A can manufacturing company is designing a can of cat food to hold 5.5 oz or about 163 cm(3). They have written out that the equation for the surface area for a can with the volume is S=2pie radius(2) + 163/r. Explain why the equation is wrong and how to fix it.

9514 1404 393

Answer:

  x = {-0.6, 1.8}

Step-by-step explanation:

Adding 33 we have ...

  4x^2 -5x = 4

Dividing by 4, we get ...

  x^2 -5/4x = 1

We can complete the square by adding the square of half the x-coefficient:

  x^2 -5/4x +25/64 = 89/64

  (x -5/8)^2 = 89/64

  x = (5 ±√89)/8 = {-0.5542, 1.8042}

The solution rounded to the nearest tenth is ...

  x = {-0.6, 1.8}

The rate that is equivalent to the rate at which John drove to San Antonio is 60 miles per hour

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

John drove from here to San Antonio which is 180 miles away in 3 hours.

This means that

Distance = 180 miles

Time = 3 hours

Using the above as a guide, we have the following:

Speed = Distance/Time

Substitute the known values in the above equation, so, we have the following representation

Speed = 180/3

Evaluate

Speed = 60

Hence. the rate that is equivalent to the rate at which John drove to San Antonio is 60 miles per hour

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Answer:

hello your question is incomplete below is the complete question

Find the minimum sample size n needed to estimate μ For the given values of​ c, σ​, and E. c=0.98​, σ=6.5​, and E=22 Assume that a preliminary sample has at least 30 members.

Answer : 48

Step-by-step explanation:

Given data:

E = 2.2,

std ( σ ) = 6.5

c ( level of confidence ) = 0.98

To find the minimum sample size

we have to first obtain the value of  \(Z_{a/2}\)  

note : a can be found using this relation :

( 1 - a ) = 0.98 ----- equation 1

a = 1 - 0.98 = 0.02

hence:  a/2 = 0.01

This means that P( Z ≤ z ) = 0.99  the value of z can be found using the table of standard normal distribution. from the table the value of z = 2.33

P( Z ≤ 2.33 ) = 0.99

To obtain the sample size n

\(n = (\frac{std*z}{E} )^{2}\)

n = \((\frac{6.5*2.33}{2.2} )^2\) =  (6.88409)^2

Therefore n ≈ 48

The area of the quarter with a diameter of 2 ⁴/₅ inches will be 6.15 square inches.

Let r be the sector's radius and be the angle subtended by the sector at its center. The region of the circle's sector will then be written as,

A = (θ/360°) πr²

A quarter has a diameter of 2 ⁴/₅ inches.

Transform the mixed fraction number into a decimal number.

2 ⁴/₅ = 2 + 0.80 = 2.8

In the quarter sector, the central angle is 90°.

A = (90°/360°) x 3.14 x (2.8)²

A = 6.15 square inches

The area of the quarter with a diameter of 2 ⁴/₅ inches will be 6.15 square inches.

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The graph of the function f(x, y) = \(x^2\) is a three-dimensional parabolic surface that opens upwards.

It is symmetric around the x-axis. This means that the shape of the surface is the same on both the positive and negative x-values. It is also a concave-up function, which means the graph is curved upwards.

Its vertex is located at the origin (0,0) and the equation of the parabola is y =\(x^2\). This means that the x-values of the graph can be any real number, while the y-values will always be non-negative as the square of any real number is always non-negative.

As x-values increase or decrease, the y-values will also increase, resulting in a smooth and continuous surface. Overall, the graph represents the upward parabolic shape of x squared.

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As the number of degrees of freedom for t-distribution increases, the difference between the t-distribution and standard deviation becomes smaller. The correct answer is B.

A t-distribution is described by one parameter, that is, degrees of freedom (df) v = n – 1, where n is the sample size. Its variance = v, where v represents the number of degrees of freedom and v ≥ 2.

To calculate degrees of freedom of a 1-sample t-test, we have to determine the size of our sample (N). Then, subtract 1. The result is the number of degrees of freedom.

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Answer:

the length of each side of the equilateral triangle = 17

Step-by-step explanation:

suppose the side length of equilateral triangle = x

The 3 side of right triangle formed (by side length): x-12 , x-13, x-14

(x-13)² + (x-14)² = (x-12)²  .... Pythagorean theorem

x² -26x + 169 + x² -28x + 196 = x² -24x + 144

x² - 30x +221 = 0

(x- 17) (x - 13) = 0

x = 17 or x = 13

if x = 13  the right triangle will have a side length of 13-13=0 ... not solution

x = 17

check: 17-12=5     17-13=4     17-14=3

3²+4² = 25 = 5²

The mistakes that were made regarding the transformation are:

It should be noted that a transformation simply means the changing of the position of an object

In this case, the transformation is incorrect as he applied the reflection to the pre-image first and used an incorrect angle of rotation around point P.

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Based on the information, we can infer that the tables are completed as follows: 5, 10, 15, 4, 8.

