What is the height of a trapezoid with an area of 24 square inches if the two bases measure 4 inches and 6 inches?.

For the given data about about inscribed right circular cone of height 2.5 units and radius 7.5 units then the dimensions of the cylinder which has maximum volume is given by height = 0.83 units and radius 5 units.

As given in the question,

Height of the right circular cone = 2.5 units

And radius of right circular cone = 7.5 units

Let r be the radius of the cylinder and h be the height of the cylinder.

Volume of a cylinder 'V' = π r² h

Cylinder is inscribed in right circular cone

From origin edge cylinder is inscribed at x distance in right circular cone.

r = 7.5 - x

h = (2.5 /7.5) x

  = x/3

V  = π ( 7.5 - x )² ( x / 3)

⇒ V = π ( x² -15x + 56.25 ) (x/3)

⇒ V = (π /3)( x³ - 15x² + 56.25x)

For maximum volume ,

dV/dx = 0

dV/dx = (π/3)( 3x² -30x + 56.25)

(π/3) ≠ 0

⇒ 3x² -30x + 56.25 = 0

⇒ 3 ( x² -10x + 18.75) = 0

3 ≠ 0

⇒ x² -10x + 18.75 = 0

x = [ - (-10) ± √ (-10)² -4(1)(18.75)]/2(1)

⇒ x = [ 10 ± √ 100 -75]/2

⇒ x=  ( 10 ± 5 ) / 2

⇒ x = 7.5 or 2.5

As r = 7.5 -x

Hence x ≠ 7.5

r = 7.5 -2.5

 = 5 units

h = x/3

  = 2.5/3

  = 0.8333 units

Therefore, for the given data about about inscribed right circular cone of height 2.5 units and radius 7.5 units then the dimensions of the cylinder which has maximum volume is given by height = 0.83 units and radius 5 units.

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Using the properties of logarithm we get the value y = 100x⁻¹ in the exponential form axⁿ

The given logarithmic equation is :

log ₁₀y + log ₁₀x = 2

Now we know that: 1 = log₁₀10

∴log ₁₀y + log ₁₀x = 2× log₁₀10

or, log ₁₀y + log ₁₀x = log₁₀10² (10 raised to the power 2)

or,  log ₁₀y + log ₁₀x = log₁₀100

we know that log p+ log q = log pq

or, log ₁₀xy =  log₁₀100

Now we take antilog on both sides of the equation:

or, xy = 100

or, y = 100 / x

or, y = 100x⁻¹

Problems that cannot be solved using the concept of basic exponents alone can be solved with a logarithm. Simply said, a logarithm is another way to talk about exponents.

A relatively simple way to remember this is that base remains the base in both forms and base does not remain solely with exponent in log form. Be aware that "b" is the base on both the left and right sides of the implies symbol, and that when an equation is written in log form, the base b and exponent x do not necessarily stay on the same side of the equation.

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The Central Angle of the sector in radians is  0.3184 π  .

In the question ,

it is given that ,

the radius of the sector = 24 m

the area of the sector = 288 m²

we know that the Area of the sector of the circle is given by the formula

Area = πr²(θ/360)

Substituting the values , we get

288 = (3.14)*(24)²*(θ/360)

θ = (288*360)/((3.14)*(24)²)

θ = 1,03,680/1808.64

θ = 57.32°

converting the angle to radian ,

we get

θ = 57.32° ×  π/180 radian

= 0.3184 π

Therefore  , The Central Angle of the sector in radians is  0.3184 π  .

The given question is incomplete , the complete question is

A sector of a circle of radius 24 m has an area of 288 m² . find the central angle of the sector in radians .

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A retaurant cutomer left ​$1. 65 a tip. The tax was 6% and the tip was ​%15 of the cot including tax. Then the total bill is $13.31.

In the given question we have to find the total bill of the customer.

A retaurant cutomer left ​$1. 65 a a tip.

The tax was 6% and the tip was ​15% of the cost including tax.

The tip was 15%(0.15) of the cost including tax.

Thus 0.15*X= 1.65

Divide both sides of the equation by 0.15.

x = 11

Now 6%(0.06) tax on meal at 11 is

11* 0.06 = 0.66

So the total bill cost = 6% tax on meal + 15% tip on meal+cost of meal

The total bill cost = $1.65 + $11+0.66

The total bill cost = 13.31

A retaurant cutomer left ​$1. 65 a tip. The tax was 6% and the tip was ​%15 of the cot including tax. Then the total bill is $13.31.

