Solve each formula for the indicated variable. A = 1/2h(b₁ + b₂) , for b₂

Pattern of the given terms -4,-3,-2,-1, . . is arithmetic progression and common difference 'd' = 1 , next three terms are 0, 1,2

As given,

Given pattern is -4,-3,-2,-1, . . .

a₁ =-4

a₂ =-3

a₃ =-2 ….

d =a₂ - a₁

  =-3 - (-4)

  =1

Pattern is arithmetic progression with d=1.

aₙ =a₁ + (n-1)d

a₅ =a₁ + (5-1)d

  =-4 +4(1)

  =0

a₆ =-4 + 5(1)

    =1

a₇ =-4 +6(1)

   =2

Therefore, pattern of the given terms -4,-3,-2,-1, . . is arithmetic progression and common difference 'd' = 1 , next three terms are 0, 1,2

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.

Answer:

he will take the same time as its the same flow of water so he will spend 9 min and 2 sec

We can use the pythagorean theorem to answer this question.

We know that [tex]l[/tex] is the hypotenuse, and the 2 sides are 7 and 7.

So, we can build the equation:

[tex]7^2+7^2 = l^2[/tex]

[tex]98 = l^2[/tex]

[tex]\sqrt{98} = l[/tex]

The Spaceship Earth geosphere at Epcot in Disney World in Orlando, Florida, a sphere building measuring 165 feet in diameter, has a volume of 2,352,071 cubic feet.

Volume refers to the amount of space occupied by a three-dimensional object.

Based on the problem, the Spaceship Earth geosphere at Epcot in Disney World in Orlando, Florida is a sphere building measuring 165 feet in diameter. If radius is half of the diameter, then it has a radius of 82.5 feet.

The volume of the Spaceship Earth geosphere can be calculated using the formula for the volume of a sphere given by:

V = 4/3 π r^3

V = 4/3 π (82.5 feet)^3

V = 4/3 π (561,5151.625 cubic feet)

V = 2,352,071.15 cubic feet

Rounding off to the nearest cubic foot,

V = 2,352,071 cubic feet

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Answer:

Step-by-step explanation:

3

2

​

−

2

3

​

y+

3

1

​

y+4=0

Combine −

2

3

​

y and  

3

1

​

y to get −

6

7

​

y.

3

2

​

−

6

7

​

y+4=0

Convert 4 to fraction  

3

12

​

.

3

2

​

−

6

7

​

y+

3

12

​

=0

Since  

3

2

​

 and  

3

12

​

 have the same denominator, add them by adding their numerators.

3

2+12

​

−

6

7

​

y=0

Add 2 and 12 to get 14.

3

14

​

−

6

7

​

y=0

Subtract  

3

14

​

 from both sides. Anything subtracted from zero gives its negation.

−

6

7

​

y=−

3

14

​

Multiply both sides by −

7

6

​

, the reciprocal of −

6

7

​

.

y=−

3

14

​

(−

7

6

​

)

Multiply −

3

14

​

 times −

7

6

​

 by multiplying numerator times numerator and denominator times denominator.

y=

3×7

−14(−6)

​

Do the multiplications in the fraction  

3×7

−14(−6)

​

.

y=

21

84

​

Divide 84 by 21 to get 4.

y=4

By solving for the density of the two metal cubes, we can determine that the two metal cubes are not made from the same material.

Density, denoted by ρ, is a property of any substance that is defined as the ratio between the mass and volume of the substance.

ρ = m/v

where ρ = density

m = mass

v =  volume

Solving the density of each cube.

Cube 1 :

ρ = m/v

ρ = m/e^3

ρ = 43. 63 g/(3. 2 cm)^3

ρ = 1.3315 g/cm^3

Cube 2 :

ρ = m/v

ρ = m/e^3

ρ = 683. 5 g/(8. 34 cm)^3

ρ = 1.1783 g/cm^3

If two objects have the same density, then they are made from the same material. Since the density of the two cubes are not equal, then they are not made form the same material.

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Answer:

search up

Step-by-step explanation:

A

The position function x(t) of a moving particle with the given acceleration a(t)=3t is 3 *t^2 / 2.

