Triangle ABC below is an obtuse triangle. What is m∠ C?

The sequence for the nth term = 5n+6 is: 11, 16, 21, 26, 31,...

The sequence for the nth term = 5n+6 is:

n = 1, the nth term is 5(1)+6 = 11

n = 2, the nth term is 5(2)+6 = 16

n = 3, the nth term is 5(3)+6 = 21

n = 4, the nth term is 5(4)+6 = 26

n = 5, the nth term is 5(5)+6 = 31

and so on.

Therefore, the sequence for the nth term = 5n+6 is: 11, 16, 21, 26, 31,...

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Answer:

1/9

Step-by-step explanation:

The formatting is quite weird since there is no * for multiplication and only x's which can confuse people between the multiplication sign and the variable. In general, try to use * for multiplication in the future! :)

Evaluate inside the parentheses:

Assuming the x on top is multiplication and xy 3 meanings 3 times xy:

(4*2/3xy)^2

= (8/3xy)^2

= [8/(3)(4)(2)]^2

= (8/24)^2

= (1/3)^2

= 1/9

You will be required to pay $130.92 in interest. So, option 2 is correct.

Simple interest is calculated using the following formula: Simple Interest (SI) is calculated as P R T / 100. P stands for the principal sum, R for the interest rate, and T for the interest period. The total amount due is the sum of the principal plus the simple interest, or P + SI.

This specific percentage represents the loan's interest rate. The cost of borrowing money is called interest, and it is usually expressed as a percentage, such as an annual percentage rate (APR). Interest may be paid to lenders for the use of their money.

You shell out $875.00 for a PC plus 5% sales tax.

Thus, the final price is 875+(0.05875)

= $918.75.

Rate per month: 14.25/12/100

= 0.011875

So, the rate for a year is 12 x 0.011875

=$130.92.

Therefore, you will be required to pay $130.92 in interest.

Hence, option 2 is correct.

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The maximum volume is achieved when the radius is 10/π cm and the height is 10 cm.

The answer is E.

Let's call the height of the cylinder h and the radius r. The sum of the height and circumference is given by:

h + 2πr = 30 (equation 1)

The volume of a right circular cylinder is given by:

V = π\(r^2\)h

We want to maximize the volume of the cylinder subject to the constraint in equation 1. We can solve equation 1 for h in terms of r as:

h = 30 - 2πr

Substituting this expression for h into the formula for V, we get:

V = π\(r^2\)(30 - 2πr)

Simplifying, we have:

V = 30π\(r^2\) - 2π\(^2r^3\)

To find the maximum volume, we can take the derivative of V with respect to r and set it equal to 0:

dV/dr = 60πr - 6π\(^2\)\(r^2\) = 0

Solving for r, we get:

r = 10/π

Substituting this value of r back into equation 1, we get:

h + 2π(10/π) = 30

h + 20 = 30

h = 10

Therefore, the maximum volume is achieved when the radius is 10/π cm and the height is 10 cm.

The answer is E.

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The expression that shows how much Diego saves in the third month is 2³ which equals 8.

To determine how much Diego saves in the third month, to consider the pattern established in the problem that Diego saves $2 in the first month, and each subsequent month he saves twice as much as the previous month.

Let's break it down:

First month: $2

Second month: Twice as much as the first month = 2 * $2 = $4

Third month: Twice as much as the second month = 2 * $4 = $8

From the pattern that Diego saves $8 in the third month.

To represent this pattern algebraically,  use the following expression:

2 × 2 × 2

This simplifies to:

2³

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Here is some info that might help


-2 factors is a hint



+0 +2 +4 is a fractor of 4/1


if not 41

Answer:

depends on the genre.... so sometimes.... Have a good day

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Rate of change forumla

\(m = \frac{y2 - y1}{x2 - x1} \)

We have our X points, -7 and -2. Now to find the Y value at those places.

For -7, Y is 5

For -2, Y is 25

Now we plug this into the equation

\( = \frac{25 - 5}{ - 2 - ( - 7)} = \frac{20}{5} = 4\)

A bicycle repair shop that offers two service packages: a tune-up and a complete overhaul.

The shop operates for 60 hours per week and receives an average of 180 bicycles each week. To analyze the capacity and utilization of the process, we need to consider the time taken at each stage and the demand for each service option. We'll break down the problem into multiple parts and provide a detailed explanation using mathematical terms.

a) Creating the Demand Matrix:

To create a demand matrix, we need to determine the number of bicycles going through each stage of the process. Let's denote the demand for tune-up as T and the demand for additional services as A.

Given that the average number of bicycles received per week is 180 and 25% of customers opt for additional services, we can calculate the demands as follows:

Demand for tune-up (T) = Total demand - Demand for additional services

T = 180 - (0.25 * 180)

T = 180 - 45

T = 135

Demand for additional services (A) = 0.25 * Total demand

A = 0.25 * 180

A = 45

Now, we can create a demand matrix based on the demand for each service option:

Demand Matrix:

Tune-up Additional Services Wheel Balancing

Tune-up  [135  0  0]

Additional [0  45  0]

Services

Total [ 135  45  0 ]

The demand matrix shows the number of bicycles flowing through each stage of the process.

b) Daily Capacity at Each Stage:

To calculate the daily capacity at each stage, we need to consider the time taken for each service option. Given that the shop operates for 60 hours per week, we can calculate the daily capacity at each stage:

Tune-up technician time per bicycle (\(T_{tuneup}\)) = 75 minutes

Additional services technician time per bicycle (\(T_{additional}\)) = 72 minutes

Wheel balancing specialist time per bicycle (\(T_{balancing}\)) = 20 minutes

Daily Capacity (C) = (60 hours * 60 minutes) / (\(T_{tuneup}\) + \(T_{additional}\) + \(T_{balancing}\))

Substituting the given values:

C = (60 * 60) / (75 + 72 + 20)

C = 21600 / 167

C ≈ 129.34 bicycles per day

Therefore, the daily capacity at each stage of the process is as follows:

Tune-up: 129 bicycles per day

Additional Services: 129 bicycles per day

Wheel Balancing: 129 bicycles per day

c) Implied Utilizations:

To find the implied utilizations, we need to compare the demand and the capacity at each stage of the process. Utilization can be calculated as the demand divided by the capacity.

Implied Utilization (U) = Demand / Daily Capacity

For the Tune-up stage:

\(U_{tuneup}\) = 135 / 129 ≈ 1.05

For the Additional Services stage:

\(U_{additional}\) = 45 / 129 ≈ 0.35

For the Wheel Balancing stage:

\(U_{balancing}\) = 0 / 129 = 0

The implied utilizations show how efficiently each stage of the process is being utilized. Utilization values greater than 1 indicate that the stage is operating beyond its capacity.

d) Weekly Capacity of the Process:

To calculate the weekly capacity of the process, we multiply the daily capacity by the number of days the shop is open per week:

Weekly Capacity = Daily Capacity * Number of days shop is open per week

Given that the shop is open for 60 hours per week, the number of days the shop is open per week can be calculated as follows:

Number of days shop is open per week = 60 hours / 24 hours per day = 2.5 days

Therefore, the weekly capacity of the process is:

Weekly Capacity = Daily Capacity * Number of days shop is open per week

Weekly Capacity = 129 bicycles per day * 2.5 days

Weekly Capacity = 322.5 bicycles per week

e) Flow Rate and Constraint Analysis:

To determine if the flow rate of the process is capacity-constrained or demand-constrained, we compare the weekly capacity to the demand for each service option.

Demand for Tune-up (\(T_{demand}\)) = 135 bicycles per week

Demand for Additional Services (\(A_{demand}\)) = 45 bicycles per week

Comparing the demands with the weekly capacity:

\(T_{demand}\) < Weekly Capacity (135 < 322.5)

\(A_{demand}\) < Weekly Capacity (45 < 322.5)

Since both the demands for tune-up and additional services are less than the weekly capacity, the flow rate of the process is demand-constrained. This means the shop has the capacity to handle the current demand without operating beyond its limits.

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A function that forms an arithmetic sequence include the following: D. F(x) = 2x - 4.

In Mathematics and Geometry, the nth term of an arithmetic sequence can be calculated by using this equation:

aₙ =  a₁ + (n - 1)d

Where:

Next, we would determine the common difference as follows.

Common difference, d = a₂ - a₁

Common difference, d = -6 + 8 = -4 + 6 = -2 + 4

Common difference, d = -2.

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The total cost before the sales tax was 19.828 pounds.

For a party, Jordan purchased 3.8 pounds of turkey, 2.2 pounds of cheese, and 3.6 pounds of egg salad.

We have to determine the total cost before sales tax.

As per the question, we have prices as:

cost of turkey = 3.95 per pound

cost of egg cheese = 1.3 per pound

cost of egg salad = 0.89 per pound

The total cost of turkey = 3.8 × 3.95  = 15.01 pounds

The total cost of cheese = 2.2 × 1.3 = 2.86 pounds

The total cost of egg salad = 2.2 × 0.89 = 1.958 pounds

The total cost before sales tax = 15.01 + 1.958 +2.86

Apply the addition operation, and we get

The total cost before sales tax = 19.828 pounds

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The question seems to be incomplete the correct question would be:

Jordan bought 3.8 pounds of turkey, 2.2 pounds of cheese, and 3.6 pounds of egg salad for a party. If prices are 3.95 per pound turkey, 1.3 per pound cheese and 0.89 per pound egg salad What was the total cost before sales tax?

Answer:

Passes through (0,1) and (1,3).

3-1/1-0=2/1=2

The slope of this line is 2

Step-by-step explanation:

The missing terms in the arithmetic sequence are: \(a_3 = 82, a_5 = 2032\)

To find the missing terms in the sequence, we can use the recursive formula provided:

\(a_1 = 4\\a_{n+1} = 5a_n - 3\)

Using this formula, we can calculate the next terms:

\(a_2 = 5a_1 - 3 = 5(4) - 3 = 20 - 3 = 17\\a_3 = 5a_2 - 3 = 5(17) - 3 = 85 - 3 = 82\\a_4 = 5a_3 - 3 = 5(82) - 3 = 410 - 3 = 407\\a_5 = 5a_4 - 3 = 5(407) - 3 = 2035 - 3 = 2032\)

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Sample size and the confidence level width have an inverse relationship. As the sample size increases, the confidence level width decreases.

When determining a confidence interval for a population parameter, such as the mean or proportion, a larger sample size provides more information about the population. This increased information leads to a narrower confidence interval.

The confidence level width is influenced by two factors: the sample standard deviation (or the variability of the data) and the critical value associated with the desired confidence level. As the sample size increases, the sample standard deviation becomes a more accurate estimate of the population standard deviation. This reduces the variability and leads to a narrower confidence interval.

A larger sample size leads to a decrease in the confidence level width, providing a more precise estimate of the population parameter with a higher level of confidence.

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Answer:

189.3cm2

Step-by-step explanation:

Divide the whole figure into 2 parts. One part as a rectangle and the other as a semicircle  ( half a circle). First find the area of the rectangle, 10 times 15 which will get you 150cm2. Next to find the area of the semicircle do \(\pi\) times 5 times 5 times half. You will get an amount like 39.26990817 but do not worry for now. Just keep it like that. Then add this amount with 150 and you will get an amount like 189.2699082

Then round it of to one decimal place and you will get 189.3cm2

Answer:

  10

Step-by-step explanation:

The restriction m < 0 means we can multiply by -7m/2 without changing the direction of the inequality symbol

  \(\dfrac{3}{m}\le-\dfrac27\\\\-\dfrac{21}{2}\le m\qquad m<0}\)

Then the solution is the number of negative integer values between -10.5 and 0. There are 10 negative integer values of m that satisfy the inequality.

Answer:

5.499 = h   likely if you used a better value for pi, it would be 5.5 = h

Step-by-step explanation:

Givens

V = 155.4

r = 3

pi = 3.14

Formula

V = pi*r^2*h   Solve for h

Solution

155.4 = 3.14 * 3^2 * h               3^2 = 9

155.4 = 3.14 * 9 * h                   Combine the right

155.4 = 28.26 * h                     Divide by 28.26

155.4/28.26 = 28.26*h/28.26

5.499 = h

By first identifying the critical points of this function by determining the first derivative, and then calculating the second derivative at the crucial points, you may determine the volume's maximum. The critical point is a maximum if the second derivative is negative.

