This lab is designed to introduce concepts frequently used in physical geogra as significant figures, units, graphing, and isolining Part 1: Math Significant Figures la. Addition (3) 1203.2 11.3 0.024 14.7 +13.0218 aligned 28.8\\ underline 1+48.2 aligned . Multiplication (4) 7.2 * 3.208 =; 1.512 * 26 = 1; 72 * 32.08 = 1; 15.12*26=\ How many significant figures do the following numbers have? (3) 7.8 45600 12.8 * 10 ^ 3 15.030 420 2.177 Exponents Exponents are convenient ways of indicating very large or small numbers For example , or 0.1 10 ^ 1 = 10; 10 ^ 2 = 100 (10) (10 * 10); 10 ^ - 1 = 1/10; 10 ^ - 2 = 1/100 0.01 etc. etc. or Scientific notation uses exponents to express large and small numbers . 230000000 10000km = 2.3 * 10 ^ 8 * km 0.0000314 m = 3.14 * 10 ^ - 5 * m 2. Convert to/from scientific notationNote that scientific notation creates a number between and 10 and then multiplies that number by the appropriate power of ten.

The point (x, y) = (7, - 1) lies on the line whose equation is y + 4 = (3 / 5) · (x - 2). (Correct choice: E)

In this problem we find five different points of the form (x, y), each of which has to be checked in the linear equation given in the statement. A point is a solution of the linear equation if and only an equality exists, that is, the reflexive property of equalities is guaranteed by evaluating the expression.

Now we proceed to check the expression for each case:

(x, y) = (1, - 5)

- 5 + 4 = (3 / 5) · (1 - 2)

- 1 = (3 / 5) · (- 1)

- 1 = - 3 / 5     (FALSE)

(x, y) = (- 8, - 12)

- 12 + 4 = (3 / 5) · (- 8 - 2)

- 8 = (3 / 5) · (- 10)

- 8 = - 30 / 5

- 8 = - 6    (FALSE)

(x, y) = (- 3, - 8)

- 8 + 4 = (3 / 5) · (- 3 - 2)

- 4 = (3 / 5) · (- 5)

- 4 = - 3    (FALSE)

(x, y) = (12, 10)

10 + 4 = (3 / 5) · (12 - 2)

14 = (3 / 5) · 10

14 = 30 / 5

14 = 6     (FALSE)

(x, y) = (7, - 1)

- 1 + 4 = (3 / 5) · (7 - 2)

3 = (3 / 5) · (5)

3 = 3    (TRUE)

The point (x, y) = (7, - 1) lies on the line whose equation is y + 4 = (3 / 5) · (x - 2).

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Answer:

2(34 + 12) > 5b

Step-by-step explanation:

A) 16

B) 18

Pls mark Brainliest :D

Answer:

(-3, 4)

it passes thru (-3, 4)

Answer:

y = 2x - 7

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 2x + 2 ← is in slope- intercept form

with slope m = 2

• Parallel lines have equal slopes , then

y = 2x + c ← is the partial equation

to find c substitute (3, - 1 ) into the partial equation

- 1 = 2(3) + c = 6 + c ( subtract 6 from both sides )

- 7 = c

y = 2x - 7 ← equation of parallel line

Given :

Line WX bisects YZ at point W.

\(WZ=9\dfrac{5}{8}=\dfrac{77}{5}\) .

To Find :

The length of YZ .

Solution :

Since , the point W bisect YZ .

So , it cuts YZ into two equal parts i.e YW and WZ .

Therefore , YW = WZ

Also , YZ = YW+WZ = 2WZ

\(YZ = 2\times \dfrac{77}{5}\\\\YZ=\dfrac{154}{5}\\\\YZ=30\dfrac{4}{5}\)

Hence , this is the required solution .

Answer:

The sale price is $13. 75% of 52 is $39, and it is 75% off

Step-by-step explanation:

The sale price is $13. 75% of 52 is $39, and it is 75% off

I know this because 75% is that much from 52.

The domain is the set of all real numbers, while the range is defined by:

R: y ≥ -4

Here we have a quadratic function:

f(x) = (x + 6)*(x + 2)

We want to study the domain and range of this function. Trivially, we know that the domain is the set of all real values, and the range is the set of all real values larger than the y-value of the vertex (in the case that the parabola opens up, like here).

