexive, Symmetric and transitive

since |A|=|B|;  

Every element in A is in B then R is reflexive

If f(1) = g(1), then g(1) = f(1), so R is symmetric.

If f(1) = g(1) and g(1) = h(1), then f(1) = h(1), so R is transitive.

R is reflexive, symmetric, and transitive,

thus R is an equivalence relation.

Answer:

2 tan theta & sin2theta/cos^2theta

Step-by-step explanation:

Final answer:

The simplified forms of the expression sec^2(theta) sin(2theta) are 2 tan(theta) and sec^2(theta) - 1. These correspond to answer choices (c) and (d) respectively, by utilizing trigonometric identities to simplify the expression.

Explanation:

To find the simplified forms of the expression sec^2(theta) sin(2theta), we can use trigonometric identities. The identity for sin(2theta) is 2sin(theta)cos(theta). Since sec(theta) is the reciprocal of cos(theta), we can write sec^2(theta) as 1/cos^2(theta).

Therefore, the expression becomes:

sec^2(theta) sin(2theta) = (1/cos^2(theta)) * (2sin(theta)cos(theta))

We can simplify this further by canceling one cos(theta) from the numerator and denominator, which yields:

2sin(theta)/cos(theta)

Simplified, this is equal to 2 tan(theta), since tan(theta) = sin(theta)/cos(theta).

Using another trigonometric identity, sec^2(theta) = 1 + tan^2(theta), we can also express the original expression as:

sec^2(theta) - 1 which simplifies to tan^2(theta).

This means that the correct answers from the provided choices are (c) and (d).

Answer:

The total income after 29 days is $16,106,127.33

Step-by-step explanation:

This is a geometric progression with the first element being 0.03 and the ratio is 2. So if we want to know the total income after 29 days we can use the formula for the sum of elements in a series of that kind, this is given by:

sum(29 elements) = [(first element)*(1 - r^(29))]/(1 - r)

sum(29 elements) = [0.03*(1 - 2^(29))]/(-1)

sum(29 elements) =(0.03*(-536870911))/(-1)

sum(29 elements) = -16106127.33/(-1) = 16106127.33

The total income after 29 days is $16,106,127.33

Answer:

It makes the solution of the equation easier

Step-by-step explanation:

Here we have the formula relating Celsius and Fahrenheit given as follows;

[tex]C = \frac{5\times (F - 32)}{9}[/tex]

From the above Celsius to Fahrenheit equation, we have that to solve for F we rearrange the formula as follows

[tex]C =\frac{5F}{9} - \frac{32\times 5}{9}[/tex]

Which is the same as

[tex]C =\frac{5F}{9} - 17\frac{7}{9}[/tex]

It is then seen that rearranging the equation between Celsius and Fahrenheit makes it easier to solve for either °C or °F.

Answer:

It’s easier to find the solution to a variable when that variable is by itself on one side of the equal sign. Rearranging formulas before substituting values for each variable makes calculations more straightforward. With this approach, we only need to perform operations such as multiplication, division, addition, and subtraction on one side of the equal sign, and we simplify instead of solving by using the properties of equality.

Step-by-step explanation:

Answer:

30 fruits

Step-by-step explanation:

Let

x ----> number of plums on the plate

y ----> number of apples on the plate

we know that

The ratio of the number of plums to the number of apples was 3:2

so

[tex]\frac{x}{y} =\frac{3}{2}[/tex]

[tex]x=1.5y[/tex] ----> equation A

After Ed took 6 plums from the plate, the number of plums remaining on the plate became the same as the number of apples

so

[tex]x-6=y[/tex] ----> equation B

substitute equation A in equation B

[tex]1.5y-6=y[/tex]

solve for y

[tex]1.5y-y=6\\0.5y=6\\y=12[/tex]

Find the value of x

[tex]x=1.5(12)=18[/tex]

therefore

Mon put on the table

[tex]x+y=18+12=30\ fruits[/tex]

Answer:

30

Step-by-step explanation:

Final answer:

When Mai turns 65, the value of her individual Retirement Account will be $61,917.28.

Explanation:

To calculate the future value of an investment with compound interest, we can use the formula:

FV = P(1+r)^n

Where FV is the future value, P is the principal amount (initial investment), r is the interest rate (as a decimal), and n is the number of compounding periods.

In this case, Mai invested $2000 and the interest rate is 10% compounded annually.

So, when Mai turns 65, the number of compounding periods would be 65 - 21 = 44 years.

Plugging in the values into the formula:

FV = $2000(1+0.10)^44 = $61,917.28

Therefore, the value of Mai's individual Retirement Account when she turns 65 will be $61,917.28.

