A tour group has $83 to buy train tickets. Each ticket costs $18. How many train tickets can
the group buy?

The proposal is as follows

Part III  -  The distance between buoys A and B is 12.8 kilometers.

Part IV  -  The length of the other two triangle legs are 10.2 kilometers and 8.4 kilometers.

Part V  - The total length of the race course is 31.4 kilometers.

Part VIII  - The winner's speed during last year's race was 10.8 knots.

See the proposal attached.

Dear Sponsor,

I'm seeking sponsorship for the San Francisco sailboat race.

With a proven track record and the determination to win, your investment of $5,500 covers travel costs and potential hazards.

By associating your brand with a winning sailor, you'll gain significant exposure to thousands of spectators. Join me in this thrilling race for success.

Sincerely,

[Your Name]

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The nurse should administer 4 Lasix 20 mg tablets to the patient to achieve the prescribed dose of 80 mg.

To determine the number of Lasix 20 mg tablets that should be administered to the patient, we need to calculate how many tablets are equivalent to the prescribed dose of 80 mg.

Given that each Lasix tablet contains 20 mg of the medication, we can divide the prescribed dose (80 mg) by the dosage strength of each tablet (20 mg) to find the number of tablets needed.

Number of tablets = Prescribed dose / Dosage strength per tablet

Number of tablets = 80 mg / 20 mg

Number of tablets = 4 tablets

Therefore, the nurse should administer 4 Lasix 20 mg tablets to the patient to achieve the prescribed dose of 80 mg.

It is important to note that this calculation assumes that the Lasix tablets can be divided or split if necessary. However, it is crucial to follow the specific instructions provided by the prescribing physician or consult with a pharmacist if there are any concerns about the appropriate administration of the medication.

Additionally, it is important to consider any additional instructions, such as the frequency and timing of administration, as specified by the physician's order.

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The midpoint of AB is M(-4,2). If the coordinates of A are (-7,3), and the coordinates of B is (-1, 1).

To find the coordinates of point B, we can use the midpoint formula, which states that the coordinates of the midpoint between two points (A and B) can be found by averaging the corresponding coordinates.

Let's denote the coordinates of point A as (x1, y1) and the coordinates of point B as (x2, y2). The midpoint M is given as (-4, 2).

Using the midpoint formula, we can set up the following equations:

(x1 + x2) / 2 = -4

(y1 + y2) / 2 = 2

Substituting the coordinates of point A (-7, 3), we have:

(-7 + x2) / 2 = -4

(3 + y2) / 2 = 2

Simplifying the equations:

-7 + x2 = -8

3 + y2 = 4

Solving for x2 and y2:

x2 = -8 + 7 = -1

y2 = 4 - 3 = 1

Therefore, the coordinates of point B are (-1, 1).

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Answer:

A: the probability that a 1 is received is 0.56.

B:  the probability that a 0 was sent given that a 1 is received is (2/25) * (1 - P(0 sent)).

Step-by-step explanation:

To solve this problem, we can use conditional probabilities and the concept of Bayes' theorem.

a. To find the probability that a 1 is received, we need to consider the two possibilities: either a 1 was sent and remained unchanged, or a 0 was sent and got flipped to a 1 by the random error.

Let's denote:

P(1 sent) = 0.6 (probability a 1 is sent)

P(0→1) = 0.2 (probability a 0 is flipped to 1)

P(1 received) = ?

P(1 received) = P(1 sent and unchanged) + P(0 sent and flipped to 1)

= P(1 sent) * (1 - P(0→1)) + P(0 sent) * P(0→1)

= 0.6 * (1 - 0.2) + 0.4 * 0.2

= 0.6 * 0.8 + 0.4 * 0.2

= 0.48 + 0.08

= 0.56

Therefore, the probability that a 1 is received is 0.56.

b. If a 1 is received, we want to find the probability that a 0 was sent. We can use Bayes' theorem to calculate this.

