Draw and label a rectangle with an area of 32 square units and a perimeter of 36 units

The dimensions of the can of greatest volume that can be made with 150 square inches of tin are a radius of approximately 5.78 inches and a height of approximately 3.85 inches.

The dimensions of the soup can of greatest volume that can be made with 150 square inches of tin are given by the formula [tex]V = \pi r^2h[/tex], where V is the volume of the can, r is the radius of the base, and h is the height of the can. We can solve for the radius and height of the can using the given information.

Let the radius of the base be r and the height of the can be h. Then, the surface area of the can is given by the formula [tex]A = 2\pi rh + 2 \pi r^2[/tex]. We are given that the surface area of the can is 150 square inches, so we can write the equation [tex]2 \pi rh + 2 \pi r^2 = 150[/tex]. We need to find the dimensions of the can that maximize its volume, V. To do this, we can use the formula for the derivative of V with respect to r, which is [tex]dV/dr = 2 \pi rh + \pi r^2 dh/dr[/tex].

Setting this equal to zero and solving for h, we get [tex]h = -2r/3[/tex]. Substituting this into the equation for A, we get the equation [tex]2 \pi r(-2r/3) + 2 \pi r^2 = 150[/tex], which simplifies to [tex]-4 \pi r^2/3 + 2 \pi r^2 = 150[/tex]. Solving for r, we get [tex]r = 5.78[/tex] inches. Substituting this into the equation for h, we get [tex]h = -3.85[/tex] inches.

Since we cannot have a negative height, we must discard this value and take the positive value of h, which is approximately 3.85 inches. Therefore, the dimensions of the can of greatest volume that can be made with 150 square inches of tin are a radius of approximately 5.78 inches and a height of approximately 3.85 inches.

See more about volume at: https://brainly.com/question/27710307

#SPJ11

Answer:

You didn't give any options, but I'm guessing one of them has a 3 in the tens digits, which should be the right answer

Step-by-step explanation:

300?

Answer:

x = - 2

Step-by-step explanation:

the equation of a vertical line parallel to the y- axis is

x = c ( c is the value of the x- coordinates the line passes through )

the line passes through all points with an x- coordinate of - 2 , then

x = - 2 ← equation of line

Explanation:

2n is greater than 20, so 2n > 20. This solves to n > 10 after dividing both sides by 2. That inequality is the same as 10 < n.

5n is less than 60. It leads to 5n < 60. That solves to n < 12 after dividing both sides by 5.

To summarize:

Combine 10 < n with n < 12 to write a compound inequality:

10 < n < 12

The value n is between 10 and 12. We exclude each endpoint.

The only possible whole number that works here is n = 11

(a) The present value of an annuity formula can be used to calculate the monthly payment: Payment is equal to (PV x I / (1 - (1 + i)(-n)).

Where PV is the loan's present value, I is its monthly interest rate (0.035 / 12), and n is the number of payments (15 years multiplied by 12 months every year = 180 months).

Applying the values provided, we obtain:

(136,000 x 0.002917) / (1 - (1 + 0.002917)(-180)) is the amount to be paid.

Amount paid: $1,054.63

Hence, the installment will be $1,054.63 per month.

(b) By deducting the loan amount (PV) from the total amount paid over the loan's lifetime, it is possible to get the total interest payment:

Total interest equals PV minus (Payment x n)

Applying the values provided, we obtain:

$1,054.63 multiplied by 180 equals $136,000 in interest.

Interest totaled $88,833.40.

The total interest payment will therefore be $88,833.40.

(c) The Turners will have paid 120 times over the course of 10 years (10 years x 12 months/year). To determine their equity, we can apply the formula for calculating a loan's remaining balance:

The remaining balance is calculated as follows: PV x (1 + i)n - Payment x (1 + i)n - 1)/i

Where n denotes how many payments are still due (180 - 120 = 60).

