How many non zero digits should numbers written in scientific notation have

Answer:

AB=2AM

3x-4=2(x+3)

3x-4=2x+6

3x-2x=4+6

x=10

So length AB 3x-4=3(10)-4

30-4=26

The length of AB is 26 units.

A line segment is denoted by two endpoints.

According to the given question M is the midpoint of segment AB.

Given, AM = x + 3 and AB = 3x - 4.

As AM is the midpoint if we take twice of AM that will be equal to AB.

∴ 2(AM) = AB

2(x+3) = 3x - 4.

2x + 6 = 3x - 4.

2x - 3x = -4 - 6.

-x = - 10.

x = 10.

So the length of the line segment AB will be (3x - 4) = 3(10) - 4 units.

= 30 - 4

= 26 units.

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Answer:

Step-by-step explanation:

Combine like terms

\(2a + \frac{5b}{4}+3a + \frac{2b}{8}=2a + 3a +\frac{5b}{4}+\frac{2b}{8}\\\\ = 2a + 3a + \frac{5b}{4}+\frac{b}{4}\\\\= 5a + \frac{5b+b}{4}\\\\= 5a +\frac{6b}{4}\\\\= 5a + \frac{3b}{2}\)

Answer:

\(2a+5\frac{b}{4}+3a+2\frac{b}{8}\)

First multiply by 8

\(2\cdot8a+5\cdot8\cdot\frac{b}{4}+3\cdot8\cdot a+2\frac{b}{8}\cdot8\)

We multiple and divide where we can

\(16a+10b+24a+2b\)

And now it's simple

30a+12b

The total FICA amount and tax deducted from Mia is A = $42.81.

Given data,

To calculate the amount deducted from Mia's paycheck each week for FICA and tax withholding, we need to follow these steps:

Step 1: Calculate FICA deduction:

FICA deduction = (FICA rate x Mia's weekly income)

FICA deduction = (6.25/100) x $325

FICA deduction = $20.31 (rounded to the nearest cent)

Step 2: Calculate tax withholding:

Tax withholding is based on the number of exemptions claimed. Each exemption reduces the taxable income by a certain amount. Let's assume that each exemption reduces the taxable income by $50.

On simplifying the equation , we get

Taxable income = Mia's weekly income - (number of exemptions * exemption amount)

Taxable income = $325 - (2 x $50)

Taxable income = $325 - $100

Taxable income = $225

The specific tax withholding rate can vary depending on the tax bracket and other factors. For the purpose of this calculation, let's assume a tax withholding rate of 10%.

On simplifying the equation , we get

Tax withholding = (tax withholding rate x taxable income)

Tax withholding = (10/100) x $225

Tax withholding = $22.50

So, the amount deducted from Mia's paycheck each week for FICA and tax withholding is $20.31 + $22.50 = $42.81.

Hence , the amount deducted is A = $42.81

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Answer:

C

Step-by-step explanation:

Since the sectors all meet at the centre of the circle, then

The angles around a point sum to 360° → A

90°... See More

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The five number summary and interquartile range for the data-set is given by:

In this problem, we have that:

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Answer:

y - 2 = 2(x + 3)

Step-by-step explanation:

the equation of a line in point- slope form is

y = b = m(x - a)

where m is the slope and (a, b ) a point on the line

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 3, 2 ) and (x₂, y₂ ) = (2, 12 )

m = \(\frac{12-2}{2-(-3)}\) = \(\frac{10}{2+3}\) = \(\frac{10}{5}\) = 2

using (a, b ) = (- 3, 2 ) , then

y - 2 = 2(x - (- 3) ) , that is

y - 2 = 2(x + 3)

Answer:

Option (3)

Step-by-step explanation:

From the given figure,

\(a_n=a_1+(n-1)d\)

where \(a_n\) = nth term of an arithmetic sequence

\(a_1\) = first term of the sequence

n = number of term

d = common difference

When n = 1 : \(a_1=-1\)

When n = 2 : \(a_2=-6\)

common difference 'd' = -6 - (-1) = -5

Formula for the nth term for the given sequence will be,

\(a_n=-1+(n-1)(-5)\)

    = -1 - 5n + 5

\(a_n\) = 4 - 5n

Now the 12th term of this sequence will be,

\(a_{12}=4-5(12)\)

     = 4 - 60

     = -56

Therefore, Option (3) will be the answer.

