Postal regulations specify that a parcel sent by priority mail may have a combined length and girth of no more than 171 in. Find the dimensions of the cylindrical package of greatest volume that may be sent via priority mail. (Hint: The length plus the girth is 2r + l.)
r =
l =
volume =

The percentage of having a probability of a non-vowel letter is 44%

Probability is the measure of the likelihood that an event will occur in a given set of circumstances. It is a quantifiable measure of the chance of something happening. Probability is expressed as a number between 0 and 1 (or 0% to 100%) where the higher the number, the more likely the event is to occur.

The probability to select a vowel letter is = 15 + 22 + 11 + 6 + 2 = 56%

The probability of selecting any vowel is 56%

In the English alphabet, we have 26 letters and 5 vowel letters.

The probability of not having a vowel letter is calculated as;

26 - 5 = 21

P = 21 / 28

In percentage, we can simply say the probability of having a non-vowel is 100 - 56 = 44

The percentage of having a non-vowel is 44%

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Answer: X= -2

Step-by-step explanation:

Regroup means regrouping refers to rearranging integers into place value-based groupings to facilitate operations.

Given that,

We have to find what does it mean to regroup.

We know that,

When performing operations like subtraction and addition, regrouping is accomplished by creating groups of tens. Regrouping refers to rearranging integers into place value-based groupings to facilitate operations.

Because you must rearrange the numbers into place value to complete the procedure, it is known as regrouping. Regrouping is an excellent approach to simplify complicated mathematics, especially for kids. Regrouping with subtraction is sometimes referred to as "borrowing."

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Answer:
a) Provider B would be cheaper
b) [tex]10m^3[/tex]

Step-by-step explanation:
a) Input 6 into both equations and solve. For Provider A, it would go like this: [tex]y = 6 + 15[/tex]. For Provider B, it would be this: [tex]y = 2(6) + 5[/tex]. The first provider adds up to £21 Pounds ($25.56 USD). The second provider adds up to £17 Pounds ($20.69 USD).

b) All you really need to do is just plug in numbers until both equations contain the same answer. The way I did it was: [tex]x + 15 = 2x + 5[/tex]. If your teacher asks how you got the answer, follow these steps:

[tex]x+15=2x+5\\x-5=2x-5\\x+10=2x[/tex]

Rounded to the nearest cent, the final value of Irlene's investment at the end of the third year is $4,431.78.

A percentage of the principal, or the amount loaned, is what a lender charges a borrower as interest. The annual percentage rate, or APR, is the usual unit used to express the interest rate on a loan (APR).

To calculate the value of Irlene's investment at the end of the third year, you can use the formula for compound interest:

FV = PV * (1 + r/n)^(n*t)

Where:

FV is the future value of the investment (what you want to find)

PV is the present value of the investment (the initial amount, $3,500)

r is the annual interest rate (the rate for the third year is 5.25%)

n is the number of compounding periods per year (for the first year it was 2, for the second year it was 2, and for the third year it was 4)

t is the number of years the money is invested (3 years in this case)

Plugging the values into the formula, you get:

FV = $3,500 * (1 + 5.25%/2)^(23) * (1 + 5.25%/4)^(41)

= $3,500 * (1.0263)^6 * (1.0131)^4

= $3,500 * 1.1496 * 1.0534= $4,431.77

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The equation of the tangent line to the curve at the given point (−3, 3, 1) (asteroid) is y-[tex]\sqrt{3}[/tex] = [tex]\sqrt{3}(x+3)[/tex]

Applying implicit differentiation, the equation of the tangent line is given by:

y - [tex]\sqrt{3}[/tex] = [tex]\sqrt{3}[/tex] (x+3)

The equation of a line tangent to a function f(x) at a point (x0, y0) is given by:

y-y0 = f'(x0,y0)(x-x0)

In this problem, point (-3, [tex]\sqrt{3}[/tex]), thus x0 = -3, y0 = [tex]\sqrt{3}[/tex]

The function is:

[tex]x^{2} /3+ y^{2}/3 = 4\\[/tex]

To find the derivative, we have to apply implicit differentiation, thus:

[tex]2x/3* dx/dx + 2y/3*dy/dx = 0[/tex]

[tex]2y/3*dy/dx = -2x/3[/tex]

[tex]dy/dx = -x/y[/tex]

Thus:

[tex]f(-3, \sqrt{3)} = -(-3/\sqrt{3} * \sqrt{3}/\sqrt{3})[/tex] = [tex]\sqrt{3}[/tex]

Then, the equation to the line tangent is:

y-y0 = f'(x0,y0)(x-x0)

y-[tex]\sqrt{3}[/tex] = [tex]\sqrt{3}(x+3)[/tex]

Refer to this complete question:

Use implicit differentiation to find an equation of the tangent line to the curve at the given point x2/3 + y2/3 = 4 (−3, 3, 1) (asteroid).

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The circumcenter theorem states that the circumcenter of a triangle is the point of intersection of the perpendicular bisectors of the sides of the triangle. In other words, the circumcenter is the center of a circle that passes through all three vertices of the triangle.

The circumcenter theorem is a fundamental theorem in geometry and is used in the construction of the circumcenter of a triangle. The circumcenter is the point of intersection of the perpendicular bisectors of the sides of the triangle, and its coordinates can be determined by the coordinates of the triangle's vertices.

This theorem is useful in many applications, such as in: the construction of a triangle from its circumcenter, or in determining the distance between two points. It can also be used to determine the area of a triangle from its three vertices. The circumcenter theorem has been studied for centuries, and it is still an important tool for geometers and mathematicians today.

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The factored form of the equation x² + 3x - 10 is  (x - 2)(x + 5)  .

In the question ,

it is given that ,

the equation is x² + 3x - 10 , we have to express it in factor form ,

So , rewriting the equation by using the split the middle term method .

= x² + 3x - 10

= x² + 5x - 2x - 10     , ...because   5x - 2x = 3x

taking  x common from the first two terms ,

we get ,

= x(x + 5) - 2(x + 5) taking (x+5) common from both the terms ,

we get ,

= (x - 2)(x + 5)

Therefore , the factor form is  (x - 2)(x + 5) .

The given question is incomplete , the complete question is

What is the factored form of x² + 3x - 10  ?

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a) Amy's monthly budget for Rent based on the total budget for housing and food is $853.

b) Amy's monthly budget for Utilities based on the total budget for housing and food is $142.

c) Amy's monthly budget for Food based on the total budget for housing and food is $427.

The total budget for Housing, Utilities, and Food for nine months = $12,798

Rent = 60%

Utilities = 10%

Food = 30%

Budget period = 9 months

Budget for rent = $7,679 ($12,798 x 60%)

Monthly budget for Rent = $853 ($7,679/9)

Budget for utilities = $1,280 ($12,798 x 10%)

Monthly budget for Utilities =  $142 ($1,280/9)

Budget for food = $3,839 ($12,798 x 30%)

Monthly budget for Food =  $427 ($3,839/9)

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Answer:17/30 lbs

Step-by-step explanation:

Answer: ABC and AED are congruent by SSS. SSS is if three sides of a triangle are congruent to 3 sides of another triangle, then the triangles are congruent. AB and AE are both 7, BC is congruent to ED and CA is congruent to DA because of the tick marks.

Answer:

26

Step-by-step explanation:

The simplified form of the given algebraic expression is 3x²√5x. The correct option is с. 3x²√5x

From the question, we are to simplify the given algebraic expression.

The given expression is

√45x^5

First, we will write the given expression properly

The expression written properly is

√45x⁵

Simplifying

√45 × √x⁵

√9×5 × √x⁴×x

√9 × √5 × √x⁴ × √x

3 × √5 × x² × √x

3 × x² × √5 × √x

3x² × √5×x

3x² × √5x

3x²√5x

Hence, the simplified expression is 3x²√5x

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Answer:

400 square feet

Step-by-step explanation:

1.  Opposite angles are equal in measure.

and

2. Diagonals bisect each other.

3. Any two adjacent angles add up to 180 degrees.

Properties of rhombus:

1.   All sides are equal in length.

2.  Opposite angles are equal.

3.   Diagonals bisect each other at 90°.

4.   Diagonals are respective angle bisectors.

5.   Any two adjacent angles add up to 180 degrees.

6.  The area of the rhombus is a product of the lengths of the 2  diagonals divided by 2.  

Properties of rectangle:

1.  Opposite sides are equal in length.

2.  All the angles are 90°.

3.  Diagonals bisect each other.

4.  Any two adjacent angles add up to 180 degrees.

Hence, the common properties are

1.  Opposite angles are equal in measure.

and

2. Diagonals bisect each other.

3. Any two adjacent angles add up to 180 degrees.

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The composition of two isometries is an isometry.

