A dog is standing 5 feet from the base of a tree, looking up at a cat that has climbed 16 feet up the tree. What is the angle of elevation from the point the dog is standing on the ground to the cat?

Check the picture below.

so the rectangle's perimeter is pretty much just 4 + 6 + 6 = 16, now let's notice the semi-circle, is really just half of a circle whose diameter is 4, meaning that its radius is 2, so let's simply get the circumference of that semi-circle and add it to 16.

[tex]\textit{circumference of a semi-circle}\\\\ C=\cfrac{1}{2}\cdot 2\pi r \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=2 \end{cases}\implies C=\cfrac{1}{2}\cdot 2\pi (2)\implies C=2\pi \\\\[-0.35em] ~\dotfill\\\\ \stackrel{Perimeter}{16~~ + ~~2\pi} ~~ \approx ~~ \text{\LARGE 22.3}[/tex]

According to the following Venn diagram, the number students surveyed is 2063

The term Venn diagram in math is defined as overlapping circles or other shapes to illustrate the logical relationships between two or more sets of items

Here we have given that anonymous survey of college students was taken to determine behaviors regarding​ alcohol, cigarettes, and illegal drugs.

While we looking into the Venn diagram we have identified that 875 drank alcohol​ regularly, 665 smoked​ cigarettes, 207 used illegal​ drugs, 422drank alcohol regularly and smoked​ cigarettes, 113 drank alcohol regularly and used illegal​ drugs,126 smoked cigarettes and used illegal​ drugs, 97 engaged in all three​ behaviors, and 217 engaged in none of these behaviors.

Then the number of students is calculated as,

=> 875 + 667 + 207 + 97 + 217

=> 2063

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The angle pairs that forms corresponding angles are angles 1 and 5. Option B

Corresponding angles are defined as angles formed when two parallel lines are both intersected by a transversal.

They are also described as any pair of angles in which each of the angles are on the same side of one of two lines that is cut by another line and on the same side of that other line.

The types of corresponding angles are;

Hence, the pairs that are corresponding are 1 and 5

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The cowpox infection will prevent the child from being infected by the small pox virus.

Hypothes is a tentative assumption made in order to draw out and test its logical or empirical consequences

A simple hypothesis suggests only the relationship between two variables: one independent and one dependent. Examples: If you stay up late, then you feel tired the next day. Turning off your phone makes it charge faster.

Given paragraph is "dr. edward jenner realized that cows have a disease called cowpox, which is like a disease that infects humans called smallpox; jenner noticed that milkmaids whose hands were infected with cowpox were not contracting smallpox. jenner infected a child with the pus from a cowpox blister, and found that the child did not contract smallpox."

In this supporting hypothesis is "The cowpox infection will prevent the child from being infected by the small pox virus."

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Bryan owns a clothing store,  Insurance: F , Internet bill: F , Clothes: V ,Employees' salaries: F

F is for fixed and V is for variable used .

Fixed cost :

Regardless of production output, fixed costs remain constant. Lease and rental payments, insurance, and interest payments are examples of fixed costs. Costs that are not affected by volume are known as fixed costs. Costs that are usually based on time rather than on how many products or services your company sells or produces are known as fixed costs. Rent and lease payments, salaries, utility bills, insurance, and loan repayments are all examples of fixed costs.

Costs that do not change when production or sales volumes increase or decrease are known as fixed costs. This is because they are not directly involved in providing a service or manufacturing a product. Consequently, fixed costs are regarded as indirect costs.

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Answer:

Step-by-step explanation:

All parts of the problem given have been explained and provided below.

Variables in any particular dataset are defined as any characteristics, numbers, or quantity that can be measured or counted to give information about any object, on which the dataset is based.

