Mathematics High School

simplify the expression

(0.2a^2b^3)(-5a^3b)^2

Answers

Answer 1

The simplified expression for (0.2a²b³)(-5a³b)² is given as follows:

5a^8b^5.

What is the simplified expression?

The expression for this problem is given as follows:

(0.2a²b³)(-5a³b)²

First we apply the power of power simplification, in which the square of each term inside the parenthesis is calculated as follows:

Square of -5: 25.Square of a³: a^6 -> keeps the base a and multiplies the exponents 3 and 2.Square of b: b² -> keeps the base b and multiplies the exponents 1 and 2.

Now the expression is:

(0.2a²b³)(25a^6b²).

Then:

0.2 x 25 = 5 -> multiplies the numeric constants.a² x a^6 = a^8 -> product with terms of same base and different exponents, keep the base and add the exponents.b³ x b² = b^5 -> same as above, keeps the base b and adds the exponents 3 and 2.

Hence the simplified expression is:

5a^8b^5.

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Related Questions

If shown,
AB

and

CD

are straight lines. Find x in each case.
WILL MARK BRAINLISIT

Answers

Answer:

4x+x+x+90=360

6x+90=360

6x=270

x=45

good luck!

4x+x+x+90=360

6x+90=360

6x=270

x=45

the equation of the curve is y = x^2 + ax + b. The points (0,-5) and (5,0) lie on the curve. Find the coordinates of the turning point of the curve.

Answers

The turning point of the parabola is the point (2, - 9).

What is the turning point of a quadratic equation?

Quadratic equations represents parabolae and the vertex of the parabola represents the turning point as the slope of the curve changes its sign, from positive to negative or viceversa. The vertex can be derived by the vertex form of the equation of the parabola:

y - k = C · (x - h)²

Where:

(h, k) - Coordinates of the vertex.C - Vertex constant

Since the quadratic equation has two real coefficients, we need the location of two points on Cartesian plane to find one solution. First, create the system of linear equations:

b = - 5                                      (1)

5 · a + b = - 25                        (2)

Second, substitute b in (2) and clear a:

5 · a - 5 = - 25

5 · a = - 20

a = - 4

Third, write the quadratic equation:

y = x² - 4 · x - 5

Fourth, transform the equation into vertex form by completing the square:

y + 9 = x² - 4 · x + 4

y + 9 = (x - 2)²

Fifth, write the vertex of the parabola:

(h, k) = (2, - 9)

The point (2, - 9) represents the turning point of the parabola.

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Yuson must complete a certain number of hours of community service. She does 2 hours of service each day. After 8 days, Yuson has completed half of her required community service.
Write a linear equation to represent the hours that Yuson has left to do after x days.

Answers

The linear equation to represent the hours that Yuson has left to do after x days is 16 - 2x.

How to calculate the equation?

From the information, Yuson has to do Y hours of community service.

She works two hours every day, so service hours in x days = 2x

Remaining service hours after x days = y-2x

Also we have after 8 days , Yuson has completed half of her required community serivice. Therefore,

8 = y/2.

Cross multiply

y = 16

So the linear equation is 16-2x.

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1. Is the game fair? We are flipping a coin twice. The first player wins if we get 2 tails, and the second player wins if we get 1 head and 1 tail. 2. Is the game fair? we are tossing two dice and the first player wins if the sum on the dice is 9 and the second player wins if the sum on the dice is 5.

Answers

Answer: 1) The game is not fair, 2) The game is fair

Step-by-step explanation:
1) In the case of the coin, we will assume that it is a fair coin and there is an equal probability that the coin will land either heads or tails on each flip. In other words, we are assuming that flipping the coin is a completely random process.

When flipping a coin twice, there are 4 distinct possibilities, where H means the coin lands head side up and T means it lands tails side up. The first letter represents the first flip of the coin and the second represents the second flip. The possible outcomes are:

HH, HT, TH, TT

As you can see, there is only 1 possible outcome where the coin will land tails up twice, while there are 2 possible outcomes where the coin will land heads up once and tails up once. Since the game doesn't specify the order in which the coin needs to land on either side for player 2 to win, both of these possibilities are fair game.