Answer:

\(\qquad\quad {:}\leadsto\sf {3}^{\dfrac {x}{2}}\times {3}{}^{\dfrac {x}{4}}=3^6 \)

\(\qquad\quad {:}\leadsto\sf 3{}^{\dfrac {x}{2}+\dfrac {x}{4}}=3^6 \)

\(\qquad\quad {:}\leadsto\sf 3 {}^{\dfrac {2x+x}{4}}=3^6 \)

\(\qquad\quad {:}\leadsto\sf 3 {}^{\dfrac {3x}{4}}=3^6 \)

\(\qquad\quad {:}\leadsto\sf \dfrac {3x}{4}=6 \)

\(\qquad\quad {:}\leadsto\sf 3x=24 \)

\(\qquad\quad {:}\leadsto\sf x=\dfrac {24}{3}\)

\(\qquad\quad {:}\leadsto\sf x=8\)

Answer:

x=8

Step-by-step explanation:

It just is, no explanation.

Answer:

1/3

Step-by-step explanation:

First we have to find the coordinates of the two points that are plotted,

(6,-3), (3,-4)

Then we need to calculate the change in Y over the change in X

\(\frac{-4-(-3)}{3-6}\)

=\(\frac{-4+3}{-3}\)

=\(\frac{-1}{-3}\)

=1/3 (since the negative cancel out)

1/3 is your answer!

Hope this helped :)

Answer:

41.309 kg, 41.32 kg, 41.236 kg

Step-by-step explanation:

I think these are the correct answers.

Answer:

3.1 degrees celcius

Step-by-step explanation:

5.6C-2.5C=3.1C

The number the interval of convergence is `[3, 3]` or `{3}`.

The function `f(x) = 8/3x + 2` and `c = 3`. We need to find the power series for the function centered at c.

The power series for `f(x)` centered at `x=c` is given by `sigma^infinity_n = 0 [(f^n(c)/n!) * (x - c)^n]`.

First we need to find the first few derivatives of the given function as follows.

`f(x) = 8/3x + 2``f'(x) = 8/3``f''(x) = 0``f'''(x) = 0``f''''(x) = 0``....`

The derivative of the function is a constant function. This tells us that the Taylor series centered at `c` will involve only the constant term of the Taylor series.

Let's evaluate this constant term using `n = 0`.`f(3) = 8/3(3) + 2 = 10/3`

Since all the remaining terms are `0`, the Taylor series will simply be a constant term. Therefore, the power series is given by:

`f(x) = 10/3`.

Next, we need to determine the interval of convergence. Since the power series is just a constant term, the interval of convergence is the singleton set `{3}`.Therefore, the interval of convergence is `[3, 3]` or `{3}`.

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The reasonable models of disease spread among a finite number of people are given by the equations:

dN/dt = alpha N

dN/dt = alpha (N_T - N)

dN/dt = alpha (N - N_T)

In the context of epidemiology, these differential equations represent different scenarios for the spread of a disease within a population. The variable N represents the number of infected individuals, and N_T represents the total population size. The parameter alpha represents the rate at which the disease spreads.

In the first model (1), the rate of change of infected individuals is proportional to the current number of infected individuals (N). This model assumes that the disease spreads based on the existing infected population alone.

In the second model (2), the rate of change of infected individuals is proportional to the difference between the total population (N_T) and the current number of infected individuals (N). This model assumes that the disease spreads based on the susceptible population size.

In the third model (3), the rate of change of infected individuals is proportional to the difference between the current number of infected individuals (N) and the total population (N_T). This model assumes that the disease spreads based on the immune or recovered population.

These models provide a mathematical framework to understand and study the dynamics of disease spread within a finite population. The choice of model depends on the specific characteristics and assumptions about the disease being studied.

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The total time Elise spent riding Maximum Velocity on her last visit to Adventure Island can be expressed as: 145d seconds.

In mathematics, an expression is a combination of numbers, symbols, and/or variables that can be evaluated to produce a value. Expressions can also include functions, such as sin(x) or log(y), as well as operators like multiplication (*), division (/), and exponentiation (^). Expressions can be used to represent mathematical formulas, equations, and relationships in a concise and symbolic way, making them easier to work with and manipulate using mathematical tools and techniques.

Here,

If we know the value of d, we can calculate the total time Elise spent riding Maximum Velocity by simply multiplying the ride time by the number of rides.

For example, if Elise rode Maximum Velocity 3 times, the total time she spent on the ride would be:

145 seconds/ride x 3 rides = 435 seconds

So, using the expression from the previous answer, we can substitute the value of d to get the actual calculation:

Total time = 145d seconds

For instance, if Elise rode Maximum Velocity 5 times during her last visit, the total time spent on the ride would be:

Total time = 145 x 5 = 725 seconds

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The relation in option (a) is Transitive , in option (b) is Reflexive and Transitive and option (c) is Symmetric .

