I, myself self am not too good at Sin, Con, and Tan so I could use some help on double-checking if this is correct??

Answer:

Mean-6.3 (3 repeating)

Median-5

Mode-1

Step-by-step explanation:

Mean-Add all numbers together and divide by 12 (because is 12 numbers)

Median- List numbers From least to greatest and cross one off of each end until you meet in the middle

Mode- find the number that occurs the most

Answer:

x=2

hope it helps !!

Step-by-step explanation:

Answer:

55

Step-by-step explanation:

To find the average you add up all numbers given then divide by the amount of numbers there were. The mean, or average, of the original 5 people was 13 since their ages added was 65, which you divide by 5 for 13. The new mean once the 6th person entered the room was 20. So, you do 6 [number of people] times 20 [average] to get 120. Taking 65 [added amount of original ages of the 5 people] away from 120 [the new added up ages of all 6 people], you get 55. This means 55 would be the 6th person's age.

Sorry if the explanation is confusing!

Call the total ages of the 6 people, x

To calculate the mean age of 6 people, we take the total age (x) and divide by the amount of people (6)

So, x : 6 = 20

-> The total ages of the 6 people are 20 x 6 = 120

We can calculate the 6th person's age by taking 120 and minus the total age of the other 5

-> 120 - (13+12+13+15+12) = 55

So, the 6th person's age is 55.

Numeric data can be used to present facts, show relationships between variables, and support an argument.

Numeric data is a powerful tool that can be used to present facts, demonstrate relationships between variables, and support an argument. It is often used to provide evidence for a particular point of view, and it can be used to persuade an audience or inform them about a particular topic. Numeric data can be presented in various forms such as graphs, tables, and charts, and when used effectively, it can be a very effective tool for conveying information. It is important to understand how to interpret numeric data correctly, as it can be used to draw false conclusions if the data is misinterpreted.

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Answer:

The wire required to fence is 530 m.

Step-by-step explanation:

Length, L = 180 m

Width, W = 85 m

The perimeter of the wire is

P = 2 (L + W)

P = 2 (180 + 85)

P =  530 m

So, the wire required to fence is 530 m.

Answer:

the bigger the handspan the more jolly ranchers they can pick up with one hand

Step-by-step explanation:

Answer:$3.19

Step-by-step explanation:

Answer: $3.32

Step-by-step explanation: Can be done 2 ways:

$3.25 x 0.02 (same as 2 %) = $0.065  

$3.25 + $0.065 = $3.315 (round up to $3.32)

or

$3.25 x 1.02 (same as 100% cost plus 2% tax) = $3.315 (round up to $3.32)

(x, y) is an element of the set c × d, since x is an element of c and y is an element of d.

Since (x, y) was an arbitrary element in a × b, we can conclude that every element in a × b is also in c × d. Thus, we have shown that if a ⊆ c and b ⊆ d, then a × b ⊆ c × d.

To show that if a ⊆ c and b ⊆ d, then a × b ⊆ c × d, follow these steps:

Step 1: Understand the notation.
a ⊆ c means that every element in set a is also in set c.
b ⊆ d means that every element in set b is also in set d.

Step 2: Consider the Cartesian products.
a × b is the set of all ordered pairs (x, y) where x ∈ a and y ∈ b.
c × d is the set of all ordered pairs (x, y) where x ∈ c and y ∈ d.

Step 3: Show that a × b ⊆ c × d.
To prove this, we need to show that any ordered pair (x, y) in a × b is also in c × d.

Let (x, y) be an arbitrary ordered pair in a × b. This means that x ∈ a and y ∈ b.

Since a ⊆ c, we know that x ∈ c because every element in set a is also in set c.
Similarly, since b ⊆ d, we know that y ∈ d because every element in set b is also in set d.

Now, we have x ∈ c and y ∈ d, so the ordered pair (x, y) belongs to c × d.

Step 4: Conclusion
Since any arbitrary ordered pair (x, y) in a × b also belongs to c × d, we can conclude that a × b ⊆ c × d.

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To find the density of the metal, we need to calculate the mass of the metal and the volume of the metal.

Step 1: Calculate the mass of the metal:

Mass of metal = Mass of cylinder with all its contents - Mass of empty graduated cylinder

Mass of metal = 390.98 g - 45.7 g

Mass of metal = 345.28 g

Step 2: Calculate the volume of the metal:

Volume of metal = Final volume of water + metal - Initial volume of water

Volume of metal = 70.7 mL - 42.0 mL

Volume of metal = 28.7 mL

Step 3: Calculate the density of the metal:

Density = Mass of metal / Volume of metal

Density = 345.28 g / 28.7 mL

Density ≈ 12.01 g/mL

Therefore, the density of the metal is approximately 12.01 g/mL.

To determine the density of the metal, we use the principles of water displacement. The student first measures the mass of the empty graduated cylinder and records it as 45.7 g. Then, 42.0 mL of water is added to the cylinder, which has a known density of 1.00 g/mL. After placing the metal into the cylinder, the student measures the final volume of water and metal as 70.7 mL.

To calculate the mass of the metal, we subtract the mass of the empty cylinder from the mass of the cylinder with its contents. This gives us a mass of 345.28 g. To calculate the volume of the metal, we subtract the initial volume of water (42.0 mL) from the final volume of water and metal (70.7 mL), resulting in a volume of 28.7 mL.

Finally, we can calculate the density by dividing the mass of the metal (345.28 g) by the volume of the metal (28.7 mL). The density of the metal is approximately 12.01 g/mL.

Using the water displacement method, the student successfully determined the density of the unknown piece of metal.

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The value for x in the given equation x = (1.38-1.21)/1.23 is 0.1382.

The density of the metal is 10.56 .

To solve for x in the given equation x = (1.38-1.21)/1.23 ,follow the steps below:

Subtract the values in the parenthesis: 1.38-1.21=0.172.

Divide the result from step 1 by the divisor: 0.17/1.23=0.138(rounded off to 3 decimal places).

Therefore, the solution for x in the given equation x = (1.38-1.21)/1.23 is 0.1382.

Now to find the density of the metal, the volume of the metal must be found by subtracting the volume of the water from the final volume of water and metal (which gives the volume of the metal). Also, the mass of the metal must be found by subtracting the mass of the cylinder and water from the mass of the cylinder, water, and metal.

With these values the density can be found by dividing the mass by the volume of the metal.To find the volume of the metal, subtract the volume of the water from the final volume of water and metal:

70.7 mL - 42.0 mL = 28.7

Therefore, the volume of the metal is 28.7 .

To find the mass of the metal, subtract the mass of the cylinder and water from the mass of the cylinder, water, and metal:

390.98 g - 45.7 g - 42.0 g = 303.28

Therefore, the mass of the metal is 303.28 .

Now that the volume and mass of the metal have been found, the density can be calculated by dividing the mass by the volume:

density = mass/volume= 303.28 g/28.7 mL= 10.56

Therefore,  the density of the metal is 10.56 .

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Answer: 13.74m

Step-by-step explanation:

Perimeter of shaded region:

Perimeter of shaded region=area of rectangle- area of semicircle

l×w‐(πr²) - -> diameter of circle‐6m; Radius‐3

=8×6‐(3.14×3×3)

=42— 28.26=13.74m

a) The recurrence relation for the number of ways to deposit n dollars in the vending machine can be expressed as follows:

W(n) = W(n-1) + W(n-1) + W(n-5)

b) The initial conditions for the recurrence relation are as follows:

W(0) = 1 , W(1) = 2 , W(2) = 4

c) There are 17 ways to deposit $10 for a book of stamps.

a) The recurrence relation for the number of ways to deposit n dollars in the vending machine, where the order matters, can be defined as follows: Let f(n) be the number of ways to deposit n dollars. We can break down the problem into three cases: depositing a $1 coin, depositing a $1 bill, or depositing a $5 bill. The recurrence relation is f(n) = f(n-1) + f(n-1) + f(n-5), where f(n-1) represents the number of ways to deposit n-1 dollars and f(n-5) represents the number of ways to deposit n-5 dollars.

b) The initial conditions for the recurrence relation are as follows: f(0) = 1 (there is one way to deposit $0, which is not depositing anything), f(1) = 1 (one way to deposit $1, using a $1 coin), f(2) = 2 (two ways to deposit $2, either using two $1 coins or a $1 coin and a $1 bill), f(3) = 4 (four ways to deposit $3, using three $1 coins, a $1 coin and a $1 bill, or a $1 coin and a $5 bill).

c) To find the number of ways to deposit $10 for a book of stamps, we use the recurrence relation. Plugging in n = 10, we get f(10) = f(9) + f(9) + f(5). Using the initial conditions and recursively applying the relation, we can calculate f(10) to find the answer.

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Answer:

Step-by-step explanation:

The total volume of the batter is the same in both cases:

(33 cm)(23 cm)(3 cm) = 2277 cm^3.

The volume-of-a-cone formula is V = (1/3)(pi)r^2h

In this case the cone diameter is given as 4 cm, so the radius is 2 cm (this does not sound right!).  The area of the base of this cone is (pi)(2 cm)^2.  Finally, the cone volume is (area of the base)(height), which works out to (pi)(4 cm^2)(9 cm) = 113.1 cm^3.

Divide this individual cone volume into the total 2277 cm^3 volume of the batter:

2277 cm^3

------------------- = 20 with a remainder

  113.1 cm^3

Alandra can fill 20 cones full and have a small fractional remainder.

The distance travelled  in 4 seconds while driving at a constant speed of 50 mph is equal to 0.0556 miles (approximately).

Driving speed is equal to 50mph

And driving at a constant speed of 50 miles per hour ,

Then your speed in miles per second is ,

Since there are 60 minutes in an hour

⇒50 mph = 50/60 miles per minute

⇒50/60 miles per minute = 5/6 miles per minute

Since there are 60 seconds in a minute

⇒ 5/6 miles per minute = 5/360 miles per second

⇒ 5/360 miles per second = 0.0138888... miles per second

⇒ 5/360 miles per second  ≈0.0139 miles per second

When look down for 4 seconds while driving at 50 mph,

Travel a distance of,

distance = speed x time

Substitute the value we get,

⇒ distance = 0.0139 miles per second x 4 seconds

⇒ distance ≈ 0.0556 miles

Therefore,  travel a distance of  0.0556 miles approximately in 4 seconds while driving at a constant speed of 50 mph.

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Answer:

a) 0

Step-by-step explanation:

Given that TRAP × 9 = PART and  T, R, A, P all have different integer values (that is their values are different). TRAP and PART are both made up of four integers digits, that means 1000 ≤ TRAP and PART ≤ 9999. This means that TRAP × 9 ≤ 10000. The value of R can be gotten from:

\(TRAP<\frac{10000}{9}<1112(rounding \ to \ the \ next \ whole \ number)\)

T cannot be 0, therefore T= 1, Since their values are different, R cannot be equal to T, we get that R can only be 0

Answer:

5 servings

Step-by-step explanation:

there is not enough juice for 6 or more servings

The probability of a radiation measurement of 599 or higher from a mountain known to have terrorists, assuming no nuclear danger, is about 0.0668.

We are given that the radiation levels observed by the satellite are normally distributed with a mean of 490 and a variance of 2916. We want to find the probability of a random radiation measurement being 599 or higher, assuming there is no nuclear danger.