Let's denote:

P(0 sent) = ?

P(1 received) = 0.56

We know that P(0 sent) + P(1 sent) = 1 (since either a 0 or a 1 is sent).

Using Bayes' theorem:

P(0 sent | 1 received) = (P(1 received | 0 sent) * P(0 sent)) / P(1 received)

P(1 received | 0 sent) = P(0 sent and flipped to 1) = 0.4 * 0.2 = 0.08

P(0 sent | 1 received) = (0.08 * P(0 sent)) / 0.56

Since P(0 sent) + P(1 sent) = 1, we can substitute 1 - P(0 sent) for P(1 sent):

P(0 sent | 1 received) = (0.08 * (1 - P(0 sent))) / 0.56

Simplifying:

P(0 sent | 1 received) = 0.08 * (1 - P(0 sent)) / 0.56

= 0.08 * (1 - P(0 sent)) * (1 / 0.56)

= 0.08 * (1 - P(0 sent)) * (25/14)

= (2/25) * (1 - P(0 sent))

Therefore, the probability that a 0 was sent given that a 1 is received is (2/25) * (1 - P(0 sent)).

A message is coded into the binary symbols 0 and 1 and the message is sent over a communication channel. The probability a 0 is sent is 0.4 and the probability a 1 is sent is 0.6. The channel, however, has a random error that changes a 1 to a 0 with probability 0.2 and changes a 0 to a 1 with probability 0.1. (a) What is the probability a 0 is received? (b) If a 1 is received, what is the probability a 0 was sent?

Answer:

We don't need to worry about the displaystyle- {3} −3 anyway, because we dcided in the first step that displaystyle {x}ge- {2} x ≥ −2. So the domain for this case is displaystyle {x}ge- {2}, {x}ne {3} x≥ −2,x≠ 3, which we can write as displaystyle {left [- {2}, {3}right)}cup {left ({3},inftyright)} [−2,3)∪(3,∞).

Step-by-step explanation:

The function Sam can use to figure his total earnings for the day, based on the number of people he serves, is E(n) = 42 + 5n.

To calculate Sam's total earnings for the day, we need to consider both his hourly wages and the tips he receives based on the number of people he serves. Let's break it down step by step.

First, we know that Sam earns $7 per hour as his wage. Since he works for 6 hours, his earnings from wages alone would be $7 multiplied by 6, which equals $42.

Next, Sam also earns about $5 in tips for each person he serves. We can represent the number of people Sam serves as "n". Therefore, his total tip earnings would be $5 multiplied by "n", which gives us 5n.

To calculate Sam's total earnings for the day, we add his earnings from wages and tips together. So the function representing his total earnings, "E", can be written as:

E(n) = 7(6) + 5n

Simplifying further, we get:

E(n) = 42 + 5n

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The correct value of volume of the pyramid is 48 cubic inches.

To find the volume of the solid oblique pyramid, we can use the formula V = (1/3) * Base Area * Height. The base of the pyramid is a triangle, and the height is given as 6 inches.The formula for the area of a triangle is (1/2) * base * height. In this case, the base length is 8 inches and the height is 6 inches. Base Area = (1/2) * 8 * 6 = 24 square inches

Now, we can calculate the volume of the pyramid:

V = (1/3) * Base Area * Height

V = (1/3) * 24 * 6

V = 48 cubic inches

Therefore, the volume of the pyramid is 48 cubic inches.

None of the provided options (a, b, c, d) match the calculated volume of 48 cubic inches. Please double-check the given options or provide the correct options for further comparison.

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Answer:

56

Step-by-step explanation:

f(x)=4x^2-7

f'(x)=8x

f'(7)=56

Answer:

Step-by-step explanation:

The correct answer is A. A rectangle the same size as the base.

When a rectangular pyramid is sliced parallel to the base, the resulting cross-section is a rectangle that is the same size as the base. The parallel slicing ensures that the cross-section maintains the same dimensions as the base of the pyramid. Therefore, option A, a rectangle the same size as the base, represents the cross-section.