Applying the values provided, we obtain:

The remaining balance is calculated as follows: $136,000 x (1 + 0.002917)60 - $1,054.63 x (1 + 0.002917)60 - 0.002917

Balance remaining: $71,587.90

As a result, their equity will be $170,000 (the original purchase price) less $71,587.90 (the outstanding balance) = $98,412.10 after ten years.

Learn more about Simple interest here:

brainly.com/question/25845758

#SPJ1

Each pair of numbers (m, h) which meet the inequality is the answer to the inequality. m < h plus 2.

A factor pair is a collection of two factors that, when multiplied together, produce a certain result in mathematics. In those other words, it's a pair of integers that we multiply to produce a result. For instance, the factor pair that yields the result in the multiplication formula 6 7 = 42 is composed of the numbers 6 and 7. 42

By adding 14 to both sides, starting with -14 + 7m 7h, we may simplify the left side:

-14 + 7m plus 14 < 7h plus 14

Even more condensed, we get at:

7m < 7h plus 14

The inequality can then be divided by 7 on both sides: m h + 2.

To know more about pairs of numbers visit:

https://brainly.com/question/16823918

#SPJ1

Answer:

Step-by-step explanation:

which band?

The principal sum is Rs. 1640 if the difference in simple interest between 3 years and 4 years is Rs. 82 at a rate of 5% per annum.

Let x be the principal sum. According to the problem, the difference in simple interest between 3 years and 4 years is Rs. 82. This means that the interest earned in the fourth year is Rs. 82 more than the interest earned in the third year.

Using the formula for simple interest, we can calculate the interest earned in each year:

Simple interest for 3 years = (x * 5% * 3) = 0.15x

Simple interest for 4 years = (x * 5% * 4) = 0.2x

The difference between the two is:

0.2x - 0.15x = 0.05x

We are given that this difference is equal to Rs. 82, so:

0.05x = 82

Solving for x, we get:

x = 82 / 0.05 = 1640

Therefore, the principal sum is Rs. 1640.

Learn more about the simple interest here: brainly.com/question/25845758

#SPJ4

The sugar concentration would be approximately 62.5%.

To find the concentration of sugar in the solution, we need to use the formula:

In this case, the solute is sugar and the solvent is water. We are given that the mass of sugar is 50 grams and the mass of water is 30 grams. However, we need to convert the mass of water to volume since we need the volume of the entire solution to calculate the concentration.

We can assume that the density of water is 1 g/mL, so the volume of water is 30 mL. The total volume of the solution is therefore 50 mL + 30 mL = 80 mL.

Now we can use the formula to find the concentration of sugar:

So the concentration of sugar in the solution is approximately 0.625 grams per milliliter.

learn more about Sugar:

https://brainly.com/question/501165
#SPJ4

Value of angle x is 41 degree.

A straight line is a one-dimensional geometric object that extends infinitely in both directions. It can be defined as the shortest path between two points in a plane, and it has a constant slope (i.e., rate of change) between any two points on the line.

The standard equation for a straight line in slope-intercept form is y = mx + b, where m is the slope of the line and b is the y-intercept (the point where the line intersects the y-axis). Another commonly used form is the point-slope form, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line.

Given, total angle=236°

236°=76°+119°+x

x=236°-76°-119°

x=41°

Hence, Value of angle x is 41 degree.

To know more about slope, visit:

https://brainly.com/question/3605446

#SPJ1

The figures created are a square and a right triangle, and the perimeter of the entire figure is (13x/3) + x × sqrt(10).

When Namandu divides the top side of the square into three equal parts, he creates two segments of length x/3 each. By connecting the first point of division with the vertex of the parallel side, he creates a right triangle with legs of length x/3 and x, and hypotenuse of length y.

Using the Pythagorean theorem, we can solve for y:

y^2 = (x/3)^2 + x^2

y^2 = x^2/9 + x^2

y^2 = (10x^2)/9

y = x×sqrt(10)/3

Now we can find the perimeter of each figure that is created

Perimeter of the original square = 4x

Perimeter of the right triangle = x + x/3 + y = x + x/3 + xsqrt(10)/3

Perimeter of the entire figure = 4x + x + x/3 + xsqrt(10)/3 = (13x/3) + x×sqrt(10)

Learn more about Pythagorean theorem here

brainly.com/question/14930619

#SPJ4

The coordinates of the point P is (-1,2) .