Here we can see that the y-value of the vertex is -4, then the range is:

R: y ≥ -4

Then the correct option is third one.

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Answer:

\(0.625kg\)

Step-by-step explanation:

we are given half-life of PO-210 and the initial mass

we want to figure out the remaining mass after 420 days

in order to solve so we can consider the half-life formula given by

\( \displaystyle f(t) = a {0.5}^{t/T} \)

where:

since it halves every 140 days our T is 140 and t is 420. as the initial mass of the sample is 5 our a is 5

thus substitute:

\(\displaystyle f(420)=5\cdot{0.5}^{420/140}\)

reduce fraction:

\(\displaystyle f(420)=5\cdot{0.5}^{3}\)

By using calculator we acquire:

\(\displaystyle f(420)=0.625\)

hence, the remaining sample after 420 days is 0.625 kg

Nine ears of sweetcorn will cost $2.25 at this store.

To determine the cost of nine ears of sweetcorn, given that four ears cost one dollar, you can follow these steps:

1. Determine the cost of one ear of sweetcorn: Since four ears cost one dollar, we can calculate the cost per ear by dividing the total cost by the number of ears: $1 / 4 ears = $0.25 per ear.

2. Calculate the cost of nine ears: Multiply the cost of one ear by the number of ears desired: $0.25 per ear × 9 ears = $2.25.

So, nine ears of sweetcorn will cost $2.25 at this store.

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Answer:

x=54

Step-by-step explanation:

55+54= 109

180-109=71

x+17=71

=54

The function f(x) = (1/3)x³ - (1/2)x² - (199/6)x + (211/6).

To find f(x) based on the given information, we can use integration.

Given that f′′(x) = 2x² - x, integrating once gives:

f′(x) = (2/3)x³ - (1/2)x² + C₁

where C₁ is a constant of integration.

Using the given information that f′(2) = 163, we have:

f′(2) = (2/3)2³ - (1/2)2² + C₁ = 8/3 - 2 + C₁ = 163

Solving for C₁, we get:

C₁ = 163 + 2 - 8/3 = 521/3

Substituting this value of C₁, we get:

f′(x) = (2/3)x³ - (1/2)x²+ 521/3

Integrating f′(x) once more, we get:

f(x) = (1/2)x⁴ - (1/6)x³ + (521/3)x + C₂

where C₂ is a constant of integration.

Using the given information that f(1) = 3, we have:

f(1) = (1/2)1⁴ - (1/6)1³ + (521/3)1 + C₂ = 3

Solving for C₂, we get:

C₂ = 3 - (1/2) + (1/6) - (521/3) = -169/3

Substituting this value of C₂, we get the final expression for f(x):

f(x) = (1/2)x⁴ - (1/6)x³ + (521/3)x - 169/3

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Answer:

x = 0

Step-by-step explanation:

4 ( 2x - 9 ) = 5 ( 3x - 7 ) - 1

8x - 36 = 15x - 35 - 1

-7x = 36 - 35 - 1

-7x = 0

x = 0

Answer:b

X= 0

Step-by-step explanation:

See work below

a) the dimension of its column space is also 2. b) the rank of A is 2. c) the nullity of matrix A is 1. d) the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.

(a) The dimension of the row space of a matrix is equal to the dimension of its column space. So, if the dimension of the row space of matrix A is 2, then the dimension of its column space is also 2.

(b) The rank of a matrix is defined as the maximum number of linearly independent rows or columns in the matrix. Since the dimension of the row space of matrix A is 2, the rank of A is also 2.

(c) The nullity of a matrix is defined as the dimension of the null space, which is the set of all solutions to the homogeneous equation Ax = 0. In this case, the matrix A is a 3 x 3 matrix, so the nullity can be calculated using the formula:

nullity = number of columns - rank

nullity = 3 - 2 = 1

Therefore, the nullity of matrix A is 1.

(d) The dimension of the solution space of the homogeneous system Ax = 0 is equal to the nullity of the matrix A. In this case, we have already determined that the nullity of matrix A is 1. Therefore, the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.

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The distance between the ship and the base of the lighthouse can be calculated using trigonometry. By applying the tangent function to the angle of depression, we can determine that the ship is approximately 54.49 feet away from the base of the lighthouse.