The expression (3√2) / (3√6) with a rationalized denominator is 3√9 / 6. Option C is the correct answer.

To rationalize the denominator in the expression (3√2) / (3√6), we can multiply both the numerator and denominator by the conjugate of the denominator. The conjugate of √6 is -√6, so we multiply the expression by (-√6) / (-√6):

(3√2 / 3√6) * (-√6 / -√6)

This simplifies to:

-3√12 / (-3√36)

Further simplifying, we have:

-3√12 / (-3 * 6)

-3√12 / -18

Finally, we can cancel out the common factor of 3:

- 3√9 / - 6.

Simplifying further, we get:

3√9 / 6.

Option C is the correct answer.

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The computed mean of 52.4 and the actual mean of 52.7 suggest a close relationship in terms of central tendency.

A computed mean is a statistical measure calculated by summing up a set of values and dividing by the number of observations. In this case, the computed mean of 52.4 implies that when the values are averaged, the result is 52.4.

The actual mean of 52.7 refers to the true average of the population or data set being analyzed. Since it is higher than the computed mean, it indicates that the sample used for computation might have slightly underestimated the true population mean.

However, the difference between the computed mean and the actual mean is relatively small, with only a 0.3 unit discrepancy.

Given the proximity of these two values, it suggests that the computed mean is a reasonably accurate estimate of the actual mean.

However, it's important to note that without additional information, such as the sample size or the variability of the data, it is difficult to draw definitive conclusions about the relationship between the computed mean and the actual mean.

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┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈

✦ The number is - 5

┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈┈

[tex]\begin{gathered} \; \sf{\color{pink}{Let \; the \; other \; number \; be \; (x)::}} \\ \end{gathered}[/tex]

Atq,,

[tex]\begin{gathered} \; \color{skyblue} :\dashrightarrow \: \tt{3 \times \bigg \lgroup \: x + ( - 7) \bigg \rgroup = - 36} \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered} \; \color{skyblue} :\dashrightarrow \: \tt{3 \times \bigg \lgroup \: x - 7 \bigg \rgroup = - 36} \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered} \; \color{skyblue} :\dashrightarrow \: \tt{3x - 21 = - 36} \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered} \; \color{skyblue} :\dashrightarrow \: \tt{3x = - 36 + 21} \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered} \; \color{skyblue} :\dashrightarrow \: \tt{3x = - 15} \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered} \; \color{skyblue} :\dashrightarrow \: \tt{x = \dfrac{\cancel{ - 15}}{\cancel{ \: 3}}} \qquad \bigg \lgroup \sf{Cancelling \: by \: 3} \bigg \rgroup \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered} \; \color{pink} :\dashrightarrow \underline{\color{pink}\boxed{\colorbox{black}{x = - 5}}} \: \pmb{\bigstar} \\ \\ \end{gathered}[/tex]

The answer is:

Work/explanation:

The product means we multiply two numbers.

Here, we multiply 3 and a number increased by -7; let that number be z.

So we have

[tex]\sf{3(z+(-7)}[/tex]

simplify:

[tex]\sf{3(z-7)}[/tex]

This equals -36

[tex]\sf{3(z-7)=-36}[/tex]

[tex]\hspace{300}\above2[/tex]

[tex]\frak{solving~for~z}[/tex]

Distribute

[tex]\sf{3z-21=-36}[/tex]

Add 21 on each side

[tex]\sf{3z=-36+21}[/tex]

[tex]\sf{3z=-15}[/tex]

Divide each side by 3

[tex]\boxed{\boxed{\sf{z=-5}}}[/tex]

To find an object's maximum height, we need to find the vertex of this quadratic equation.

Answer: 5.50 seconds

Terms to know:

Quadratic function: A quadratic function is a polynomial function of degree 2, which means the highest power of the variable in the equation is 2.

