the length of a side of a rectangle is 6 cm. what should the length of the other side be so that the perimeter of the rectangle is smaller than the perimeter of a square with a side of 4cm?

Your viewing angle α is approximately 46.34 degrees when sitting in the classroom next to the wall and looking at the blackboard.

To show that your viewing angle α is determined by the length of the blackboard and its distance from the wall, we can use geometry and trigonometry.

Let's consider a right triangle formed by your line of sight, the distance from the wall to the blackboard, and the length of the blackboard.

The adjacent side of the triangle is the distance from the wall to the blackboard, which is 5 ft. The opposite side is half the length of the blackboard since you are looking at the midpoint of the blackboard. Therefore, the opposite side is (11 ft)/2 = 5.5 ft.

We can use the tangent function to calculate the viewing angle α:

tan(α) = opposite/adjacent

tan(α) = (5.5 ft)/(5 ft)

tan(α) = 1.1

To find α, take the arctan (inverse tangent) of both sides:

α = arctan(1.1)

Using a calculator, we find that α ≈ 46.34 degrees.

Therefore, your viewing angle α is approximately 46.34 degrees when sitting in the classroom next to the wall and looking at the blackboard.

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Answer:

<3 = 112 degrees

<4 = 68 degrees

Step-by-step explanation:

<3 = 112 degrees (Alternate angles are congruent)

And,

<4+<3 = 180 (Angles on a straight line add up to 180)

=> <4 + 112 = 180

=> <4 = 180-112

=> <4 = 68 degrees

Answer:

Step-by-step explanation:

Area is equal to the product of the length and the width

The length is 10 inches and the width is 5 inches.

Thus the Area = 10in * 5in = 50\(in^{2}\)

Answer:

144

Step-by-step explanation:

6(14+8)+12, Use distributive property

84+48+12, Just add all of them up

To make the expression x * equivalent to the C expression (x << 3) + (x << 1), the blank should be filled with 10.

In the given C expression, (x << 3) represents left-shifting the value of x by 3 bits, and (x << 1) represents left-shifting the value of x by 1 bit. To achieve an equivalent expression using multiplication, we need to determine the multiplication factor that corresponds to the left shifts.

The left shift by 3 bits is equivalent to multiplying by 2 raised to the power of 3, which is 8. Similarly, the left shift by 1 bit is equivalent to multiplying by 2 raised to the power of 1, which is 2.

Therefore, to make the expression x * equivalent to (x << 3) + (x << 1), the blank should be filled with 10, as x multiplied by 10 gives the same result as the given C expression.

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Answer:

161ft^2 is answer

Step-by-step explanation:

area of rectangle = l ×b

=7ft ×23ft

=161ft^2

Answer:

B. 1/2, -1/8, 1/32

Step-by-step explanation:

We know that since we have a negative common ratio, our terms in the sequence will alternate the sign. So we know that our second term is positive, third term is negative, and ultimately fourth term is positive.

We also know that 2/1 * 1/4 = 1/2

1/2 * -1/4 = -1/8

-1/8 * -1/4 = 1/32

Hope this helps

Edit: I fixed the answer

Answer:

Y=-65.25x

Step-by-step explanation:

Answer:

a) 38.40 yd  (2 dp)

b) 211.18 yd²  (2 dp)

Step-by-step explanation:

Formula

\(\textsf{Arc length}=2 \pi r\left(\dfrac{\theta}{360^{\circ}}\right)\)

\(\textsf{Area of a sector}=\left(\dfrac{\theta}{360^{\circ}}\right) \pi r^2\)

\(\quad \textsf{(where r is the radius and}\:\theta\:{\textsf{is the angle in degrees)}\)

Calculation

Given:

\(\begin{aligned}\implies \textsf{Arc length} &=2 \pi (11)\left(\dfrac{200^{\circ}}{360^{\circ}}\right)\\ & = 22 \pi \left(\dfrac{5}{9}\right)\\ & = \dfrac{110}{9} \pi \\ & = 38.40\: \sf yd \:(2\:dp)\end{aligned}\)

\(\begin{aligned} \implies \textsf{Area of a sector}& =\left(\dfrac{200^{\circ}}{360^{\circ}}\right) \pi (11)^2\\& = \left(\dfrac{5}{9}\right)\pi \cdot 121\\& = \dfrac{605}{9} \pi\\& = 211.18\: \sf yd^2 \:(2\:dp)\end{aligned}\)

Please note:  As you have not specified if π should be approximated, I have not used an approximation for π.

we need to multiply this number by 100 to get the  as a percentage:

0.1806 * 100 = 18.06%

The probability of choosing a senior can be calculated using the formula:

P(senior) = (102/562) * 100

P(senior) = 18.06%

This means that there is an 18.06% chance of choosing a senior if a student is randomly selected from the school.