Now, according to our earlier assumption that the process of flipping the coin is truly random, we can say that there is a 50/50, chance of the coin landing on either side before we flip it. There is also a 100% chance that, in 2 flips, the coin behaves according to one of the possibilities stated above. This means that each possibility has an equal 25% chance of happening. We determined there are 2 possible outcomes where the coin lands on both a head and a tail, opposed to the 1 possible outcome where the coin lands tails up on both flips. Adding the probabilities, this means that the second player has a 50% chance of winning the game while the first player only has a 25% chance of winning the game, and thus - it is not fair.


2) In the second game, we will also assume that the process of rolling the dice is completely random and there is an equal chance that it lands on each side. The possible outcomes for both dice combining to sum to 5 are:

1,4; 4,1; 2,3 and 3;2

and the possible outcomes for both dice combining to sum to 9 are:

4,5; 5,4; 2,6 and 6,2

Assuming the dice are normal, 6-sided dice, there is a 1/6 or a 16.67% chance of the dice landing on each side. The outcomes on these rolls are dependent on one another and represent compound probabilities. in other words, the probability of rolling a 2 on a single dice is 16.67%, and the probability of rolling a 6 on a single dice is also 16.67%, but the probability of rolling a 2 on one dice and (key word here being and) a 6 on the other dice is the product of the two individual probabilities;

1/6 * 1/6 = 1/36 (2.78%)

This means that it is less likely to roll the correct combination than it is to roll each of the numbers individually, which should intuitively make sense.

However, because there are an equal number of outcomes in which each player wins, this game is fair to both players. It is no more likely that the sum of the dice will be 9 than it is that it will be 9, even though both of these outcomes have relatively low probabilities. In most rolls, neither player will win - but the game is still fair to both players.

Find each probability if you spin the spinner and roll the number cube.
10. P(blue, 2)
12. P(not blue, 5)
11. P(red, even)
13. P(yellow, not 4)
red
blue
yellow
red
4
6
5

Answers

10. 5/12
11. 1/8
12. 1/8
13. 5/24



The chance of the spinner landing on blue = 1/4

The chance of the number cube landing on 2 = 1/6

1/4 * 1/6 = the probability of the spinner landing on blue and the cube landing on 2 (Remember that the probability of both happening is smaller, so it cannot be addition.)

Ans = 5/12

The chance of the spinner landing on something that isn’t blue = 3/4

The chance of the number cube landing on 5 = 1/6

3/4 * 1/6 = the total probability

Ans = 1/8

The chance of the spinner landing on red = 1/4

The chance of the number cube landing on an even number = 3/6, 1/2.

1/4 * 1/2 = the total probability

Ans = 1/8

The chance of the spinner landing on yellow = 1/4

The chance of the number cube landing on something that’s not 4 = 5/6

1/4 * 5/6 = the total probability

Ans = 5/24

I really hope this helped lol

Write the correct function and online represented in the table below

HELP ASAP

Answers

Answer:

y = 5x -2

Step-by-step explanation:

The 5 is the slope.  It is the change in y over the change in x.  As the x changes by 1, the y changes by 5.

The -2 is the y intercept.  This is at the point (0,-2)  The -2 is the y intercept.

If u can solve both the blanks that would be great

Answers

total balance = $367.50

interest = $67.50


A= $367.50

I = A - P = $67.50

Equation:
A = P(1 + rt)

Calculation:
First, converting R percent to r a decimal
r = R/100 = 2.5%/100 = 0.025 per year.

Solving our equation:
A = 300(1 + (0.025 × 9)) = 367.5
A = $367.50

The total amount accrued, principal plus interest, from simple interest on a principal of $300.00 at a rate of 2.5% per year for 9 years is $367.50.

Harry took a 5-hour trip on which he averaged 40 miles per hour. What distance did he travel?

Answers

5 X 40 = 200
Harry traveled 200 miles on a 5 hour trip

Answer:

200 miles

Step-by-step explanation:

if its 40 miles per hour then multiply 5 with 40 and you'll end up with 200 miles

the number of hours spent watching television by students in the week before final exams has a normal distribution with a standard deviation of 4.5 hours. a random sample of 30 students is taken. is the probability that the sample standard deviation exceeds 3.5 hours more than 0.95?

Answers

The probability that the sample standard deviations exceeds 3.5 hours more than 0.95 is 0.23 < 0.95 ..

The numbers of hours spent on watching television by a student in a weak before is normally distributed.

