3.1 Create an activity where procedural and conceptual understanding co- exists. Revisit your content areas and choose a problem to solve and demonstrate how procedural and conceptual knowledge can be linked to the teaching and learning process. (6)​

Applying the central angle theorem, we have:

a. m<CBD = 70°   b. m<A = 50°      c. m<CBD = 2x

The central angle theorem states that the measure of the central angle is equal to the measure of its intercepted arc, similarly, the inscribed angle has half of the measure of the intercepted arc and also half of the central angle.

a. m<A = 35°

m<CBD = m(CD)

Find arc CD:

m(CD) = 2(35)

m(CD) = 70 degrees.

m<CBD = 70°

b. m<CBD = m(CD) = 100°

m<A = 1/2(CD)

m<A = 1/2(100)

m<A = 50°

c. If m<A = x, therefore:

m<CBD = 2x

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The actual length of roof of house is 25 feet.

The basic formula to find the scale factor of a figure is expressed as,

Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.

From the given figure, model has 24 inches and roof has 15 inches and the base angle of roof is 37°.

The actual house dimension is 40 feet.

40 feet = 480 inches

a) Scale factor = 24/480

= 1/20

So, measure of actual roof is 1/20 = 15/x

x=300 inches

300 inches = 300/12 = 25 feet

b) Using cosine rule formula

25=√(40²+25²-2×40×25 cosC)

625=2225-2000cosC

-1600=-2000cosC

cosC=4/5

cosC=0.8

∠C=37°

Therefore, the actual length of roof of house is 25 feet.

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Answer:[tex]\sqrt{\frac{14}{5} }[/tex]  or [tex]\frac{\sqrt{70} }{5}[/tex]

Step-by-step explanation:

(f o g )(x) means f(g(x)) so take g(x) and put it into f every time you see an x

f(g(x))[tex]=\sqrt{\frac{2(4+\sqrt{x} )}{5} }[/tex]

now plug in 9 for this answer  =[tex]\sqrt{\frac{14}{5} }[/tex]  or [tex]\frac{\sqrt{70} }{5}[/tex]

The function is solved for the given intervals and the values are noted

Given data ,

Let the function be represented as f ( x )

when x ≤ -2 , f ( x ) = -2

when -2 ≤ x ≤ 2 , f ( x ) = - ( x + 1 )²

And , when x > 2 , f ( x ) = - ( 1/4 )x + 1

Now , the function is defined as

a)

f ( -2 ) = -2

b)

f ( -1 ) = - ( -1 + 1 )²

f ( -1 ) = 0

c)

f ( 3 ) = ( -1/4 )(3 ) + 1

f ( 3 ) = -3/4 + 1

f ( 3 ) = 1/4

Hence , the function is solved

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The required width of the aquarium is 1.5033 feet.

To find the width of the aquarium, we can use the formula for the volume of a rectangular prism:

Volume = Length x Width x Height

We are given the length and height of the aquarium, as well as its volume (33.75 gallons). However, the volume is in gallons, while the dimensions are in feet. We need to convert the volume to cubic feet so that we can use the formula.

1 gallon is equivalent to 0.13368 cubic feet (approximately). Therefore, we have:

Volume = 33.75 gallons x 0.13368 cubic feet/gallon

Volume = 4.51 cubic feet

Now we can substitute the given values into the formula and solve for the width:

4.51 cubic feet = 2 feet x Width x 1.5 feet

Simplifying the equation, we have:

Width = 4.51 cubic feet / (2 feet x 1.5 feet)

Width = 1.5033 feet (rounded to four decimal places)

Therefore, the width of the aquarium is approximately 1.5033 feet.

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Answer:

Step-by-step explanation:

Area is equal to 1/2 times base times height

1/2 × 4 × 8= 16 m²

Answer:

16m

Step-by-step explanation:

area = base x height x 1/2

4 x 8 x 1/2

4 x 8 = 32

32 x 1/2= 16

The domain of the function in the graph is the set of all real numbers.

For an equation of the form:

y = f(x)

We define the domain as the set of possible inputs for the equation, that is, the possible values of x.

Remember that the values of x appear on the horizontal axis. Now, if you look at the given graph, you can see that the function keeps going in both directions (left and right). Then it covers the whole horizontal axis, which means that the domain is the set of all real numbers.

So the correct option is the last one.