First, we need to calculate the total number of students in the school by adding together the number of students in each class:

Total = 165 + 145 + 114 + 102 = 562

Next, we need to calculate the probability of choosing a senior by taking the number of seniors enrolled in the school (102) and dividing it by the total number of students in the school (562).

102/562 = 0.1806

Finally, we need to multiply this number by 100 to get the probability as a percentage:

0.1806 * 100 = 18.06%

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Answer:

that one is already correct

Answer:

hmm

Step-by-step explanation:

Answer:

\(the \: rational \: number \: is \: \sqrt{100} \)

Step-by-step explanation:

The reason why

\( \sqrt{97} \)

isn't a rational number is because, when simplified, it results in 9.848857802.... its decimal doesn't terminate(stop).

The reason why

\( \sqrt{98} \)

isn't a rational number is because, when simplified, it results in 9.899494937.... it's decimal doesn't terminate(stop).

The reason why

\( \sqrt{99} \)

isn't a rational number is because, when simplified, it results in 9.949874371.... it's decimal doesn't terminate(stop).

The reason why

\( \sqrt{100} \)

is a rational number is because, when simplified, it results in 10, its decimal terminates (stops).

\(\frac{f}{g}(2) = \frac{2}{11}\\\)

\(\frac{f}{g}(2) = \frac{f(2)}{g(2)} \\ \frac{f}{g}(2) = \frac{(2)^2}{5(2)^2 +2} \\ \frac{f}{g}(2) = \frac{4}{5(4) +2} \\ \frac{f}{g}(2) = \frac{4}{20 +2} \\ \frac{f}{g}(2) = \frac{4}{22} \\ \frac{f}{g}(2) = \frac{2}{11}\)

To add fractions with different denominators, we need to find a common denominator. By adding the fractions 1/2 and 7/8, we got the final answer is 11/8.

A fraction is part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator.

First, we can see that 3 and 8 have no common factors, so we can find their least common multiple (LCM), which is 24.

Then we can convert both fractions so that they have a denominator of 24:

1/3 = 8/24

4/8 = 3/6 = 12/24

Now we can add the fractions:

8/24 + 12/24 = 20/24

However, we should simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 4 in this case.

So the final answer is 5/6.

First, we can find the least common multiple (LCM) of the denominators, which is 8 in this case.

Then we can convert both fractions so that they have a denominator of 8:

1/2 = 4/8

7/8 = 7/8

Now we can add the fractions:

4/8 + 7/8 = 11/8

However, we should simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 1 in this case.

So the final answer is 11/8.

similarly,

3/4 + 2/3 = 17/12

7/16 + 9/16 = 1

1/6 + 4/9 = 11/18

1/2 + 1/6 = 2/3

3/10 + 1/2 = 4/5

4/15 + 1/3 = 3/5

3/4 + 7/12 = 4/3

5/6 + 3/10 = 17/15

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Yahtzee is a game of chance like dice or poker. The numbers of ways the outcomes ( straight rolling ) is 240 .

Probability of hitting a large straight is 240 / 7776 = 1/32

Yahtzee is the one of dice game that uses five standard six-sided dice. After rolling each die, the player can decide which die to keep and which to reroll. Goals include many different types of combinations, many of which originate from poker.

The two types of combinations that players must roll are called roads: small roads and large roads. Similar to poker straights, these combinations consist of consecutive dice. A small straight uses 4 out of the 5 dice and a large straight uses all 5 dice. Since the dice rolls are random, we can use probability to analyze the likelihood of hitting large straight on a single roll. Assumes that the dice used are fair and independent of each other. Now, you need to know how many ways you can roll a big/ large straight. Here it is more difficult than calculating the sample size. Big straights are harder to roll than small straights, but it’s easier to count the number of times you’ve rolled a big straight than the number of times you’ve rolled a small straight.

Next, determine the number of ways to get a straight by rolling the given dice. To get a nice straight with dice {1, 2, 3, 4, 5}, you can arrange the dice in any order. It turns out that you just swap the five dice. There are 5! = 120 ways to do this. There are two dice combinations that form the large Straight, each with 120 ways to roll, so there are 2 x 120 = 240 ways to roll the large Straight.

Now the probability of hitting a big/ large straight can be calculated with simple division. Since there are 240 ways to get the big straight in one roll, and 7776 rolls 5 dice, the odds of getting the big straight are 240/7776, close to 1/32, and lie 3.1%.

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Answer: x=3 ; y=13

Step-by-step explanation:

1. isolate y from equation to substitute into the second equation

y= 16-x ---> (16-x) = 3x+4

2. move to one side and solve for x

4x=12 --> x=3

3. plug in x value to solve for y

3+y=16 or 3(3)+4

y=13

A=200in² is the area of the shaded polygon so 200in² ➗ 30in

Answer:

56 pennies

Explanation:

You should find 20% of 70 to get 14 and subtract that from 70 to get your answer.

Answer:

56

Step-by-step explanation:

The velocity of the particle is ⟨-2sin(t)-2tcos(t), -2cos(t)+2tsin(t), -4t⟩, the acceleration of the particle is ⟨(2t-2)cos(t)-2sin(t), -(2t+2)sin(t)-2cos(t), -4⟩, and the speed of the particle is 2√(5t^2+1).

To find the velocity of the particle, we need to take the derivative of the position function r(t):

r(t) = ⟨-2tsin(t), -2tcos(t), -2t^2⟩

v(t) = r'(t) = ⟨-2sin(t)-2tcos(t), -2cos(t)+2tsin(t), -4t⟩

To find the acceleration of the particle, we need to take the derivative of the velocity function v(t):

a(t) = v'(t) = ⟨-2cos(t)+2tcos(t)-2sin(t), -2sin(t)-2tsin(t)-2cos(t), -4⟩

Simplifying this expression, we get:

a(t) = ⟨(2t-2)cos(t)-2sin(t), -(2t+2)sin(t)-2cos(t), -4⟩

To find the speed of the particle, we need to find the magnitude of the velocity vector at any given time t:

∣v(t)∣ = √((-2sin(t)-2tcos(t))^2 + (-2cos(t)+2tsin(t))^2 + (-4t)^2)

Simplifying this expression, we get:

∣v(t)∣ = 2√(5t^2+1)

Therefore, the velocity of the particle is ⟨-2sin(t)-2tcos(t), -2cos(t)+2tsin(t), -4t⟩, the acceleration of the particle is ⟨(2t-2)cos(t)-2sin(t), -(2t+2)sin(t)-2cos(t), -4⟩, and the speed of the particle is 2√(5t^2+1).

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The probability that her 10th roll is her last roll in the expression of a decimal to the nearest thousandth is 0.039.

As per information given, the condition of the event will be:

As we can find the value of each probability, the probability of the tenth roll is the last roll will be:

Last roll in tenth = 1 x (5/6)⁸ x 1/6

Last roll in tenth = 0.03876133989

Since, the question is asking for the nearest thousandth, the answer will be 0.039

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to measure exactly 4 quarts well first fill the 3 quart pail 2 times and pour it into the 5 quart pail and remaining answer is below.

1 US liquid quart is the same as 2 pints, 4 cups, and 32 ounces in terms of volume. It's vital to remember that a dry quart equals 4.6546 cups when converting any dry component.

A liter contains 1.057 quarts, and a quart contains 0.946 liters. This is what? Because the measurements are so similar, you can treat liters and quarts the same for many conversions.

As we an infinite supply of water and a 5 quart and 3 quart pail, and we have to measure exactly 4 quarts

so, first we'll first fill the 3 quart pail and pour it into the pail of 5 quart.

now we'll again fill the 3 quart pail and pour it into the pail of 5 quart

this time the 5 quart pail will be filled before the 3 quart pail get completely empty.

at this time; 3 quart pail is containing the 1 quart in it. now pouring into the 3 quart pail and combining with the 3 quart, it will make 4 quarts after pouring into the 5 quart pail.

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The probability that the mean weekly wage of a randomly selected group of 16 workers from the factory will be within $3 of the population mean wage is 0.98

To solve this problem,

We can use the central limit theorem which states that the sample means from a large sample will be approximately normally distributed with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

First, we need to find the standard error of the mean, which is equal to the standard deviation divided by the square root of the sample size:

Standard error of the mean = 5 / sqrt(16) = 1.25

Next, we need to find the z-score for the lower and upper bounds of the sample mean:

lower z-score = (402 - 405) / 1.25 = -2.4

upper z-score = (408 - 405) / 1.25 = 2.4

We can use a standard normal distribution table or a calculator to find the probabilities associated with these z-scores:

lower probability = 0.0082

upper probability = 0.9918

To find the probability that the sample mean is within $3 of the population mean we need to subtract the lower probability from the upper probability:

Probability = 0.9918 - 0.0082 = 0.9836

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Answer:

a. 10560

b. 63360 in.

c. 10000 m

d. 100000 cm

e. 3.107 miles

f. 42.165 km

Step-by-step explanation:

a. 2 miles contain how many feet?

