surface area of a hemisphere is 154 cm2, find its volume.

If the difference between the total **surface area **and **curved surface area **of a **hemisphere **is 154 cm2, then its **volume **is 718.66 cm³

In general, the term "**hemisphere**" refers to the lower half of the earth, such as the northern or southern **hemispheres**. A **hemisphere**, however, is a 3D figure that is created by splitting a sphere into two equal halves, each with one flat side, and is known as such in geometry.

In everyday life, we encounter a variety of objects that have a **hemisphere **shape, such as a cherry that is shaped like a **hemisphere** when cut in half or a grapefruit that has a **hemisphere **shape when cut in half.

The difference between the **total surface area **and **curved surface area **of a **hemisphere **is 154cm.

Total Surface Area of **Hemisphere **= 3πr²

And Curved Surface Area of **Hemisphere **= 2πr²

It is Given that

**Total Surface Area **of **Hemisphere **- **Curved Surface Area **of **Hemisphere**. = 154.

Substituting the values, we get,

⇒ 3πr² - 2πr² = 154

⇒ πr² = 154

⇒ r² = 154/π

⇒ r² = 154 × (7/22)

⇒ r² = 7 × 7

⇒ r = 7.

Now, lets find the **volume **which is

**Volume** of **Hemisphere **= 2/3πr³

V = 2/3π(7)³

V = 2/3(22)(7)²

V = 2156/3

V = 718.66 cm³

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Kelly drove 238 miles on 6 1/6 gallons of gasoline. Calculate how many miles per gallon she gets in her vehicle.

**Kelly** gets 38.59 miles per **gallon** of **gasoline**

**Miles** drove by Kelly = 238 miles

Gasoline used by the car = 6 1/6 gallons

**Gasoline** used in the car in improper fraction = 37/6 gallons

Average fuel economy: Average fuel economy of a car gives the distance covered by the car in one gallon of gasoline. This is an important factor to consider while buying or using a car as it is a major source of expenditure for the car.

To calculate miles per **gallon** we use the following formula:

Miles per gallon = Miles driven/ Gasoline used in the car

= 238/(37/6)

= 238*6/37

= 38.59

Miles per gallon = 38.59

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Write the quadratic function [tex]f(x)=\frac{1}{7} (x^{2} +14x+35)[/tex] in standard form and use it to find the axis of symmetry and the vertex.

**Answer:**

f(x) = 1/7 * (x + 7)^2 - 2

axis of symmetry: x = -7

vertex: (-7 | -2)

**Step-by-step explanation:**

f(x) = 1/7 * (x^2 + 14x + 35)

f(x) = 1/7 * (x^2 + 14x) + 5

f(x) = 1/7 * (x^2 + 14x + 7^2 - 7^2) + 5

f(x) = 1/7 * (x^2 + 14x + 7^2 - 49) + 5

f(x) = 1/7 * (x^2 + 14x + 7^2) + 5 - 7

f(x) = 1/7 * (x + 7)^2 + 5 - 7

f(x) = 1/7 * (x + 7)^2 - 2

A rectangle has an area of 40 square units. The length is

6 units greater than the width.

Mark this and return

What are the dimensions of the rectangle?

O 8 by 5

O 10 by 4

O11 by 9

O 13 by 7

Save and Exit

Next

Submit

The **dimensions** of the **rectangle **will be equal to 10 by 4.

A **rectangle** may be defined as the closed figure having **four sides** with the interior angles equal to 90°. it has two dimensions the length and the width. The** area** of a rectangle may be defined as the **product** of its length and width. According to the question the area of the rectangle is given as 40 square units. Let us assume the **length** as 'l' units and **width** as 'b' units. It is given that length is 6 units greater than the width that is l = (b + 6).

Now, the **area of the rectangle** = l×b

40 = (b + 6)×b

40 = b² + 6b

=> b² + 6b - 40 = 0

=> b = [-6 ± √(36 + 160)]/2

=> b = (-6 ± 14)/2

=>b = 4 units, since width cannot be **negative**.

Now, length = b + 6 = 10 units.