Answer:

y = [tex]\frac{1}{2}[/tex]x+1

Step-by-step explanation:

To find a right angle we need to find the perpendicular line. The trick here is to do the flip of your slope and since there is no "that passes through the point (#, #) you're done after that. So the answer is

y = [tex]\frac{1}{2}[/tex]x+1

Answer: There’s a .35 % chance that the marble will be green. When drawing all 3, the chance is .04%

Step-by-step explanation:

Answer:

x=31

Step-by-step explanation:

The interior angles of a triangle must add to 180 degrees, so

81+68+x=180

Add on the left

149+x=180

Now, solve for x by getting it by itself. To do this, subtract 149 from both sides

149-149+x=180-149

x=31

Answer:

Refer below.

Step-by-step explanation:

True statements for Approximately 25 men in the sample weigh are:

More than 150 lbs.

More than 162 lbs.

Between 150 and 155 lbs.

Between 155 and 162 lbs.

Based on the experimental data, approximately 25 men in this sample weigh:

A boxplot simply refers to a type of chart that can be used for the graphical representation of the five-number summary of any data set, especially based on skewness, locality, and spread.

Additionally, the five-number summary of a data comprises the following:

In this scenario, the true statement is that approximately 25 men in this sample would weigh:

Read more on boxplots here: https://brainly.com/question/14277132

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Answer:

C is the answer

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

x =(3-√37)/2=-1.541

x =(3+√37)/2= 4.541

Step-by-step explanation:

to long to explain sorry but trust me

Answer:

The answer to your question is below

Step-by-step explanation:

Data

Equation     x² + 3x + 7 = 0

Let's solve this equation by two methods.

1) Completing the perfect square trinomial

                 x² + 3x      = -7

                 x² + 3x + (3/2)² = -7 + (3/2)²

                (x + 3/2)² = -7 + 9/4

                 (x + 3/2)² = -19/4

                 x + 3/2 = √-19/√4

                 x = -3/2 + √-19/2         It has imaginary solutions.

2.- Graph the equation

See the graph below.

In the graph we notice that the equation does not cross the x-axis so it does not have real solution.

Answer:

23

Step-by-step explanation:

Answer:

31.42 yards

Step-by-step explanation:

The formula for the circumference is pi multiplied by the diameter.

To work this out you would first multiply 5 by 2, which would be 10 yards. This is because the radius is half of the diameter. Then you would multiply pi by 10, which would be 31.416.

radius=[tex]\frac{1}{2}[/tex] of diameter

Circumference=[tex]\pi d[/tex]

1) Multiply 5 by 2.

[tex]5*2=10[/tex]

2) Multiply pi by 10.

[tex]\pi *10=31.416[/tex]

3) Round to 2 decimal places.

[tex]31.42[/tex]

When x=0 we get y=1

1 = 3(0) + ?

1 = ?

Answer: 1

Answer:

1

Step-by-step explanation:

This equation is written in slope intercept form, which is y=mx+b

This is where m is the slope, and b is the y intercept. What we need to find here, is the y intercept.

The y intercept is what y equals when x is 0.

Based on the table, we know that y is 1, when x is 0.

Therefore, the equation completed, would be y=3x+1

Answer:

1.17e+16

hope this helps! (if right pls mark brainy) thanks!

Answer:

The sample size required is 102.

Step-by-step explanation:

The (1 - α)% confidence interval for population mean μ is:

[tex]CI=\bar x\pm z_{\alpha/2}\times\frac{\sigma}{\sqrt{n}}[/tex]

The margin of error for this interval is:

[tex]MOE= z_{\alpha/2}\times\frac{\sigma}{\sqrt{n}}[/tex]

Given:

σ = 9.2

(1 - α)% = 90%

MOE = 1.5

The critical value of z for 90% confidence level is:

[tex]z_{0.10/2}=1.645[/tex]

*Use a z-table.

Compute the value of n as follows:

[tex]MOE= z_{\alpha/2}\times\frac{\sigma}{\sqrt{n}}[/tex]

      [tex]n=[\frac{z_{\alpha/2}\times \sigma}{MOE}]^{2}[/tex]

         [tex]=[\frac{1.645\times 9.2}{1.5}]^{2}\\=101.795\\\approx102[/tex]

Thus, the sample size required is 102.

To calculate the sample size for a 90% confidence interval with a 1.5 margin of error using a known standard deviation of 9.2, you would need a sample size of approximately 101.

90% Confidence Interval Sample Size Calculation

To determine the required sample size for a 90% confidence interval with a maximum margin of error of 1.5, and a known population standard deviation of 9.2, you can use the following formula:

n = (Z*σ/E)^2

Here, 'n' is the sample size, 'Z' is the Z-score corresponding to the desired confidence level, 'σ' is the population standard deviation, and 'E' is the maximum margin of error. For a 90% confidence level, the Z-score is approximately 1.645 (since 5% is in each tail of the normal distribution). Plugging in the values we have:

n = (1.645 * 9.2 / 1.5)^2

The calculation yields:

n = (15.074 / 1.5)^2

n = (10.049)^2

n = 101.0

Therefore, you would need a sample size of approximately 101 to ensure the sample mean does not deviate from the population mean by more than 1.5 with a 90% confidence interval.

Answer:

c

Step-by-step explanation:

plz mark me brainlesssss