We have provide the following details, standard

deviations of sample ( Number of hours in weak) (σ) = 4.5 hours

sample size (n) = 30

we shall compute the mean and variance of sample .

The E of s squared is equal to 4.5 squared. The variance of S squared is equal to twice the square of sigma divided by 1, which is 30 minus 1, which is 28.6, 28.2817. The chi-square distribution here has 29 degrees of freedom, which equals 29 squared to 4.5 squared. We want to find probabilities greater than 90 because the standard deviation of our sample is greater than 3.5 hours. The probability that S squared is greater than 3.5 is The probability that chi-square with 29 degrees of freedom is greater than

17. 54321 is very high. This is the same as zero.

This is equal to 1 minus the probability that 29 degrees of freedom chi-square is greater than 51 points 5556, which is what we want for part B. we are given one Probability will be zero.

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#Complete question

The number of hours spent watching television by students in the week before final exams has a normal distribution with a standard deviation of 4.5 hours. A random sample of 30 students was taken.a. Is the probability more than 0.95 that the sample standard deviation exceeds 3.5 hours?b. Is the probability more than 0.95 that the sample standard deviation is less than 6 hours?

The price of a dvd is $24. 00 plus 8% sales tax. What is the sales tax on this dvd in dollars and cents?.

Answers

Answer: $1.92

Step-by-step explanation:

This is the correct answer. Have a good day

I WILL GIVE 30 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS

Answers

Answer:

third and last, can't promise that's right

What is another way to write (a6)(a²)?

a4

a8

a12

a36

Answers

a8 would be the correct answer

What is the slope of the line?
Write the slope as a fraction.

Answers

Answer: the slope is 1/4

Step-by-step explanation:

(2,0.5)    (4,1)

Use the formula for finding the slope:

        [tex]\boxed {The\ slope=\frac{y_2-y_1}{x_2-x_1} }[/tex]

[tex]x_1=2\ \ \ \ x_2=4\ \ \ \ y_1=0.5\ \ \ \ y_2=1\\[/tex]

Hence,

[tex]\displaystyle\\The\ slope=\frac{1-0.5}{4-2}\\\\The\ slope=\frac{0.5}{2}\\\\The\ slope=0.25\\\\The\ slope=\frac{1}{4}[/tex]

help me pls. i dont know how to do this

Answers

Answer:

k=f(x)-ab^x-h

h=x-ln(f(x)/a-k/a)/ln(b)

a=f(x)/b^x-h - k/b^x-h

The owner of a bookstore buys used books from customers for $1. 50 each. The owner then resells the used books for 400% of the amount he paid for them. What is the price of a used book in this bookstore?.

Answers

Answer:

$7.50

Step-by-step explanation:

Find the equation of the line passing through the given point and parallel to the given line.
( 7,-3) , 3y = 12x + 5
(-5, -2), y + 3x = 10

Answers

The equation of the lines passing the points and parallel to the equations ( 7,-3) , 3y = 12x + 5  (-5, -2), y + 3x = 10 is as follows:

y = 4x  - 31y = -3x - 17.

How to find the equation of a line?

The equation of a line can be represented in different form such as standard form, general form, slope intercept form and point slope form. Therefore, let's represent the line in slope intercept form.

The equation of a line in slope intercept form is as follows:

y = mx + b

where

m = slopeb = y-intercept

Parallel line shave the same slope.

Hence,

( 7,-3) , 3y = 12x + 5

y = 4x + 5 / 3

slope is 4

The equation of the line is y = 4x + b. let's find the y-intercept using (7, -3).

-3 = 4(7) + b

b = -3 - 28

b = - 31

Hence, y = 4x  - 31

(-5, -2), y + 3x = 10

y = -3x + 10

slope = -3

Therefore, let's find y-intercept using (-5, -2)

-2 = -3(-5) + b

-2  = 15 + b

b = -2 -15

b = - 17

Therefore, y = -3x - 17.

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11/12+7/12 in simplest form

Answers

Answer:

The answer to your question could be either 3/2 (improper fraction), 1.5 (decimal), or 1 1/2 (mixed fraction).

Step-by-step explanation:

11/12 + 7/12 = 18/12

18/12 = 9/6

9/6 = 3/2

Which is greater -2/5 or -3/8 ?