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simplify 0.027^2/3 PLEASE

**Answer:**

Hope the picture will help you

**Answer:**

2.718

**Step-by-step explanation:**

let x = .027^2/3

x=.027^.67

applying natural log on both sides

lnx = ln.027^.67

lnx = .67ln.027

lnx = 2.42004

applying antilog on both sides

x = e^2.42004

x = 2.718

thus, .027^2/3 = 2.718

The gas mileage m(x) (in mpg) for a certain vehicle can be approximated by m(x) = -0. 028x² + 2. 688x – 35. 012, where x is the speed of the vehicle in mph. A. Determine the speed at which the car gets its maximum gas mileage. B. Determine the maximum gas mileage

The **speed** for maximum car mileage will be 48 mph. The maximum gas **mileage** will be 29.5 mpg.

We are provided with an equation for **mileage** of car as

m(x) = -0.028x² + 2.688x -35.012

here , variable 'x' is the speed of the car.

Now

for the maximum speed of the car we have to first take the derivative of m(x) and then for the boundary value condition by putting the **derivative** equal to zero.

comparing to the equation ax² + bx + c , if the value of

'a' is positive, then we have minimum value at 1st derivative = 0

'a' is negative we have maximum value .

in this case a = -0.028 ( -ve) so we will have a maxima at 1st derivative.

so, dm/dx = -0.056x + 2.688

putting the 1st derivative = 0 , we have

x = 48

therefore , car gets maximum gas mileage at **speed** of 48 mph.

Also , putting this value in equation (1) we will get max. mileage.

so max. mileage = -0.028 (48)² + 2.688 x 48 - 35.012

= -64.512 + 129.024 - 35.012

= 29.5

so the maximum gas mileage will be 29.5 mpg .

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beth wants to paint a circular tabletop that has a radius of 3 feet. a small can of paint covers 15 square feet. how many cans will beth need to buy?

To paint the **circular** table top **Beth need** to buy 2 **cans** of paint .

In the question ,

it is given that ,

the** radius **of the **circular table top** is = 3 feet

So , the **area **of the circular table top is = π*r² = π*(3)²

= 9π

= 28.26

also given that

area covered by 1 **small can** of paint = 15 sq. feet

So , the number of cans needed to **paint **the table top is = (area of table top)/(area covered by 1 small can of paint)

On substituting the values , we get

number of cans needed to paint the table top is = 28.26/15

= 1.884

≈ 2

Therefore , To** paint** the** circular **table top Beth need to buy **2 cans **of paint .

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can someone please help me answer this im really confused. Thank you so much if you help!!

**Answer:**

y=2X - 6

**Step-by-step explanation:**

find the slope using the 2 points

m = 8-2/7-3 = 2

substitute 4,2 in the equation y=mx+b and solve for b.

2 = 2x4+b

b=-6

y = 2x - 6

**Answer:**

Slope intercept formula: y = 2x -6

Point Slope formula y = 2x-6

**Step-by-step explanation:**

1) Find the slope

2) Choose a point and plug it into the equation y = mx+b

3) Solve for b

4) Plug-in new slope (m) and new y-intercept (b) into equation y = mx+b

**Solving:**

4 = x1

2 = y1

7 = x2

8 = y2

to find slope with slope formula:

m = y2-y1/x2-x1 = 8-2/7-4 = 6/3 = 2

now plug in,

y = 2x+b

to find b, take any one of the pair

(i will choose (4,2) )

2 = 2(4) + b

now solve for b,

2 = 8+b

b = -6

**Slope intercept formula: y = 2x -6**

for point slope: y-y1 = m(x-x1)

as we know our slope is 2 and points are (0,-6) where 0 is x1 and -6 is y1

now we plug in,

y-(-6) = 2(x-0)

y+6 = 2x

**Point Slope formula y = 2x-6**

**Hope this helps! Please like!!**

:)

What type of pay is modeled below?

A. Hourly pay with a bonus. B. Hourly pay without a bonus. C. Commission pay D. Piece rate

The type of pay which is modeled in the image attached below is: D) **piece rate.**

Money or something paid for a purpose and especially as a salary or wage

The types of **pay.**

In Mathematics, there are four 5) different types of pay and these include:

The different types of compensation include:

Salary.

**Hourly Wages.**

Sales Commission.

Tips.

Stock Options.

Bonuses.