Proof:

Let T1 and T2 be isometries. T1(A) = A' and T1(B) = B'. Therefore by isometry T1, AB = A'B'

T2(A) = A'' and T2(B) = B''. Therefore by isometry T2, AB = A''B''

T2 º T1 = T2(T1(A)) = T2(A') = A'''. T2 º T1 = T2(T1(A)) = T2(B') = B'''. Therefore under composition AB = A'''B''' and distance is preserved.

The inverse of an isometry is an isometry.

Proof:

Given T and isometry. This means T(A) = A' and T(B) = B' with AB = A'B'

The inverse of T, T⁻¹maps A' to A and B' to B, so A'B' maps to AB.

But A'B' = AB and so the inverse is an isometry

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Answer: Barry's Swimwear sold a greater fraction of the bathing suits in stock as long as the store had fewer than 72 bathing suits in stock.

Step-by-step explanation:

Barry's Swimwear sold 15 out of an unknown number of bathing suits in stock, so we can express this fraction as 15/x, where x is the total number of bathing suits in stock at Barry's Swimwear. Similarly, Philip's Sun Wear sold 5 out of 72 bathing suits in stock, so we can express this fraction as 5/72.

To compare these two fractions, we need to express them with a common denominator. One way to do this is to find the least common multiple of the two denominators, which in this case is 72. To express 15/x with a denominator of 72, we can multiply both the numerator and the denominator by a factor of 72/x. This results in the fraction 15*(72/x)/72 = 15/x. Similarly, we can express 5/72 with a denominator of 72 by multiplying both the numerator and the denominator by a factor of 72/72, which results in the fraction 5*(72/72)/72 = 5/72.

Now that we have both fractions expressed with a common denominator of 72, we can compare them directly. 15/x is greater than 5/72 as long as x is less than 72. This means that Barry's Swimwear sold a greater fraction of the bathing suits in stock as long as the store had fewer than 72 bathing suits in stock.

Answer:

Point slope: y - 115 = 2(x -30)

Slope intercept: y = 2x + 55

Step-by-step explanation:

I choice the first point to write the equation in the point slope form of a line.

(30,115)

Slope is the change in y over the change in x.  I see that the y's are increasing by 10, while the x's are increasing by 5

10/5 = 2

The slope is 2

y = y = m( x + x)

y - 115 = 2(x - 30)

Slope intercept form of a line

We already found the slope to be 2.  Use the slope and the point (30,115) to find x

y = mx + b

115 = 2(30) + b

115 = 30 + b    Subtract 30 from both sides

55 = b

y = 2x + 55

Watching basketball games and liking the flavor of coconut "are" independent events because the probability of a teenager from the group watching basketball games "is not equal to" the probability of a teenager from the group watching basketball games given that they like the flavor of coconut.

Independent events is the events which occur freely of each other. An event A is said to be independent of another event B if the probability of occurrence of one of them is not affected by the occurrence of the other.

We observe that the event of watching basketball games does not affect liking the flavour of coconut, hence they are independent events their probabilities are most likely not the same.

Therefore, we use "are" for the first statement to show the two events are independent and "is not equal to" for the probability statement.

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Cumulative markup percent for department at the end  is 23.1%.

The men's furnishing department had an opening inventory of $168,000 at cost  with a markup of 48.5%

Cumulative markup is  the difference between the total wholesale cost and total retail price of all merchandise handled during a given period of time.

cumulative markup dollars are the total markup dollars on all merchandise for a selected selling period. To calculate cumulative markup dollars and cumulative markup percent, the following formulas are utilized by the retailer:

Cumulative Markup $ = Total Retail $ - Total Cost $

Cumulative Markup % = Cumulative Markup $ ÷ Cumulative Retail $

Steps for calculating cumulative markup percentage for the specified period of time:

Step 1. Calculate the unknown retail value for either opening inventory or purchases.

Step 2. Calculate total retail of opening inventory and purchases.

Step 3. Calculate the unknown cost value for either opening inventory or purchases.

Step 4. Calculate total cost of opening inventory and purchases.

Step 5. Calculate total markup dollars.

Step 6. Calculate cumulative markup percent for the specified period of time.

For opening inventory

retail = $168,000

cost = 168,000*48.5/100 = $81480

For purchases

retail = 80,000*52.5/100 = $42000

cost  = $80,000

total retail of opening inventory and purchase =

168,000+42000 = $210000

total cost of opening inventory and purchase =

81480+80,000 = $161480

total markup = total retail - total cost

total markup  = 210000-161480 = 48520

cumulative markup percent = (total markup/ total retail)

= (48520/210000)*100

= 0.23104761904*100

=23.1%

So cumulative markup percent for department at the end  is 23.1%.

