100 gallons of water at $1.19 per gallon

Answer:

75°

Step-by-step explanation:

B=105° (corresponding angles)

Straight line=180°

180°-105°=75°

The tangent line approximation, ln(0.98) is approximately -0.02 and ln(1.02) is approximately 0.02.

Here, we have,

To approximate both ln(0.98) and ln(1.02) using one tangent line approximation, we can first find the equation of the tangent line to the function f(x) = ln(x) at the point x = x₀ = 1.

The derivative of f(x) is f'(x) = 1/x. Evaluating this derivative at x = x₀ = 1 gives us f'(1) = 1/1 = 1.

The equation of the tangent line is given by:

y = f(x₀) + f'(x₀)(x - x₀)

Plugging in x₀ = 1 and f(x₀) = ln(1) = 0 into the equation, we have:

y = 0 + 1(x - 1)

Simplifying further:

y = x - 1

Now we can use this tangent line equation to approximate both ln(0.98) and ln(1.02), which are close to ln(1).

Substituting x = 0.98 into the equation, we get:

ln(0.98) ≈ 0.98 - 1 = -0.02

Similarly, substituting x = 1.02 into the equation, we get:

ln(1.02) ≈ 1.02 - 1 = 0.02

Therefore, using the tangent line approximation, ln(0.98) is approximately -0.02 and ln(1.02) is approximately 0.02.

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Answer:

5/3 or 1.67

Step-by-step explanation:

Find the slope of the original line

3x+5y=4                Subtract 3x from both sides

5y = - 3x + 4           Divide both sides by 5

y = (-3/5)x + 4

The original line has a slope of - 3/5 or - 0.6

Find the slope of the perpendicular line

m1 * m2 = - 1

m1 = - 3/5

m2 = -1/(-3/5)

m2 = 5/3

The slope of the perpendicular line is

5/3 or 1.67

To derive the slope for a single variable regression from the slope in a multiple regression, you can use the concept of partial derivatives.

In a multiple regression model, we have several independent variables (predictors) that are used to predict a dependent variable. Let's say we have a multiple regression model with two independent variables: X1 and X2, and a dependent variable Y. The regression equation can be written as:

Y = b0 + b1X1 + b2X2

To find the slope for the variable X1, we need to hold all other variables constant and differentiate the regression equation with respect to X1. The partial derivative of Y with respect to X1 (denoted as ∂Y/∂X1) gives us the slope for X1 in the multiple regression model.

∂Y/∂X1 = b1

Therefore, the slope for X1 in the multiple regression is simply equal to b1, the coefficient of X1 in the regression equation.

So, to derive the slope for X1 in the simple regression model, you can directly use the coefficient b1 obtained from the multiple regression analysis.

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Answer:

Reflection

Step-by-step explanation: A reflection is a transformation that acts like a mirror.

Answer:

Reflection

Step-by-step explanation:

Translations are a horizontal and/or vertical movement of a shape. In this case, the points wouldn't match up. A dilation is either growth or reduction, which this pretty obviously is not. A rotation also wouldn't properly match the points up. If we reflect this shape across a line directly in between the two, all the points will match up.

The multiplier is 1 + growth percentage or 1- decrease percentage rage.

1) 1 + 5% = 1.05

2) 1-12% = 0.88

3) 1-0.85% = 0.9915

4) 1 + 200% = 3

Answer:

Calculate the probability that a randomly selected egg weighs between 62.5g and 68.75g. Show your work. My work: Dont you need a population of how many eggs are produced by a hen before you start

Answer:

B

Step-by-step explanation:

5/2=2.5

7.5/3=2.5

10/4=2.5

12.5/5=2.5

B. 2 and OD. 15 are not possible lengths for the third side of the triangle.

To determine the possible values for the length of the third side of a triangle, we need to consider the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Given that two sides have lengths 6 and 9, we can analyze the possibilities:

6 + 9 > x

x > 15 - The sum of the two known sides is greater than any possible third side.

6 + x > 9

x > 3 - The length of the unknown side must be greater than the difference between the two known sides.

9 + x > 6

x > -3 - Since the length of a side cannot be negative, this inequality is always satisfied.

Based on the analysis, the possible values for the length of the third side are:

A. 7

C. 4

□E. 10

O F. 12

B. 2 and OD. 15 are not possible lengths for the third side of the triangle.

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The model which properly represent the information in given axioms is Cross geometry (+).

In the given question we have following information,

by using the above axioms we draw a geometry of Cross sign Geometry as seen above .

We can draw a line which contains three points and these points are only from given five points another line also follow this . this geometry follows all given axioms . The two lines intersect each other at a point . The point of intersection is one of point from five points . both of lines are linear and consists three points .