So, the variables in this given dataset are;

Overall score

Recommended

owner satisfaction

Overall miles per gallon

Acceleration (0-60) sec

Categorical or qualitative variables are those which can't be quantified or measured. Their values are defined by an order relation between the different categories.

the categorical variables in this dataset are,

Recommended

Owner satisfaction

Quantitative variables are those which can be measured in an order to provide information about an object.

the quantitative variables in this dataset are,

Overall score

Overall miles per gallon

Acceleration (0-60) sec

In the given dataset, 7 vehicles are recommended,

So their percentage would be,

7/15 × 100 = 46.67%

The average overall miles per gallon of these 15 vehicles is 25.4.

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The range of the function (f+g)(x) = x² - 1 will be ( -1, ∞ ). The correct option is B.

The range of values that we are permitted to enter into our function is known as the domain of a function.

The x values for a function like f make up this set (x). A function's range is the set of values it can take as input. After we enter an x value, the function outputs this set of values.

Given that the function is f(x) = x²+2x-5. The function g(x) will be calculated by the data given in the table.

x           -6    -3     -1    4

g(x)       16    10    6   -4

The function g(x) will be:-

g(x) = mx + c

m = ( 10 - 16 ) / ( -3 + 6 )

m = -6 / 3

m = -2

c = y - mx

c = 10 - 6

c = 4

g(x) = -2x + 4

The function ( f + g)(x) will be:-

( f + g)(x) = f(x) + g(x)

( f + g)(x) = x²+ 2x - 5 - 2x + 4

( f + g)(x) = x² - 1

At x = 0, the value ( f + g)(x) is -1. The range of the function is ( -1, ∞).

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The value of 223,692 divided by 42 using the standard algorithm and showing work is 5326.

The value of 223,692 divided by 42 using the standard algorithm and showing work is given below:

Dividing the two values by 2, a common factor

223,692 / 42 = 111,846 / 21

Dividing the two values by 3, a common factor

111,846 / 21 = 37282 / 7

Dividing the two values by 7, a common factor

37282 / 7 = 5326 / 1

Hence, the value of the division is 5326.

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Answer:

5/18

Step-by-step explanation:

1. to get to the fractions you need to subtract make them have the same denominator. make 1/2=9/18 and 2/9=4/18

2. 9/18-4/18=5/18

Based on the analysis, we can be conclude that (C) Driving behavior and gender are related.

The link between variables is described by correlation. It can be viewed positively or negatively, as well as strong or weak. A correlation does not prove a cause. When the variable on the x-axis rises as the variable on the y-axis rises, there is a positive linear association. An upward-sloping straight regression line illustrates this.

When one variable rises while the other falls, there is a negative linear correlation. A straight regression line with a falling slope illustrates this. When there is a relationship between variables, but the relationship is not linear, there is a non-linear correlation (straight).

Hence, according to correlation theory, Driving behavior and gender are related.

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The cost of one DVD to Hector is $11.8.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

Hector spent $26.75 for 2 DVDs that cost the same amount.

The sales tax on his purchase was $4.15.

That means,

the cost of 2 DVDs = 26.75 - 4.15 = $22.6

Hector also used a coupon for $1.00 off his purchase.

That means,

the cost of 2 DVDs = $23.6

The cost of one DVD = 23.6 /2 = $11.8

Therefore, the cost of one DVD is $11.8.

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what do you want help with?

Answer:

36 adult and 94 student tickets

Step-by-step explanation:

x = adult ticket              y = student ticket

5x + 3y = 462

x + y = 130

x + y = 130

y = 130 - x

5x + 3y = 462

5x + 3(130 - x) = 462

5x + 390 - 3x = 462

2x + 390 = 462

2x = 72

x = 36

x + y = 130

36 + y = 130

y = 94

For the scenario, the null and alternate hypotheses are as follows:

H(0) : p = 0.75

H(a) : p ≠ 0.75

In the question, a hospital director believes that 75% of the lab reports contain errors.

A sample of 140 reports found 98 errors.

We have to explain there is sufficient evidence at the 0.10 level to refute the hospital director's claim or not and we have to state the null and alternative hypotheses for the above scenario.