**Incentive Pay.**

Other Variable Pay.

Salary

Commission

Bonuses

**Piece rate**

Method of wage payment that remunerates the employees on the basis of quantity they produced is known as **piece rate.**

Plucking tea

The number of tee-shirts produced.

Pruning fruit trees

Sorting second-hand clothes (garments)

Hence the** **graph of a** piece** **rate** model is characterized by a **straight line **with the slope upwards as represented in the image attached.

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Below are ten scores for two different students. Students have a choice: they can take the median of their scores as their final grade, or they can take the mean of their scores as a final grade. Scores are rounded to the nearest whole number. For each student tell which option would result in the highest grade.

Student A: 25, 78, 80, 82, 85, 86, 88, 89, 96, 99

Student B: 71, 77, 77, 79, 79, 80, 88, 89, 91, 96

Find the median and mean for both students.

**Answer:**

**Step-by-step explanation:**

Student A:

**Mean** 80.8

**Median**: 85.5

*The Median is a higher score.*

Student B:

**Mean **82.7

**Median: **79.5

*Mean is a higher score*

**Answer:**

**Student A's median **and** Student B's mean** would result in the highest grade.

**Step-by-step explanation:**

*How to find the mean:*

The mean is the **average.**

Therefore, you must **add** all numbers listed, then **divide** the added numbers by the amount of numbers you added together. Lastly, as instructed round to the nearest whole number.

- Student A : **Mean = 81**

Step 1 : 25+78+80+82+85+86+88+89+96+99 = 808

Step 2: 808 ÷ 10 = 80.8

Step 3: 80.8 ---> 81

- Student B: **Mean = 83**

Step 1: 71+77+77+79+79+80+88+89+91+96 = 827

Step 2: 827 ÷ 10 = 82.7

Step 3: 82.7 ---> 83

*How to find the median:*

The median is the **middle number** in a sorted list of numbers.

Therefore, you list all of the numbers from **least to greatest**. Then, you get rid of a number from each side until you finally get to the **center** number. If there are **two numbers left in the center** you then **find the mean**(average) of those numbers.

- Student A: **Median = 86**

Step 1: Knock off a number from each side until you reach the center number(s)

25, 78, 80, 82, 85, 86, 88, 89, 96, 99 ---> 85, 86

Step 2: Find the mean(average) of the two central numbers

85 + 86 = 171 ---> 171 ÷ 2 = 85.5

Step 3: Round your answer

85.5 ---> 86

- Student B: **Median = 80**

Step1: Knock off a number from each side until you reach the center number(s)

71, 77, 77, 79, 79, 80, 88, 89, 91, 96 ---> 79, 80

Step 2: Find the mean(average) of the two central numbers

79 + 80 ---> 159 ÷ 2 = 79.5

Step 3: Round your answer

79.5 ---> 80

give two examples of each of linear equations

Some of the examples of linear equations are 2x – 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, 3x – y + z = 3.

Answer:

(2x + 5)/(x + 4) = 1

and

6x - 19 = 3x - 10

Step-by-step explanation

Linear euqations are the equation for the straight line. When graphed both equations will be straight lines.

Hope this helps you!

Complete the following statement. Use the integers that are closest to the number in the middle.

? < 90 < ?

The **integers** that are closest to the number in the middle will be 89 < 90 < 91.

It should be noted that an **integer** simply means a whole number that can be positive, negative, or zero.

It should be noted that on this case, we have to look for the **numbers** that are closest to 90 one has to be less than 90 and the other one should be **greater** than it.

Therefore, the **numbers** that fits the information will be 89 and 91.

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If you earn $7.50 per hour at your job how much will you earn if you work 25 hours?

**Answer:**

$187.5

**Step-by-step explanation:**

.

Answer:

187.50

Step-by-step explanation:

7.5(25)=187.50

hope this helped

have a good day^^

Idil is deciding between two different movie streaming sites to subscribe to. Plan A costs $18 per month plus $1 per movie watched. Plan B costs $8 per month plus $3 per movie watched. Let AA represent the monthly cost of Plan A if Idil watches x per month, and let B represent the monthly cost of Plan B if Idil watches x movies per month. Write an equation for each situation, in terms of x, and determine which plan would be cheaper if Idil plans on watching 6 movies each month.

