1.Which quadrant will the terminal ray falls for an angle of rotation equal to 1.2 radians.

A.) QIV
B.)QII
C.)QI
D.)QIII

Answer:

A semicircle can be drawn by first drawing a diameter of a circle, which is a line segment connecting two points on the circumference that passes through the center of the circle. Then, the semicircle can be constructed by drawing an arc that is half of the circumference of the circle and connecting the ends of the arc to the endpoints of the diameter.

A quarter circle can be drawn in a similar way, but instead of drawing an arc that is half of the circumference, you would draw an arc that is a quarter of the circumference. To do this, you would need to find the central angle that subtends the arc and divide it by 4. The quarter circle can then be constructed by drawing an arc with this central angle and connecting the ends of the arc to the endpoints of a radius of the circle, rather than the diameter.

In both cases, you can use a compass or a protractor to accurately draw the arcs.

Answer: The statement "The mean height of the students in Juan's math class is equal to the mean height of the students in his English class" means that the center or average of both groups is the same. However, the statement "the standard deviation of the heights of students in his math class is 3.2 inches, the standard deviation of the heights of students in his English class is 6.1 inches" implies that the heights of the students in the English class are more spread out than the heights of the students in the math class.

Therefore, the answer is:

D) The heights of the students in Juan's math class are less variable than the heights of the students in his English class.

Step-by-step explanation:

The second situation costs less by

The cost of the first situation is

Adult = 8 * 2 = 16

drink = 2 * 2 = 4

popcorn = 2 * 2 = 4

Total = $24

Second situation

rent a video = $3.50

buy a 2 liter of cola = $1.60

a bag of microwave popcorn = $1.98.

Total = $7.03

The second situation costs less by

$24 - $7.03

= $16.92

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From the total of 300 workers in the factory :

a. Number of men = 200 and Women = 100

b. Number of workers works in the morning = 225

c. Number of workers unionized are 150.

d. Number of workers trustworthy are 50.

Total number of workers in the factory are 300.

a. Fraction of men in the factory are ( 2/3)

= 2/3 of 300

= 200

Women

= 300 -200

= 100

b. Number of workers in the morning shift are

= 3/4 of 300

= 225

c. Total number of workers unionized

= 1/ 2 of 300

= 150

d. Number of trustworthy workers

= 1/6 of 300

= 50

Therefore, out of 300 workers in the factory answer of the following questions are:

a. Number of men and women work in the factory are 200 and 100 respectively.

b. Number of workers works in the morning is 225.

c. Unionized workers = 150

d. Trustworthy workers = 50.

The above question is incomplete , the complete question is :

The Factory has 300 workers of which 2/3 are men, 3/4 work in the morning, 1/2 are unionized and 1/6 are trusted personnel.

a. How many men work in the factory and how many women?

b. How many workers work in the morning?

c. How many are unionized?

d. How many are trustworthy?

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A

im going to guess that the top of the graph has a flat line.

its easy to visualize since the graph looks like a hill, and the story describes the graph the most accurately

The exponential function that best models the number of game systems sold, in million, x years since 2015 is given as follows:

y = 30.5(0.7)^x.

The standard definition of an exponential function is given as follows:

y = ab^x.

In which:

Considering the graph, the parameters for this problem are given as follows:

Hence the function is defined as follows:

y = 30.5(0.7)^x.

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Answer: 20

Step-by-step explanation:

30-60-90 triangles are special: Their side lengths fall in a ratio of 1:2:[tex]\sqrt{3}[/tex], in order of Shortleg : hypotenuse : longleg

Since we know the short leg is 10, the hypotenuse must be double, or 20.

answer:

if you multiply the 2 sides of the ratio by a number it will give you an equivalent ratio

5:8 = 10:16 multiplying by 2

5:8 = 15:24 multiplying by 3

5:8 = 20:32 multiplying by 4

5:8 = 25:40 multiplying by 5

5:8 = 30:48 multiplying by 6

5:8 = 35:56 multiplying by 7

and so on ...

The distance that a person with a height of 6 feet can see is given as follows:

10.5 feet.

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

The function for this problem is defined as follows:

d = 1.75h.

For the person with a height of 6 feet, the distance is obtained replacing the lone instance of h by 6, hence:

d = 1.75 x 6

d = 10.5 feet.

The problem asks for the distance that a person with a height of 6 feet can see.

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Answer:

See below.  The answer is 8.8 feet, but none of the options offers this value.

Step-by-step explanation:

I get 8.8 feet.

