Your team has contracted to design and build a 500 ft, square-based, open-top, rectangular steal holding tank for a paper company. The tank is to be made by welding thin stainless steel plates together along their edges. As the production engineer, your job is to find dimensions for the base and height that will make the tank weight as little as possible.

Answer: 9x - 20

Step-by-step explanation:

You can graph 2(3x - 10) + 3x.

Here is how I would do it:

First, Distribute

2(3x - 10) + 3x (Original)

6x - 20 + 3x (Distribute)

Second, Combine like terms

6x - 20 + 3x

9x - 20

Therefore, the solution to your problem is 9x - 20

The value of c should be 20.2 so that 99% of all parcels are at least 1 lb under the surcharge weight (that is, only 1% are beyond c-1 lb).

What is surcharge?

Surcharges are extra fees or taxes, as the name implies. A 10% surcharge on a 30% tax rate effectively increases the total tax burden to 33%. A 10% surcharge is added to the tax obligation for people whose net taxable income exceeds Rs 1 crore. The surcharge is increased to 5% if the net income is greater than Rs 10 crore. If a company's net income surpasses Rs. 1 crore and Rs. 10 crore, they are both provided a margin of relief.

Solution Explained:

Given,

m = 12

d = 3.5

P(z<x) = 0.99 = ¢(Z)

Z = 2.33

Since Z = (x - m)/d

x = dZ + m

x = 3.5*2.33 + 12

x = 20.155 lb approximately

x = 20.2 lb

Therefore, the highest weight for 99% if the parcels is 20.2 lb.

That is, the surcharge weight = 20.2 + 1 = 21.2 lb

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Answers to both the subparts are as follows:

(A) In order to factor A(t), we obtain A(t) = -cost + 1.

(B) t = 1.57 after solving the equation A(t) = 0 for 0 ≤ t ≤ 2.

Two expressions are combined by the equal sign to form a mathematical statement known as an equation.

For instance, a formula might be 3x - 5 = 16.

After solving this equation, we learn that the value of the variable x is 7.

(A) Factorize A(t):

A(t) = 2cost - 3cost + 1

After assembling the cost terms, we have:

A(t) = cost(2 - 3) + 1

A(t) = cost(- 1) + 1

A(t) = -cost + 1

In order to factor A(t), we obtain A(t) = -cost + 1.

(B) Solving equation A(t) = 0 for 0 ≤t≤ 2:

Since A(t) = -cost + 1

When we solve A(t) = 0 for 0 ≤ t ≤ 2, we get:

A(t) = 0

-cost + 1 = 0

-cost = -1

cost = 1

If we take the inverse cosine, we get:

t = cos⁻¹(1)

t = π/2

t = 3.142/2

t = 1.571

t ≅ 1.57

t = 1.57 after solving A(t) = 0 for 0 t 2

Therefore, answers to both the subparts are as follows:

(A) In order to factor A(t), we obtain A(t) = -cost + 1.

(B)  t = 1.57 after solving the equation A(t) = 0 for 0 ≤ t ≤ 2.

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Complete question:
Let A (t) = 2 cost-3 cost+1, 0 ≤t ≤ 2

A. Factorize A(t).

B. Hence, solve the equation A(t) = 0 for 0 ≤t≤ 2.

Answer:

Step-by-step explanation:

=w + 2 + 2w + 6

= 3w + 8

3w = -8

w =-8/3

The conclusion does not change if the significance level went from 7% to 5%.

According to the given situation, 79% of the fruits sold are good and whether there is an increase in the percentage of good fruit is to be tested. If there is no increase in percentage of good fruit, p = 0.79 and if there is an increase in percentage of good fruit, p > 0.79.

The test statistic is given by z = (X - µ)/(σ/√n)

In the given data, µ = 0.79 and σ = √(0.79(1-0.79) = 0.407

In a random sample n = 475 and 85 are bad.

Good fruits = 475 – 85 = 390

X = 390/475 = 0.8211

Hence,

z = (0.8211 – 0.79)/(0.407/√475) = 1.66

From the z-table, p value is 0.9515.

The p value of the test that no increase in percentage of good fruits = 1 – 0.9515 = 0.0485

If the p-value is less than 0.05 it is statistically significant. As 0.0486 is less than 0.05 and 0.07 there is sufficient evidence to conclude that there is a statistically significant increase in the percentage of good fruit. It is true for each significance level. Hence, the change in significance levels does not change the conclusion.

Note: The question is incomplete. The complete question probably is: In recent years, only 79% of the fruit sold at Fred's Fruit stand has been any good. Fred recently started buying fruit from new farmers and wants to know if there is a statistically significant increase in the percentage of good fruit. In a random sample of 475 pieces, 85 were bad. How would the conclusion change if the significance level went from 7% to 5%?