Vertex: The vertex of a quadratic function is the point on the graph where the function reaches its highest or lowest point. In the case of a quadratic function in the form f(x) = ax^2 + bx + c, the vertex is given by the coordinates (x, f(x)).

Step-by-step explanation:

The vertex of a quadratic equation can be represented as [tex](\frac{-b}{2a}, f(\frac{-b}{2a})[/tex]

Since we only are looking at the time it takes to reach maximum height we will only look at the x value.

[tex]x= \frac{-176}{2(-16)}[/tex]

[tex]x= 5.50[/tex]

Let's use the fact that the sum of the angles of a triangle is always 180 degrees to solve this problem. Let the two equal angles be x, then the third angle is x + 45.Let's add all the angles together:x + x + x + 45 = 180Simplifying this equation, we get:3x + 45 = 180Now, we need to isolate the variable on one side of the equation. We can do this by subtracting 45 from both sides of the equation:3x = 135Finally, we can solve for x by dividing both sides of the equation by 3:x = 45Therefore, the value of x is 45 degrees.

Answer:

Step-by-step explanation:

180 = x + x + x + 45

180 - 45 = 3x

135 = 3x

x = 135 : 3

x = 45°

------------------

check

180 = 45 + 45 + 45 + 45

180 = 180

same value the answer is good

Answer: [tex](-\infty, 0) \cup (0, \infty)[/tex]

Step-by-step explanation:

The graph of [tex]\frac{\sin x}{x}[/tex] is continuous for all real [tex]x[/tex] except [tex]x=0[/tex], and multiplying this by [tex]1/3[/tex] does not change this.

Answer:

Hope this helps and have a nice day

Step-by-step explanation:

To find the value of x, we can use the formula:

Time = Distance / Speed

Let's calculate the time taken to travel from Q to P and back to Q.

From Q to P:

Distance = 12 km

Speed = 6 km/h

Time taken from Q to P = Distance / Speed = 12 km / 6 km/h = 2 hours

From P to Q:

Distance = 12 km

Speed = (6 + x) km/h

Time taken from P to Q = Distance / Speed = 12 km / (6 + x) km/h

Given that the total time taken for the round trip is 3 hours 20 minutes, we can convert it to hours:

Total time = 3 hours + (20 minutes / 60) hours = 3 + (1/3) hours = 10/3 hours

According to the problem, the total time is the sum of the time from Q to P and from P to Q:

Total time = Time taken from Q to P + Time taken from P to Q

Substituting the values:

10/3 hours = 2 hours + 12 km / (6 + x) km/h

Simplifying the equation:

10/3 = 2 + 12 / (6 + x)

Multiply both sides by (6 + x) to eliminate the denominator:

10(6 + x) = 2(6 + x) + 12

60 + 10x = 12 + 2x + 12

Collecting like terms:

8x = 24

Dividing both sides by 8:

x = 3

Therefore, the value of x is 3.

Answer:

x = 3

Step-by-step explanation:

speed  = distance / time

time = distance / speed

Total time from P to Q to P:

T = 3h 20min

P to Q :

s = 6 km/h

d = 12 km

t = d/s

= 12/6

t = 2 h

time remaining t₁ = T - t

= 3h 20min - 2h

=  1 hr 20 min

= 60 + 20 min

= 80 min

t₁ = 80/60 hr

Q to P:

d₁ = 12km

t₁ = 80/60 hr

s₁ = d/t₁

[tex]= \frac{12}{\frac{80}{60} }\\ \\= \frac{12*60}{80}[/tex]

= 9

s₁ = 9 km/h

From question, s₁ = (6 + x)km/h

⇒ 6 + x = 9

⇒ x = 3

Step-by-step explanation:

a linear relationship or function is described in general as

y = f(x) = ax + b

Because the variable term has the variable x only with the exponent 1, this makes this a straight line - hence the name "linear".