To determine the distance between the ship and the base of the lighthouse, we can use trigonometry. The angle of depression of 15° represents the angle formed between the horizontal line from the top of the lighthouse and the line of sight to the ship in the ocean. We can consider the height of the lighthouse (158 ft) as the opposite side of the right triangle, and the distance between the ship and the base of the lighthouse as the adjacent side.

Using the tangent function, we can set up the equation tan(15°) = opposite/adjacent, where the opposite side is 158 ft and the angle is 15°. Rearranging the equation, we have tan(15°) = 158/adjacent. Solving for the adjacent side, we find that the ship is approximately 545.51 feet away from the base of the lighthouse.

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Answer:

5 inches

Step-by-step explanation:

We need to converver the cm to inches.

\(\frac{12.5 cm}{1}\) · \(\frac{1 in}{2.54 cm}\) = \(\frac{12.5 in}{2.54}\) = 4.92125984252 Rounded to the nearest whole number is 5 inches.

Helping in the name of Jesus.

Answer:

\(\angle EAB = 85\)

Step-by-step explanation:

Given

\(\angle EBC = 148\)

\(\angle ADC = 63\)

See attachment for triangle

Required

Find EAB

\(\angle AEB = \angle ADC = 63\)  --- corresponding angles

\(\angle ABE + \angle EBC = 180\) --- angle on a straight line

So:

\(\angle ABE + 148 = 180\)

This gives:

\(\angle ABE =- 148 + 180\)

\(\angle ABE =32\)

Considering: \(\triangle ABE\)

\(\angle ABE +\angle AEB +\angle EAB = 180\) --- angles ina triangle

So:

\(32 +63+\angle EAB = 180\)

\(95+\angle EAB = 180\)

Collect like terms

\(\angle EAB = 180-95\)

\(\angle EAB = 85\)

Answer:

no solution

Step-by-step explanation:

Answer:

-15$

30 ft

6*c

I hope this helps

Answer:

Step-by-step explanation:

a. → Mary had a debt of $30. She earned $15 more now she has _x = $30 + $15_______.

b.→ A diver was at the depth of 10ft . Then he sank 5ft. then he sank 15ft more . now he is at depth of _x = 10 + 5 + 15 ft.

c.→ The temperature was 2*c and feel 7* . Then it rose 4*. Now the Temperature is _x = 2 + 4__________ *c.

The rug with a diameter of 24.8 meters has an area of approximately 476.456 square meters when using 3.1 as the value of pi.

To find the area of a rug with a diameter of 24.8 meters, we need to calculate the area of a circle using the given value of pi as 3.1. The formula to find the area of a circle is A = πr^2, where A represents the area and r represents the radius of the circle.

Since we have the diameter, which is twice the length of the radius, we need to divide 24.8 meters by 2 to find the radius. Thus, the radius is 12.4 meters.

Now we can substitute the values into the formula: \(A = 3.1 \times (12.4)^2\). First, we square the radius, which is \(12.4 \times 12.4 = 153.76\). Then we multiply it by 3.1: \(A = 3.1 \times 153.76\).

Calculating the product, we have A = 476.456.

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The largest area that can be enclosed by a fence of 240 m and a wall is 7200m²

It is given that the rectangular area will be fenced up against a long rectangular wall. Therefore, the fencing will be done on just three sides.

Let one side be x

Then the side opposite to it must be x cm as well

The sum of the three sides should be equal to 240 m

Hence the third side must be 240 - 2x m

Therefore the area of the region fenced must be

A = x(240 - 2x)

or, A = 240x - 2x²

Now we need to maximize the above equation

Taking the first derivative zero we get

A' = 0

or, 240 - 4x = 0

or, 60 - x = 0

or, x = 60

Now we will test whether the above output is maximum or not. The second derivative of A is

A'' = -4

Since A'' is a constant function,

Now, A''(60) = -4

Therefore, the maximum side will have lengths of 60 m and 120 m.

Hence the largest area that can be enclosed with the fence is

60 X 120 m²

= 7200 m²

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The side length of each corner square must be 2 inches.

A piece of cardboard measuring 8 inches by 11 inches can be used to make an open-top box by removing squares from each of its corners, and then folding up the edges.

The resulting box will have the dimensions (8-2x) by (11-2x) by x, where x is the side length of each of the squares removed from the corners, as shown below:

                                                \((8-2x) \times (11-2x) \times x\).