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Answer:

f(7)= 42

Step-by-step explanation:

we fill in 7 where x is

f(7)=5(7)+7

f(7)=35+7

f(7)=42

Hopes this helps please mark brainliest

Jay is incorrect in doing addition first.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Given the expression as;

3x (3 +12 divided by 3) -4.

To simplify this expression, then must follow PEMDAS.

3x(3+12÷3)

3x(3+4)

3x(7)

21x

Which means that Jay is incorrect in doing addition first.

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The function y = 2x² - 5 is a nonlinear equation and the table of values is

x    0     1    2    3

y    -5    -3   5    13

From the question, we have the following equation that can be used in our computation:

y = 2x² - 5

As a general rule, a linear equation can take any of the following forms

By comparing y = 2x² - 5 to the above forms, we can see that the equation does not take any of the forms represented above

This means that the function is not a linear function

i.e. The function is a nonlinear function

Also, we set x = 0, 1, 2 and 3

So, we have

y = 2(0)² - 5= -5

y = 2(1)² - 5= -3

y = 2(2)² - 5= 5

y = 2(3)² - 5 = 13

So, the table of values is

x    0     1    2    3

y    -5    -3   5    13

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Step-by-step explanation:

A group of friends wants to go to the amusement park. They have no more than $115 to spend on parking and admission. Parking is $15, and tickets cost $25 per person, including tax. Write and solve an inequality which can be used to determine x, the number of people who can go to the amusement park.

115 ≥ 25p + 15

115 ≥ 25p + 15

subtract 15 from both sides:

115 - 15 ≥ 25p + 15 - 15

100 ≥ 25p

divide both sides by 25:

100/25 ≥ 25p/25

4 ≥ p

4 people

The number of people who can go to the amusement park is 4.

In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number lineby their size.

Given that, the money to be spend, is no more than $115 to spend on parking and admission.

Parking is $15, and tickets cost $25 per person, including tax.

we need to determine the maximum number of people that can go to the park,

115 ≥ 25p + 15

115 ≥ 25p + 15

subtract 15 from both sides:

115 - 15 ≥ 25p + 15 - 15

100 ≥ 25p

divide both sides by 25:

100/25 ≥ 25p/25

4 ≥ p

Hence, the number of people who can go to the amusement park is 4.

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There's not enough evidence to refute the publisher's claim.

Here, we are given that a newsletter publisher believes that 29% of their readers own a personal computer.

The testing firm believes this is inaccurate and hence conducts hypothesis testing to verify the claim.

They take a significance level of 0.02 and fail to reject the null hypothesis.

The null hypothesis of the testing firm would be- 29% of the readers own a personal computer because this is what is established by the publisher.

They fail to reject this null hypothesis which means that there is not enough evidence at 0.02 significant level that the percentage is not 29%.

Thus, there's not enough evidence to refute the publisher's claim.

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The number of terms that must be added together to achieve this series s is 5000.

Given that,

The remainder of the following convergent series must be less than 10 Superscript negative 5 in magnitude.

We have to calculate the number of terms that must be added together to achieve this.

Given

S= summation n=0 to infinity (-1)ⁿaₙ.

An upper bound for the error of the series Rₙ is aₙ₊₁ so

Rₙ=|s-sₙ|≤aₙ₊₁

In this case we have

1/2n+1≤1/10⁴

10⁴≤2n+1

(10⁴-1)/2≤n

(10⁴-1)/2 is approximately 5000.

Therefore, the number of terms that must be added together to achieve this series s is 5000.

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The complex numbers will be 3-i and I and the coordinates will be (-1,-3) or C point on the coordinate plane.

Two number lines combine to generate the two-dimensional surface known as the coordinate plane. The x-axis is a single horizontal number line. The y-axis is the name of the vertical number line that is the other number line. The origin is where the two axes come together. The coordinate plane can be used to graph points, lines, and other things.

Here,

A=(1,3)

B=(-3,1)

C=(-1,-3)

D=(3,-1)

=(3-i)/i

=-1-3i

The coordinates will be (-1,-3) that is C point on the coordinate plane and the complex numbers be 3-i and i.

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Website B is cheaper then website A.

What are headphones?

A user wears headphones, which are a pair of small loudspeaker drivers, on or near their head over their ears.

They function as electroacoustic transducers, converting an electrical signal into an associated sound.

People can listen to music and carry on conversations at any time and from any location thanks to headphones. It is impossible to overstate how simple it is to use headphones and how much mobility they provide.

There are two types of headphones, website A and website B.

First to find the cost for website A.

Cost of website A = Cost of headphone + cost of postage

                              = 47.68 + 16.96

Cost of website A = 64.63

Cost of website B = Cost of headphone + cost of postage

                              = 49.95 + 14.39

Cost of website B = 64.34

The cost of website B is less than the cost of website A.