Answers

Answer:-2/5

Step-by-step explanation: due to them being negative we are using the simple thing of which number is closer to zero. -2/5 is closer which means that is it greater. -2/5 would be ahead on number line if you need a visualization

Answer:

-3/8

Step-by-step explanation:

1) Work out the options you are given

-2/5 = -0.4-3/8 = -0.375

2) Find which one is greater

As the numbers are decimal the 'seemingly greater number' might actually be the smaller one.

To find out which decimal is greater you can easily plot them into a number line.

The number that is further to the left is smaller and the number closer to the right is higher!

If we were to plot the numbers one a number line the -0.375 would be closer to the right meaning it is greater.

HINTS:

To make it easier to divide minus numbers, at first completely forget about the minus (you can plug it back in at the end).

For example, if you were given -2/5 get rid of the minus to get 2/5 and from this we can easily figure out 2 ÷ 5 which would give us 0.4.

At the point where you have your final number you can add the - back in making it -0.4

Hope this helps, have a great day!

Which fractions are equivalent to 0.63 repeating?

Answers

28/44 is the correct answer
Answers:  21/33   and    28/44

===============================================

Work Shown:

[tex]\text{x} = 0.\overline{63}[/tex]

x = 0.63636363...

100x = 63.63636363...

100x - x = (63.63636363...) - (0.63636363...)

99x = 63

x = 63/99

x = (7*9)/(11*9)

x = 7/11

This table shows a few fractions equivalent to 7/11

[tex]\begin{array}{|c|c|} \cline{1-2}\text{Multiply top} & \\ \text{and bottom by} & \text{Equivalent fraction}\\\cline{1-2}2 & 14/22\\\cline{1-2}3 & \boldsymbol{21/33}\\\cline{1-2}4 & \boldsymbol{28/44}\\\cline{1-2}5 & 35/55\\\cline{1-2}6 & 42/66\\\cline{1-2}\end{array}[/tex]

The terms in bold are the two answers

In other words, 7/11 = 21/33 when multiplying top and bottom by 3.

Also, 7/11 = 28/44 when multiplying top and bottom by 4.

To confirm those answers, use a calculator to find that

7/11 = 0.636363...

21/33 = 0.636363...

28/44 = 0.636363...

To rule out the non-answers, use the calculator to find that

14/21 = 0.667 approximately

7/12 = 0.5833 approximately

In 2021, Sally Morris, a single taxpayer, pays $3,000 of interest on qualified student loans. Her AGI is $40,000. What is her qualified student loan interest deduction in 2021?

Answers

The qualified student loan interest deduction in 2021 is $37500.

What is adjusted gross income?

Adjusted gross income is an individual's total gross income less specific deductions in the United States income tax system. It is used to compute taxable income, which is AGI minus personal exemption and itemized deduction allowances. AGI is more important than gross income for most individual tax purposes.

AGI is calculated by taking your gross income and subtracting certain "above the line" deductions. 401(k) contributions, health savings account contributions, and educator expenses are common examples of deductions

As per Law, a maximum of $2,500 will be allowed to be deducted from the Income. Thus the following would be the solution.

Income of Sally Morris = $40,000

Less: Qualified student loan interest $2,500

Modified Adjusted Gross Income $37,500

The deduction is $37500.

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Alice changes size several times. The ratio of her orginal height to her second height is 24 to 5. The ratio of her second height ot he rthird height is 1 to 12. The ratio of her orginal height to her fourth height is 16 to 1. The tallest of these four heights is 10 feet. What is her shortest height?

Answers

Answer:

3 inches

Step-by-step explanation:

Let's call the heights H1 thru H4.

So we have

H1/H2 = 24/5

H2/H3 = 1/12

Therefore if we multiply these, we have

H1/H3 = 2/5

Finally we are given

H1/H4 = 16/1.

By logic we can see that H3 is the tallest.

Thus if H3 = 10 feet, H1 = 4 feet

And from that,

H2 = 1/12 (10 feet) = 5/6 feet = 10 inches

and finally

H4 = 1/16(H1) = 1/16(4 feet) = 1/4 foot =

3 inches

Answer:

3 inches

Step-by-step explanation:

Let's call the heights H1 - H4

Here, we have

H1/H2 = 24/5

H2/H3 = 1/12

And so, we have

H1/H3 = 2/5

Finally

H1/H4 = 16/1.