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The volume of the tissue box is 85⅓ cubic inches.

The correct answer option is option D

Volume of the tissue box = Base area of the rectangular prism × Height of the rectangular prism

= 16 square inches × 5⅓ inches

= 85⅓ cubic inches

Therefore, the rectangular prism has a volume of 85⅓ cubic inches

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Answer: the first one is 30 ml

Therefore ,the true bearing of the plane and its speed is ∝=-71.9° and 324.31 mph

A thing with both magnitude and direction is called a vector. A vector can be visualized geometrically as a directed line segment, where the direction is indicated by an arrow and the length of the segment equals the magnitude of the vector. From the vector's tail to its head is the direction of motion. According to the definition of a resultant vector, a single vector is one that has the same result as several other vectors taken together.

Here,

To find the true bearing of the plane and its speed.

We find the vector component,

Since  N75°W is same as 95°+90°=165°

Thus,

f(x)=300cos100 +50cos165 = -100.39

f(y)=300sin100 +50sin165= 308.38

next we find resultant

R=[tex]\sqrt{f(x)^{2}+f(y)^{2} }[/tex]

R=[tex]\sqrt{(-100.39)^{2}+(308.38)^{2} }[/tex]

R=[tex]\sqrt{105178.35}[/tex]

R=324.31 mph

The bearing of the plane=> ∝=[tex]tan^{-1}[/tex](308.38/-100.39)

So  ∝=-71.96°

Therefore ,the true bearing of the plane and its speed is ∝=-71.96° and 324.31 mph

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Answer:

$77.50

Step-by-step explanation:

Since each cookie cake feeds 6, she can buy enough cakes to feed 6, 12, 28, 24, 30, 36, etc. people.

The smallest number above 29 she can feed is 30.

Each cookie cake feeds 6.

30/6 = 5

She needs to buy 5 cookie cakes.

5 × $15.50 = $77.50

Answer:

D: f(x) · g(x) =12x^2-25x+12

Step-by-step explanation:

we multiply the 2 equations

(3x-4)(4x-3)

12x^2-9x-16x+12

12x^2-25x+12

so d is the answer

hopes this helps please mark brainliest

The restriction on the variables x and y are given as follows:

x ∈ W, y ∈ W.

The three sets of numbers that appear in this problem are given as follows:

The number of tickets sold cannot assume decimal values, hence we know two things:

The number of tickets also assumes only values of zero or positive numbers, they cannot be negative, hence it is a whole number and the second option is correct.

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The monthly take home pay if your take-home pay is calculated as 46 hours per week; is $2,606.6.

What is monthly take home pay?

The amount of money left over after taxes, benefits, and other deductions from a paycheck is known as take-home pay. It is the difference left over after subtracting all gross income deductions.

Let,

Number of hours per week = 46 weeks.

Regular hourly wage up to 40 hours = $15.90

Wage up to 40 hours = 40 x 15.90 = $636

Hours over 40 hours, wage is 1.5 times as much

Wage of hour  41 - 46 = 6 x 1.5 x 15.90 = $143.10

Total weekly wage = 636 + 143.10 = $779.10

Since 1 month = 4.345 weeks.

Therefore,

Monthly wage = Weekly wage x 4.345

                        = 777.10 x 4.345

Monthly wage = $3385.19

Now maximum and assurance = 23% of monthly wage

= 23% of 3385.19

= 0.23 x 3385.10

= $778.59

Therefore,

Monthly take home pay = Monthly wage - Tax

                                        = $3385.19 - $778.59

Monthly take home pay = $2606.6

Hence, the monthly take home pay if your take-home pay is calculated as 46 hours per week; is $2,606.6.

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Answer:

24 square units

Step-by-step explanation:

1/2 times base times height is the formula for the area of a triangle

the base is 12

the height is 4

1/2(12)(4)

6(4)

24

hopes this helps please mark brainliest

After reflecting the quadrilateral EFGH across the line y = 2, the x-coordinates of the corresponding points in the image and the preimage will be the same.

Generally,  Reflection is an isometry, which means that it preserves distance and angles. Therefore, the x-coordinates of the points in the image and the preimage will not be changed by the reflection. The y-coordinates will change since the reflection flips the points over the line of reflection.

For example, if quadrilateral EFGH has a vertex at (x, y), then the corresponding vertex in the image will be at (x, 2 - y). The x-coordinate remains the same, but the y-coordinate is reflected across the line y = 2.

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