Hence, website B is cheaper then website A.

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Answer:

  B/A = 1/2

Step-by-step explanation:

You want the scale factor between the two figures shown.

The scale factor is the ratio of the length in one figure to the corresponding length in the other figure. Often, we're interested in the scale factor B/A, which is what A dimensions need to be multiplied by in order to match the B dimensions.

You can pick any corresponding dimensions. Often, it is convenient to choose a short one, so you don't have to count so many grid squares.

We can choose the line from the center, where the lines cross, up and to the right to the upper right corner. In the A figure, that line goes 2 squares to the right and 2 squares up. In the B figure, that line goes 1 square right and 1 square up. Then the scale factor is ...

  (B dimension)/(A dimension) = 1/2

We can choose to look at the lengths of that line (A: 2√2; B: √2), or the x-dimension (A: 2; B: 1) or the y-dimension (A: 2; B: 1). All the measurements are proportional, so we get the same ratio for any pair of corresponding measures.

The scale factor B/A is 1/2.

__

Additional comment

The horizontal magenta lines in the attached figure are another possibility for determining the scale factor. B/A = 2/4 = 1/2.

You need to be careful to understand what scale factor you want. Sometimes it is described as "A to B", which can be ambiguous.

Here, the ratio of an A dimension to a B dimension is A : B = 2 : 1. The same wording can be interpreted to mean "the scale factor that multiplies A to transform it to B." That is the scale factor we have shown.

The chart can be completed by substituting the value of x and y in the given equation in two variable y = 1/2 x

What are Linear Equations in Two Variables?

The linear equations in two variables are the equations in which each of the two variables are of the highest exponent order of 1 and have one, none, or infinitely many solutions. The standard form of a two-variable linear equation is ax + by + c = 0 where x and y are the two variables.

According to the given question:

(Check the attachment below for complete question)

The given function is y = x/2

Let x be the minutes taken by the student and y be the pages read by him.

The chart can be completed by substituting the value of x that is minutes taken in the given equation to find the value of y. (Check attachment below)

If the teacher recommended that student must be read 20 min each night then the page read by the student is y = 20/2 = 10 pages.

If he reads 18 pages then time taken by him is x = 2×18 = 36 min.

If there are 245 pages then the time taken by the student is  

x= 2×245 = 490 min        

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Via Gelato total revenue for the month of June as the the details of expenses is equal to $7870.

As given in the question,

Total revenue is:

= (6200 × 13) - 72,540

=$ 8060

Details of all expenses are as follow:

Expense on raw material:

= (6200 × 4.75) -30,330

= -$880

Wages :

= (6200 ×1. 50) + 5,700 - 14,560

= $440

Utilities:

= (6200 × 0.30) +1730 - 3,800

= -$210

Rent:

= (2700-2700)

= 0

Insurance :

= (1450-1450)

= 0

Miscellaneous :

= (6200 × 0.45) + 660 -2,990

= $460

Total expense

=-$190

Net operating income :

=$ [8060-190]

=$7870

Therefore, Via Gelato's  total revenue of the June month is equal to $7870.

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Answer:

As a decimal:0.016

As a percentage:1.6%

Step-by-step explanation:

The area of the triangle is 3/4 units.

What is area of the triangle?

The total area that is bounded by a triangle's three sides is referred to as the triangle's area. In essence, it is equal to 1/2 of the height times the base, or A = 1/2 b h. Therefore, we need to know the triangular polygon's base (b) and height (h) in order to calculate its area.

Suppose

x is the shorter leg of the triangle.

As the longer leg of a right triangle is three times as long as the shorter leg.

⇒ 3x is the longer leg of the triangle.

The hypotenuse of the triangle is, √5.

By using Pythagorean theorem,

[tex]x^2 + (3x)^2 = (\sqrt{5} )^2\\x^2 + 9x^2 = 5\\10x^2 = 5\\x^2 = \frac{5}{10}\\ x^2 = \frac{1}{2} \\x = \frac{1}{\sqrt{2} }[/tex]

⇒ Shorter leg of the triangle is 1/√2.

⇒ Longer leg of the triangle is 3/√2.

Now to find the area of the triangle.

Area of triangle = [tex]\frac{1}{2}(\frac{1}{\sqrt{2} })(\frac{3}{\sqrt{2} } )[/tex]

[tex]A = \frac{3}{4}[/tex]

Hence, the area of the triangle is 3/4 units.

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A sample observation results in a point estimate of 0.53 for the mean value of paint thickness.

The mean value theorem states that there is one point on a curve where the tangent is parallel to the secant running through the two points.

A low-viscosity paint sample with the following thickness is provided to us.