The position is the object can depend on where you are, and the description might also change if it is based on where other objects are.

The velocity is the time rate of change of position of a body in a specified direction. the rate of speed with which something happens.

Acceleration is the act or process of moving faster or happening more quickly: the act or process of accelerating rapid acceleration is the acceleration of economic growth.

a(t) = 3t

d^2/dx^2=(3t)

x(t) = [tex]\int\limits {3t} \, dt[/tex]

    = 3 *t^2 / 2

Hence the position function x(t) of a moving particle with the given acceleration a(t)=3t is 3 *t^2 / 2.

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Answer:

4/12

Step-by-step explanation:

If the ratio 4:8 is a part-to-part ratio, it means that there are 4 of something and 8 of something else with a total of 12. To convert a part-to-part ratio such as 4:8 as a fraction, you make the left side of the colon the numerator and the total the denominator: 4:8 → 4/12

Based on the time that Rex walked and the time that Samir walked, we can say that Samir walked TWO times as many hours as Rex walked.​

To find out how many times more Samir walked than Rex, divide the number of hours walked by Samir by the hours walked by Rex.

Solving gives:

= 3¹/₃ ÷ 1²/₃

= 10/ 3 ÷ 5/3

= 10/3 x 3/5

= 30/ 15

= 2 times more

In conclusion, Samir walked two times more.

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Answer:

Step-by-step explanation:

Based on the time that Rex walked and the time that Samir walked, we can say that Samir walked TWO times as many hours as Rex walked.​

How many times more did Samir walk?

To find out how many times more Samir walked than Rex, divide the number of hours walked by Samir by the hours walked by Rex.

Solving gives:

= 3¹/₃ ÷ 1²/₃

= 10/ 3 ÷ 5/3

= 10/3 x 3/5

= 30/ 15

= 2 times more

In conclusion, Samir walked two times more.

The value of x is 4.89 ≈ 5 units

Given,

The figure includes two right angled triangles.

Consider the first right angled triangle:

Hypotenuse = 7 units

Base = 3 units

Altitude = a

By using Pythagorean theorem, we can find a.

That is,

Hypotenuse² = Altitude² + Base²

7² = a² + 3²

49 = a² + 9

a² = 49 - 9

a² = 40

Altitude = [tex]\sqrt{40}[/tex]  units

Now consider second right angled triangle:

Hypotenuse = [tex]\sqrt{40}[/tex] units

Altitude = 4 units

Base = x units

Apply Pythagorean theorem:

Hypotenuse² = Altitude² + Base²

([tex]\sqrt{40}[/tex])² = 4² + x²

40 = 16 + x²

x² = 40 - 16

x² = 24

x = [tex]\sqrt{24}[/tex]

Base, x = 4.89 ≈ 5 units.

Therefore, the value of x is 4.89 which is approximately equals to 5 units.

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The equation of the line in standard form passing through the points (-4 , 6) and (2 , -2) is 4x + 3y = 2.

The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.

The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant.

Given two points, (-4 , 6) and (2 , -2), use the two-point form to generate the equation of the line.

y - y2 = [(y2 - y1)/(x2 - x1)] (x - x2)

y - -2 = [(-2 - 6)/(2 - -4)](x - 2)

y + 2 = (-8/6)(x - 2)

y + 2 = -4/3 x + 8/3

To write the equation in standard form, arrange the variable(s) in one side and the constant(s) in the other.

y + 2 = -4/3 x + 8/3

4/3 x + y = 8/3 - 2

4/3 x + y = 2/3

Multiply both sides by 3 to have integer coefficients.

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

4x + 3y = 2

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Answer:

A. F/5 = 4

Step-by-step explanation:

F is the total of fish so F is divided by the total of dolphins, which is 5

so F/5 = 4

Answer:

F/5=4

Step-by-step explanation:

F is the total amount of fish. Since there are 5 dolphins to feed, you should divide F by 5.

By determining the conjecture is not valid by the law of detachment.

A statement in mathematics that has not been formally proven is referred to as a conjecture. Observing a pattern that holds true in numerous instances leads to conjectures. But just because a pattern appears frequently, it does not imply that it will appear frequently in all instances. The mathematical observation cannot be fully accepted unless conjectures are proven. A conjecture becomes a theorem if it has been thoroughly proven.