2^2 + x^2 = 9^2

4 + x^2 = 81

x^2 = 77

x = 8.77496 to be exact.

The completed statements with regards to the projectile motion of the football are presented as follows;

This graph is a nonlinear function

The hang time of the football is 3 seconds

The football reaches its maximum height when t = 1.5 seconds

The maximum height is about 11 meters

For t between t = 0 and t = 1.5, the height is increasing

The motion of a projectile is one that involves an object thrown into the air or into space, which is acted upon by only gravitational force.

The graph in the question, showing the scale on the x-axis obtained from a similar question on the internet, indicates that we get;

The x-intercept of the graph are; (0, 0), and (3, 0)

Therefore;

The time the football is in the air, which is the hang time of the football can be obtained from the difference between the x-values of the x-intercept as follows;

Hang time = 3 - 0 = 3

The graph indicates that the coordinates of the maximum height is (1.5, 11). Therefore;

The height at t = 0 is 0 meters, and the height at t = 1.5 seconds is 11 meters, therefore; the height is increasing between t = 0 and t = 1.5 seconds

For t between t = 0 and t = 1.5, the height is increasing

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Answer:

Nonlinear

3

1.5

11

increasing

Step-by-step explanation:

The value of x that makes the shape a parallelogram is 2/3

A quadrilateral is a polygon that has four sides and four angles. Types of quadrilaterals are kite, square, rectangle, parallelogram and so on.

A parallelogram is a quadrilateral with two pairs of parallel sides. Each parallel sides are equal. Also, the diagonals of a parallelogram bisect each other.

From the diagram, the diagonals bisect each other in other to be a parallelogram, hence:

6x = 3x + 2

3x = 2

x = 2/3

The value of x is 2/3

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The time taken by population of bacteria to be doubled whose normal growth is six fold in 10 hours is equal to 3.87 hours.

Let us consider 'n' is the time taken by the bacteria populations.

And P(n) represents the population of the bacteria in time 'n'

Using exponential growth function we know,

P(n) = K e^(a× n)

Where K and 'a' are the constants.

From the given condition we have :

P(10 ) = 6 P(0)

⇒ K e^ (10a) = 6k e^(0 × a )

⇒ e^(10a) = 6

⇒ 10a = log 6

⇒ a = ( log 6 ) / 10

Now required time when population is double :

P(n ) = 2P(0)

⇒  K e^ (n × a) = 2k e^(0 × a )

⇒ e^ [ n ×( log 6 ) / 10 ] = 2

⇒ n ×( log 6 ) / 10 = log 2

⇒ n = ( 10 × log 2 ) / log 6

⇒ n =  ( 10 × 0.3010 ) / 0.7782

⇒ n = 3.8679 hours

⇒ n = 3.87 hours

Therefore, the population of the bacteria will take 3.87 hours to get double.

The above question is incomplete , the complete question is:

A bacteria population increases sixfold in 10 hours. Assuming normal growth, how long did it take for their population to double?

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The required measure of angle m∠Q is 42 degrees, as of the given condition.

The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should equal to 180°

Here,
In a triangle, the sum of the angles is always equal to 180 degrees. Therefore, for triangle OPQ,

m∠O + m∠P + m∠Q = 180°

Using the given information,

m∠O = (6x - 14)°

m∠P = (2x + 16)°

m∠Q = (2x + 8)°

(6x - 14)° + (2x + 16)° + (2x + 8)° = 180°

10x + 10 = 180°

10x = 170

x = 17

Substituting the value of x back into the expression for m∠Q,

m∠Q = (2x + 8)°

m∠Q = (2 * 17 + 8)°

m∠Q = 42°

So the value of m∠Q is 42 degrees.

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Answer:

29.22

Step-by-step explanation:

The scale factor of abcde to zyxwv is obtained dividing one side length of zyxwv by the equivalent side length of abcde, for example:

k = zy/ab.

A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.

The figures for this problem are given as follows:

Hence the scale factor of abcde to zyxwv is obtained dividing one side length of zyxwv by the equivalent side length of abcde, for example:

k = zy/ab.

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When ever the area is calculated the units will have a degree of two.

The area is defined as the space covered by any two-dimensional body. The unit if the area is calculated as square units. The square units come because the area is calculated by the two parameters of length.

The area of the rectangle is calculated by the multiplication of the two lengths like length and width.

Similarly, the area of the circle is calculated by taking the square of the radius of the circle it means that the length here is also multiplied by two times.

Therefore, the area is calculated in an square units.