The** cheaper plan** here would be** plan A. **The equation that is written in terms of the plans on movies is 0 < x < 5

For the plan A, we would have the function to be given as

A = 1x + 18

This is due to thge fact that this plan is said to cost $18 per month plus $1 per movie watched.

For plan B the function would have to be:

B = 3x + 8

The equation that we would have here would be

1x + 18 < 3x + 8

= x - 3x < 8 - 18

= -2x < -10

x < 5

Hence we would have the **equation** as 0 < x < 5

Cheaper plan

1x6 + 18 = 24

3x 6+ 8 = 18 + 8 = 26

Plan A id **cheaper**

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The half-life of a certain medication is 2 hours, and a patient takes a single 400-milligram dose of the medication.

After 6 hours, there will be X milligrams of medication left in the patient's body.

After 7 hours, there will be X milligrams of medication left in the patient's body. Round your answer to the nearest hundredth.

After 8 hours, there will be X milligrams of medication left in the patient's body.

The number of **milligrams** of medication medication left after 6 hours is; 50 milligrams.

The number of **milligrams** of medication medication left after 7 hours is; 35.36 milligrams.

The number of **milligrams** of medication medication left after 8 hours is; 25 milligrams.

It follows from the task content that the amount of medications left in the patient's body be determined in each case.

Recall the formula for the amount of substance remaining for half life situations is as follows;

A = N (1/2)^(t/half-life)

Since **half life** = 2 hours and **N** = 400 milligrams;

Hence;

At t = 6hrs; A = 400(1/2)^(6/2) = 400(1/2)³ = 50millograms.At t = 7hrs; A = 400(1/2)^(7/2) = 400(1/2)^(3.5) = 35.36 millograms.At t = 8hrs; A = 400(1/2)^(8/2) = 400(1/2)⁴ = 25 millograms.Read more on **half-life**;

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A right pyramid has a surface area of 258 cm2. A right cone has a base radius of 4 cm. The cone and pyramid have equal surface areas. What is the height of the cone to the nearest tenth of a centimetre?

The **height of the cone** to the nearest tenth of a centimeter is** 17.40 cm.**

From the given information provided in the question, we can solve this problem by following a few steps.

The surface area of a right pyramid is** 258 cm²** according to the question.

The surface area of the cone is equal to the surface area of the right pyramid. Therefore the surface area of the cone is also **258 cm².**

The surface area of a cone is denoted as** ( πrh + πr² )**.

Where h is denoted as the **height **and, r is denoted as the **radius of the cone** which is **4 cm.**

Hence the surface area of the cone is,

**SA = (π× 4× h+ π× 4² ) cm²**

Now, we can generate an equation, as **both represent **the value of the **surface area** of the cone.

(π× 4× h+ π× 4² ) = 258

Or, (12.56h + 39.44) = 258 [ **The value of π is 3.14 **]

Or, 12.56h = 258 - 39.44 [ subtracting 39.44 from both sides ]

Or, 12.56h = 218.56

Or, h = 218.56/12.56 [ dividing both sides by 12.56]

Or, h = 17.40

Now, we can conclude that the** **height of the cone is **17.40 cm.**

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keisha's basketball team must decide on a new uniform. the seventh-graders will pick the color of the shorts (black or gold) and the eighth-graders will pick the color of the jersey (black, white, or gold), but the two groups of players will not confer together. if, for both garments, each possible color is equally likely to be chosen, what is the probability that the shorts will be a different color than the jersey? express your answer as a common fraction.

The **probability **that the shorts of the basketball team will be of a different color than the jersey is **2/3**.

Probability can be found using the following formula;

probability = number of favorable outcomes or events ÷ total number of outcomes or events

In order to calculate the probability that the **shorts **will be of a different color than the **jersey**, we first determine the total number of combinations that are possible;

1- Black-Black

2- Black-White

3- Black-Gold

4- Gold-Black

5- Gold-White

6- Gold-Gold

Hence there are a total of 6 possible combinations of shorts and jerseys out of which 2 are the same and 4 are different.