Hypothesis: Tommy makes cookies tonight.

Conclusion: Tommy must have an oven.

Even though the stated statement, "Tommy has an oven," matches the conclusion, the hypothesis is not always true. Tommy might own an oven, but he could bake something other than cookies in it.

Hence, the hypothesis is unfounded.

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A)  x, i.e. price of each ticket should be charged 20 dollars to maximize revenue.

B) The maximum revenue is 6060 dollars.

C) Two prices between which a profit is made are $19 and $21.

Given:

profit function P(x)= -15x² + 600x + 60

The value of a is -15, which is negative, so the graph is opening downwards.

The graph of the function is a parabola and it opens downward therefore it has a maximum point. The formula used to find the vertex of the parabola  f(x) is given by

x-coordinate of the vertex = -b/2a

y-coordinate of the vertex =  f(-b/2a)

We have the x-coordinate of the parabola as:

⇒  -600 / 2(-15)

⇒ -600/-30 = 20

A)  x, i.e. price of each ticket should be charged 20 dollars to maximize revenue.

B) y-coordinate of the vertex is given by

    f(20) = -15(20)² + 600(20) + 60

             = 6060

The maximum revenue is 6060 dollars.

C)   f(21) = -15(21)² + 600(21) + 60

             = 6045

       f(19) = -15(19)² + 600(19) + 60

             = 6045

   at $21, the profit is $6045

   at $19, the profit is $6045

Two prices between which a profit is made are $19 and $21.

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answer in the form a√2 where a is an integer.​  √18 √50= 4 root 2

Solution:

Mean

Mean is one of the important and most commonly used measures of central tendency. There are several types of means in mathematics. In statistics, the mean for a given set of observations is equal to the sum of all the values of a collection of data divided by the total number of values in the data. In other words, we can simply add all the values in a data set and divide it by the total number of values to calculate the mean. However, the general method and formulas vary depending upon the type of data given, grouped data, or ungrouped data.

Grouped data is the data set formed by aggregating individual observations of a variable into different groups, while ungrouped data is a random set of observations

Observation :

An observation is a fact or figure we collect about a given variable. It can be expressed as a number or as a quality. An example of a number is the observation "25" for the age of a mother at the birth of her first child.

Using mean formula

Mean = {Sum of Observation} ÷ {Total numbers of Observations}

= [tex]\sqrt{18} +\sqrt{50}[/tex]

=[tex]3\sqrt{2} + 5\sqrt{2}\\ = 5\sqrt{2}[/tex]

sum of observation is 8[tex]\sqrt{2}[/tex]

total number of observation = 2

[tex]8\sqrt{2} /2\\=4\sqrt{2}[/tex]

Answer in the form a√2 where a is an integer.​ = 4 [tex]\sqrt{2}[/tex]

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ans = [tex]4\sqrt{2}[/tex]

Using basic mathematical operations such as addition and subtraction, the art club have $358 after the show.

Basic mathematical operations includes addition, subtraction, multiplication, and division.

Addition is combining two or more values to come up with a total or sum. On the other hand, subtraction, the opposite of addition, is removing a value from another resulting to their difference.

If the art club raised $248 through fundraisers, spent $206 to set up an art show, and raised another $316 at the art show, adding the total amount they raised and subtracting the amount they have spent, we can solve how much money they have after the show.

$248 - $206 + $316 = $358

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Answer:

it is as follows:

5x2=10

5x3=15

5x4=20

5x5=25

5x6=30

5x7=35

5x8=40

5x9=45

Step-by-step explanation:

Answer: 5   10   15   20   25   30   35   40   45   50   55   60    65   70   75   80   85   90   95   100   105   110   115   120   125   130   135   140   145   150

Step-by-step explanation:

The integer that makes the expression, (____ + -3 = -4), true is -1.

According to the question,

We have the following expression:

__ + (-3) = -4

Now, let's take the integer to be filled in the blank as x.