In statistics, a two-tailed test is a procedure that determines if a sample is larger than or less than a particular range of values by using a two-sided critical area of a distribution. It is utilized in tests for statistical significance and null hypotheses.

So this is a two tailed test.

The null and alternative hypotheses for the above scenario is:

H(0) : p = 0.75

H(a) : p ≠ 0.75

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Answer: The wall that Randy is painting is 20 feet long and 6 feet high. The two corners that he is not painting are triangular in shape and are each 6 feet high and 4 feet wide.

So the area of the wall that Randy is going to paint is:

20 ft * 6 ft = 120 sq ft

The area of the two corners that Randy is not painting is:

(1/2) * 4 ft * 6 ft = 12 sq ft

Therefore, the total area that Randy needs to paint is:

120 sq ft - 12 sq ft = 108 sq ft

One gallon of paint will cover 100 square feet.

So Randy will need to purchase 108 sq ft / 100 sq ft/gallon = 1.08 gallons of paint.

Randy will have to purchase 1.08 gallons of paint.

Step-by-step explanation:

Answer:

The answer should be 6.6 and -12.4. The first and last one. I wish you the best of luck!

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

as u pit it in the mirrror and u can see

The two positive coterminal angles are 180° and 540°, the two negative ones are -900° and -180°.

For any given angle A, the family of coterminal angles can be written as:

B = A + n*360°

Where n can be any integer number.

Here we want to find angles coterminal to -540°, so we have the relation:

B = -540° + n*360°

if n = -1 we get:

B = -540° - 1*360° = -900°

if n = 1

B = -540° + 1*360° = -180°

if n = 2

B = -540° + 2*360° = 180°

if n = 3

B =  -540° + 3*360° = 540°

These are the 4 coterminal angles on the given range.

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Answer: 10 magdalenas

espero que esto ayude

The number of years from 2020 to 2050 will be 30 years. Then the average temperature in 2050 will be - 15.25 °F.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

In 2020, the normal temperature in certain pieces of the Artic was about - 19.3F. The temperature in the cold expanded around 0.135 degrees each year somewhat recently.

Let 'x' be the number of years and 'y' be the temperature. Then the equation is given as,

y = 0.135x - 19.3

The number of years from 2020 to 2050 will be given as,

x = 2050 - 2020

x = 30

Then the average temperature in 2050 will be given as,

y = 0.135(30) - 19.3

y = 4.05 - 19.3

y = - 15.25F

The number of years from 2020 to 2050 will be 30 years. Then the average temperature in 2050 will be - 15.25 °F.

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The area of the shaded region is 251 m^2.

the solution is attached with this,

parallelograms

A parallelogram is a two-dimensional geometrical shape whose sides are parallel to each other.

The Sum of adjacent angles of a parallelogram is equal to 180 degrees.

It is a type of polygon having four sides, where the pair of parallel sides are equal in length.

polygon

A polygon can be defined as a flat or plane, two-dimensional closed shape bounded with straight sides. It does not have curved sides. The sides of a polygon are also called its edges.

The points where two sides meet are the vertices of a polygon.

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11 is a 35.3% decrease of 17.

17 - 11/((17 + 11)/2) = 6/14 = 0.42857142857143 = 42.857142857143%

20 litres of regular milk must be mixed with 90 l of milk with 1% butterfat to have milk with 2% butterfat.

From the data given,

Let us assume that the x litres of regular milk which have 4% butterfat is mixed.

The amount of butterfat in 40 L of milk with 1% butterfat will be = (40*.01)=0.4 L

The amount of butterfat in x L of milk with 4% butterfat will be =x *0.04=0.04 x

The amount of butterfat in (40+x) L  (when both are mixed) of milk with 2% butterfat will be =(40+x)*(0.02)=0.02(40+x)

Since we are aware that the total quantity of butterfat in each type's individual milk will match the total amount of butterfat in the final milk.