Therefore the probability that the shorts will be of a different color can be calculated as follows;

probability = number of favorable outcomes or events ÷ total number of outcomes or events

probability = 4 ÷ 6

probability = 2/3

Hence, 2/3 is the probability that the shorts will be of a different color than the jersey.

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Leo has three times as many colored marbles as he has clear-glass marbles. In total, he has 60 marbles. How many clear-glass marbles does he have?

**Answer:**

15

**Step-by-step explanation:**

Supposing:

Coloured marbles = x

Glass marbles = y

According to Question

x = 3y

As,

x + y = 60

3y + y = 60 (putting value of x = 3y)

4y = 60

y = 60/4

y = 15

Hence, Leo has 15 Clear-glass marbles

3. A tomato sauce company currently sells tomato sauce in a

cylindrical can that has a radius of 5 cm and a height of 12 cm.

They have plans to use larger cans to sell tomato sauce in bulk.

The new cylindrical cans are to be similar to the original cans

and have a height of 60 cm.

If the original can holds 1487 cm³ of tomato sauce,

how much tomato sauce will the new can hold?

√x cm³

V=

** Tomato sauce will the new can hold is ** 743[tex]cm^{3[/tex]

**let take us take,**

**V = Sh **

[tex]S_{1} =S_{2}[/tex]** **

** **[tex]h_{1[/tex] = 12 cm

[tex]h_{2}[/tex] = 60 cm

[tex]\frac{V_{1} }{V_{2} } = \frac{h_{1} }{h_{2} }[/tex]

[tex]\frac{1487}{v_2} } = \frac{12}{60}[/tex]

= 743[tex]cm^{3[/tex]

What is Height? **Height** means the vertical **distance**, either between the top and bottom of something or between the bottom and the thing above it. height refers to being tall or short as measured **vertically**.

Height is a way of measuring someone or something from the bottom to the top or from the **head** to the **feet**. In other words, height indicates how tall someone or something is. We can compare how tall we will be when we grow up. We often compare the** average height** of men and women in different countries.

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PLEASE HELP!!!!! It’s algebra

Answer:

k=3/10

Step-by-step explanation:

8y=12x+6 >>>>(÷8) both sides

y= (3/2)x+(3/4)

if x=0, y=3/4

4y=k(3x+10) >>> plug in (0, 3/4)

4(3/4)= k(0+10)

3= 10k >>> (÷10) both sides

k=3/10

Nura made a square poster with a side length of 13 inches. Latrice made a square poster with a side length of 15 inches. Whats the difference in square inches between the area of Latrice's poster and the area of Nura's poster?

The **difference **between the **areas **of the posters is **56 in²**.

There are different quadrilaterals, for example: square, rectangle, rhombus, trapezoid, and parallelogram. Each type is defined accordingly to its length of sides and angles. For example, in a square, all angles are 90° and all sides present the same value.

The **area **of a **square **is given by: **A= a²**, where a=the **length of the sid**e.

A=(13 in)²

A= 169 in²

Area of square poster's LatriceA=(15 in)²

A= 225 in²

Therefore, the difference in square inches between the area of Latrice's poster and the area of Nura's poster is 225 - 169=56 in²

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Referring to the image how does 2 become 8?

**Answer:**

see explanation

**Step-by-step explanation:**

each term inside the parenthesis is raised to the exponent outsie, that is

(2xy)³

= 2³ × x³ × y³ ← 2³ = 2 × 2 × 2 = 4 × 2 = 8

= 8x³y³

Perpendicular to y=-5x+1 passing through (2,-1)

The **equation** of the line** perpendicular **to the given line will be equal to 5y = x - 3.

A **line** may be defined as a straight figure which is drawn and has no **end points**. The **equation** of line in **slope intercept** form may be written as **y = mx + c** where m is the** slope** and c is the** y intercept**. The equation of line passing through a point (x₁, y₂) will be given as (y - y₁) = m(x - x₁). The slope of line **perpendicular** to a line having slope m is given by -1/m. The equation of line in the question is y = -5x + 1. The **slope** of the line is -5. The slope of line perpendicular to this line is 1/5.** Equation **of line passing through (2, -1) and slope 1/5 is given by

(y + 1) = 1/5(x - 2)

5y + 1 = x -2

5y = x - 3 which is the required **equation**.