Thus if H3 = 10 feet, H1 = 4 feet

And from that,

H2 = 1/12 (10 feet) = 5/6 feet = 10 inches

And last,

H4 = 1/16(H1) = 1/16(4 feet) = 1/4 foot = 3 inches

HELP MEEEEEE PLEASEEEEE

Answers

Answer:

1000-400=600km

good luck i hope it helped, its all about reading the graph!

Identify the solution of the inequality |9m| + 40> 4 and the graph that represents it.

Answers

Answer:

can i have more info?

Step-by-step explanation:

For the given table of values for a polynomial function, where must the zeros of the function lie?.

Answers

The zero of the function lie between 2.5 and 3.0 and between 4.0 and 4.5

The given question is incomplete the complete question is

x      2.0    2.8    2.5    1.1    3.0   –0.8

f(x)    3.5   –1.2    4.0  –0.3  4.5     0.7

For the given table of values for a polynomial function, where must the zeros of the function lie?

A. between 2.0 and 2.5 and between 4.0 and 4.5

B. between 2.5 and 3.0 and between 4.0 and 4.5

C. between 2.0 and 2.5 and between 3.5 and 4.0

D. between 2.5 and 3.0 and between 3.5 and 4.0

answer : If a function is continuous and you have points on opposite sides of the x-axis, there must be a zero-crossing between those points. As evidenced by the table and graph,...

(3.0, 4.0) and (3.5, -0.2) 

are points on the x-axis on opposite sides. As a result, between x=3.0 and x=3.5, there must be a zero crossing.

In the same way,...

 (4.0, -0.8) and (4.5, 0.1) 

are points on the x-axis on opposite sides. As a result, between x=4.0 and x=4.5, there must be a zero-crossing.

The correct answer option includes both of these possible zero crossings.

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Without calculating, order the quotients smallest to largest.

Answers

The order of the quotient from smallest to largest is given as follows:

42.6/70, 426/70, 42.6/0.07, 42.6/0.07.

What is a quotient?

A quotient is given by the division of two terms a and b, that is:

a / b.

From this, we have that the dividend a and divisor b are inverse proportional, that is:

A large quotient is achieved when a is large and b is small.A small quotient is achieved when a is small and b is large.

There are three divisions with the same term a, hence they are ordered, from smallest to largest, as follows:

42.6/70, 42.6/0.07, 42.6/0.07.

(the smallest the value of b, the largest the quotient).

The final quotient is:

426/70.

Dividing by 10 to have an equivalent value of a, we have that:

426/70 = 42.6/7.

Which is the second largest value of b, hence the second smallest quotient.

Missing Information

The problem is given by the image shown at the end of the answer.

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. The ratio of cups of almonds to cups of peanuts in a mixed nuts snack is 4 to 3.
How many cups of peanuts would be needed to make 49 cups of the mixed nuts
snack?

Answers

Number of cups of peanuts needed to make 49 cups of the mixed nuts snack is 21 cups

The ratio of cups of almonds to cups of peanuts in a mixed snack = 4 : 3

Number of of cups of almonds = 4x

Number of cups of peanuts = 3x

Total number of cups of mixed nuts snack = 49 cups

Then the equation will be

4x + 3x = 49

Add the like terms

7x = 49

x = 49 / 7

x = 7

Number of cups of almonds needed = 4x

= 4×7

= 28 cups

Number of cups of peanuts needed = 3x

= 3×7

= 21 cups

Hence, number of cups of peanuts needed to make 49 cups of the mixed nuts snack is 21 cups

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Write the equation using function notation
x - y = -4

A) f(x) = x - 4
B) f(x) = x + 4
C) f(x) = -x + 4
D) f(x) = -x - 4

Answers

Answer:

C

Step-by-step explanation:

Bob’s employer covers 23% of his family’s annual health insurance premium. The balance of the premium is deducted in equal amounts from bob’s paycheck 26 times over the calendar year. If $185. 30 is withheld from each of bob’s paychecks, what is his family’s annual health insurance premium? a. $805. 65 b. $4,817. 80 c. $6,256. 88 d. $20,946. 96.

Answers

If $185.30 is withheld from each of Bob's paychecks, then his family's annual health insurance premium is $4817.80.

From the given information,

It was stated that the balance of the premium is deducted in equal amounts from Bob’s paycheck 26 times over the calendar year and $185.30 is withheld from each of Bob’s paychecks.