In the question ,

it is given that ,

Option(a) ,  

R is a relation on set of all people where (a,b) is in R if a is taller than b .

Reflexive : NO , because "a" cannot be taller than "a" itself .

Symmetric : NO , because if "a" is taller than "b" , then "b" will be shorter than "a" .

Transitive : YES , because if "a" is taller than "b" and "b" is taller than "c" , then "a" is taller than "c" .

Option(b)

R is a relation on set of integers > 0 where (a,b) is in R if a divides b .

Reflexive : YES , because every number divides itself .

Symmetric : NO , because if "a" divided "b" , then "b" may not divide "a" .

Transitive : YES , because if "a" divided "b" and "b" divides "c" , then "a" must divide "c" .

Option(c)

R is a relation on set of all people where (a,b) is in R if a is married to b .

Reflexive : NO , because marriage is between two people , and "a" cannot marry "a" .

Symmetric : YES , because if "a" is married to "b" , then "b" is married to "a" .

Transitive : NO , because if "a" is married to "b" and "b" is married to "c" , then "a" is not married to  "c" .

Therefore , The relation in option (a) is Transitive , in option (b) is Reflexive and Transitive and option (c) is Symmetric .

The given question is incomplete , the complete question is

Write in the space provided the property or properties that each relation possesses (reflexive, symmetric, transitive).

(a) R is a relation on the set of all people, (a,b) is in R if a is taller than b .

(b) R is a relation on the set of integers > 0 , (a,b) is in R if a divides b .

(c) R is a relation on the set of all people , (a,b) is in R if a is married to b .

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(aA+bB)t = aAt + bBt for any A,B\epsilonMmxn(F) and any a,b\epsilonF. is

for any A,B∈Mmxn(F) and any a,b∈F, (aA+bB)t = aAt + bBt.  

Proving that (aA+bB)t = aAt + bBt for any A,B∈Mmxn(F) and any a,b∈F is fairly straightforward. First, let's take a look at the definition of matrix transpose: the transpose of a matrix A is the matrix At obtained by interchanging its rows and columns.

From this definition, it can be seen that At can be obtained by multiplying each element of A by its corresponding scalar in the set {a, b}. Thus, for any given A,B∈Mmxn(F) and any a,b∈F, (aA+bB)t = aAt + bBt.

Furthermore, multiplying each element of A by its corresponding scalar can be generalized to any number of matrices. That is, given any n matrices A1, A2, A3, ..., An and scalars a1, a2, a3, ..., an (all ∈F), (a1A1+a2A2+a3A3+...+anAn)t = a1A1t + a2A2t + a3A3t +...+anAnt.

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Answer: solve for x

x ∈ R, h = 0 and g = 0

Step-by-step explanation:

Term 11=a+10d

Here

a=10

d= 7-10= -3

Term 11;

=10+(10×-3)

=10+(-30)

= -20 is the answer

Thank you Hope it helps dear

Answer: -32

Step-by-step explanation:

a=10, d = 7-10 = -3

First find which term is -62

an = -62

a = (n-1) d= -62

Putting values

10 + (n-1)(-3) = -62

10 + (n(-3) -1 (-3) = -62

10 - 3n + 3 = -62

13 - 3n = -62

-3n = -62-13

n = 75/3 = 25

We need to find out 11th term from the last term ie., 25 - 10 = 15th term

So we need to find a14

an = a +(n-1) d

a15 = 10+ (15-1) (-3)

= 10 + 14 (-3)

= 10 -42

= -32

So the 11th term from the 15th term from the first = -32

Answer: \((x-7)^2+(y+2)^2=11^2\) ; \(A=121\pi\)

Step-by-step explanation:

I have never done a problem like this, so this is my first time attempting it.

The standard form for the equation of a circle is:

\((x-a)^2+(y-b)^2=r^2\)

Begin by grouping the 'x' terms and 'y' terms:

\((x^2-14x)+(y^2+4y-68)=0\)

Complete the square for the second polynomial:

\((\frac{b}{2} )^2=(\frac{4}{2} )^2=4\)

\((x^2-14x)+(y^2+4y+4-4-68)=0\)

\((x^2-14x)+(y^2+4y+4)-4-68=0\)

\((x^2-14x)+(y^2+4y+4)-72=0\)

\((x^2-14x)+(y+2)^2-72=0\)

Do the exact same process with the other polynomial:

\((x^2-14x-72)+(y+2)^2=0\)

Complete the square:

\((\frac{14}{2} )^2=49\)

\((x^2-14x+49-49-72)+(y+2)^2=0\)

\((x^2-14x+49)-49-72+(y+2)^2=0\)