To complete the table of the ratios we must take into account the information provided in the fragment. According to the above, in box A for every two markers there are 5 pencils and in box B for every three markers there are 4 pencils. Then the ratios would be the following:

Box A

box B

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Answer:

Every numbered angle is 90 degrees

Step-by-step explanation:

Using the right angle we are given, linear pairs and a vertical angle give us that angles 1, 2, and 3 are also right angles.

Then using corresponding angles we can find that one of the 4-7 angles. From there we can use linear pairs the same as the first step.

Answer:

they are equal

Step-by-step explanation:

adding a 0 to a number that is a . doesn't change it's value unless it is infront of the number

Answer:

Step-by-step explanation:

c

Answer:

\(\frac{7^2}{p^8 \cdot q^9}\)

Step-by-step explanation:

\(\frac{p^{-8}}{7^{-2}} \cdot q^{-9} = \frac{\frac{1}{p^8}}{\frac{1}{7^2}} \cdot \frac{1}{q^9} = \frac{7^2}{p^8 \cdot q^9}\) by the definition of negative exponents: \(a^{-b} = \frac{1}{a^b}\) for all \(a,b\) so long as \(a\ne 0\).

The value of the exponential equation is A = 7²q⁹ / p⁸

When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.

The different Laws of exponents are:

mᵃ×mᵇ = mᵃ⁺ᵇ

mᵃ / mᵇ = mᵃ⁻ᵇ

( mᵃ )ᵇ = mᵃᵇ

mᵃ / nᵃ = ( m / n )ᵃ

m⁰ = 1

m⁻ᵃ = ( 1 / mᵃ )

Given data ,

Let the exponential equation be represented as A

Now , the value of A is

A = p⁻⁸ / 7⁻² ( q ) ⁻⁹   be equation (1)

On simplifying the equation , we get

A = 7² ( q ) ⁹ / p⁸

Therefore , the value of A is 7²q⁹ / p⁸

Hence , the exponential equation is A = 7²q⁹ / p⁸

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The function of the object height is an illustration of a projectile motion

The object will never hit the ground

The function is given as:

h=16t^2+80t+96.

When the object hits the ground, h = 0

So, we have:

16t^2+80t+96 = 0

Divide through by 16

t^2+5t+6 = 0

Expand

t^2 + 3t + 2t + 6 = 0

Factorize

t(t + 3) + 2(t + 3) = 0

Factor out t + 3

(t + 2)(t + 3) = 0

Solve for t

t = -2 or t = -3

The time (t) cannot be negative.

Hence, the object will never hit the ground

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Answer:

6

Step-by-step explanation:

did this question in savvas

Answer:

i think A

Step-by-step explanation:

correct me if I wrong k

(A) The required down payment is $48,000.

(B) The amount of the mortgage is $192,000.

(C) Monthly payment = $192,000 * (0.085/12) * (1 + (0.085/12))^(3012) / (((1 + (0.085/12))^(3012)) - 1)

(a) To find the required down payment, we need to calculate 20% of the house price.

Down payment = 20% of $240,000

Down payment = 0.2 * $240,000

Down payment = $48,000

The required down payment is $48,000.

(b) The amount of the mortgage is equal to the total cost of the house minus the down payment.

Mortgage amount = Total cost of the house - Down payment

Mortgage amount = $240,000 - $48,000

Mortgage amount = $192,000

The amount of the mortgage is $192,000.

(c) To find the monthly payment for the mortgage, we can use the formula for the monthly payment on a fixed-rate mortgage:

Monthly payment = P * r * (1 + r)^n / ((1 + r)^n - 1)

Where:

P = Principal amount (mortgage amount)

r = Monthly interest rate (8.5% annual interest divided by 12 months and converted to a decimal)

n = Total number of monthly payments (30 years multiplied by 12 months)

Monthly payment = $192,000 * (0.085/12) * (1 + (0.085/12))^(3012) / (((1 + (0.085/12))^(3012)) - 1)

Using this formula and performing the calculation will give you the monthly payment amount.

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The relationship in this problem is not proportional, as there are different ratios between the number of people and the number of cars washed.

A proportional relationship is a relationship in which a constant ratio between the output variable and the input variable is present.

The equation that defines the proportional relationship is a linear function with slope k and intercept zero given as follows:

y = kx.

The slope k is the constant of proportionality, representing the increase or decrease in the output variable y when the constant variable x is increased by one.

The ratios between the output and the inputs are given as follows:

Different ratios, hence the relationship is not proportional.

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Answer:

no solution

Step-by-step explanation:

2|x-1|=½X+8

|x-1|=x+1

2(x+1)=½X+8

2x+2=½X+8

multiple both side by 2

4x+4=x+16

4x-x=16-4

3x=12

x=4

The correct statement about the graph of the function f(x) = 2x²-x-6 is: "The range of the function is all real numbers; The function has two x-intercepts.

What is a function?

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

Here, we have

The given statements about the graph of the function f(x) = 2x² – x – 6 that are true include: The range of the function is all real numbers; The function has two x-intercepts.

Hence, the correct statement about the graph of the function f(x) = 2x²-x-6 is: "The range of the function is all real numbers; The function has two x-intercepts.

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The solution is, After decreasing £16870 by 3% we get, £16363.90.

Here, we have,

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%".

First, find the percentage of £16870 by 3%

%value = 3% * 16870

           = (3 / 100) * 16870

           = 506.1

Now, just minus with actual value

New value = actual value - %value

We know, actual value = £16870 and %value = 506.1

so, New value = 16870 - 506.1

we get, New value = £16363.90

Therefore, After decreasing £16870 by 3% we get, £16363.90

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complete question:

Decrease £16870 by 3%

Give your answer rounded to 2 DP.

Answer:

(5x)^2=5x^2

Step-by-step explanation:

you just remove the parenthsis.

ASA stands for "Angle-Side-Angle." Triangles classified as ASAs have two known angles and a common side. The ASA triangle ABC, with provided angles B and C and their common side a between them, is depicted below.

What does a congruence mean in mathematics?

If two numbers can be placed exactly over one another, they are said to be "congruent." When placed one on top of the other, the two bread slices are the same size and form. Things that are precisely the same size and shape are said to be congruent.

Describe ASA congruence through an example.

ASA (Angle-Side- Angle) 

According to the ASA rule, two triangles are said to be congruent if any two angles and the side included between the angles of one triangle are equal to the corresponding two angles and side included between the angles of the second triangle.

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Answer:

1.43

Step-by-step explanation:

12 tenths ⇒ 1.2

23 hundredths ⇒ 0.23

0.23 + 1.2 = 1.43

Answer:

100, 197, 13

Step-by-step explanation:

Total revenue from 1st movie

16×100 = 1600

Revenue from 2nd and 3rd movie = 4980 - 1600 = 3380

Total number of tickets sold = 310

Number of tickets sold for 2nd and 3rd movie combined = 310 - 100 = 210

Let x be number of 2nd movie tickets, y be number of 3rd movie tickets

x + y = 210, multiplying this by 13,

13x + 13y = 2730   (1)

13x + 18y = 3380   (2)

(2) - (1)

5y = 650

y = 13

x = 197

The slope of the line tangent to the graph of h(x) = 1/x + 3 at the point when x is -6 is -1/36.

To determine the slope of the line tangent to the graph of the given function when x = -6;

Using alternative form of the definition of derivative.

f'(a) = lim (h->0) [f(a+h) - f(a)] / h

Using this formula for the given function;

h'(a) = lim (h->0) [h(a+h) - h(a)] / h

Now, substitute a = -6 into the formula:

h'(-6) = lim (h->0) [h(-6+h) - h(-6)] / h

Next, simplify the expression by plugging in the values:

h'(-6) = lim (h->0) [1/(-6+h) + 3 - (1/-6 + 3)] / h

Simplifying further:

h'(-6) = lim (h->0) [1/(-6+h) - 1/-6] / h

Now, let's combine the fractions with a common denominator:

h'(-6) = lim (h->0) [(-6 - (-6+h))/((-6+h)(-6))] / h

Simplifying the numerator:

h'(-6) = lim (h->0) [-h / ((-6+h)(-6))] / h

Canceling out the h's:

h'(-6) = lim (h->0) [-1 / ((-6+h)(-6))]

Taking the limit as h approaches 0:

h'(-6) = -1 / ((-6)(-6))

Simplifying further:

h'(-6) = -1 / 36

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To ensure that there is an equal number of glass bears in each group, Mrs. Dryson constructed a total of 17 groups, which can be calculated using arithmetic operations.

What is arithmetic operations?

The study and application of numbers in all other fields of mathematics are covered in the area of mathematics known as arithmetic operations. Addition, subtraction, multiplication, and division are included in the basic operations.

As given in the question,

Mrs. Dryson divided her collection of 52 glass bears into equal groups and She had one bear left over

The steps listed below can be used to calculate the total amount of Mrs. Dryson's products:

Step 1: Arithmetic operations can be utilized to calculate Mrs. Dryson's overall output.

Step 2: Keep in mind that there are 52 glass bears in all, and after separating them into equal groups, she was left with just one bear.

Step 3 - The total bear population to divide into groups of an equal number is calculated as follows:

= 52 - 1 = 51

Step 4: The number that is divided by 51 such that the result is an integer is 3.

Step 5 - As a result, Mrs. Dryson created a total of the following groups:

= 51/3 = 17.

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The equivalent decimal and mixed number for given letter C is,

⇒ C = 8.2 ; 8 2/10

We have to given that,

A number line is shown in image.

Since,

A number lines are the horizontal straight lines in which the integers are placed in equal intervals.

And, All the numbers in a sequence can be represented in a number line. This line extends indefinitely at both ends.

Now, By given number line,

Point C is two point left from point 8.

Hence, The point C is denoted as,

⇒ C = 8.2

⇒ C = 82/10

⇒ C = 8 2/10

Therefore, the equivalent decimal and mixed number for given letter C is,

⇒ C = 8.2 ; 8 2/10

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