First, we need to standardize the radiation level of 599 using the formula:

z = (x - mu) / sigma

where x is the radiation level, mu is the mean, and sigma is the standard deviation. Substituting the values we have:

z = (599 - 490) / √(2916) = 1.5

Now, we can use a standard normal distribution table or calculator to find the probability of a z-score of 1.5 or higher. The table or calculator will give us the area under the standard normal curve to the right of 1.5.

Using a calculator, we can find this probability as follows:

P(Z > 1.5) = 0.0668 (rounded to four decimal places)

Therefore, the probability of a random radiation measurement being 599 or higher is approximately 0.0668, assuming there is no nuclear danger.

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The model's fit to the data is weak, indicated by a correlation coefficient of -0.34. There is a weak negative relationship between the variables, with the model's predictions being imprecise and scattered around the line of fit.

A relationship coefficient of - 0.34 shows a frail negative connection between's the factors in the information. This intends that as one variable expands, the other variable will, in general, diminish, however, the relationship isn't a serious area of strength for exceptionally.

The line of fit for the information recommends that there is a general pattern or example, however, it doesn't fit the information focuses intently. The scatterplot of the information would show focuses spread around the line, for certain focuses straying a considerable amount from it.

The model's capacity to foresee the specific upsides of the reliant variable in light of the free variable(s) is restricted. In outline, the attack of the model to the information isn't an area of strength for extremely, there is a frail negative connection between the factors.

The model's forecasts may not be profoundly precise, and there may be different elements or factors not caught by the model that impact the information.

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Answer:

-9/8

Hope this helps

The right answer is - 9/8

please see the attached picture for full solution

Hope it helps..

The area of the sector OAB of the circle is 9 square meters

From the question, we have the following parameters that can be used in our computation:

Using the above as a guide, we have the following:

Sector area = central angle/360 * Circle area

Substitute the known values in the above equation, so, we have the following representation

Sector area = 45/360 * 72

Evaluate

Sector area = 9

Hence, the area of the sector is 9 square meters

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Answer:

11² = 121

Step-by-step explanation:

When you divide powers with the same base, subtract the exponents.

\( \dfrac{11^6}{11^4} = 11^{6 - 4} = 11^2 = 121 \)

Answer:

121

Step-by-step explanation:

11 to the 6 power = 1771561

11 to the 4 power = 14641

1771561/14641 = 121

Answer:

c

Step-by-step explanation:

in order for it to be a triangle the smaller sides have to add up to be greater than the longest side

for a 5+14=19 so that is not a triangle because the  side dont add up to be greater than 19

for b 14+8=22 so that is also not a triangle because the sides dont add up to be greater than 24

for c 5+15=20 so that is a triangle because to 2 shorter sides added are greater than the longest side

for d 14+9=23 so that is not a triangle because the two smaller sides dont add up to be greater than 24

The total number of counters in the bag is given as follows:

23 counters.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The probability of taking a blue counter is of 0.8, while there are 18 blue counters in the bag, hence the total number of counters in the bag is obtained as follows:

0.8 = 18/n

0.8n = 18

n = 18/0.8

n = 23 counters. (rounding up).

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R is transitive. it is an equivalence relation. We used direct proof technique to prove this.

To prove that R is an equivalence relation, we need to show that it is reflexive, symmetric, and transitive.

Since for every x in A there is a y in A such that x R y, we know that R is reflexive. This is because every element in A is related to itself by R, as given by the premise of the problem.

To show that R is symmetric, let x and y be arbitrary elements in A such that x R y. Since R is symmetric, we know that y R x. But since x R y, and R is transitive, it follows that x R x. Therefore, R is symmetric.

Finally, to show that R is transitive, let x, y, and z be arbitrary elements in A such that x R y and y R z. Since R is transitive, it follows that x R z. Therefore, R is transitive.

Since R is reflexive, symmetric, and transitive, it is an equivalence relation. We used direct proof technique to prove this.

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Assuming the track is straight, the distance at which they are apart one hour before they meet is; 30 km

We are told that a Nonstop trains leave Toronto and Montreal at the same time each day going to the other city along the main line.