\((x^2-14x+49)-121+(y+2)^2=0\)

\((x-7)^2-121+(y+2)^2=0\)

Bring the 121 to the other side to get:

\((x-7)^2+(y+2)^2=121\)

\((x-7)^2+(y+2)^2=11^2\)

The above expression is the equation of our circle in standard form. It is centered at the coordinates (7, -2) and has a radius of 11 units. The area of a circle if given by:

\(A=\pi r^2=121\pi\)

The function which represents the cost to drive a car from this agency miles x a day is :

C(x) = 15, if 0 ≤ x ≤ 200

      = 15 + 0.05x, if x > 200

Given that,

A car rental agency charges $15 a day for driving a car 200 miles or less.

The function can be written as,

C(x) = 15 if 0 ≤ x ≤ 200

If a car is driven over 200 miles, the renter must pay $0.05 for each mile over 200 driven.

C(x) = 15 + 0.05x, if x > 200

Hence the correct option is D.

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To determine if a matrix is a linear combination of other matrices, we need to check if it can be written as a weighted sum of those matrices where the weights are scalar values (numbers).

If a matrix can be expressed in this way, it is said to be a linear combination of the other matrices.

For example if we have matrices: A, B & C and we can write matrix D as follows:

Then D is a linear combination of matrices A, B and C. This concept is important in linear algebra as it allows us to express one matrix in terms of others. Making it easier to manipulate & analyze the matrices. A matrix is a linear combination of other matrices if it can be expressed as a weighted sum of those matrices where the weights are scalar values.

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Given:

Cost of 2 DVDs before tax = $19.99

Tax rate = 8.25%

To find:

The cost of 2 DVDs after the tax was added.

Solution:

We have,

Cost of 2 DVDs before tax = $19.99

Tax rate = 8.25%

So,

Tax = 8.25% of Cost of 2 DVDs before tax

\(Tax=\dfrac{8.25}{100}\times 19.99\)

\(Tax=1.649175\)

\(Tax\approx 1.65\)

Now,

Cost of 2 DVDs after tax = Cost of 2 DVDs before tax + Tax

                                         = $19.99 + $1.65

                                         = $21.64

Therefore, the cost of 2 DVDs after the tax is $21.64.

Answer:

a

Step-by-step explanation:

Step-by-step explanation:

The area of a rectangle is 1,872 ft2. The ratio of the length to the width is 9:13. Find the perimeter of the rectangle.

176 ft

You want to make a scale drawing of your bedroom to help arrange your furniture. You decide on a scale of 3 in. = 2 ft. Your bedroom is a 12 ft by 14 ft rectangle. What should the dimensions of your drawing be?

18 in. by 21 in.

If 5/y + 7/x=24 and 12/y + 2/x=24, find the ratio of x to y.

5/7

Simplify the ratio 8ft/12in. Use the conversion 12 in. = 1 ft.

8/1

Analyze the proportion below and complete the instructions that follow.

2x+5/3 = x-5/4

-7

If a+b/2a-b = 5/4 and b/a+9 = 5/9, find the value of b.

30

Analyze the ratio below and complete the instructions that follow.

$30:$6

Simplify the ratio.

5:1

If 14/3 = x/y then 14/x =

3/y

Analyze the diagram below and complete the instructions that follow.

In the diagram, AB:BC is 3:4 and AC = 42. Find BC.

24

Analyze the diagram below and complete the instructions that follow.

If AB:BC is 3:11, solve for x.

9

If a, b, c, and d are four different numbers and the proportion a/b = c/d is true, which of the following is false?

b/a = c/d

Analyze the diagram below and complete the instructions that follow.

Find the ratio of the width to the length of the rectangle, then simplify the ratio. Use the conversion 100 cm = 1 m.

3/4

Simplify the ratio 3 gal./24 qt. Use the conversion 4 qt = 1 gal.

1/2

The area of a rectangle is 4,320 ft2. The ratio of the length to the width is 6:5. Find the length of the rectangle.

72 ft

Analyze the diagram below and complete the instructions that follow.

Given that CB/CA = DE/DF, find BA.

10.5

Analyze the proportion below and complete the instructions that follow.

2/3 = 8/x

3, 8

Analyze the diagram below and complete the instructions that follow.

Are the polygons shown here similar? Justify your answer. The images are not drawn to scale.

Yes, PQR ~TSV with a scale factor of 1:√3

All __________ are similar.

squares

Analyze the diagram below and complete the instructions that follow.

Determine which 2 triangles are similar to each other. The images are not drawn to scale.

GHI ~ JKL

Analyze the diagram below and complete the instructions that follow.