0.810.870.901.051.111.141.301.301.481.481.591.601.661.691.781.84

a) Point estimate of the mean value of coating thickness.

To estimate the mean coating thickness, we use the mean value of the sample.

mean= sum of all observations/total number of observations

mean=8.16/16

mean=0.53

Construct a normal probability plot for the following sample of observations on coating thickness for low-viscosity paint. 0.810.870.901.051.111.141.301.30 1.481.481.591.601.661.691.781.84 Determine the z percentile associated with each sample observation. (Round your answers to two decimal places.)

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the regression line indicates whether the slope of the regression line is positive or negative is a proportion will be between 0 to 1

Regression is a statistical method that links a dependent variable to one or more independent (explanatory) variables. A regression model can demonstrate whether variations in the dependent variable are related to variations in one or more of the explanatory variables.

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Step-by-step explanation:

let's use the formula .......

[tex]x \: = \: \frac{ - 6 \sqrt{3} \frac{ + }{} \sqrt{36 \times 3 - 4(1)( - 9)} }{2(1)} [/tex]

[tex]x \: = \: \frac{ - 6 \sqrt{3} \frac{ + }{} \sqrt{108 \: + 36} }{2} [/tex]

[tex]x \: = \: \frac{ - 6 \sqrt{3} \frac{ + }{} \sqrt{144} }{2} [/tex]

[tex]x \: = \: \frac{ - 6 \sqrt{3} \frac{ + }{} 12 }{2} [/tex]

[tex]x \: = \: \frac{ - 6 \sqrt{3} - 12 }{2} [/tex]

Answer: no i need this too :(

Step-by-step explanation:

Answer:

x ≤ -5

Step-by-step explanation:

Treat this EXACTLY like you would an equation:

-3(x+4) ≥ x+8

-3x - 12 ≥ x + 8

-4x - 12 ≥ 8

-4x ≥ 20

Except here (when dividing BOTH sides by a negative):

-4x ≥ 20  ⇒  x ≤ -5

The unit rate per batch of cookies is 2.75 as Lennon uses 5 1/2 cups of flour for every 2 batches of cookies she bakes.

To calculate the unit rate, divide the denominator by the numerator so that the denominator equals 1. For example, if 50 kilometers are reached in 5.5 hours, the unit rate is 50 kilometers/5.5 hours = 9.09 kilometers per hour.

When expressed as a fraction, a unit rate has a denominator of one unit. To write a rate as a unit rate, divide the rate's numerator and denominator by the rate's denominator.

Based on the given conditions, formulate:

(5 1/2)/2

We have to find the common denominator and write the numerators above the common denominator.

(((5×2)/2)+(1/2))/2

Now, we have to calculate the product or quotient:

((10/2)+(1/2))/2

Now, write the numerators over common  denominator,

((10+1)/2)/2

Then, calculate the sum or difference:

(11/2)/2

=11/4

=2.75 (or) 2 3/4

Therefore, the unit rate per batch of cookies is 2.75.

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Answer:

ITS A

Step-by-step explanation:

Answer:

n=15

Step-by-step explanation:

The value of sides of the right triangle are a = 3 units, b = 12.47 units and c = 11.21 units.

For the given question-

The length of the side are-

a = 3 units

Angle B = 64°.

Then,

Applying trigonometric properties-

Tan B = b/a

b = a tan B

b = 3 tan 64°

b = 12.47 units

Now,

Sin B = b/c

c = b sin B

c = 12.47 sin 64°

c = 11.21 units.

Thus, the value of sides of the right triangle are a = 3 units, b = 12.47 units and c = 11.21 units.

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70% of students had scores that were within (±) one standard deviation of the mean.

For the stated question-

Total number of students = 20

Scores received; 70, 60, 75, 68, 85, 86, 78, 72, 82, 88, 88, 73, 74, 79, 86, 82, 90, 92, 93, 73.

Mean = Sum of all/ Total number

Mean x = 79.7

standard deviation = 8.7

Thus, (±) one standard deviation SD of the mean becomes;

-1 SD; 79.7 - 8.7 ≈ 70.994

+1 SD; 79.7 + 8.7 ≈ 88.406

Thus, 71 to 88

Percentage = scores between  71 to 88/ total scores

Percentage = 14/20 x 100 %

Percentage = 70%

Thus, 70% of students had scores that were within (±) one standard deviation of the mean.

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The domain and the range of the functions are given by the images at the end of the answer.

The domain of a function is composed by the set that contains all possible values assumed by the input of the function. Hence, on the graph, it will be given by the values of x of the graph, the values assumed by the horizontal axis of the graph.

The range of a function is composed by the set that contains all possible values assumed by the output of the function. Hence, on the graph, it will be given by the values of y of the graph, the values assumed by the vertical axis of the graph.

The notations are given as follows:

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