Therefore we can set up the equation which will be like this:

0.4+0.04 x=0.02(40+x)

Now solving the above equation for getting the value of "x"

0.4+0.04 x=0.02(40+x)

=>0.4+0.04x=0.8+0.02x

=>0.04x-0.02x=0.8-0.4

=>0.02x=0.4

=>x=(0.4/0.02)=20

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To make milk with 2% butterfat, 20 liters of ordinary milk must be combined with 90 liters of 1% butterfat milk.

Assume that 4% butterfat normal milk in an amount of X litres is combined. 40 L of milk with 1% butterfat will contain (40 x 0.01)=0.4 L of butterfat. In X L of milk containing 4% butterfat, the amount of butterfat is equal to =(X liter) x (0.04)=0.04 X.

When both are combined, (40+X) L of milk with 2% butterfat will contain =(40+X)*(0.02)

=0.02(40+X) grams of butterfat.

We know that the overall amount of butterfat in each type's individual milk will be the same as the total amount of butterfat in the finished milk.

As a result, we may construct the equation, which looks like this:

0.4+0.04X = 0.02(40+X)

To find the value of "X," solve the equation above.

0.4+0.04 X=0.02(40+X)

= 0.4+0.04X=0.8+0.02X

= 0.04X-0.02X=0.8-0.4

= 0.02X=0.4

= X=(0.4/0.02)

=  20

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Total area of the roof top garden is 272 ft² .

Rooftop planters can have soil depths ranging from six inches at the very least, to allow for little groundcovers and shrubs, to three to four feet, which is necessary for huge shade and coniferous trees. Divide the length by the width of a rectangle or square to find its area.

The square footage of the area is calculated by multiplying the length and width. Please maintain the same unit size (feet or inches). For a rectangular garden area, multiply the length by the width to get the square footage. A suitable garden is often one that is roughly 10 feet by 10 feet, if your landscape permits it (3 x 3 meters).

Given, the figure comprises of triangle and rectangle,

Area of rectangle = length × breadth

= 12 ft × 20 ft

= 240 ft²

Area of triangle = 1/2 × base × height

= 1/2 × 8 × (20 - 12)

= 1/2 × 8 × 8

= 32 ft²

Total area of the figure = Area of rectangle + Area of triangle

= 240 + 32

= 272 ft²

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For the graphed function we have:

The domain

D: {-3, -2, -1, 0, 1, 2}

And the range

R: {0.25, 0.5, 1, 2, 4, 8}

For a function y = f(x), we define the domain as the set of possible inputs and the range as the set of possible outputs.

Remember that the notation in point form is (input, output).

Now, the graphed points are:

(-3, 8), (-2, 4), (-1, 2), (0, 1), (1, 0.5), (2, 0.25)

The domain is the set of the first values:

D: {-3, -2, -1, 0, 1, 2}

And the range is the set of the second values:

R: {0.25, 0.5, 1, 2, 4, 8}

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Answer: I believe it's 30 vehicles

Step-by-step explanation:

If you divided by 40 you get 30. There's for 4 rows of 10 which is 40 so you would divide, I think? I hope this helps! Been so long since I did this math.

To determine whether the variable is qualitative or quantitative, the reasoning for the following question will be:

a) qualitative, State of residence describes an attribute or characteristic, making the variable qualitative. Because the state of residence can be determined through measurement or counting, the variable is qualitative.

b) quantitative, The state of residence serves as a description of an attribute or characteristic, so the variable is quantitative. Since determining the state of residence requires measuring or counting, the variable is quantitative.

c) qualitative, Your variable will be quantitative if it is something like, say, your age or salary, which is typically something that can be discovered by counting or using mary-screw analysis. However, in this case, the state of residence is obviously a qualitative factor.

d) qualitative, If your variable is something like, say, your age or salary, or if it's something that is typically discovered by counting or Mary, then these kinds of variables are quantitative. But in this case, the state of residence is categorically important for this question.

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