Pentagon PQRST ~ pentagon XYZVW. Find the value of b. The images are not drawn to scale.

3

Analyze the diagram below and complete the instructions that follow.

If ABC ~ XYZ, find XY. The images are not drawn to scale.

24

ABC is a right triangle. The legs of ABC are 9 ft and 12 ft. The shortest side of XYZ is 13.5 ft, and ABC ~ XYZ How long is the hypotenuse of XYZ?

22.5 ft

Answer:

0.6 or 40/1

Step-by-step explanation:

Oki 5/7 x 8/9 = 40/63 = 0.63 Do you mean like this way or the other ?

5/7 x 9 = 45/63 and 8/9 x 7 = 56/63 x 45\63 = 2520\63 = 40/1

Hope that this will help you.

Answer:

The law of demand says that at higher prices, buyers will demand less of an economic good. The law of supply says that at higher prices, sellers will supply more of an economic good. These two laws interact to determine the actual market prices and volume of goods that are traded on a market.

Supply is generally considered to slope upward: as the price rises, suppliers are willing to produce more. Demand is generally considered to slope downward: at higher prices, consumers buy less. ... The relationship between the supply and demand for a good (or service) and changes in price is called elasticity.

Answer:

A) 10

B) (C+10)/2 = n

Step-by-step explanation:

A) We know that the total cost is represented by the variable C. So, basically the problem is saying that the variable C is equal to 30. If we plug that into the equation, we get 30 = 2n + 10. Solving this, we get n = 10.

B) Isolating a variable means to only have the specified variable on one side and have all other integers and variable on the other side. So, the final answer would be (C+10)/2 = n.

Answer:

k = 5/6

Step-by-step explanation:

First, we can make this have the form of a quadratic function, or ax²+bx+c=0. To do this, we can first subtract 10x from both sides to get

(2k+1)x²-8x=-6

Next, we can add 6 to both sides, resulting in

(2k+1)x²-8x+6 = 0

For a quadratic function of form ax²+bx+c=0, we can see that a=2k+1, b=-8, and c=6. We can then apply the quadratic equation, or

x= (-b ± √(b²-4ac))/(2a) to get our roots to be

x= (8 ± √(64-4(6)(2k+1)))/(2*(2k+1))

=  (8 ± √(64-(48k+24)))/(4k+2)

=  (8 ± √(40-48k))/(4k+2)

For the roots to be equal, we must have the two roots equal to each other. We can write this as

(8 + √(40-48k))/(4k+2) = (8 - √(40-48k))/(4k+2)

multiply both sides by (4k+2) to remove the denominator

8+√(40-48k) = 8 - √(40-48k)

subtract 8 from both sides to isolate the square roots

√(40-48k) = - √(40-48k)

The only number that is equal to its negative self (and is real) is 0. Therefore, √(40-48k) = - √(40-48k) = 0, so we have

√(40-48k) = 0

square both sides to remove the square root

40-48k = 0

add 48k to both sides to isolate the k and its coefficient

40 = 48k

divide both sides by 48 to isolate k

k = 40/48 = 5/6

a. The volume of the spherical container is approximately 37,785.41 cubic centimeters.

b. It will take approximately 62.98 minutes to fill the container with a flow rate of 600 cubic centimeters per minute.

a. To find the volume of the spherical container, we can use the formula:

V = (4/3)πr^3

where V is the volume and r is the radius of the sphere. However, we need to first find the radius of the sphere using the given surface area.

The surface area of a sphere is given by the formula:

A = 4πr^2

Given that the surface area is approximately 5,538.96 square centimeters, we can equate the formula for surface area to the given value and solve for r:

4πr^2 = 5,538.96

r^2 = 5,538.96 / (4π)

r^2 ≈ 441.57

Taking the square root of both sides, we get:

r ≈ √441.57 ≈ 21.02

Now that we have the radius, we can substitute it into the formula for volume to find the volume of the container:

V = (4/3)π(21.02)^3 ≈ 37,785.41 cubic centimeters

Therefore, the volume of the container is approximately 37,785.41 cubic centimeters.

b. If 600 cubic centimeters of water flow into the container in one minute, we can calculate the time it takes to fill the container by dividing the volume of the container by the flow rate:

Time = Volume / Flow rate

Time ≈ 37,785.41 / 600 ≈ 62.98 minutes

Therefore, it will take approximately 62.98 minutes to fill the container.

The correct question should be :

A spherical container has a surface area of about 5,538.96 square centimeters.

a. What is the volume of the container?  

b. If 600 cubic centimeters of water flow into the container in one minute, about how many minutes will it take to fill the container?

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Answer:510

Step-by-step explanation: