Line AB intersects line CD at point F. If m<AFC=(7x-8)° and m<BFD=(5x+6)°, what is m<BFD?
82°
48°
41°
7°​

The data modelling function is Price required to recoup printing expenses is equal to 0.1 * (numbers of yearbooks sold) + 45.

A yearbook is a collection of images and text that is issued by an organisation once a year to remember and highlight the happenings at a particular school during the previous academic year. Yearbooks were used in elementary, middle, high, and college and university settings throughout the 20th century.

Using the information in the table,

[tex]n = 5[/tex]

Σ[tex]x = 1175[/tex]

Σ[tex]y = 145[/tex]

Σ[tex](xy) = 41000[/tex]

Σ[tex](x^2) = 287500[/tex]

When these values are inserted into the formula,

[tex]m = (541000 - 1175145) / (5*287500 - 1175^2)[/tex]

[tex]= -0.1[/tex]

Therefore, the slope of the linear function is [tex]-0.1[/tex].

[tex]b = y - mx[/tex]

where we can use any of the data points. Let's use[tex](250, 20)[/tex]

[tex]b = 20 - (-0.1*250)[/tex]

[tex]= 45[/tex]

Therefore, the y-intercept of the linear function is [tex]45[/tex].

[tex]y = -0.1x + 45[/tex]

Therefore,

Price needed to cover the costs of printing [tex]= -0.1*[/tex](number of yearbooks sold) [tex]+ 45[/tex].

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Answer:

C). 8/9n - 1 1/3

Step-by-step explanation:

Answer:

[tex]\frac{8}{9} n - 1\frac{1}{3}[/tex]

Step-by-step explanation:

Using the distributive property [tex]\frac{4}{9}[/tex] times 2 equals [tex]\frac{8}{9}[/tex] and [tex]\frac{4}{9}[/tex] times 3 equals [tex]\frac{4}{3}[/tex] which simplifies to [tex]1\frac{1}{3}[/tex]

Answer:

x = 45

Step-by-step explanation:

since the lines are congruent, then the opposite angles will be the same.

2x+90=180

Hope this helps

Answer:

To find the 9th term of a geometric sequence, we can use the formula:

an = a1 * r^(n-1)

where:

an = the nth term of the sequence

a1 = the first term of the sequence

r = the common ratio of the sequence

n = the term number we want to find

In this case, we are given that the common ratio is 2/3, the first term is 6, and we want to find the 9th term. So we can plug in those values and get:

a9 = 6 * (2/3)^(9-1)

Simplifying the exponent, we get:

a9 = 6 * (2/3)^8

Using a calculator, we can evaluate the exponent:

a9 = 6 * 0.015625

Multiplying, we get:

a9 = 0.09375

Therefore, the 9th term of the geometric sequence is 0.09375.

Step-by-step explanation:

here's a step-by-step explanation:

We are given the first term of the geometric sequence, a1 = 6, and the common ratio, r = 2/3. We need to find the 9th term, which we can do using the formula:

an = a1 * r^(n-1)

where n is the term number we want to find.

Step 1: Substitute the given values into the formula

a9 = 6 * (2/3)^(9-1)

Step 2: Simplify the exponent

a9 = 6 * (2/3)^8

The exponent 9-1 simplifies to 8.

Step 3: Evaluate the exponent

a9 = 6 * 0.015625

We can use a calculator to evaluate (2/3)^8, which is 0.015625.

Step 4: Multiply to find the 9th term

a9 = 0.09375

Multiplying 6 by 0.015625 gives us the 9th term of the geometric sequence, which is 0.09375.

Therefore, the 9th term of the geometric sequence whose common ratio is 2/3 and whose first term is 6 is 0.09375.

The average number of siblings for the group is 1.3.

We must compute the total number of siblings and divide it by the total number of children in the group to determine the average number of siblings for the group.

There are a total of: siblings in the bunch.

3 + 8 + 9 = 20 (1 sibling times 3 children) + (2 siblings times 4 children) + (3 siblings times 3 children)

The total number of kids in the group is: 5 + 3 + 4 + 3 = 15

As a result, the group as a whole has an average of:

20/15 = 1.33 (rounded to the nearest tenth) (rounded to the nearest tenth)

So, the group as a whole has 1.3 siblings on average.

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Answer:

1065.09 square meters

Step-by-step explanation:

The inner circle has a diameter of 21.4 cm

Its radius is half that = 21.4/2 = 10.7 m

Area of the inner circle = π (10.7)² = 114.49π  m²

The outer circle has a radius
= radius of inner circle + 10.6
= 10.7 + 10.6

= 21.3 m

Therefore the area of the outer circle
= π(21.3)² = 453.6π m²

Area of shaded region
= Area of outer circle - Area of inner circle

= 453.6π - 114.49π  
= 339.2 π

Taking π = 3.14

Area of shaded region
= 339.2  x 3.14
= 1,065.088 m²
= 1065.09 m² (rounded to nearest hundredth)

The equation for the relationship between the total fee and vertical distance is: y = 100 + x/3000.

Vertical distance is the measurement of the straight line distance between two points in a vertical plane. It is the difference between the higher and lower altitudes of two points and is measured in a straight line from the highest point to the lowest point.

This equation can be explained as follows. The total fee for a trip to climb Mount Kilimanjaro is split into two parts. The first part is the initial fee of $100, which is a fixed cost independent of the distance climbed. The second part is the cost per vertical meter, which is calculated by dividing the vertical distance climbed (x) by 3000 (the constant fee for each vertical meter climbed) and then multiplying the result by the constant fee. Therefore, the equation for the relationship between the total fee and vertical distance is y = 100 + x/3000.

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In this case, the population is children from 6 to 18 years old who had nonlethal scorpion sting; on the other hand, the sample is the 245 children selected.

In a research study, the population is considered as the group of individuals being studied. However, as this number is often high, researchers often select a small random percentage that should be representative of the population, which is known as the sample.

Based on this, the population can be children  from 6 to 18 years old who had nonlethal scorpion sting, while the sample are those children selected (245) to carry out the research study.

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Answer:

B

Step-by-step explanation:

The function that models the situation is an exponential decay function of the form:

t(m) = a(1 - r)^m

where:

t(m) is the number of trees after m months

a is the initial number of trees (5,500 in this case)

r is the monthly rate of decrease (3.2% or 0.032 as a decimal)

Substituting the values given in the options, we get:

A) t(m) = 5,500(0.032)^m

B) t(m) = 5,500(1-0.032)^m = 5,500(0.968)^m

C) t(m) = 5,500(1.032)^m

D) t(m) = 5,500(1-0.968)^m = 5,500(0.032)^m

Option B is the correct answer as it correctly models the situation with exponential decay with a starting value of 5,500 trees and a monthly rate of decrease of 3.2%.

Answer: The formula for exponential decay is given by:

t(m) = a(1-r)^m

where

a = initial value

r = decay rate

Here, the initial value is 5,500 and the monthly decay rate is 3.2% or 0.032. So the function that can be used to find the number of trees in the forest at the end of m months is:

t(m) = 5,500(1 - 0.032)^m

t(m) = 5,500(0.968)^m

Therefore, the answer is (D) t(m) = 5,500(0.968)^m.

Your welcome (;

Answer: 85.5

Step-by-step explanation: divide 855 by ten or move the decimal to the left one place for every zero

The set of data that Zoey should use for the linear graph is given as follows:

D the temperature of a water sample increasing 2° every hour.

The graph represents a linear function, meaning that the rate of change of the output variable relative to the input variable must be constant.

The input and output variables of the graph are given as follows:

As the rate of change must be constant, the correct option is given by option d, which has a rate of change of 2º every hour. For the other options, the rate of change is not constant.

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Answer:

Step-by-step explanation:

To determine the mean number of water tanks supplied to the construction site in March 2022 during weekdays, we need to add up the number of tanks supplied during weekdays and divide by the number of weekdays in March 2022:

March 2022 had 23 weekdays.

From the information given, we don't know the number of tanks supplied during weekdays in March 2022. Therefore, we cannot calculate the mean number of tanks supplied during weekdays in March 2022.

The numerical data recorded on the calendar in ANNEXURE A by the contractor was the number of water tankers supplied to the construction site on each day of the month.

To determine the modal number of water tankers that were supplied to the construction site in June 2022, we need to find the number that appears most frequently in the data:

From the information given, we don't have the data on the number of water tankers supplied to the construction site in June 2022. Therefore, we cannot determine the modal number of water tankers supplied in June 2022.

Given that the water tanker has a fuel capacity of 460 litres and the rate of fuel consumption of the Mercedes water tanker averages 5 km/l, we can calculate the distance traveled on a full tank of fuel:

The distance traveled on a full tank of fuel is 460 litres x 5 km/l = 2,300 km.

Finally, we are given the prices of fuel per litre in March and June 2022:

In March 2022, the price of diesel 50 ppm was R19.55 per litre.

In June 2022, the price of diesel 50 ppm was R24.14 per litre.

Answer: is mature enough to vote

Step-by-step explanation: the second drop box is asking about the opposing claim, which is the one that the professor gives.

Answer:

the last option, " is mature enough to vote".

Step-by-step explanation:

Professor Steinberg believes that 16 old can vote as their brains are mature enough to make informed decisions like voting.

Answer:

Hmm.. not quite sure why you multiplied A with 10 yds. I am going to assume M=meters.

A.) You can convert to whatever units you like, but I am going to convert into meters.

0.89/yd * 0.9144yd/m = $0.97 > $0.94.. So.. A Lumber yard is selling the same rope for less expensive.

B.) You convert feet until you get to the correct units. like this....

550 ft * 1yd/3ft * .9144m/yd * $.97/m = $162.62

550 ft * 1yd/3ft * .9144m/yd * $.94/m = $157.58

taking the difference would be $5.03.

I believe for answer A, you forgot to convert...or converted differently. Hope this helps.

Step-by-step explanation:

Answer:

Since $0.973/m is greater than $0.94/m, the lumber yard sells the rope for a lower price

So Jim would save $6.19 if he purchased 650 ft of the less expensive rope before taxes.

Step-by-step explanation:

According to the given information, measure of angle FNL is given by 234 - 13x.

What is angle ?

In geometry, an angle is a figure formed by two rays, or line segments, that share a common endpoint, called the vertex of the angle. The two rays are called the sides or legs of the angle.

line FN || line EM || line DL,

line FD and line NL intersects line FN,line EM and line DL at pts F,E,D and N,M,L respectively

FE = ED ,NM = ML

angle FNL = (9x-40)deg

angle FDL = (4x-14)deg

Since line FN is parallel to line EM, we have:

angle FNM = angle FEL (corresponding angles)

Since line FN is parallel to line DL, we have:

angle FNL = angle FLD (alternate interior angles)

Similarly, since line FD intersects line FN and line EM at points F and E, we have:

angle FEL + angle FED = 180 degrees (linear pair)

Since FE = ED, we have:

angle FEL = angle FED (opposite angles of a parallelogram are equal)

Combining the above equations, we get:

angle FNL = angle FLD = angle FED = 180 - angle FEL

Also, since NM = ML, we have:

angle NML = angle MLM

Now, applying the angle sum property in triangle FNL, we get:

angle FNL + angle FLD + angle FEL = 180 degrees

Substituting the given values, we get:

(9x-40) + (4x-14) + (180 - angle FEL) = 180

Simplifying, we get:

13x - 54 + 180 - angle FEL = 180

13x - angle FEL = 54

Solving for angle FEL, we get:

angle FEL = 13x - 54

Substituting this value in the equation we derived earlier, we get:

angle FNL = angle FLD = angle FED = 180 - angle FEL

= 180 - (13x - 54)

= 234 - 13x

Therefore, measure of angle FNL is given by 234 - 13x

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Answer:

4[tex]\frac{3}{8}[/tex]

Step-by-step explanation:

Answer:

4 3/8

Step-by-step explanation:

4*8=32 35-32=3

Through the given statement we can say that the vertical distance travelled by the ball  is 84 m.

One limitation of this model is that it assumes that the ball rebounds to the same percentage of its previous maximum height after every bounce.

The formula for vertical distance from the earth is y = - 1 2 g t 2 y = - frac 1 2 g t 2 y=-21gt2, where g is the acceleration of gravity and h is an elevation.

So :

C) the required total vertical distance that the given dropped ball travels until its bouncing stops:

= (12 m) + 2*(12 m)*(3/4)*[1 + 3/4 + (3/4)^2 + (3/4)^∞] [the factor 2 is for equal distance being covered up and down after each bounce of the ball]

= (12 m) + (24 m)*(3/4)*

(sum of an infinite GP series whose 1st term is 1 and common ratio is 3/4)

= (12 m) + (24 m)*(3/4)*[1/(1 - 3/4)]

= (12 m) + (24 m)*(3/4)*4

= (12 m) + (72m) = 84 m

D) This model's assumption that the ball will always bounce back to a certain proportion of its maximum height is one of its limitations. In fact, the rebound height can differ from one bounce to the next due to factors like air resistance, the ball's elasticity, and the surface it bounces on.

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The function is positive on the interval (-1, 1)," is the only answer that is accurate. Due to the fact that the function accepts positive values for x between -1 and 0, accepts 0 at x = 0, and then accepts positive values.

When a function is specified at each point along an interval without any gaps, leaps, or interruptions, the interval is said to be continuous for that function.

When we examine the function's graph, we can observe that:

Because the function accepts negative values for x > 1 and positive values for x -1, it does not have a maximum value of 0.

The function does not approach as x approaches. Instead, as x rises, the function alternates between positive and negative values.

There are times when the function increases. Rather, it is rising on the interval (1, ) and falling on the intervals (-, 1). At x = -1, it has a local minimum, while at x = 1, it has a local maximum.

Due to the fact that it accepts negative values for x between -1 and 0, the function is not positive on the range (-1, 1).

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The translation of f(x) to g(x) is described by - translation of 4 units up.

As you translate a figure, you slide it left, right, up, or down. This implies that the coordinates for such vertices of the figure will alter on the coordinate plane.

Apply the identical modification to every point in order to graph a translation.

As there is the shift of coordinates on y axis upward by 4 units units.

Thus, the translation of f(x) to g(x) is described by - translation of 4 units upward.

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[tex]4x^2+20x-24 = 4x^2-4x+24x-24 = 4x(x-1)+24(x-1) = (4x + 24)(x-1)\\[/tex]

[tex]= 4(x+6)(x-1)[/tex]

By solving the increase in percentage, the projected number of students in an associate degree program in 2024-2025 is approximately 7,897,500.

What is an increase in percentage?

An increase in percentage is a measure of the change in a quantity expressed as a percentage of the initial value. It is calculated by subtracting the initial value from the final value, dividing the result by the initial value, and then multiplying the quotient by 100 to express the result as a percentage. The formula for calculating the percentage increase is:

percentage increase = (final value - initial value) / initial value * 100

To find the increase in the number of students enrolled in an associate degree program from 2014-2015 to 2024-2025, we can first calculate the amount of increase as a percentage of the initial enrollment:

Increase = 21.5% * 6,500,000 = 1,397,500

Therefore, the increase in the number of students is approximately 1,397,500.

To find the projected number of students in an associate degree program in 2024-2025, we can add the increase to the initial enrollment:

Projected enrollment = 6,500,000 + 1,397,500 = 7,897,500

Therefore, the projected number of students in an associate degree program in 2024-2025 is approximately 7,897,500.

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Answer:

$839.95

Step-by-step explanation:

To get the amount of tax Ella would have to pay for, multiply the price of the computer by the tax rate

785 x .07 = 54.95

Then add the computer price and tax to get how much she paid for in total

785 +54.95= $839.95

The measure of the angles is 143°

From the given diagram, the given measures are alternate exterior angles and they are equal.

Given the following parameters

∠A =7x + 24

∠B = 3x + 92

Equate

7x + 24 = 3x + 92

7x - 3x = 92 - 24

4x = 68

x = 17

Determine the measure of the angles

∠A = ∠B = 7x + 24

∠A = ∠B = 7(17) + 24

∠A = ∠B = 143 degrees

Hence the measure of the angles is 143°

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Answer: true

Step-by-step explanation:

6:8 = 12:16

12:16 less than 14:16

When 1. 384 is divided by 0. 4, the quotient would be 3. 46.

One way to divide 1. 384 by 0. 4 is to use the fact that division is the same as multiplying by the reciprocal of the divisor. The reciprocal of 0. 4 is 1 / 0. 4 or 2. 5. Therefore, we can rewrite the division as:

1. 384 / 0. 4 = 1. 384 x 2.5

We can then use multiplication to get the result:

1. 384 × 2. 5 = 3. 46

Therefore, 1. 384 divided by 0. 4 equals 3. 46.

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According the Question the value οf x will be 6.

The measurement οf the circle's bοundaries is called as the circumference οr perimeter οf the circle. whereas the circumference οf a circle determines the space it οccupies. The circumference οf a circle is its length when it is οpened up and drawn as a straight line. Units like cm οr unit m are typically used tο measure it.

The circle's radius is cοnsidered while calculating the circumference οf the circle using the fοrmula. As a result, in οrder tο calculate the circle's perimeter, we must knοw the radius οr diameter value.

The side οf the circle JH . JG = JK . JM

JM = 7*16/8 = 14

X = 14-8 =6

Hene the value οf x will be 6.

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hii

what's the best way to recreate the incident as it happened and to picture

The quotient gives (f/g)(4) = -16/3 and the value that is not in the domain is x = 1.

Here we know that:

f(x) = (x + 4)(x - 6)

g(x) = x - 1

And we want to find the quotient between these functions:

(f/g)(4)

So first let's find the values of the functions when x = 4.

f(4) = (4 + 4)*(4 - 6) = 8*-2 = -16

g(4) = 4 - 1 = 3

Then the quotient is:

(f/g)(4) = -16/3

Now, the values that are not in the domain of f/g are the values that make the denominator equal to zero, because we can't divide by zero.

g(x) = 0 = x - 1

         1  =x

The denominator is zero for x = 1, so that value is not in the domain.

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Answer: The answer is B!

Step-by-step explanation:

If you multiply 22.2 by 8.3, you get 84.36 (if you move the decimal point one space, otherwise you'd get 843.6.) Then if you estimate it, you would get 84.58.

Answer:

Third choice
π = 1/2 and 1 - π = 1/2

Step-by-step explanation:

Formula for binomial distribution is
[tex]P(x) = \dfrac{n!}{x!(n-x)!} \pi^x (1-\pi)^{n-x}[/tex]

where
x is the number of successes

n = number of trials

π = probability of success on a single trial

The variance of the binomial distribution is
[tex]\sigma^2 = n \cdot \pi(1-\pi)[/tex]

The maximum variance occurs when
[tex]\pi = (1- \pi) = 1/2[/tex]

Hence the correct choice is the third choice
π = 1/2 and 1- π = 1/2