Modeling Real Life A train ride from Chicago to Emeryville, California, is 2,438 miles. It is about 8 times as long as a train ride from Chicago to Port Huron, Michigan. About how long is the train ride from Chicago to Port Huron?

The value of cosθ = 0.5

The correct option is (A).

Now, According to the question:

Basic Trigonometric Function Formulas:

By using a right-angled triangle as a reference, the trigonometric functions and identities are derived: sin θ = Opposite Side/Hypotenuse. cos θ = Adjacent Side/Hypotenuse. tan θ = Opposite Side/Adjacent Side.

Remember that in a right triangle, we have that:

cos(θ) = (adjacent cathetus)/(hypotenuse)

Here we have:

Replacing all that in the equation we get:

cos(60°) = 1/2 = 0.5

Hence, the value of cosθ = 0.5

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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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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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Answer: plane a is faster than plane b because it has more speed than plane b

Step-by-step explanation:

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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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 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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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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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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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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Here to solve the probability of this sum, it is difficult to say that the probability without no information.

(a)The probability that the team wins the debate with a junior giving the closing argument is 0.083.

(b) To design a simulation to estimate the probability that a sophomore is never selected to give the closing argument in the next 3 debates, one could randomly assign a closing argument speaker for each debate using a table of random digits. The table would have two columns: one for sophomores and one for juniors and seniors. The probability of a sophomore being selected would be 20%, and the probability of a junior or senior being selected would be 80%. The simulation would be run for 3 debates and the number of times a sophomore is never selected would be recorded. This process would be repeated a number of times to estimate the probability of a sophomore never being selected. (e) Based on the dot plot, it appears that there is some evidence that the sophomores were purposely ignored, as there are several simulated sets of 5 debates where a sophomore was not selected to give the closing argument. However, without more information, it is difficult to say for certain if this is enough evidence to support the claim that the sophomores were purposely ignored.

A larger sample size or a more detailed analysis of the simulation results may be needed to make a more convincing determination.

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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]

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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The length of the chalk outline is 19 feet.

The field is circular and the line drawn by chalk is the length of the rim of the circular field and is called the circumference. It can be calculated from the radius(or diameter) of the circle.

The formula of the circumference of a circle:

Circumference of circle [tex]= 2 * \pi * r = \pi * d[/tex]

where r means the radius of the circle and d means the diameter of the circle.

The diameter d = 2 times of radius

Thus, we have:

Length of a chalk outline [tex]= \pi * d = \pi * 6 = 3.14 * 6 = 18.84 = 19 feet[/tex]

So,  the length of the chalk outline is 19 feet.

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The height of the wall decal when my actual height is 5.5 inches, is equals to the 110 inches.

We have, My height in the portrait measures = 3 1/2 inches = 7/2 = 3.5 inches

According to the scale used by company,

one inch measurement on portrait = 20 inches on the wall decal. That is portrait measurement / wall decal = 1/20 ( in inches) . We have to determine the height on the wall decal if my actual height is 5.5 inches. Let the height of wall decal be "h inches" when my actual height is 5.5 inches. Write the proportion like this to calculate the value of h , 1/20 = 5.5/ h

Cross multiply we get,

=> 1× h = 5.5 × 20

=> h = 110.0

Hence, the required height of the decal is 110 inches.

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Complete question:

Your height in the portrait measures 3 1/2 inches, if the company uses a scale where 1 inch on the portrait represents 20 inches on the wall decal, find the height on the wall decal if your actual height is 5.5 inche?

When compared to my actual height of 5.5 inches, the wall decal's height is 110 inches.

We've got My height in the image is 3 1/2 inches plus 7/2, which is 3.5 inches.

On the basis of the scale:

20 inches are equal to one inch in a portrait on the wall decal. That is a portrait measurement divided by a 20-inch wall decal. If my real height is 5.5 inches, we must determine the height on the wall decal. Let the wall decal's height be "h inches" even though my height is 5.5 inches. To compute the value of h, write the ratio as 1/20 = 5.5/h.

When we cross multiply,

1× h = 5.5 × 20

h = 110.0

Therefore, 110 inches is the minimum height for the decal.

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Note: The complete question would be as bellow,

Your height in the portrait measures 3 1/2 inches, if the company uses a scale where 1 inch on the portrait represents 20 inches on the wall decal, find the height on the wall decal if your actual height is 5.5 inche?

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 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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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:

Answer:

Step-by-step explanation:

a)
Because if you visualize the formation of it size x will fit perfectly on the 6cm side therefore x = 6cm

b)
6 x 9 = 54cm

what do you want help with?

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:

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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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

Country B is more efficient than Country A when it comes to producing cars and tanks.

Country A takes twice as long to produce a car (30 minutes) than Country B (12 minutes). However, Country A takes 20 minutes to produce a tank while Country B takes 10 minutes, cutting the amount of time in half.

We can measure the efficiency of each country by calculating the number of cars and tanks each country can produce in an hour. We can do this using the following formula:

Cars per hour = (60 minutes/minutes to produce car)

Tanks per hour = (60 minutes/minutes to produce tank)

For Country A, the number of cars produced in an hour is (60 minutes/30 minutes) = 2 cars per hour and the number of tanks produced in an hour is (60 minutes/20 minutes) = 3 tanks per hour.

For Country B, the number of cars produced in an hour is (60 minutes/12 minutes) = 5 cars per hour and the number of tanks produced in an hour is (60 minutes/10 minutes) = 6 tanks per hour.

Therefore, Country B is more efficient than Country A when it comes to producing cars and tanks.

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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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Answer:

9π inches

Step-by-step explanation:

we know clock start from 12 o'clock to 9 o'clock, it will be 270 degree. Then we convert it to radian is 3π/2. We get the radian and the radius. So we can apply the formula of the lenghth of an arc.

l = rθ

l=6*3π/2=9π inches