When a cone and cylinder have comparable heights, the cylinder's volume is three times greater than a cone's volume. Determine the cone's volume. To the tenth of a cubic centimetre nearest, round.

Therefore, a cylinder with the same base radius and height has a volume that is equal to one-third that of a cone.Learn more about cylinder.

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Answer:

Brand C

Step-by-step explanation:

Brand A: 1.77/6=$0.30

Brand B: 3.75/12=$0.31

Brand C: 5.24/18=$0.29

Brand D: 7.10/24=$0.30

Based on the price per egg of each brand (calculated above), the best price per egg would be brand C.

The length of the shortest straight  is approximately 28.01 ft.

What is the right triangle?

A right triangle is" a type of triangle that has one angle measuring 90 degrees (a right angle). The other two angles in a right triangle are acute angles, meaning they are less than 90 degrees".

To find the length of the shortest straight beam,we can use the Pythagorean theorem.

Let's denote the length of the beam as L and  a right triangle formed by the beam, the wall, and the ground. The wall is 28 ft tall, and the distance from the wall to the building is 1 ft.

Using the Pythagorean theorem,

\(L^2 = (28 ft)^2 + (1 ft)^2\)

Simplifying the equation:

\(L^2 = 784 ft^2 + 1 ft^2\\ L^2 = 785 ft^2\)

\(L = \sqrt{785}ft\)

Calculating the value of L:

L ≈ 28.01 ft

Therefore, the length of the shortest straight beam  is approximately 28.01 ft.

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This refers to the ratio between the scale of a given original object and a new object. It is its representation but of a different size (bigger or smaller). For example, if we have a rectangle of sides 2 cm and 4 cm, we can enlarge it by multiplying each side by a number, say 2.

Solving for the area and scale factor we have:

L= 5 units

W = 2 units

A = (5 x 2)

A = 10 square units.

A= (Scale factor of  L * W)*  L * W

= (2 x 2 x 5 x 2)

A = 40 square units.

A= (Scale factor of  L * W)*  L * W

= (3 x 3 x 5 x 2)

A= 90 square units

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The Roman numeral number I means the number "1".

In roman numerals, the counting is represented by using the basic English alphabets in the Upper Case.

The roman numeral I means the number "1". For representing 10 we use "X".

When we have to write 1, 2, 3 we use I, II, III respectively and when we use want to show 5 we use "V" in roman numerals. More English letters like L, C etc. are also used to depicts certain other big numbers in the roman numbers. It is to be noted that one alphabet cannot be used more than three times in an number.

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Answer: 1280

Step-by-step explanation: LxWxH = 16 X 10 X 8

The Area of Triangle is 30.85 unit².

Heron's formula, formula credited to Heron of Alexandria (c. 62 ce) for finding the area of a triangle in terms of the lengths of its sides.

In symbols, if a, b, and c are the lengths of the sides:

Area = √s(s - a)(s - b)(s - c) where s is half the perimeter, or (a + b + c)/2.

The semi perimeter

s =(16 + 10 + 8)/2 = 34/2 = 17

So, the Area of Triangle

= √s(s- a)(s -b )(s-c)

= √17 (17-16)(17-10)(17-8)

= √17 x 1 x 7 x 9

= 30.85 unit²

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Answer:

Step-by-step explanation:

The given trigonometric expression is :

11 cos^2 x +3 sin^2 x+6sinx cosx +5

or, we can write it as,

(9 cos^2 x + 2 cos^2 x) + (2 sin^2 x + sin^2 x) + 6sinx cosx +5

Again, after rearranging the terms, we can write the whole expression as,

(9 cos^2 x + sin^2 x + 6sinx cosx) + (2 cos^2 x + 2 sin^2 x) + 5

Then if you factor the following underlined section as you would with a polynomial:

(9 cos^2 x + sin^2 x + 6sinx cosx) + (2 cos^2 x + 2 sin^2 x) + 5

You get:

(3 cos x + sin x)^2 + 2 (cos^2 x + sin ^2 x) + 5

Now, the term inside the second bracket (cos^2 x + sin ^2 x) is a very popular trigonometric identity and it's value is equal to one.