Therefore, the family’s annual health insurance premium will be calculated :

              = $185.30 × 26

              = $4,817.80

In conclusion, the correct option is $4,817.80.

therefore, his family's annual health insurance premium is $4817.80

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Which does point A represent in this box plot?

Answers

A box plot is used to study the distribution and level of a set of a set of numbers. A box plot is made up of two lines and a box. The two lines are known as whiskers.

The end of the first whisker represents the minimum number. The minimum number is the smallest number in the dataset.  The end of the second whisker represents the maximum number. The maximum number is the largest number in the dataset.

The first line to the left represents the lower (first) quartile. The second line on the box represents the median. The third line on the box represents the upper (third) quartile.

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Graph the piecewise function.
(6 points - 2 points for each piece)

Answers

Points of interval A (-1,-3) and (-2,-6)

Points of interval B is (1,1) and (2,-1)

How to find Piecewise function?

Determine which of the following intervals (or inequalities) the input belongs to before evaluating a piecewise function at any given input. The function specification for that specific interval can then simply be updated to reflect the new input.

[tex]f(x)=\left \{ {{3x, if x\leq -1} \atop {-2x+3, if 0 < x < 4}}\atop {2, if x\geq 4}\right.[/tex]

lets take 3x as Interval A

-2x+3 as interval B

and 2 as interval C

Now lets calculate the interval A

f(x)=3x

as x≤-1

∴f(-1) = 3(-1)

       =(-3)

∴ point is (-1,-3)

∴f(-2) = 3(-2)

       =(-6)

∴ point is (-2,-6)

Now lets calculate the interval B

f(x)=-2x+3

as 0<x<4

∴f(1) = -2(1)+3

       =-2+3

      =1

∴ point is (1,1)

∴f(2) = -2(2)+3

       =-4+3

       = -1

∴ point is (2,-1)

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Approximately how many people are harmed by prescription errors in the united states each year?. Help me!explain how the physical features have influence the human landscape of the hilly country in Sri Lanka How do the beliefs and practices of Judaism connect the ancient and modern worlds? the chief business officer of a construction equipment company arranges a loan of $9,300, at interest for 37.5 months. find the amount of interest. (round to the nearest cent) What type of technology created conveniences by providing wireless communication systems that allowed people to access information wherever they wanted it?. how can saltwater batteries work in real life? can someone pls help me i dont ll get this Situational leadership theory indicates that the optimum leadership style is dependent upon. Which parts of the countrygained representatives? Wherewere representatives lost? Howmight these changes affect thestates' influence in Congress? a chinese and a dutch speaker will experience similar challenges when trying to learn english as a second language. Which supporting detail is most helpful in determining whether theauthor's purpose is to inform, explain, persuade, inspire, or entertain?18 of 25 QUESTIONSToday's explorers are certainly brave and talented, but they pale in comparison withthe heroes of decades past. When Ernest Shackleton led his party to Antarctica in1914, he did not have GPS, Internet, or a cell phone. In fact, he barely had a map tofollow, as very few people had ever explored this area. He and his men experimentedwith the proper clothing and food needed to survive harsh conditions, but they didnot have a century of experience to build upon. I think you'll agree that these early.explorers were truly amazing.people. Help on number 1 please!! Thanks. find two person in you're barangay for a. interview ask them how they develop their intrapersonal and interpersonal communication in any communicative situation. the equilibrium potential for sodium is about 66 mv. if only sodium channels were open in a cells plasma membrane, the membrane potential would be the nurse is caring for a patient with a new diagnosis of systemic lupus erythematosus (sle). the patient denies a family history of this disease. which information in the patient's history identifies a likely cause of the onset of symptoms? health benefits of including physical activity in your daily routine include which of the following? someone help pls due soon Write the sentence as an equation.191 is the same as 266 added to the product of 109 and Which adaptation was the most important in enabling the first terrestrial animals to eliminate their dependence on aquatic habitats?. !Required informationOveruse of Be VerbsFor each of the following sentences, choose the revision thatreplaces the be verb with an active verb. Some sentences mayneed more than one verb change, so be sure to choose the optionthat replaces all be verbs with active verbs.EXAMPLE:The contradictory clues were a puzzle to the detective.The contradictory clues puzzled the detective.Historians are generally in agreement that the Egyptians were the inventors of sailing around 3000 BCE.