What is translation?

In mathematics, a translation is a geometric transformation that moves every point of a figure or a space by the same amount in a given direction. The amount and direction of the movement can be described using a vector, which is a mathematical object that has both magnitude and direction.

Finding the coordinates of the point P :

The coordinates of point P can be found by subtracting the vector from point Q.

To find the coordinates of point P, we need to subtract the vector [tex]\begin{pmatrix}4\\-3\end{pmatrix}[/tex] from the coordinates of point Q, which are (3, -1).

Subtracting the x-coordinate of the vector from the x-coordinate of point Q gives us:

3 - 4 = -1

Similarly, subtracting the y-coordinate of the vector from the y-coordinate of point Q gives us:

-1 - (-3) = 2

Therefore, the coordinates of point P are (-1, 2).

So, the correct answer is (C) (-1, 2).

To know more about coordinates visit :

brainly.com/question/16634867

#SPJ1

Answer:

If the store marks up the price of the diving board by 45%, the selling price will be 100% + 45% = 145% of the cost price.

Let's calculate the selling price:

Selling price = Cost price + Mark-up

Mark-up = Selling price - Cost price

Mark-up = (145% of cost price) - cost price

Mark-up = 0.45 * cost price

We know that the store paid $261 for the diving board, so:

Mark-up = 0.45 * $261 = $117.45

Therefore, the amount of the mark-up is $117.45.

well, what's 45% of 261?

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{45\% of 261}}{\left( \cfrac{45}{100} \right)261}\implies \text{\LARGE 117.45}[/tex]

Answer:

the value of x is approximately 0.382 cm.

Step-by-step explanation:

The equation of the circle in standard form is (x-5)² + (y+1)² = 9. The center of the circle is (5,-1) and the radius is 3.

To write the equation of the circle in standard form, we need to complete the square for both x and y terms:

x² - 10x + y² + 8y + 37 = 0

(x² - 10x + 25) + (y² + 8y + 16) + 37 = 25 + 16

(x - 5)² + (y + 4)² = 6²

So the equation of the circle in standard form is (x - 5)² + (y + 4)² = 36.

The center of the circle is (5, -4), and the radius is 6.

Learn more about standard form equation here: brainly.com/question/12452575

#SPJ4

Answer:

center is 5,-4 radius is 2

Step-by-step explanation:

Answer:

Elise's average pay per hour for the year 2017 was £11.88.

Step-by-step explanation:

First, we need to calculate Elise's monthly salary in 2017 after the 3% increase:

3% of £2100 = 0.03 x £2100 = £63

Elise's new monthly salary in 2017 = £2100 + £63 = £2163

Next, we need to calculate her total earnings in 2017:

Total earnings = monthly salary x number of months worked

Elise worked for 45 weeks in 2017, which is approximately 10.4 months:

Total earnings = £2163 x 10.4 = £22,477.20

Finally, we can calculate her average pay per hour for the year:

Total number of hours worked = 42 hours/week x 45 weeks = 1890 hours

Average pay per hour = total earnings / total number of hours worked

Average pay per hour = £22,477.20 / 1890 hours = £11.88 per hour

Answer:

I got $13.73 per hour

Step-by-step explanation:

If you multiply 2100 by 12 months you get $25200 for an annual salary before percent increase.

Then you include the 3% salary increase each month 25200 x .03 = 756 then add the two 25200 + 756 = 25956 OR you can calculate the longer way by doing each individual month, either way it will be the same answer. 2100 x .03 = 63 then 2100 + 63 = 2163 then 2163 x 12 = 25956

Then you divide 25956 by the number of weeks worked in the year. 25956/45 = 576.8

So, each week $576.8 was earned.