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Answer:

Answer:

38

Step-by-step explanation:

128 + angle G= 180

angle G = 180-128= 52

m+ 52 = 90 ( complementary angles)

m= 90-52= 38

Answer:

The answer is Giechung: equation

Step-by-step Explanation:

equation consist of a dependent variable and independent variable

3x=10+5

3x=15

3x/3=15/3

x=5

The interval of hours that represents the lifespan of the middle 68% of light bulbs is 1655 hours - 1745 hours.

What is empirical rule?

A statistical principle known as the empirical rule, also known as the three-sigma rule or 68-95-99.7 rule, holds that with a normal distribution, almost all observed data will lie within three standard deviations (denoted by ) of the mean or average (denoted by ).

The empirical rule predicts that 68% of observations falls within the first standard deviation (µ ± σ), 95% within the first two standard deviations (µ ± 2σ), and 99.7% within the first three standard deviations (µ ± 3σ).

Given that, the amount of time a certain brand of light bulb lasts is normally distributed with a mean of 1700 hours and a standard deviation of 45 hours.

Thus,  µ = 1700 hours and σ = 45 hours.

The random variable X can be defined as, the amount of time a certain brand of light bulb lasts and the random variable X is normally distributed with parameters µ = 1300 hours and σ = 90 hours.

Calculate 68%:

⇒ P ( µ  - σ < X < µ  + σ ) = 0.68

⇒ P ( 1700  - 45 < X < 1700  + 45 ) = 0.68

⇒ P( 1655 < X < 1745) = 0.68

Therefore, the interval of hours that represents the lifespan of the middle 68% of light bulbs is 1655 hours and 1745 hours.

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Answer: x = -29

Step-by-step explanation:

-0.59x+0.39x=5.8

Collect like terms

-0.2x = 5.8

Divide both sides of the equation by -0.2

x = -29

Response to user in comments:

-0.59+0.39=-0.2 that is a fact

-0.2/-0.2=1 that is a fact

5.8/-0.2= - 29 that is a fact

These are the facts about the steps of the equation. Solving Steps for Solving the Equation

Answer:

Step-by-step explanation:

This is a right triangle; so you can use the Pythagorean Theorem (\(a^2 + b^2 = c^2\)), where a and b are the lengths of the legs and c is the hypotenuse.

You get: \(5^2 + 12^2 = c^2\)

Simplify the expression: \(25 + 144 = c^2\)

Combine like terms: \(169 = c^2\)

Take the square root of both sides: \(\sqrt{169} = \sqrt{c^2}\)

Evaluate: 13 = c

So the answer is letter c ... x = 13

Answer:

x^4

Explanation:

Breakdown x^4 = x · x · x · x

Breakdown x^5 = x · x ·  x · x · x

Here the common factor is x · x · x · x = x^4

Hence, the greatest common factor of x^4 and x^5 is x^4.

Answer:

\( \sqrt{58} \)

a) The campaign manager has a random sample of potential voters in a large city and records the number of individuals within each of the categories.

b) A Chi-Square goodness of fit test.

a) A campaign manager would like to show that the distribution of individuals within several social economic categories is different than what a newspaper reported and that's why we know that the campaign manager has a random sample of potential voters in a large city and records the number of individuals within each of the categories.

Chi-Square goodness of fit is used to find out how the observed value of a given phenomenon is significantly different from the expected value. In Chi-Square goodness of fit test, the sample data is divided into intervals.

In this case, we have one categorical variable which is the distribution of individuals within several social groups. We want to see if the actual distribution of the variable is significantly different from the distribution within several social groups as claimed(expected) by the newspaper.

Hence, we will use chi-square goodness of fit test for this case.

b) A Chi-Square goodness of fit test.

Here the variable is the distribution of individuals purchasing season pass at an amusement park. The variable has 4 categories based on the age group of the individuals.

A tourist company wants to test the actual distribution of individuals within each age group and wants to check if it is significantly different from the expected distribution i.e the one claimed by the amusement park.

The tourist company randomly sampled 200 individuals entering the park.

The proportion of individuals within each group as claimed by the amusement park is given.

Hence, we will use chi-square goodness of fit test to test if the actual distribution within each group is significantly different or not from the claimed distribution.

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In perimeter, The cost to frame Joy's math certificate in a fancy frame is $138.00.

The dimensions of Joy's math certificate are 10 inches tall and 13 inches wide.

Joy wants to frame it in a fancy frame that costs $3.00 per inch.

To determine the total cost of framing the certificate, we need to find its perimeter and then multiply that by the cost per inch.

The perimeter of the certificate is:

Perimeter = 2 × (height + width)

Substituting the given values, we get:

Perimeter = 2 × (10 + 13)Perimeter = 46 inches

Therefore, the total cost of framing Joy's math certificate is:

Total cost = Perimeter × Cost per inch

Total cost = 46 × 3.00Total cost = $138.00

Thus, the cost to frame Joy's math certificate in a fancy frame is $138.00.

