A bacteriologist estimates that there are 5.2×10^4 bacteria growing in each of 20 petri dishes. About how many bacteria in total are growing in the petri dishes? Express your answer in scientific notation

Answers

Answer 1

Answer:

Answer:

1X10^6

1.04x10^6

Step-by-step explanation:

You start by multiplying 5.2x10^4 by 20 because there are 20 petri dishes with this amount growing, and you get 1,040,000. Now we need to convert it to scientific notation. We know that 1,000,000 is 10^6, so we would move the decimal to the left 6 places and get 1.04x10^6. This is in scientific notation, but we need to keep in mind significant figures (sig figs), so your final answer would be 1x10^6, if that is not what your instructor is looking for, try 1.04x10^6.

Answer 2

Answer:

Final answer:

The total amount of bacteria growing in the 20 petri dishes is calculated by multiplying the amount of bacteria in each dish (5.2×10^4) by the number of dishes (20), which gives a result of about 1.04×10^6 bacteria.

Explanation:

Given that there are approximately 5.2×10^4 bacteria in each dish and there are 20 petri dishes, we can find the total amount of bacteria by multiplying these two values together. The calculation is as follows: 5.2×10^4 bacteria/dish * 20 dishes = 1.04×10^6 bacteria. Therefore, there are about 1.04×10^6 bacteria in total growing in the petri dishes.

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ABCD is a rectangle. Find the length of each diagonal.ac=2(5a+1) bd=2(a+1).

Answers

The length of the diagonal of the rectangle is d = 2

What is the diagonal of a rectangle?

The diagonal of a rectangle is calculated by the formula

From the Pythagoras Theorem , The hypotenuse² = base² + height² , and

Diagonal of a Rectangle = √ ( Length )² + ( Width )²

Given data ,

Let the rectangle be represented as ABCD

Now , the diagonal of the rectangle is AC and BD

The measure of AC = 2 ( 5a + 1 )

And , the measure of BD = 2 ( a + 1 )

For a diagonal of a rectangle ,

The two diagonals of the rectangle will be same

So , the measure of AC = measure of BD

Substituting the values in the equation , we get

2 ( 5a + 1 ) = 2 ( a + 1 )

On simplifying the equation , we get

Divide by 2 on both sides of the equation , we get

5a + 1 = a + 1

Subtracting a on both sides of the equation , we get

4a + 1 = 1

Subtracting 1 on both sides of the equation , we get

4a = 0

a = 0

Now , substitute the value of a in measure of AC , we get

The measure of diagonal AC = 2 ( 5 ( 0 ) + 1 )

The measure of diagonal AC = 2

Hence , the measure of diagonals of the rectangle = 2

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Rectangle diagonals are equal.

2(5a+1) = 2(a+1)
10a + 2 = 2a + 2
10a -2a = 2 - 2
8a = 0
⇒ a = 0

AC = 2(5a+1) = 2(5 × 0 +1)= 2(0 + 1) = 2 × 1 = 2
BD = 2(a+1) = 2(0 + 1) = 2 × 1 = 2

Ansver: AC = BD = 2

Which is another way to check the sum of 104+34+228+877?

Answers

The answer is digit sum method.

Digit sum method is method used to check the sum of sum numbers. If the sum of all of the digits of numbers is equal to the sum of all of the digits of the total sum, then the arithmetic process was correct.

We need to check the sum of 104+34+228+877:
104 + 34 + 228 + 877 = 1243

Let's first summarize the digits of individual numbers:
104 *** 1 + 0 + 4 = 5
34 *** 3 + 4 = 7
228 *** 2 + 2 + 8 = 12 *** 1 + 2 = 3
877 *** 8 + 7 + 7 = 22 *** 2 + 2 = 4

Now, let's sum these sums:
5 + 7 + 3 + 4 = 19 *** 1 + 9 = 10 *** 1 + 0 = 1

Then, let's summarize the digits of the total sum:
1243 *** 1 + 2 + 4 + 3 = 10 *** 1 + 0 = 1

Since the sums of the digits on the both sides of equation is 1, than the arithmetic process was correct and the sum of 104 + 34 + 228 + 877 is really 1243.

In the xy-plane, triangular region R is bounded by the lines x=0, y=0, and 4x+3y=60. Which of the following points lie inside region R?a. (2, 18)
b. (5, 12)
c. (10, 7)
d. (12, 3)
e. (15, 2)

Answers

Convert the equation of the line to the slope-intercept form:
$4x+3y=60 \n3y=-4x+60 \ny=-(4)/(3)x+20$

All points which lie inside region R satisfy the system of inequalities:
$x\ \textgreater \ 0 \ny\ \textgreater \ 0 \ny\ \textless \ -(4)/(3)x+20$

You can see all coordinates in your choices are positive, so the first two inequalities are satisfied. We must check which points satisfy the third inequality.
Plug the values (x,y) into the inequality and check:
$(2,18) \n18 \ \textless \ -(4)/(3) * 2+20 \n18 \ \textless \ -(8)/(3)+20 \n18\ \textless \ -2(2)/(3)+20 \n18\ \textless \ 17 (1)/(3) \nfalse \n \n(5,12) \n12\ \textless \ -(4)/(3) * 5+20 \n12\ \textless \ -(20)/(3)+20 \n12\ \textless \ -6(2)/(3)+20 \n12\ \textless \ 13 (1)/(3) \ntrue$

$(10,7) \n7 \ \textless \ -(4)/(3) * 10+20 \n7\ \textless \ -(40)/(3)+20 \n7\ \textless \ -13 (1)/(3)+20 \n7\ \textless \ 6 (2)/(3) \nfalse \n \n(12,3) \n3\ \textless \ -(4)/(3) * 12+20 \n3\ \textless \ -(48)/(3)+20 \n3\ \textless \ -16+20 \n3\ \textless \ 4 \ntrue$

$(15,2) \n2 \ \textless \ -(4)/(3) * 15+20 \n2\ \textless \ -(60)/(3)+20 \n2\ \textless \ -20+20 \n2\ \textless \ 0 \nfalse$

The answer is B and D.

[-3 x 8] + (7 - 4) exponent of 2

Answers

[-3 x 8] + (7 - 4)^2
= [-24] + (3)^2
= -24 + 9
= -15

Is relation t a function? Is the inverse of relations t a function? Relation t x 0 1 2 3
y -2 1 10 2

Answers

Relation t is a function because it has no repeating x values

the inverse of relation t is when u switch the x and y values.
ex. inverse of (0,-2) is (-2,0).

and yes, the inverse of relation t is also a function because there are no repeating x values.

Jovan is building a fort in his backyard using a 10-foot board He leans the base of the board 6 feet away from the base of the wall. How high will be bourd be able to reuch up the wall? If necessary round to the nearest tenth.

Answers

That’s a long board because 10 foot is tall

Final answer:

In the scenario, a right triangle is formed with the board, the ground, and the wall. We use the Pythagorean theorem to find the height the board will reach up the wall and get the result as 8 feet.

Explanation:

This is a geometry problem where we need to determine the height the board will reach up the wall. This appears to be a right triangle since the board is leaning against the wall. The length of the board is the hypotenuse (10 feet), and the distance from the wall is one of the legs of the triangle (6 feet).

To find the height the board will reach up the wall, which is the other leg of the triangle, we can use the Pythagorean theorem: a² + b² = c² where a and b are the legs and c is the hypotenuse.

Substitute the given values to the formula: a² + 6² = 10²

Solving this equation gives: a² = 10² - 6²

Then, a² = 64

So, a = √64 = 8

Thus, the height the board will reach up the wall is 8 feet.

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