Then to get an hourly rate, you divide this by the number of hours worked in each week. 576.8/42 = 13.73

So, the hourly rate is $13.73.

I hope this helped :)

By using the formula of a geometric sequence, the 14th term will be 125/1024

We have, the Fourth term of geometric sequence T_4= 125 and T_10 = 125/64

Let's find the first term and common ratio of the geometric sequence.

Using the formula of the nth term of a geometric sequence, we get,

T_4 = a * r^3 = 125 ....(1)

and,

T_10 = a * r^9 = 125/64 ...(2)

On dividing eq. (2) by eq. (1), we get,

(r^6) = (125/64) / 125 ⇒ 1/64

Taking the sixth root of both sides, we get:

r = (1/64)^(1/6)

r = 1/2

Now that we know the common ratio, we can use the equation for the nth term of a geometric sequence:

T_n = a * r^(n-1)

To find the 14th term, we substitute n=14 and solve:

T_14 = a * (1/2)^(14-1) ⇒ a * (1/2)^13

We don't know the value of a yet, but we can use the fact that the 4th term is 125 to solve for it:

a * r^3 = 125

a * (1/2)^3 = 125

a = 125 * 2^3

a = 1000

Substituting this value for a, we get:

T_14 = 1000 * (1/2)^13

T_14 = 1000 * 1/8192

T_14= 125/1024

Therefore, the 14th term of the geometric sequence is 125/1024.

To know more about the "geometric sequence": https://brainly.com/question/24643676

#SPJ11

The significance of a pedigree symbol consisting of a square with a diagonal slash mark through it is that it represents the male members of the family

It is a standard symbol in a pedigree chart. This symbol represents the sex of a person, in this case, it represents the male sex. In other words, a square with a diagonal slash mark through it is used to represent the male gender in pedigree charts.

A pedigree chart is a diagram that shows the genetic relationships between individuals in a family. It is used to track genetic diseases or traits through generations. A pedigree chart can provide information about a family's medical history and can help doctors to understand how genetic disorders are inherited from one generation to the next. Each symbol used in the pedigree chart has a specific meaning.

The squares represent males while the circles represent females. The horizontal line between two symbols represents marriage, and the vertical line from a symbol represents a child of that union.

See more about symbol at: https://brainly.com/question/1389310

#SPJ11

The probability that the 3rd card is a heart if the first card was a heart and the second card was a club is approximately 0.0152. It is the product of the probabilities.

The probability that the 3rd card is a heart if the first card was a heart and the second card was a club when three cards are drawn without replacement from an ordinary deck of 52 playing cards.

There are 13 hearts in a deck of 52 cards.

Therefore, P(1st card is a heart) = 13/52 = 1/4

There are 13 clubs in a deck of 52 cards. Since one heart is already drawn in the first card, there are only 51 cards left in the deck.

Therefore, P(2nd card is a club) = 13/51

There are only 12 hearts remaining in the deck since one heart is already drawn in the first card. There are only 50 cards left in the deck since two cards are already drawn.

Therefore, P(3rd card is a heart) = 12/50 = 6/25

The probability that the 3rd card is a heart if the first card was a heart and the second card was a club is:

P(3rd card is a heart | 1st card is a heart and 2nd card is a club) = P(1st card is a heart) × P(2nd card is a club) × P(3rd card is a heart) = (1/4) × (13/51) × (6/25) = 39/5,775 = 0.0152 (rounded to 5 decimal places)

Therefore, the probability that the 3rd card is a heart if the first card was a heart and the second card was a club is approximately 0.0152.

Learn more about Probability here:

https://brainly.com/question/30034780

#SPJ11

When the function d(x) = -x +(-3), then the value of d(0) is -3

In mathematics, a function is a relationship between two sets of numbers, called the domain and range. A function assigns each element of the domain to exactly one element of the range.

In the given problem, we are given a function d(x)=-x-3. The notation d(0) represents the value of the function d(x) when x = 0.