Thus, the volume of the open-top box can be calculated by multiplying the three dimensions together:

                               V(x) = \((8-2x) \times (11-2x) \times x\)

Let's find the value of x that will maximize the volume of the box by differentiating V(x) with respect to x, and then setting the resulting expression equal to zero:

                                             dV/dx = 4x² - 38x + 88 = 0

Solving for x, we get:x = 2 or x = 11/2

Since we're only interested in the positive value of x, the side length of each corner square must be 2 inches.

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There are 6 possible results for each roll: 1, 2, 3, 4, 5 or 6. Each result has a probability of 1 in 6 or 1/6. The probability of rolling a 3 is 1/6. After 3000 rolls, you would likely reach theoretical probability of 1/6 and therefore 1/6x3000 = 500 rolls would be a 3, so p(3) = 1/6.

The Python code to the expression and print the result is

Output:

60.74999999999999

The Python code is

Output:

0.5304751375515361

1. The Python code to calculate the expression and print the result is as follows:

```python

result = 3.14 * 2 * 5**0.5 + 5 * 8 * (6.4 - 1.5/6)

print(result)

```

Output:

60.74999999999999

2. The Python code to evaluate the equation `y = vt - (2/1) * gt**2 + sin(t) * (1.2 * t - e**(-t))` with given values and print the result of `y` is as follows:

```python

import math

v = 3

g = 7

t = 0.5

y = v * t - (2/1) * g * t**2 + math.sin(t) * (1.2 * t - math.e**(-t))

print(y)

```

Output:

0.5304751375515361

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Answer:

where's the data

Step-by-step explanation:

The area of the regions are

The area of the regions is calculated by dividing the regions into simper form and adding or subtraction as the case may be

1. the region is divided into semicircle and trapezoid

= area of semicircle + area of trapezoid

= 1/2 πr² + 1/2(sum of parallel lines ) * height

= 0.5 * π * 6² + 0.5(12 + 6) * 8

= 56.55 + 72

= 128.55 cm²

2. the region is divided into rectangle and trapezoid

= area of rectangle - area of trapezoid

= length * width - 1/2(sum of parallel lines ) * height

= 25 * 17 - 0.5((25 - 5 - 3) + 11) * 8

= 425 - 0.5(34) * 8

= 425 - 136

= 289 cm²

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Answer:

Answer is C

Step-by-step explanation:

Because when you go across the X- axis you are just copying the triangle just in the "box" above.

Answer:

1/15

Step-by-step explanation:

Hope it helps

The correct option is A. Write-in adjustments All above-the-line adjustments that do not have corresponding input lines on Schedule 1 (Form 1040) are indicated as write-in adjustments.

All above-the-line adjustments that do not have corresponding input lines on Schedule 1 (Form 1040) are referred to as write-in adjustments. Line 36 of Schedule 1 is where all write-in adjustments are reported. You have to provide a brief explanation of the adjustment and the corresponding amount for each write-in adjustment.If the IRS has developed an input line for a particular write-in adjustment, taxpayers must use that input line to report the adjustment. 

When writing in adjustments, taxpayers must ensure that the amount they enter is calculated and that they have a reasonable explanation for the adjustment. Taxpayers may be required to provide documentation to support the adjustment if the IRS requests it.

Miscellaneous adjustments and miscellaneous deductions are not used to describe all above-the-line adjustments that do not have corresponding input lines on Schedule 1 (Form 1040).

Therefore, options C and D are incorrect. The correct option is A. Write-in adjustments.

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The graph of y = x^2e^(-2) has a point of inflection at the values of x where the concavity of the curve changes. In mathematical terms, a point of inflection occurs where the second derivative of the function changes sign.

To find the values of x that correspond to the points of inflection, we need to find the second derivative of the function and solve for the values of x that make the second derivative equal to zero or undefined.

First, let's find the first and second derivatives of y = x^2e^(-2):

First derivative:

dy/dx = 2xe^(-2) + x^2(-2)e^(-2) = 2xe^(-2) - 2x^2e^(-2)

Second derivative:

d^2y/dx^2 = 2e^(-2) - 4xe^(-2) = 2e^(-2)(1 - 2x)

Now, set the second derivative equal to zero and solve for x:

2e^(-2)(1 - 2x) = 0

Since e^(-2) is always positive and nonzero, we can ignore it for solving this equation. Therefore:

1 - 2x = 0

2x = 1

x = 1/2

So, the graph of y = x^2e^(-2) has a point of inflection at x = 1/2.

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