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Answer:

[tex]10[/tex] four point questions and [tex]30[/tex] two point questions

Step-by-step explanation:

Let's say [tex]f =[/tex] [tex]\text{number of four point questions}[/tex] and[tex]t = \text{number of two point questions}[/tex]. The total number of questions is [tex]40[/tex], therefore [tex]t + f = 40[/tex]. We know the test is worth [tex]100[/tex] points so we can write [tex]2t + 4f = 100[/tex]. We have a system of equations: [tex]t + f = 40 \text{ and } 2t + 4f = 100[/tex]. We can rewrite [tex]t[/tex] as [tex]t = 40 - f[/tex]. We rewrite this in the equation [tex]2t + 4f = 100[/tex]. Since [tex]t = 40 - f[/tex], we have [tex]2 \cdot (40 - f) + 4f = 100[/tex]. Distributing & simplifying gives

[tex]2 \cdot (40 - f) + 4f = 100\\(80 - 2f) + 4f = 100,\\\text{Remove parentheses} 80 - 2f + 4f = 100,\\80 + (-2f) + 4f = 100\\80 + 2f = 100,\\\text{Subtract 80 from both sides} 2f = 20,\\\text{Divide 2 by both sides} f = 10.\\[/tex]

Since we determined [tex]t = 40 - f[/tex] and [tex]f = 10[/tex], subtracting [tex]10[/tex] from [tex]40[/tex] will give [tex]t = 30[/tex].

Therefore, there are [tex]10[/tex] four point questions and [tex]30[/tex] two point questions.

Hope that helps!

Answer:

5.1

Step-by-step explanation:

11.5 + 5.6 + 8.8 = 29.5

31 - 29.5 = 5.1

Percentage profit on a chocolate bar is 150%

Profit percentage is a top-level and the most common tool to measure the profitability of a business. It measures the ability of the firm to convert sales into profits. i.e., 20% means the firm has generated a net profit of $20 for every $100 sale.

%profit = (selling price - cost price)/cost price × 100

%profit =( 1.50-0.6)/0.6 × 100

%profit = 0.9/0.6 × 100

= 1.5 × 100

= 150 %

therefore the percentage profit on a chocolate bar is 150%

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Step-by-step explanation:

x current age of the father

y current age of the son

first equation (x-4)+(y-4)=27 so x=27+4+4-y=35-y

second equation (y+5) : (x+5)= 2:7

so (y+5)*7=(x+5)*2

let's replace x we found at the first equation with the one at second equation

(y+5)*7=(35-y+5)*2

7y+35=(40-y)*2

7y+35=80-2y

7y+2y=80-35

9y=45

y=5

x=35-y=35-5=30

variety of statistics for 1057 inernet users are  = (0.9180, 0.8998)  solve by given question .

population proportion is the share of a population that belongs to a particular category. Confidence intervals are used to estimate population proportions.

Let p be the population proportion of respondents who say the Internet has been a good thing for them personally.

=p +- z*[tex]\sqrt{p*(1-p)/n}[/tex]

where z* = Critical value p = Sample proportion,n = sample size.

As per given , we have

n= 1057 By z-table , Critical value for 95% confidence interval : z*= 1.96

Then, the 95% confidence interval for the proportion of respondents who say the Internet has been a good thing for them personally. will be :

=p +- z*[tex]\sqrt{p*(1-p)/n}[/tex]

=0.9+-1.96[tex]\sqrt{.9*(1-.9)/1057}[/tex]

=0.9180, .8998

Hence, the required 95% confidence interval for the proportion of respondents who say the Internet has been a good thing for them personally = (=0.918, .881)

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Answer: Since triangle QRS and triangle TUV are both triangles, we can use the fact that the sum of the interior angles in a triangle is 180 degrees.

In triangle QRS, the measure of angle Q is 117 degrees and the measure of angle R is 180 - 117 = 63 degrees. The measure of angle S is 180 - 63 = 117 degrees, since the angles in a triangle add up to 180 degrees.

In triangle TUV, the measure of angle T is 180 - 30 = 150 degrees and the measure of angle U is 30 degrees. The measure of angle V is 180 - 150 = 30 degrees, since the angles in a triangle add up to 180 degrees.

The measures of LQ and LS can be found using the fact that the exterior angle of a triangle is equal to the sum of the measures of the two interior angles that are not adjacent to it.

The measure of LQ is equal to the sum of the measures of angles R and T:

LQ = 63 + 150 = 213 degrees

The measure of LS is equal to the sum of the measures of angles Q and U:

LS = 117 + 30 = 147 degrees

So the measure of LQ is 213 degrees and the measure of LS is 147 degrees.