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Answer: 119 minutes

Step-by-step explanation:

The ratio which compares to be a whole is:

2/9

Given,

Kenny has 2 red marbles and 4 black marbles.

we are asked to determine the ratio which compares a part to whole.

Based on the given conditions, formulate:

2 ÷ (4+2+3)

Calculate the sum

2/6+3

calculate the sum:

2/9

hence ratio is:

2/9

Hence we get the ratio as 2/9.

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Answer:

$455.75

Step-by-step explanation:

End amount = 200.00(1 + 0.04)^(21) = $455.75

Answer:

at least 17 sales

Step-by-step explanation:

On Wednesday she wants to earn 128.

Per day value = 60

128-60=68

She still needs to earn 68.

68 divided by 4=The number of sales needed to get 68 dollars=17

Thus she needs to make at least 17 sales, at most means maximum but she wants to earn AT LEAST 128 which means she wants more thus, answer is 4th option.

Answer:

XZ = 21 cm

Step-by-step explanation:

since the triangles are congruent then corresponding sides are congruent, so

LN = XZ , that is

5x - 19 = 2x + 5 ( subtract 2x from both sides )

3x - 19 = 5 ( add 19 to both sides )

3x = 24 ( divide both sides by 3 )\

x = 8

then

XZ = 2x + 5 = 2(8) + 5 = 16 + 5 = 21 cm

The angles found by the given figure are:

m∠5 = 97°

m∠7 = 97°

From the graph given we can get that the two parallel lines are cut by a transversal and:

m ∠4 = m∠2

m∠2 = 83°

hence, m∠2 + m∠5 = 180°

so,:

m∠5 = 180° - m∠2

= 180 - 83

= 97°

hence m∠5 = 97°

now, m∠7 = m∠5

since the vertical angles of two increasing lines are equal

so, m∠7 = 97°

Hence we get the two angles respectively.

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The algebraic expression to represent the given situation is 24/x where x is the number of students.

According to the question,

We have the following information:

Some students equally share 2 baskets of apples. Each basket has 12 apples.

Now, this situation can be presented to find the number of apples each student had.

Let's take the number to students to be x.

(x is the variable in this case.)

Number of apples one student had = total number of apples/number of students

Number of apples one student had = (2*12)/x

Number of apples one student had = 24/x

Hence, the algebraic expression to represent the given situation is 24/x where x is the number of students.

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The value of (tanx+2cosx) = [tex]2\frac{7}{20}[/tex].

Given that

sinx = [tex]\frac{3}{5}[/tex]

sinx = [tex]\frac{opp}{hyp}[/tex]

Using the Pythagoras' theorem

[tex]hyp^{2} = opp^{2} + adj^{2} \\\\adj^{2} = 5^{2}- 3^{2} \\ \\= 25-9\\\\adj^{2} = 16\\ \\adj = \sqrt{16} \\[/tex]

adj = 4.

Now we have to find out tanx and cosx

[tex]tanx = \frac{opp}{adj}[/tex]

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

[tex]cosx = \frac{adj}{hyp}\\ \\= \frac{4}{5}[/tex]

Now we have to find out the given equation (tanx+2cox)

[tex]= \frac{3}{4} +2(\frac{4}{5})\\ \\= \frac{15+32}{20} \\\\= \frac{47}{20} \\\\or\\\\= 2\frac{7}{20}[/tex]

Hence the answer is the value of (tanx+2cosx) = [tex]2\frac{7}{20}[/tex].

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The length of each side of the square is 4x - 1 while the area for the dimensions of the rectangle is (9x + 2y) by (9x - 2y) using the factorization methods of grouping and difference in two squares respectively.

Factorization is the process of breaking down a number in which when multiplied together will arrive at the original number.

Part A: Given the area of square as 16x² - 8x + 1, applying factorization by grouping;

16x² - 8x + 1 = 16x² - 4x - 4x + 1 (group terms with common factors)

16x² - 8x + 1 = 4x(x - 1) - (4x - 1) (factor out the common factor in each group)

16x² - 8x + 1 = (4x - 1) × (4x - 1) (factor the common factor from the expression)

16x² - 8x + 1 = (4x - 1)²

Part B: For the area or rectangle given as 81x² - 4y², factorizing by the method of difference in two squares;

81x² - 4y² = 9²x² - 2²y² (express as squares)

81x² - 4y² = (9x)² - (2y)²

81x² - 4y² = (9x + 2y) × (9x - 2y)

Therefore, 4x - 1 is the length of one side of the square as all sides of a square are equal and (9x + 2y) by (9x - 2y) is the dimension of the rectangle using the factorization methods of grouping and difference in two squares.