Now, putting x in the given expression:

x + (-3) = -4

x = -4+3 (3 was negative on the left hand side. So, it is positive on the right hand side.)

x = -1

(More to know: when two numbers are given with two different signs then the smaller number is subtracted from the larger number but the sign remains of the number which is larger.)

Hence, the integer that makes the given addition sentence true is -1.

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Answer:

< - 9, 11 >

Step-by-step explanation:

consider the end points of the vector

(5, - 2 ) and (- 4, 9 )

x- direction is then - 4 - 5 = - 9

y- direction is 9 - (- 2) = 9 + 2 = 11

then vector in component form is < - 9, 11 >

2. For the given cylinders, we have that:

A. The volume is of 72π cm³ and the curved surface area is of 48π cm².

B. The volume is of 112π cm³ and the curved surface area is of 56π cm².

5. There are 330 liters of water in the container.

The volume of a cylinder of radius r and height h is given as follows:

V = πr²h.

The curved surface area of a cylinder of radius r and height h is given as follows:

S = 2πrh.

For problem 2 item a, we have that the parameters are given as follows:

r = 3, h = 8.

Hence:

The volume is of 72π cm³ and the curved surface area is of 48π cm².

For problem 2 item b, we have that the parameters are given as follows:

r = 8/2 = 4, h = 7.

Hence:

The volume is of 112π cm³ and the curved surface area is of 56π cm².

For item 5, the parameters are given as follows:

r = 0.65/2 = 0.325m, h = 1m.

Hence the volume is:

V = πr²h = π(0.325)² = 0.33 m³.

Each m³ has 1000 liters, hence:

0.33 x 1000 = 330 liters.

There are 330 liters of water in the container.

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Answer:

$1518

Step-by-step explanation:

Take the 1320 and multiply it by 0.15 (15% as a decimal) to get 198

Then add the 198 to the 1320 to get 1518

Answer:

x=1

Step-by-step explanation:

Perimeter of the square is 4 times the side = 4*(4x-1)

Perimeter of Rectangle = 2 L + 2 W = 2*(2x+2) + 2*2x

4*(4x-1) = 2*(2x+2) +4x

16x-4= 4x+4+4x

16x-4 = 8x+4

16x-8x = 4+4

8x = 8

x = 8/8

x=1

Hope this helps!^^

Step-by-step explanation:

Combine like terms on the right side,

42= 3x+6.

Subtract 6 from each side

36=3x

Divide each side by 3

x=12, which is our lowest integer.

The next two integers we find with 12+2=14 and 12+4=16. Or just simply take the next two even integers. Thus, 12+14+16=42.

Hope this helps.

g(x) = |14x + 3| is a function whose graph represents a horizontal stretch by a factor of 4 of the graph of f(x)=|x+3|.

So, we must write a function g whose graph represents a horizontal stretch of f(x)=|x+3| by a factor of 4.

Now perform horizontal stretch 4:

Therefore, g(x) = |14x + 3| is a function whose graph represents a horizontal stretch by a factor of 4 of the graph of f(x)=|x+3|.

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The correct question is given below:
Write a function g whose graph represents a horizontal stretch by a factor of 4 of the graph of f(x)=|x+3|.

g(x)=

Answer:

An army ant queen can lay 299,742 more eggs

The army ant queen will lay 120 times more eggs than the honeybee queen.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that a honeybee queen can lay 2.5 × 103 eggs per day. An army ant queen can lay up to 300,000 eggs per day.

The ratio will be calculated as,

Army ant/honeybee queen = 300,000 / (2.5 x 10³)

Army ant/honeybee queen = 300,000 / 2500

Army ant = 120 x ( honeybee queen )

Therefore, the army ant queen will lay 120 times more eggs than the honeybee queen.

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Answer:

Step-by-step explanation:

if you multiply a negative number with another negative number, it will be positive: ( - ) x ( - ) = ( + )

and if you multiply a negative number with a positive number, it will be negative: ( - ) x ( + ) = ( - )

so          -(-4) = 4                  and             +(-9) = -9

-5+9-4+4-9-12+7=-10

I hope this helps

Answer:

-60 x 2= -120

Step-by-step explanation:

Answer:

-40 * 3

Step-by-step explanation:

Just one example of many