here f(x) is P(x) :

P(x) = ax + b

now we are using both given points (ordered pairs) to calculate a and b :

20 = a×170 + b

2820 = a×220 + b

to eliminate first one variable we subtract equation 1 from equation 2 :

2800 = a×50

a = 2800/50 = 280/5 = 56

now, we use that in any of the 2 original equations to get b :

20 = 56×170 + b

b = 20 - 56×170 = 20 - 9520 = -9500

so,

P(x) = 56x - 9500

a. An equation to describe the total cost of RV rental:

Cost = (125 * d) + (0.32 * m) + 2500

b. Comparing the two costs will determine which option is cheaper.

c. For the more direct route: m ≤ 3500

For fewer overnight stays: d ≤ 14

These domains ensure that we don't exceed the original values for miles and days.

d. I recommend compromising by lessening the number of days of the rental. By reducing the rental period to 11 days, you can stay within the $5,000 budget while still allowing your little sister to take the two-week trip.

a. To write an equation for the total cost of RV rental, we can use the given information. The cost per day is $125, and there is an additional charge of 32 cents per mile. Let's denote the number of days as d and the number of miles as m. The equation for the total cost of RV rental can be written as:

Cost = (125 * d) + (0.32 * m) + 2500

b. To compare the costs of the two options, we need to calculate the total cost for each. Option 1 has 3500 miles and takes 11 days, while option 2 has 3000 miles and takes 14 days. We can substitute these values into the equation from part a to find the total costs for each option. Comparing the two costs will determine which option is cheaper.

c. To compromise and stay within a budget of $5,000, we can adjust either the number of miles or the number of days. For the more direct route, we can reduce the number of miles, and for fewer overnight stays, we can reduce the number of days. The domains for these compromises would be:

For the more direct route: m ≤ 3500

For fewer overnight stays: d ≤ 14

These domains ensure that we don't exceed the original values for miles and days.

d. To find the number of miles or days to eliminate in order to stay under the $5,000 budget, we can set up equations using the total cost equation from part a. Let's denote the reduced number of miles as m' and the reduced number of days as d'. We need to solve the following equation for each compromise:

(125 * d') + (0.32 * m') + 2500 ≤ 5000

By substituting the appropriate values into the equation and solving for m' or d', we can determine how many miles or days need to be eliminated.

Based on the given information, I recommend compromising by lessening the number of days of the rental. By reducing the rental period to 11 days, you can stay within the $5,000 budget while still allowing your little sister to take the two-week trip. This compromise ensures that you don't have to sacrifice too much scenic beauty or make drastic changes to the route.

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Answer:

Step-by-step explanation:

To solve these problems, we can use the Poisson probability formula:

P(x; λ) = (e^(-λ) * λ^x) / x!

Where:

P(x; λ) is the probability of x events occurring

e is the base of the natural logarithm (approximately 2.71828)

λ is the average rate of events occurring in the given time period

x is the number of events

(a) Probability of exactly 4 orders arriving in 30 minutes:

The average rate of orders is given as 5 orders per hour. To find the average rate of orders in 30 minutes, we divide it by 2 (since 30 minutes is half an hour):

λ = 5 orders/hour / 2 = 2.5 orders/30 minutes

Using the Poisson probability formula:

P(x = 4; λ = 2.5) = (e^(-2.5) * 2.5^4) / 4!

Calculating this:

P(x = 4; λ = 2.5) ≈ (0.082 * 39.0625) / 24

P(x = 4; λ = 2.5) ≈ 3.22265625 / 24

P(x = 4; λ = 2.5) ≈ 0.134

Therefore, the probability that exactly 4 orders will arrive in 30 minutes is approximately 0.134, or 13.4%.

(b) Probability of at least 2 orders arriving in an hour:

To find the probability of at least 2 orders, we need to calculate the probabilities of having 0 and 1 order and subtract it from 1 (since it's the complement).