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the answer is

option A

Step-by-step explanation:

(2√3)/3

The next term of the geometric sequence is A₆ = -273

Given data ,

Let the geometric progression be represented as A

Now , the value of A is

A = -1, -3, -9, -27, -81,...

The common ratio in this sequence is -3/-1 = 3.

To find the next term, we multiply the last term (-81) by the common ratio (3):

-1, -3, -9, -27, -81, -243

Hence , the 6th term of the GP is -243

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The length AC of the triangle ABC to the nearest whole number would be = 28

To calculate the missing length of the triangle, the sine rule can be used. That is , a/sinA = b/sinB.

Where;

a= 20

A= 30°

b= ?

B= 45°

That is;

20/sin30° = b/sin45°

b= 20× 0.707106781/0.5

b= 14.14213562/0.5

b= 28.28

b= 28

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If nth partial sum of series S is given by Sₙ = n+1/n²+1, the value of S is equal to 0.7834.

To find the sum S of the series, we need to take the limit of the nth partial sum as n approaches infinity. This is because the series contains an infinite number of terms, and the sum is the value that the series approaches as we add more and more terms.

We can write the formula for the nth partial sum as:

Sₙ = 1/2 + 2/5 + 3/10 + ... + n/(n²+1)

To find the sum S, we take the limit of Sₙ as n approaches infinity:

S = [tex]\lim_{n \to \infty}[/tex] Sₙ

We can use the formula for the nth partial sum to simplify Sₙ:

Sₙ = 1/2 + 2/5 + 3/10 + ... + n/(n²+1)

= [1/(1²+1)] + [1/(2²+1)] + [1/(3²+1)] + ... + [1/(n²+1)]

= Σ[1/(k²+1)], k=1 to n

Using calculus or other advanced techniques, we can find that the limit of Σ[1/(k²+1)] as n approaches infinity is approximately 0.7834. Therefore, the sum of the series S is approximately:

S ≈ 0.7834

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Answer:

C. 25; 56

Step-by-step explanation:

In a stem and leaf plot the number on the left (the stem) is the first digit, and the numbers on the right are the second digits so the first number has a 2 in the first place and a 5 in the second place and the last number has a 5 in the first place and a 6 in the last place

Therefore, the probability of selecting two Democrats and two Republicans from a committee of four people is approximately 0.476 or 47.6%.

To find the probability of selecting two Democrats and two Republicans from a committee of four people out of a city council consisting of five Democrats and five Republicans, we can use the formula for probability:

Probability = (number of ways to select two Democrats and two Republicans) / (total number of ways to select any four people)

The number of ways to select two Democrats and two Republicans can be found by multiplying the number of ways to select two Democrats from the five available Democrats and the number of ways to select two Republicans from the five available Republicans. This can be expressed as:

(Number of ways to select 2 Democrats from 5 Democrats) * (number of ways to select 2 Republicans from 5 Republicans)

= (5 choose 2) * (5 choose 2)

= 10 * 10

= 100

The total number of ways to select any four people from the city council is:

(Number of ways to select 4 people from 10 people)

= (10 choose 4)

= 210

Therefore, the probability of selecting two Democrats and two Republicans is:

Probability = (number of ways to select two Democrats and two Republicans) / (total number of ways to select any four people)

= 100 / 210

= 10 / 21

≈ 0.476 or 47.6% (rounded to the nearest tenth)

Therefore, the probability of selecting two Democrats and two Republicans from a committee of four people is approximately 0.476 or 47.6%.

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We can be 90% confident that the true population proportion lies between 0.433 and 0.567.

In statistics, proportion refers to the percentage or fraction of a population or sample that possesses an important trait.

If we wanted to know, for instance, what percentage of individuals in a particular city possessed cars, we would pick a sample of people from that city, count how many of them did, and express that number as a percentage of the whole sample size.

When drawing conclusions about a wider population from a sample, proportions are frequently used. Based on the sample proportion, one can estimate or evaluate the population proportion using confidence intervals and hypothesis tests.

A range of values used to estimate or define a population parameter, such as a mean, percentage, or variance, is referred to in statistics as an interval. The lower and upper bounds of an interval estimate are determined using the sample data and a degree of confidence or probability.

For instance, a range of values near the sample mean that we may reasonably be convinced contains the true population mean would make up a confidence interval for the population mean. The margin of error reveals the accuracy of the estimate, while the confidence level shows the likelihood that the interval contains the actual population mean.