1 mile = 5280 ft

2 miles × 5280 ft / mile = 10560 ft

b. 1 mile contains how many inches?

1 ft = 12 in

1 mile × 5280 ft/mile × 12 in./ft = 63360 in.

c. 10 kilometers contain how many meters?

1 km = 1000 m

10 km × 1000 m/km = 10000 m

d. 1 kilometer contains how many centimeters?

1 km × 1000 m/km × 100 cm/m = 100000 cm

e. How many miles are in a "5k" (five-kilometer) race?

1 in. = 2.54 cm

5 km =

= 5 km × 1000 m/km × 100 cm/m × 1 in. / (2.54 cm) × 1 ft / (12 in.) × 1 mile / (5280 ft)

= 3.107 miles

f. A marathon is 26.2 miles. How many kilometers is this?

26.2 miles =

26.2 miles × 5280 ft / mile × 0.3048 m/ft × km / (1000 m) = 42.165 km

The chances of winning a rare item at least once in 20 attempts is approximately 33.3%.

If you have a 2% chance of winning a rare item, and you want to know the chances after being multiplied by 20

To calculate the probability of winning the rare item at least once in 20 attempts, you can use the complement probability method.

First, find the probability of not winning the item in a single attempt, which is 1 - 0.02 = 0.98.

Then, find the probability of not winning the item in all 20 attempts by multiplying the probability of not winning in a single attempt (0.98) by itself 20 times, which is\(0.98^20.\)

Finally, subtract that result from 1 to find the probability of winning at least once in the 20 attempts.

Calculate the probability of not winning in a single attempt.

1 - 0.02 = 0.98

Calculate the probability of not winning in all 20 attempts.

\(0.98^20.\) ≈ 0.667

Calculate the probability of winning at least once in 20 attempts.

1 - 0.667 ≈ 0.333

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The time study analyst should account for at least 55 observations in order to calculate the mean time per item with a 95.5% confidence level and a 0.4 minute margin of error.

We can use the sample size calculation formula in a confidence interval to get the number of observations required for a time study with the specified parameters:

\(n = (Z * \sigma / E)^2\)

Where:

n = sample size

Z = The target confidence level's Z-score (95.5% translates to roughly 1.96)

σ = procedure standard variation (1.5 minutes per piece)

E = margin of error (0.4 minutes)

Plugging in the values, we can calculate the sample size:

\(n = (1.96 * 1.5 / 0.4)^2\)

\(n = (2.94 / 0.4)^2\)

\(n = 7.35^2\)

n ≈ 54.02

We round up the sample size to the next whole number because we can't have a portion of an observation:

n = 55

Therefore, the time study analyst should prepare for at least 55 observations to estimate the mean time per item with a margin of error of 0.4 minutes and a confidence level of 95.5%.

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Answer:

V shaped graph or absolute value function.

Answer:

The rate is $7.50 per hour.

The unit rate is $7.50 per hour.

This function rule represents the relationship between the number of hours worked (x) and the amount earned (y) at a rate of $7.50 per hour.

Step-by-step explanation:

To find the rate, divide the total amount earned by the number of hours worked. In this case, you earned $45 for 6 hours.

Rate = Total amount earned / Number of hours worked

Rate = $45 / 6 hours

Rate = $7.50 per hour

The rate is $7.50 per hour.

The unit rate refers to the rate per unit of one. In this case, it would be the rate per hour.

Unit Rate = Rate / Number of units

Unit Rate = $7.50 / 1 hour

Unit Rate = $7.50 per hour

The unit rate is $7.50 per hour.

To write a function rule to represent this situation, let's use "x" to represent the number of hours worked and "y" to represent the amount earned:

y = Rate * x

Since the rate is $7.50 per hour, the function rule can be written as:

y = 7.50x

This function rule represents the relationship between the number of hours worked (x) and the amount earned (y) at a rate of $7.50 per hour.

Answer:

Step-by-step explanation:

7.5