Using the Poisson probability formula:

P(x = 0; λ = 5) = (e^(-5) * 5^0) / 0! = e^(-5) ≈ 0.0067

P(x = 1; λ = 5) = (e^(-5) * 5^1) / 1! ≈ 0.0337

P(at least 2 orders) = 1 - P(x = 0) - P(x = 1) ≈ 1 - 0.0067 - 0.0337 ≈ 0.9596

Therefore, the probability of at least 2 orders arriving in an hour is approximately 0.9596, or 95.96%.

Answer:

f(3r - 1) = -6r + 6

Step-by-step explanation:

To find f(3r - 1), we substitute 3r - 1 for x in the expression for f(x) and simplify:

f(x) = 4 - 2x

f(3r - 1) = 4 - 2(3r - 1)

= 4 - 6r + 2

= -6r + 6

So, f(3r - 1) = -6r + 6.

Group A is performing most consistently in terms of quality and associate engagement compared to last month.

To determine which performance area the groups are performing most consistently compared to last month, we need to compare the scores of each performance area between the two months.

Let's analyze each performance area:

Quality:

For Group A, the quality score increased from 90 to 94, indicating an improvement in quality performance. However, for Group B, the quality score decreased from 74 to 70, indicating a decline in quality performance. Therefore, Group A is performing more consistently in terms of quality compared to last month.

Productivity:

For Group A, the productivity score decreased from 79 to 62, showing a significant decline in productivity performance. Similarly, for Group B, the productivity score decreased from 86 to 58, indicating a notable decline as well. Both groups experienced a decrease in productivity performance, but Group A had a larger decline. Therefore, neither group is performing consistently in terms of productivity compared to last month.

Associate Engagement:

For Group A, the engagement score increased from 68 to 70, suggesting a slight improvement in associate engagement. Conversely, for Group B, the engagement score increased from 76 to 72, indicating a slight decline. Both groups had minor changes in engagement scores, but Group A had a smaller change. Therefore, Group A is performing more consistently in terms of associate engagement compared to last month.

Based on the analysis, Group A is performing most consistently in terms of quality and associate engagement compared to last month. However, neither group is performing consistently in terms of productivity. It is important to address the productivity decline and identify areas for improvement to ensure consistent performance across all categories.

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When 2 items are selected without replacement from a population of 6 items, there are 15 possible samples that can be formed. Option A.

To determine the number of possible samples when 2 items are selected at random without replacement from a population of 6 items, we can use the concept of combinations.

The number of combinations of selecting k items from a set of n items is given by the formula C(n, k) = n! / (k! * (n-k)!), where n! represents the factorial of n.

In this case, we have a population of 6 items and we want to select 2 items. Therefore, the number of possible samples can be calculated as:

C(6, 2) = 6! / (2! * (6-2)!) = 6! / (2! * 4!) = (6 * 5 * 4!) / (2! * 4!) = (6 * 5) / (2 * 1) = 15. Option A is correct.

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Trent will need approximately 2.86 bottles of waterproof spray to cover his tent.

To calculate the number of bottles of waterproof spray Trent will need to cover his tent, we first need to find the surface area of the tent.

The surface area of a square-based pyramid is given by the formula:

Surface Area = Base Area + (0.5 x Perimeter of Base x Slant Height)

The base of the pyramid is a square with a side length of 14 feet, so the base area is:

Base Area = (Side Length)^2 = 14^2 = 196 square feet

To find the slant height of the pyramid, we can use the Pythagorean theorem. The slant height is the hypotenuse of a right triangle formed by one side of the base, the height of the pyramid, and the slant height. The height of the pyramid is given as 8 feet, and half the length of the base is 7 feet.