According to question,

We can apply the following formula to create a confidence interval for a population proportion:

Confidence Interval is calculated as Sample Proportion +/- Error Margin.

where the margin of error takes into account the uncertainty in calculating the population proportion from the sample proportion and the sample proportion is the portion of the sample that possesses the feature of interest.

The sample proportion in this instance is:

x/n = 75/150 = 0.5

The following formula can be used to determine the margin of error:

Error margin is equal to z*√(p(1-p)/n)).

where z is the desired level of confidence's associated z-score. Using a typical normal distribution table, the z-score is 1.645 with a 90% degree of confidence.

When we enter the values, we obtain:

1.645√(0.5(1-0.5)/150) = 0.067 is the margin of error.

the 90% confidence interval for the population proportion is:

0.5 +/- 0.067, or (0.433, 0.567)

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The relationship between pints and cups where p represents pints and n represents cups is n = 2p.

We have,

3 cups converts to 1.5 pints

and 5 cups converts to 2.5 pints.

We know from constant of proportionality

y = kx

k = y/x

Put y= 2.5 and x= 5

Then, k = 5/2.5

k = 2

So, the relationship between pints and cups where p represents pints and n represents cups is

n = 2p

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Answer: Starting with 2(tan x - sqrt(3)) = 2:

First, divide both sides of the equation by 2 to simplify:

tan x - sqrt(3) = 1

Next, add sqrt(3) to both sides:

tan x = 1 + sqrt(3)

To solve for x, we need to take the arctan of both sides:

x = arctan(1 + sqrt(3))

In degrees, this is:

x = 75 degrees

In radians, this is:

x = 5π/12 radians

Step-by-step explanation:

Answer:

A = 383 [tex]\frac{1}{4}[/tex] m²

Step-by-step explanation:

the area (A) of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )

   = [tex]\frac{1}{2}[/tex] × 42 × 18 [tex]\frac{1}{4}[/tex] ( change mixed number to improper fraction )

  = 21 × [tex]\frac{73}{4}[/tex]

  = [tex]\frac{21(73)}{4}[/tex]

   = [tex]\frac{1533}{4}[/tex]

  = 383.25

 = 383 [tex]\frac{1}{4}[/tex] m²

The maximum annual variable cost Amber Hawke can have is $2,120.

Number of miles driven by Amber Hawke in a year = 12,000 miles

The annual vehicle fixed cost Amber have is = $2,200

Cost per mile for her compact car = $0.36

To find the maximum annual variable cost we have to solve it as shown below,

(x+$2,200)/12,000 = $0.36      [x is annual variable]

By solving the above equation, we can obtain the annual variable.

(x+$2,200) = $0.36 x 12,000

(x+$2,200)  = $4,320

x = $4,320 - $2,200

x = $2,120

From the above anaylis, we can conclude that Amber Hawke can have maximum of $2,120 annual variable cost.

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[tex]\tan(A )=\cfrac{\stackrel{opposite}{15}}{\underset{adjacent}{36}} \implies \tan(A)=\cfrac{5}{12}[/tex]

The statements regarding the scatter plot are given as follows:

The scatter plot, as shown by the image given in the problem is a series of points of the data-set in the following format:

(Years of experience,  yearly income).

As the line of best fit is an increasing line, there is a positive linear association between years of experience and yearly income.

For a person with 14 years of experience, we have point (14,50) on the line of best fit, meaning that a good estimate is of $50,000.

Outliers are in fact points away from the line of best fit, which is the case for item b.

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Answer:

A

Step-by-step explanation:

using the sine ratio in the right triangle and the exact value

sin45° = [tex]\frac{\sqrt{2} }{2}[/tex] , then

sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{2}[/tex] = [tex]\frac{\sqrt{2} }{2}[/tex] ( cross- multiply )

2x = 2[tex]\sqrt{2}[/tex] ( divide both sides by 2 )

x = [tex]\sqrt{2}[/tex]

the triangle is a 45- 45- 90 and is isosceles with congruent legs, then

x = y = [tex]\sqrt{2}[/tex]

Answer:

Graph B

Step-by-step explanation:

Graph B is not a function, because it fails the "vertical line test". Which means the plots that would be placed on the line intersecting the X axis would have the same X value, and X values CANNOT repeat when it comes to functions. So the Answer is B because the X Values would repeat if you were to write the coordinates of the points down.