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Answer:

9.405

Step-by-step explanation:

Answer: quadrant II

Step-by-step explanation:

A. Using the given information, y expressed in terms of x is y = x + 50

B. The table that shows the relationship between y and x is

x               y

10             60

20            70

30             80

40             90

50             100

From the question, we are to express y in terms of x

From the given information,

There are x sparrows in a tree and 50 sparrows on the ground beneath the tree

If y represent the total number of sparrows in the tree and on the ground,

Then,

We can write that

y = x + 50

B.

We are to make a table to show the relationship between y and x

Using the equation above

y = x + 50

When x = 10

y = 10 + 50

y = 60

When x = 20

y = 20 + 50

y = 70

When x = 30

y = 30 + 50

y = 80

When x = 40

y = 40 + 50

y = 90

When x = 50

y = 50 + 50

y = 100

Thus,

The table is:

x               y

10             60

20            70

30             80

40             90

50             100

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Answer:

$360 the first month $60 a month after that

Step-by-step explanation:

The required diameter of the sphere for the given volume of the sphere is equal to 12.2 cm (rounded to one decimal place)

Volume of the sphere = 944cm^3

Let us consider V be the volume of the sphere.

And r be the radius of the sphere.

The formula for the volume of a sphere is,

V = (4/3) × π × r^3

Solve for the radius of the sphere by rearranging the formula as follows,

⇒ r^3 = (3/4) × (V/π)

⇒r = [(3/4)×(V/π)]^(1/3)

Substituting V = 944 cm^3, we have,

⇒ r = [(3/4) ⇒ (944/π)]^(1/3)

⇒r ≈ 6.08 cm

⇒r ≈ 6.1 cm (rounded to one decimal place)

The diameter of the sphere is twice the radius, so the diameter is,

d = 2r

   ≈ 12.2 cm (rounded to one decimal place)

Therefore, the diameter of the sphere with a volume of 944 cm^3 to the nearest tenth of a centimeter is 12.2 cm.

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The stem-and-leaf plot of the given data is attached. The correct options regarding percentage distribution, the distribution skewness, and gaps within the data are A, E, and F.

A stem and leaf plot refers to a technique used to to present and organize quantitative data (discrete or continuous) in a graphical format. It is displayed as table where each data value is split into a "stem" (the first digit or digits) and a "leaf" (usually the last digit). A stem and leaf plot can be used to visualize the shape of a distribution. The stem and leaf plot of the given data regarding the percentage loss of wetlands in the lower states is attached.

Based on the plot, it can be seen that:

Note: The question is incomplete. The complete question probably is: Wetlands offer a diversity of benefits. They provide a habitat for wildlife, spawning grounds for U.S. commercial fish, and renewable timber resources. In the last 200 years, the United States has lost more than half its wetlands. Environmental Almanac gives the percentage of wetlands lost in each state in the last 200 years. For the lower 48 states, the percentage loss of wetlands per state is given. i) Make a stem-and-leaf display of these data. (Use the tens digit as the stem and the ones digit as the leaf. Enter NONE in any unused answer blanks.) ii). How are the percentages distributed? Is the distribution skewed? Are there any gaps? (Select all that apply.) A) The percentages are concentrated from 20% to 60%. B) ii. The percentages are concentrated from 60% to 90%. C) There is a gap showing that none of the lower 48 states has lost from 60% to 69% of its wetlands. D) These data are strongly skewed left. E) These data are fairly symmetric, perhaps slightly skewed right. F) There is a gap showing that none of the lower 48 states has lost from 10% to 19% of its wetlands. G) There are no gaps in the data.

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Answer:

2x - 2

Step-by-step explanation:

Move the numbers to be near their mates

4x - 2x + 8 - 10

Then solve as much as you can

4x - 2 = 2x, 8 - 10 = -2

2x - 2

Answer:

There is an infinite number of solutions.

All points on line 3x - 2y = 12 are solutions.

Step-by-step explanation:

3x - 2y = 12

6x - 4y = 24

Divide both sides of the second equation by 2:

3x - 2y = 12

Both equations are the same equation, so there is an infinite number of solutions. All points on line 3x - 2y = 12 are solutions.

Hey there! :)

Answer:

Infinite solutions.

Step-by-step explanation:

Solve this system of equations by subtracting the first equation from the second:

6x - 4y = 24

3x - 2y = 12

Multiply the bottom equation by 2 to make the terms with the y variable equivalent:

6x - 4y = 24

6x - 4y = 24

Subtract:

0x + 0y = 0

0 = 0

Therefore, there are infinite solutions to the system of equations.