To find d(0), we need to substitute x = 0 in the function d(x)=-x-3, which gives:

d(0) = -(0) - 3

The first term -(0) is equal to zero, and the second term -3 is a constant value that remains the same regardless of the value of x. Therefore, we can simplify the expression as

d(0) = -3

Learn more about function here

brainly.com/question/12431044

#SPJ4

the statement "A Triangle with side lengths 20,21, and 28 is a right triangle" is invalidated.

As, You may simply rule out the first three options if you are familiar with specific Pythagorean triples and other triangle relationships.

Pythagorean triples consist of the three positive numbers a, b, and c, where a2+b2 = c2. The symbols for these triples are (a,b,c). Here, a represents the right-angled triangle's hypotenuse, b its base, and c its perpendicular. The smallest and most important triplets are (3,4,5).

So,

20² +21² = 400 +441 = 841 = 29²

The appropriate choice is  20, 21, and 29

To know more about Pythagorean triples, click the below link

https://brainly.com/question/15190643

#SPJ4

The sample size is 12 with an error calculation of 5 if 97% of the confidence interval is around a sample mean of 31. 3.

Percent confidence = 97

Sample mean =  31. 3

Standard deviation = 7. 6

Sample size = 40

Error calculation = 5

The formula for a confidence interval using the t-distribution is:

CI = x ± tα/2 * (s/√n)

CI = 31.3 ± 2.423 * (7.6/√40)

CI = 31.3 ± 3.940

CI = (27.36, 35.24)

The population mean with an error of 5,

n = (Zα/2 * σ / E)^2

Assuming a 95% confidence level, the sample size is,

n = (1.96 * 7.6 / 5)^2

n = 11.69

Therefore we can conclude that the sample size is 12 with an error calculation of 5.

To learn more about Sample size

https://brainly.com/question/30646963

#SPJ4

The total surface area of the remaining portion is approximately 23.14 in.

To find the total surface area of the remaining portion of a wooden sphere after two equal caps have been removed, use the formula SA = 4πr2. A sphere is symmetrical, and thus, the diameter of the wooden sphere is equal to the diameter of the remaining portion. The radius of the remaining portion is equal to half the diameter of the sphere minus the radius of the cap.

The diameter of the wooden sphere is 11.8 in. As such, the radius of the sphere is 5.9 in. If two equal caps are removed, the diameter of the remaining portion is equal to 11.8 in - 2x R_cap, where R_cap is the radius of the cap. Since the caps are equal, we can simplify the formula to

D = 11.8 - 2R_cap. R_cap is equal to the radius of a circle with area equal to the surface area of one cap. As such, we can use the formula SA = 2πrh + πr2 to find the surface area of the cap. We know the diameter of the sphere is 11.8 in. Thus, the radius of the sphere is 5.9 in. We also know that the height of the cap is 5.9 in. Since the caps are equal, we can use the formula to find the surface area of one cap and multiply by 2 to get the total surface area of both caps.

SA_cap = 2π(5.9 in)(5.9 in) + π(5.9 in)

2SA_cap = 2π(34.84 in2) + π(34.84 in2)

SA_cap = 2π(34.84 in2) + 109.45 in2SA_cap ≈ 219.74 in

Since the surface area of the cap is equal to 219.74 in, we can use the formula to find the radius of the cap.

219.74 in = 2πrh + πr22(219.74 in2)

= 2π(5.9 in)h + π(5.9 in)22(219.74 in2)

= 37.699 in2 + 109.45 in23r2

= 72.533 in2r ≈ 4.545 in

Using the formula D = 11.8 - 2R_cap, we can find the diameter of the remaining portion of the wooden sphere.

D = 11.8 - 2(4.545 in)D ≈ 2.71 in

The radius of the remaining portion of the wooden sphere is equal to 5.9 in - 4.545 in. Thus, the radius of the remaining portion of the sphere is 1.355 in. Finally, we can find the total surface area of the remaining portion of the sphere.