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Please help me please I’m begging I WILL GIVE YOU BRAINLEST 1-8

**Answer: have you tried m a t h w a y**

**Step-by-step explanation:**

He number of nano-related patents that are granted in the us increases by a factor of 1.21.21, point, 2 every year. in 199119911991, there were 606060 nano-related patents. which expression gives the number of patents in 199819981998?

The **exponential** function y = 60(1.2)7 yields the number of patents in 1998.

The formula for an **exponential** function is f (x) = ax, where x is a variable and an is a constant that serves as the function's base and must be bigger than 0. The **transcendental** number e, or roughly 2.71828, is the most often used **exponential** function basis. Let y be the number of nanotechnology-related patents issued in the US in year x following 1991.

There were 60 patents on nanotechnology in 1991, and since then there has been a factor of 1.2 increase.

y = 60(1.2)ˣ

y = 60 in 1998 (7 years ago) (1.2)⁷

The **exponential** function is used to calculate the number of patents in 1998.

y=60(1.2)⁷

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1. A trapezoid is pictured on the right. Its bottom base a is not changing while its top base b is increasing at the rate of 3 inches per second while its height h is decreasing at the rate of 0.5 inches per second. How fast is the area of the trapezoid changing, measured in square inches per second, at this moment?

A) -2.5

B) -.75

C) 1

D) 2

(Please explain)

Answer:

the answer is A...

Step-by-step explanation:

Calculate Area (A):

The area formula for a square is denoted below:

A = s2

Taking the square root of both sides, we get:

s = √A

s = √3

s = 1.7320508075689

May you guys/girls please help me I have to submit this before midnight and I do not fail because my parents will get me , so may y'all please help me out!?

1 over 2

1/2

Rise / run

1/2

Rise / run

**Answer:**

Slope = 1/2 or 0.5

**Step-by-step explanation:**

Picking two integer points on the line, (any)

(-3, 2) and (-1, 3)

We can find the slope

(3-2)/(-1-(-3)

=1/2

:]

Nathan eats the same amount of lunch meat everyday. If Nathan eats 2 pounds of lunch meat in 8 days, he eats pound(s) of lunch meat per day

Using **fraction**, He consumes **1/4 pound** of **lunch meat **each day.

A fraction, expresses a** piece of a whole,** a fraction, such as one-half, eight-fifths, or three-quarters, specifies the number of **components **of a respective size.

Given,

He consumes **2 pounds **of beef in** 8 days.**

We need to determine how much meat he consumes each day.

To ascertain:

He consumes** 2/4 of a pound **of beef in a day.

**= 1/4**

He thus consumes **1/4 pound **or less of lunch meat every day.

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Please help!! It’s geometry and I just need the answer quick

**Answer:**

4.5

**Step-by-step explanation:**

Here is a polygon.

Draw a scaled copy of the polygon with scale factor 3.

**Scaled copy **of the **polygon **with scale factor 3 is given below.

A **polygon **is a closed **polygonal chain **made up of a finite number of straight line segments and is a type of planar figure in **geometry**. A polygon is a region that is bounded by a bounding circuit, a bounding plane, or both.

A **polygonal circuit's **segments are referred to as its edges or sides. A polygon is a geometric object with two dimensions and a finite number of sides. A polygon's sides are made up of segments of straight lines that are joined end to end.

Polygons include shapes like **triangles**, **quadrilaterals**, pentagons, and hexagons. The shape's number of sides is indicated by the name. A quadrilateral has four sides, whereas a **triangle **has three.

To learn more about **polygon **from given link

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x^2 - xy = 14

y^2 +xy = 60

Use a calculator boom

The answer is

**x = 7, -7, √2, -√2**

**Add **the two equations to get

x2 + y2 = 74

**Eliminate **y from the first by solving for y and using that result:

(x2 − 14) = x√74 - x2

**square **both sides, then condense:

x4 − 51x2 + 98 = 0

These ready **factors**:

(x−7)(x+7)(x−√2)(x+√2)=0

I'll let you handle it from there, but keep in mind that if we square all sides, we might find roots that need to be pulled out afterward.

Therefore,

**x = 7, -7, √2, -√2**

Let's learn more about the **functions **of **Equations**

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