Step-by-step explanation:

If Benjamin invests $400 in a savings account that earns 5% interest each year, the expression that shows the correct balance is  A = 400(1 + 0.05)(1 + 0.05)(1 + 0.05)

The principal amount = $400

interest rate = 5%

The equation of the simple interest

A = P (1+ rt)

Where A is the final amount

P is the principal amount

r is the interest rate

t is the time period

The final amount after one year

= 400( 1 + 0.05×1)

= 400(1 + 0.05)

The final amount after two year

= 400(1 + 0.05)(1 + 0.05)

The final amount after three year

= 400(1 + 0.05)(1 + 0.05)(1 + 0.05)

Therefore, the balance amount after three years is A = 400(1 + 0.05)(1 + 0.05)(1 + 0.05)

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Answer: B: 15,080

Step-by-step explanation:

Alright, let's convert 20% into a decimal: 0.20

Then multiply 0.20 x 75,400  which gets you to 15080

So she needed to pay $15,080 in taxes

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Answer:

27%

Step-by-step explanation:

a percent is a part of 100

so if we get the denominator to 100, the numerator is the percent of the equation

54/200

in order to get 200 to 100, we have to divide by 2.

however we have to divide the numerator aswell as if we don't, we simply just half the equation.

54/2 = 27

200/2 = 100

27/100 is the new equation. referring back to the first statement, i made, the numerator would be the percent of the equation that is a part of 100

27%.

54/200 is equal to 27/100. all we did was divide both the numerator and denominator by 2.

The corresponding p-value for this test statistic is 0.005, which is smaller than our significance level of α=0.05.

To begin, we define the population proportion of people who shop for groceries online in region A as p₁ and the population proportion of people who shop for groceries online in region B as p₂.

Our null hypothesis is that there is no difference in these proportions, which we can write as H0=> p₁ = p₂. Our alternative hypothesis is that there is a difference, which we can write as H1=> p₁ ≠ p₂.

Next, we need to calculate the sample proportions and standard errors for each region. We can do this using the formulas:

p₁ = x₁/n₁, p₂ = x₂/n₂

where x₁ and x₂ are the number of people in each sample who shop for groceries online, and n₁ and n₂ are the sample sizes. The standard errors are given by:

=> SE₁ = √(p₁(1-p₁)/n₁),

=> SE₂ = √(p₂(1-p₂)/n₂)

Using the given data, we find that p₁ = 0.16, p₂ = 0.24, SE₁ = 0.037 and SE₂ = 0.042.

We can now calculate the test statistic, which measures the difference between the sample proportions under the assumption that the null hypothesis is true. We use the formula:

z = (p₁ - p₂) / √(SE₁² + SE₂²)

Substituting the values we calculated, we get:

z = (0.16 - 0.24) / √(0.037² + 0.042²) = -2.83

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Complete Question:

A random sample of 100 people from region A and a random sample of 100 people from region B were surveyed about their grocery-shopping habits. From the region A sample, 16 percent of the people indicated that they shop for groceries online. From the region B sample, 24 percent of the people indicated that they shop for groceries online. At the significance level of α=0.05, do the data provide convincing statistical evidence that there is a difference between the two regions for the population proportions of people who shop online for groceries? Complete the appropriate inference procedure to support your answer.

The amount of cubic feet that the storage shed can hold is 168 ft³

An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.

The volume of the storage shed is the product of the base area and the height. It is given by:

Volume = base area * height

From the diagram, the base is a triangle. Hence:

Area of base = (1/2) * base * height = (1/2) * 8 ft * 7 ft = 28 ft²

Volume = base area * height = 28 ft² * 6 ft. = 168 ft³

The volume of the storage shed is 168 ft³

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Answer:

44

Step-by-step explanation:

Answer: equation: 3/5 * 5/8 = 38 = 0.375

Spelled result in numbers/words is three eighths/ 3/8.

Step-by-step explanation:

the basketball field takes up 3/8 of the playground

3/5 * 5/8 = 38 = 0.375 = 3/8

then (simplify) 0.375 into a fraction.

3/5 * 5/8 = 38 = 3/8

Answer:

Equation: 3/8 * 5/8

Answer:3/8

Step-by-step explanation:

Equation: 3/5 * 5/8. Since it is 5/8 of 3/5, you can do 3/5 * 5/8.

Answer: 3/8. Since 3/5 * 5/8 = 3/8, the answer will be 3/8