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Perimeter of the park = 10km

Part of the wall's construction completed =

[tex] \frac{4}{5}th \: of \: perimeter [/tex]

=

[tex] \frac{4}{5} \times 10[/tex]

(cancel 5 and 10)

=

[tex] \frac{4}{1} \times 2[/tex]

= 8km

•.• Part of the wall left (to be constructed) = 10km - 8km = 2km

HOPE THIS HELPS YOU

After factorizing we get the value as:

4sinαcosα

Given,

we have the expression as:

(sinα + cosα)² - (sinα - cosα)²

open the brackets using the identity of:

(a+b)² = a²+b²+2ab

(a-b)² = a²+b²-2ab

now evaluate:

⇒ sin²α + cos²α + 2sinαcosα - (sin²α + cos²α - 2sinαcosα)

⇒ sin²α + cos²α + 2sinαcosα - sin²α - cos²α + 2sinαcosα

⇒ cancel the like terms

⇒ 2sinαcosα  + 2sinαcosα

= 4sinαcosα

hence after factorization we get the value as 4sinαcosα

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The value of z such that 0.05 of the area lies to the right of z is 1.64.

Given:

0.05 = 5%

The z score is calculated:

z = x - μ / σ

from the t table the value of z is:

= 1.64

More details is in the image uploaded.

Therefore the value of z such that 0.05 of the area lies to the right of z is 1.64.

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Answer:

D

Step-by-step explanation:

Unit rates always compare quantities with different units

Ex. 10 km per 1 hour (10kph)

Answer:

Step-by-step explanation:

(2/3)20

The ordered pair P within the line segment AB is (- 1, 1 / 2).

In this question we have a segment whose endpoints are known: A(x, y) = (- 3, 2), B(x, y) = (5, - 4), and in which we need to determine the location of point P such that the following relationship is known:

k = AP / PB

[tex]\overrightarrow {AP} = k \cdot \overrightarrow {PB}[/tex]

P(x, y) - A(x, y) = k · [B(x, y) - P(x, y)]

(k + 1) · P(x, y) = A(x, y) + k · B(x, y)

P(x, y) = [1 / (k + 1)] · A(x, y) + [k / (k + 1)] · B(x, y)

Where:

If we know that A(x, y) = (- 3, 2), B(x, y) = (5, - 4) and k = 1 / 3, then the location of the ordered pair is:

P(x, y) = [1 / (4 / 3)] · (- 3, 2) + [(1 / 3) / (4 / 3)] · (5, - 4)

P(x, y) = (3 / 4) · (- 3, 2) + (1 / 4) · (5, - 4)

P(x, y) = (- 9 / 4, 6 / 4) + (5 / 4, - 1)

P(x, y) = (- 9 / 4, 3 / 2) + (5 / 4, - 1)

P(x, y) = (- 1, 1 / 2)

The ordered pair P is (- 1, 1 / 2).

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The length of the equator is 40192 km.

The radius of the earth is approximately 6400 km.  The equator is the circle around the earth dividing it into the northern and southern hemisphere.

Let's find the length of the equator as follows:

The length of the equator is the circumference.

Therefore,

L = 2πr

where

L = 2 × 3.14 × 6400

L = 6.28 × 6400

L = 40192 km

Therefore, the equator which is the circle around the earth has a length of 40192 km.

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Answer:

Step-by-step explanation:

13n=78        /13

n= 6

The correct answer is Men continue to earn more than women.

The average yearly wages of men and women are different from one another. Men make more money than women do.

What is the annual salary?

Annual earnings may also be referred to as annual income or yearly income. It displays a person's earnings over a specific time period.

The yearly earning of a person or a corporation is calculated by dividing the monthly earnings by the number of months in a year.

Men continue to earn more than women under the situation mentioned above, hence their wages are higher. The red line is always above the blue line.

As a result, choice A is accurate which is men continue to earn more than women.

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Answer: C. women's earnings have increased in relation to men's earnings

Step-by-step explanation:

The chart shows that

The amount of money that Richard will have when he turns 27 can be found to be $3, 474.26

Convert the interest rate to a periodic rate which will be in days as the interest is compounded daily:

= 7% / 365 days a year

= 0.019178%

The number of periods is:

= (27 - 15) years x 365 days a year

= 4, 380 days

The money that Richard will have when he turns 27 is:

= 1, 500 x ( 1 + 0.019178%) ⁴³⁸⁰

= $3, 474.26

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At the ski shack, customers can rent,skis, snowboards, boots, and poles by the day Mrs.Alvarez is renting skis and poles she has a 18$ coupon off

which expression represents the total cost for Mrs.Alvarez to rent skis for s days and poles for p days

If the answer you asked is this:

48s+12p-18  the correct answer

Step-by-step explanation:

d = number of dimes

n = number of nickels

one dime = $0.10

one nickel = $0.05

d = 3n

0.1×d + 0.05×n = 3.85

0.1×3n + 0.05×n = 3.85

0.3×n + 0.05×n = 3.85

0.35×n = 3.85

n = 3.85 / 0.35 = 11

d = 3n = 3×11 = 33

she has 33 dimes (and 11 nickels).