Using the Pythagorean theorem:

[tex]Slant Height^2 = (Half Base Length)^2 + Height^2[/tex]

[tex]Slant Height^2 = 7^2 + 8^2Slant Height^2 = 49 + 64Slant Height^2 = 113Slant Height ≈ √113 ≈ 10.63 feet[/tex]

Now we can calculate the surface area of the tent:

Surface Area = 196 + (0.5 x 4 x 10.63)

Surface Area = 196 + (2 x 10.63)

Surface Area = 196 + 21.26

Surface Area ≈ 217.26 square feet

Since each bottle of waterproof spray covers 76 square feet, we can divide the total surface area of the tent by the coverage of each bottle to find the number of bottles needed:

Number of Bottles = Surface Area / Coverage per Bottle

Number of Bottles = 217.26 / 76

Number of Bottles ≈ 2.86

Therefore, Trent will need approximately 2.86 bottles of waterproof spray to cover his tent. Since we can't have a fraction of a bottle, he will need to round up to the nearest whole number. Therefore, Trent will need 3 bottles of waterproof spray to fully waterproof his tent.

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Answer:

Step-by-step explanation:

Let's calculate the expression step by step:

93 - (15 × 10) + (160 ÷ 16)

First, we perform the multiplication:

93 - 150 + (160 ÷ 16)

Next, we perform the division:

93 - 150 + 10

Finally, we perform the subtraction and addition:

-57 + 10

The result is:

-47

Therefore, 93 - (15 × 10) + (160 ÷ 16) equals -47.

Answer:

  4

Step-by-step explanation:

You want the sum of digits of the largest number that divides 1305, 4665, and 6905 with the same remainder.

We can look at 4665/1305 ≈ 3.57 and 6905/1305 ≈ 5.29 for a clue as to the divisor of interest. These quotients tell us that one possibility is the value that would give quotients of 4 and 6 after the remainder is subtracted from each of the numbers.

For 1305 and 4665, if r is the remainder, we require ...

  4(1305 -r) = 4665 -r

  5220 -4665 = 4r -r

  555/3 = r = 185

If 185 is the remainder in this scenario, then 1305 -185 = 1120 is the divisor. Checking the remainder with 6905, we find ...

  6905/1120 = 6 r 185

The sum of digits of this divisor is 1 + 1 + 2 + 0 = 4.

The sum of the digits in N is 4.

After a long study, tree scientists conclude that a eucalyptus tree will grow at the rate of 3ft per year, where t is time in years. So, the tree will grow 5 feet in the first year.

We have to find the number of feet the tree will grow in the first year, given that 5(t + 1)³. The rate of growth of a tree is given as 3ft/year. Therefore, in the first year, the tree will grow 3 feet.

To find the number of feet the tree will grow in the first year, we substitute t = 0 in the given expression.

5(t + 1)³ = 5(0 + 1)³= 5(1)³= 5(1)= 5. Therefore, the tree will grow 5 feet in the first year.

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Answer:

Step-by-step explanation:

The given expression is: 14x^(2n+1) + 7x^(n+3) - 21^(n+2)

Unfortunately, it seems there is a missing exponent for the term "21" in the expression. Please provide the correct exponent for 21, and I'll be happy to help you further simplify the expression.

The z-score for Brazil is given as follows:

Z = 0.87.

The z-score formula is defined as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In which:

The parameters for this problem are given as follows:

[tex]X = 6.24, \mu = 4.8, \sigma = 1.66[/tex]

Hence the z-score for Brazil is given as follows:

Z = (6.24 - 4.8)/1.66

Z = 0.87.

More can be learned about z-scores at https://brainly.com/question/25800303

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Answer:

AB = √3

Step-by-step explanation:

Since ABCD is a rectangle, all angles are 90°

∠CDA = 90°

⇒ ∠CDB + ∠BDA = 90

⇒ ∠BDA = 60

In ΔABD,

sin(∠BDA) = opposite/ hypotenuse = AB / BD

⇒ sin(60) = AB/2

⇒ AB = 2 sin(60)

⇒ AB = 2 (√3)/2

AB = √3