Speed of Train 1 = 120 km/h

Speed of Train 2 = 90 km/h

Time spent by train 1 = 1 hour

Time spent train 2 = 1 hour

Formula for distance is;

Distance = Speed * time

If they leave the same time each day, it means that;

Distance of train 1 = 120 * 1 = 120 km

Distance of train 2 = 90 * 1 = 90 km

Thus, distance at which they will be apart before meeting each other is;

Distance apart = 120 - 90

Distance apart = 30 km

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Answer:

\( {x}^{2} - 12x + 23 = 0\)

\( {x}^{2} - 12x = - 23\)

\( {x}^{2} - 12x + 36 = 13\)

\( {(x - 6)}^{2} = 13\)

x - 6 = +√13

x = 6 + √13

The limit value is equal to 2 .

Given,

2x ≤ g(x) ≤ \(x^{4}\) − x² +  2

According to sandwich theorem,

g(x)≤ f(x) ≤ h(x)

\(\lim_{x \to \ a} g(x) = \lim_{x \to \ a} h(x) = L\)

Then,

L= \(\lim_{x \to \ a} f(x) = L\)

Here we have,

2x ≤ g(x) ≤ \(x^{4}\) − x² +  2

And so if we take the limit as x→1; then

\(\lim_{x \to \ 1} 2x = 2\\\\ \lim_{x \to \ 1} x^{4} - x^{2} + 2 = 2\\\)

Thus we can apply the sandwich theorem,

\(\lim_{x \to \ 1} g(x) = 2\)

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Correct expression:

2x ≤ g(x) ≤ \(x^{4}\) − x² +  2

Statement: ∠ABC ≅ ∠EDC

Reason: Given (or Angle equality postulate)

In line 5, we can state that ∠ABC is congruent to ∠EDC because it is given in the paragraph proof. The reason for this statement is the "Given" or "Angle equality postulate," which states that if two angles are given to be congruent, then they are congruent.

Statement: Triangle ABC and Triangle EDC are congruent.

Reason: ASA (Angle-Side-Angle) congruence criterion.

In a two-column proof, each line consists of a statement and a reason. To complete the proof, we need to determine the appropriate statement and reason for line 5.

The given paragraph proof should provide information leading to the conclusion that Triangle ABC and Triangle EDC are congruent. The most likely reason for this congruence would be the ASA (Angle-Side-Angle) criterion.

The ASA criterion states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

Therefore, in line 5, we can state "Triangle ABC and Triangle EDC are congruent" and provide the reason as "ASA (Angle-Side-Angle) congruence criterion." This indicates that the two triangles are congruent based on the given information and the ASA criterion.

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The probability of getting 3 or more who were involved in a car accident last year is 0.126.

Given 9% of the drivers were involved in a car accident last year.

We have to find the probability of getting 3 or more who were involved in a car accident last year if 14 were selected randomly.

We have to use binomial theorem which is as under:

n\(C_{r}p^{r} (1-p)^{n-r}\)

where p is the probability an r is the number of trials.

Probability that 3 or more involved in a car accident last year if 14 are randomly selected=1-[P(X=0)+P(X=1)+P(X=2)]

=1-{\(14C_{0}0.9^{0} (0.1)^{14} +14C_{1} (0.9)^{1} (0.1)^{13} +14C_{2} (0.9)^{2} (0.1)^{12}\)}

=1-{1*0.2670+14!/13!*0.9*0.29+14!/2!12!*0.0081*0.2358}

=1-{0.2670+0.3654+0.2358}

=1-0.8682

=0.1318

Among the options given the nearest is 0.126.

Hence the probability that 3 or more are involved in the accident is 0.126.

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Answer:

A, \({x | x<-2}\)

Step-by-step explanation:

We have the inequality as

\(3x<-6\)

We can simplify this inequality a little bit more by dividing 3 from both sides.

That gets us

\(x<-2\)

We can see the only answer that has this is A.