So, now the whole expression becomes,

(3 cos x + sin x)^2 +7

Now, the maximum and the minimum value of the whole expression depends upon the maximum and the minimum value of the term (3 cos x + sin x), which is of the form (a cosx + b sinx),

The maximum and minimum value of (a cosx + b sinx) is relatively easy to find.

So, I've attached a screenshot from a relevant document below:

Here, a=3 and b=1,

So, R= √10

As the value of cosine of any angle lies between -1 to 1, so the value of the value of expression cos(x − α) will lie between -1 to 1.

Hence, the maximum and the minimum value of (a cosx + b sinx) will be -R and R and all the values of the expression will lie between them.

i.e., in our case between (-√10) to √10.

Again, coming back to our original expression,

(3 cos x + sin x)^2 +7

The value of the term in bracket will lie between (-√10) and √10.

But, there is a catch here, as the squares of negative terms come out be positive, hence we can't take the negative term to find the minimum value of our expression. the minimum value of the expression will be at the minimum non-negative value in the range, which is zero.

So, the minimum value will be,

(0)^2 + 7=7

and the maximum value will be,

(√10)^2 +7 = 17

Applying law of sine and law of cosine, the unknown values x and y are 16.2 units and 37.1 degrees respectively.

To determine the value of x and y in the given triangle, we can use law of sine or law of cosine depending on the variables available and what we need to determine.

Applying law of cosine;

x² = 15² + 10² - 2(15)(10)cos78

x² = 225 + 100 - 300cos78

x² = 225 + 100 - 62.4

x² = 262.6

x = √262.6

x = 16.2 units

From this, we can apply law of sine to determine y;

x / sin X = y / sin Y

Substituting the values into the formula above;

16.2 / sin78 = 10 / sin y

Cross multiply both sides and solve for y;

16.2siny = 10sin78

sin y = 10sin78 / 16.2

sin y = 0.6038

y = sin⁻¹ (0.6038)

y = 37.14°

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True, it is often not feasible to study the entire population because it may be impossible to observe all the items in the population. This is especially true in larger populations where it may be impractical or too costly to collect data on every single item. Therefore, researchers often use statistical sampling techniques to select a representative subset of the population. This sample is then studied and used to make inferences about the population as a whole. While sampling is not perfect, it can provide a reliable estimate of the population parameters with a certain level of confidence. Therefore, it is essential to carefully choose the sample to ensure that it accurately represents the population.

The question is about the feasibility of studying the entire population. It is often not possible to observe all the items in a population due to various constraints such as time, money, and practicality. Therefore, researchers use sampling techniques to select a representative subset of the population, which can provide a reliable estimate of the population parameters.

In conclusion, it is true that it is often not feasible to study the entire population. However, researchers can use statistical sampling techniques to select a representative subset of the population, which can provide a reliable estimate of the population parameters. It is essential to carefully choose the sample to ensure that it accurately represents the population.

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A statement that correctly compares the areas of these two rectangles is that the area of the yellow rectangle is greater than the area of the blue rectangle by 8 square units.

In Mathematics and Geometry, the area of a rectangle can be calculated by using the following mathematical equation:

A = LW

Where:

Based on the information provided about these rectangles, we have the following:

Area of blue rectangle = 10 × 4

Area of blue rectangle = 40 square units.

Area of yellow rectangle = 6 × 8

Area of yellow rectangle = 48 square units.

Difference = Area of yellow rectangle - Area of blue rectangle

Difference = 48 - 40

Difference = 8 square units.

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Answer: y = 3 (x -4)^3

Step-by-step explanation: horizontal shift of 4 units to the right (subtract 4 units from the x):   y = 3(x - 4)^3

Vertical shift 3 units down (subtract 3 units from the function):   y = 3(x - 4)^3 - 3

Answer:

you multiply both sides by 2.

Step-by-step explanation:

Im in advanced math and we have been doing this for a while.