All the rays in tiffany's designs that she is going to use on a stained glass window above her front door are EA , ED , EB , GC GH

Rays are a part of a line that has a fixed starting point but no endpoint.

Rays are written in a specific form

first letter should be the fixed point and the second letter should be point with no endpoint

E is fixed point A is no end point = EA

E is fixed point D is no end point = ED

E is fixed point B is no end point = EB

G is fixed point C is no end point = GC

G is fixed point H is no end point = GH

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In the Venn diagram , the given statement is valid.

What is Venn diagram?

Venn diagrams are frequently used in mathematics, statistics, logic, teaching, linguistics, computer science, and business. They are also known as Set diagrams or Logic diagrams.

Here the given Venn diagram , the Jimmy is one of the kids. because from all kids  some are rude and some are not rude .Then the given statement is Valid.

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To find the equation of a line perpendicular to d: 3x − 6y = 1, we need to determine its slope. We can rewrite d in slope-intercept form as:

y = (1/2)x - 1/6

The slope of d is then 1/2. A line perpendicular to d will have a slope that is the negative reciprocal of 1/2:

slope of perpendicular line = -2

Since the line passes through (0, 7), we know that when x = 0, y = 7. We can use this point and the slope of the line to find its equation using point-slope form:

y - 7 = -2(x - 0)

y - 7 = -2x

2x + (y - 7) = 0

2x + (y - 7) = c

where c is a constant.

To find the value of c, we need another point on the line. Since the line is perpendicular to d, we know that their intersection point will be the midpoint between (0, 7) and the x-intercept of d. To find the x-intercept of d, we let y = 0:

3x - 6(0) = 1

x = 1/3

So the midpoint between (0, 7) and (1/3, 0) is:

((0 + 1/3)/2, (7 + 0)/2) = (1/6, 7/2)

This point lies on the line, so we can substitute its coordinates into the equation 2x + (y - 7) = c:

2(1/6) + (7/2 - 7) = c

1/3 = c

Therefore, the value of c is 1/3. The equation of the line passing through (0, 7) and perpendicular to d: 3x − 6y = 1 is:

the value of c is 1/3. The equation of the line passing through (0, 7) and perpendicular to d: 3x − 6y = 1 is:2x + (y - 7) = 1/3

The value of c=7.

The equation of a straight line is given by y = mx + c where m represents the slope of the line and c is the height at which the line crosses the y-axis.

The equation of the given line is l:2x+by=c and it is perpendicular to d:3x-6y=1 and also the given line l passes through point (0,7)

The slope of two mutually perpendicular lines is related as per the following formula:

m1*m2=-1

Slope for line d = 1/2. Therefore, m*(1/2)=-1

i.e. slope of line l will be m=-2.

So, the given equation becomes [tex](y-y_1)=m(x-x_1)[/tex]

[tex](y-y_1)=-2(x-x_1)[/tex]

For point (0,7) the equation will be

[tex](y-7)=-2(x-0)[/tex]

y=-2x+7

Upon comparing the obtained values will be b=1 and c=7

Hence, the value of c will be 7 for the given equation.

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Bulk Pete's has the smaller unit price, so that coffe has the better price.

First, we know that five pounds of Kroger Dark Ground at $17.81, then the cost of a single pound of this cofee is given by the quotient:

$17.81/5 lb = $3.56 per lb.

That is the unit price of this coffe

While we know that Bulk Pete's Italian Roast at $3.11 per pound.

So we already can see that Bulk Pete's coffec has a smaller cost per pound, so that one has the better price.

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The requried ball reached a maximum height of approximately 62 feet

Let the ball is thrown vertically upward, we can use the following formula to find the maximum height it reaches:

[tex]h(t) = -16t^2 + vt + h_0[/tex]

here, h(t) is the height of the ball at time t, v is the initial velocity of the ball (in feet per second), and h0 is the initial height of the ball (in feet). We can also use the fact that the ball remains in the air for 3.8 seconds, which means that the time it takes to reach the maximum height is half of that or 1.9 seconds.

At the highest point, the ball's velocity is zero, so we can find the initial velocity by setting v = 0 in the above formula and solving for h₀:

h₀ = h(t) + 16t²

   = 4 + 16(1.9)²

   ≈ 4 + 57.76

   ≈ 61.76

Therefore, the ball reached a maximum height of approximately 62 feet

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