The dimensions of the box that minimizes the total cost is side of the square base is 7.23 m and height of the box is 4.82 m   .

In the question ,

it is given that ,

the bottom of the box is =  square ,

let the side of the square bottom be = "s" ,

so , the base area [tex]=[/tex] s²

let the height of the box [tex]=[/tex] h ,

Volume of the box = height × (base area)

So , the Volume of the box [tex]=[/tex] s²h

given that the volume of the box is 252 m³ , that means

s²h = 252

h = 252/s²

given that the Cost of bottom = $40 per m²

and the Cost of sides = $30 per m²

So , the total cost = 40s² + 30×(4sh)

substituting the value of h= 252/s² , we get

C = 40s² + 120s×252/s²

C = 40s² + 30240/s

to minimize the cost we differentiate with respect to s , and equating it  to 0 ,

we get ,

80s - 30240/s² = 0

s³ = 30240/80

s³ = 378

s = 7.23
again differentiating C = 40s² + 30240/s with respect to s , and equating it  to 0 ,

we get ,

d²C/ds² = 80 + (30240*2)/s³

at s=7.23 , d²C/ds² > 0

So , the minimum is at s = 7.23 ,

we have h = 252/(7.23)²

h = 4.82 .

Therefore , The dimensions of the box that minimizes the total cost is side of the square base is 7.23 m and height of the box is 4.82 m   .  

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From the equations , the company A is selling the phone for less money

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

The equations for Company A :

The smart phone price per month = $ 35.50

The smart phone price for 1 year = $ 35.50 x 12

                                                      = $ 426

The price for 1/12 th of a phone = $ 35.50

The price for the entire phone = ( Price for 1/12 th of a phone ) x 12

                                                   = $ 35.50 x 12

                                                   = $ 426

Now , The equations for Company B :

The smart phone price per month = $ 18.00

The smart phone price for 2 year = $ 18.00 x 24

                                                        = $ 432

The price for 1/24 th of a phone = $ 18.00

The price for the entire phone = ( Price for 1/24 th of a phone ) x 24

                                                   = $ 432

Therefore , we can clearly see that price of the smart phone offered by Company A is lesser than price of the phone offered by Company B

And , $ 426 < $ 432

Hence , from the equations , the company A is selling the phone for less money

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Tension in each string in the 3 - box system is T1 =  m2 * f/m, T2 = m3 *f/m, a = f/m1+m2+m3.

In 3 - box system:

There are two tensions and two strings, let T1 and T2 be the tensions.

Let mass of boxes be m1,m2,m3

total mass m = m1+m2+m3

Acceleration a = force / m

a = f/m1+m2+m3

T1 = m2 * f/m

T2 = m3 * f/m.

Therefore Tension in each string in the 3 - box system is T1 =  m2 * f/m, T2 = m3 *f/m, a = f/m1+m2+m3.

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The area of the composed rectangle and the semicircle is 92.56 square units.

Area of rectangle and semicircle

The formula for the Area of a Rectangle.

A = l × w.

where l refers length and w refers width of the rectangle

The area of a semicircle refers the half of the area of the circle. Therefore, the area of a semicircle is 1/2(πr²), where r is the radius.

Given,

Here we have the figure below composed of a rectangle and a semicircle And we need to find the area of this figure then round to the nearest tenth place.

Here we know the following values,

Length of the rectangle = 10

Width of the rectangle = 8

Diameter of the circle = 8

Through the given diameter we have identified the radius as 4.

Now, the area of the rectangle is calculated as,

A = 10 x 8

A = 80 square units.

Similarly, the area of the semicircle is

A = 1/2 (π x 4²)

A = 1/2 x π x 8

A = π x 4

We know the value of π = 3.14, then the area of the semicircle is,

A = 3.14 x 4

A = 12.56 square units.

Therefore, the are of the figure is,

Total area = area of rectangle + area of semicircle

Total area = 80 + 12.56

Therefore, the total area of the figure is 92.56 square units.

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