SA = 4πr2SA = 4π(1.355 in)2SA ≈ 23.14 in

Therefore, the total surface area of the remaining portion is approximately 23.14 in.

To learn more about total surface area of sphere refer :

https://brainly.com/question/14692728?

#SPJ11

Answer:

When x = 0, y = 2^0 + 6 = 7. So the first point is (0, 7).

When x = 1, y = 2^1 + 6 = 8. So the second point is (1, 8).

When x = 2, y = 2^2 + 6 = 10. So the third point is (2, 10).

When x = -1, y = 2^-1 + 6 = 6.5. So the fourth point is (-1, 6.5).

When x = -2, y = 2^-2 + 6 = 6.25. So the fifth point is (-2, 6.25)

The measurement of  of angle c is (4x-24. 6) and measure of angle d is (x+11. 3). If the angles are supplementary, the value of x is 38.66.

The measure of angle c is (4x-24. 6)

The measure of angle d is (x+11. 3)

If both angles are supplementary angles then,

angle c + angle d = 180

(4x-24. 6) + (x+11. 3) = 180

5x - 13.3 = 180

5x = 180 + 13.3

5x = 193.3

x = 193.3/5

x = 38.66

So, the value of x is 38.66

What distinguishes complimentary from supplementary angles?

Two angles are said to be supplementary angles because they combine to generate a linear angle when their sum is 180 degrees. When two angles add up to 90 degrees, however, they are said to be complimentary angles and together they make a right angle.

To know more about supplementary angles, click the below link

https://brainly.com/question/13045673

#SPJ4

Therefore, the volume of the solid obtained by rotating the region bounded by the curves y = x^2, y = 0, x = 0, and x = 1 about the line x = 2 is (5/6)π cubic units.

To find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line, we use the method of cylindrical shells. The formula for the volume of a cylindrical shell is given as,
Volume = 2πrh * Δx

Where, r is the distance of the shell from the axis of rotation, h is the height of the shell, and Δx is the thickness of the shell. The factor 2π accounts for the entire circumference of the shell.
Example problem: Find the volume of the solid generated by rotating the region bounded by the curves y = x^2, y = 0, x = 0, and x = 1 about the line x = 2.
Solution:
Step 1: Draw the graph of the region to be rotated
Step 2: Identify the shell radius and height
For a shell at position x, the radius is given by r = 2 - x (the distance of the line x = 2 from the axis of rotation)
The height of the shell is given by h = x^2 (the difference between the top and bottom curves)
Step 3: Write the volume formula
Volume = 2πrh * Δx
Step 4: Integrate to find the total volume
The limits of integration are from 0 to 1 since the curves intersect at (0,0) and (1,1).
[tex]∫ 2π(2 - x)(x^2) dx from 0 to 1[/tex]
= [tex]2π [∫ 2x^2 - x^3 dx from 0 to 1][/tex]
= [tex]2π [(2/3) - (1/4)][/tex]
= 2π [5/12][tex]2π [5/12][/tex]
= (5/6)π cubic units
for such more questions on  integration

https://brainly.com/question/22008756

#SPJ11

The probability that a person chosen at random at age 40 or older has only completed high school is 0.2912.

Probability is the chance or likelihood that something will occur. It is quantified using numbers, ranging from 0 (no chance) to 1 (certainty). It also helps us to draw conclusions about the chances of something happening based on the available data.

The total number of people who have only completed high school

=(5394)

the total number of people in the age group 40 and over =(18521)

By dividing both the data, we get

5394/18521= 0.2912

From the given data in the table, we can calculate the probability that a person chosen at random at age 40 or older has only completed high school.

For more questions related to data

https://brainly.com/question/19243813

#SPJ1

Answer:

15/x * 100 %

Step-by-step explanation:

Since we don't know the total, we have 15/x * 100 % as the percent of how many people passed the test. (x is amount of people, 15 or greater.)

209 went to the first game.

192+17=209

Happy to help.