Find the area of a circle with diameter, d = 5.8m. Give your answer rounded to 1 DP.

The man's journey took 43 minutes.

The distance traveled divided by the motion's duration gives the average speed, or vavg. Time is calculated as distance divided by average speed. Time is calculated as distance divided by average speed. distance = v avg 150 kilometers in time 3.2 h = 47 km/h.

Take the start time and subtract the end time.

The man was supposed to arrive at 12:25, but he was 15 minutes late, thus his actual arrival time was 12:40 (12:25 plus 15).

The man's journey began at 11:57, therefore we can calculate how long it took by deducting the start time from the end time.

End time - Start time = Journey time

12:40 - 11:57 = 43 minutes

So, The man's journey took 43 minutes.

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[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{-8})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{-4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-4}-\stackrel{y1}{(-8)}}}{\underset{\textit{\large run}} {\underset{x_2}{6}-\underset{x_1}{(-3)}}} \implies \cfrac{-4 +8}{6 +3} \implies \cfrac{ 4 }{ 9 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-8)}=\stackrel{m}{ \cfrac{ 4 }{ 9 }}(x-\stackrel{x_1}{(-3)}) \implies y +8 = \cfrac{ 4 }{ 9 } ( x +3)[/tex]

The probabilities of the events are

a. 0.43

b. 0.27

c. 0.1161

d. 0.2444.

According to the question,

Statistics classes require a statistical calculator = 43% = 0.43

Statistics classes require a computer that has statistical software = 27% = 0.27

Of the classes that require a statistical calculator, classes also require the use of a computer = 17% = 0.17

a. P(Statistical Calculator)

= 0.43

b. P(Statistical Software)

= 0.27

c. P(Require a Statistical Calculator and Statistical Software)

⇒ (0.43)(0.27)

= 0.1161

d. P(Require a Statistical Calculator GIVEN Require Statistical Software)

⇒ 0.066/0.27

⇒ 0.2444

Hence we can conclude that the probabilities of the events are

a. 0.43

b. 0.27

c. 0.1161

d. 0.2444

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The solution of the trigonometric function sin(x) + 1 = cos(x) in the interval of [0, 2) will be 0.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The trigonometric function is given below.

sin(x) + 1 = cos(x)

Simplify the equation, then we have

sin(x) + 1 = cos(x)

(sin(x) + 1)² = cos² (x)

(sin(x) + 1)² = 1 - sin² (x)

sin² (x) + 2sin x + 1 = 1 - sin² (x)

2sin² (x) = 0

sin (x) = sin 0

x = 0

The solution of the trigonometric function sin(x) + 1 = cos(x) in the interval of [0, 2) will be 0.

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As per the given half life the approximate mass of the sample after 20 hours is 0.03125

The term half life is defined as the interval of time required for one-half of the atomic nuclei of a radioactive sample to decay.

Here we have know that Sean is conducting an experiment with an isotope of a particular element that has a half-life of 4 hours.

And here we also know that he begins with a sample of the isotope with a mass of 92 grams and then measures the mass of the object every hour.

Then the approximate mass of the sample after 20 hours is calculated as,

=> 20/4 = 5

Then the value after 5 hours of time is calculated as,

=> 1/2⁵

=> 0.03125

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Answer:

real

Step-by-step explanation:

-5 is real. It is not complex because it is not in the form a+bi. It also has no imaginary part so it is neither of the other two.

Hope that helps, let me know if you have any other questions!

Answer:

1.26 meters

Step-by-step explanation:

Answer:

[tex]x = 4\sqrt{3}[/tex]

Step-by-step explanation:

[tex]a^{2}+b^{2} =c^{2}[/tex]

[tex]x^{2} + 12^{2} =c^{2}[/tex]

Equilateral --> c = 2x

[tex]x^{2} +144 = (2x)^{2} \\x^{2} +144 = 4x^{2} \\3x^{2} =144\\x^{2} =48\\x=4\sqrt{3}[/tex]

There will be a bias in the data samples in favor of the opinions of a limited subset of the research community.

To find patterns and trends in the broader data set being reviewed, data sampling is a statistical analysis approach that is used to choose, modify, and analyze a representative selection of data points.

a. Under coverage happens when some members of the population are less likely to be selected for the sample or are not eligible for selection. Bias results from under coverage when the "under covered" individuals' differences from the general population have an impact on their responses.

Undercover prejudice may lead to bias in the voluntary response. This suggests you run the risk of obtaining information from a small number of people who are enthusiastic about the research issue. Your data samples will be biased toward the opinions of a tiny subset of your research population as a result.

b. People who don't have a phone number listed in the phone book are probably more worried about privacy issues than the ordinary person. The results would have probably revealed a higher percentage of people who were concerned about privacy if they had been included in the sample.

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So you need 14.58 liters of 80% solution and 10.42 liters of 54% solution. To convert these to grams, you need to multiply by density of the solution.

To obtain 25 liters of a 42% solution, you would need to mix a certain amount of an 80% solution with a certain amount of a 54% solution. To determine the specific amounts, you would need to set up and solve a system of equations.

x + y = 25

(0.8x) + (0.54y) = 0.42(x + y)

x = (0.42*25) / (0.8 + 0.54) = 14.58 liters

y = 25 - x = 10.42 liters

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After clockwise rotation 90°, we obtain vertices of image as (-2, -2), (-3, -6) and (3, -4). Therefore, option D is the correct answer.

Here are the rotation rules: 90° clockwise rotation: (x, y) becomes (y, -x) 90° counterclockwise rotation: (x, y) becomes (-y, x) 180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y).

Given that, triangle LMN with vertices L(2, -2), M(6, -3) and N(4, 3).

After clockwise rotation 90° we get

Here, L(2, -2) →L'(-2, -2)

M(6, -3) →M'(-3, -6)

N(4, 3) →N'(3, -4)

Therefore, option D is the correct answer.

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Nominal scale- A nominal scale is a discrete classification of data, in which data are neither measured nor ordered but subjects are merely allocated to distinct categories.

Measurements on an interval scale have substantial differences between the values. In other words, the disparities between the scale's points are exact and measurable.

Ratio scales are interval scales where lengths are expressed in relation to a rational zero.

Ordinal scale: a scale where data is presented merely in terms of order of magnitude because there is no accepted method for determining differences.

Since there are 5 categories: Blue, Red, Green, Yellow, Orange, so by the above definition we can say that for this question we would use Nominal scale for measurement.

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Answer:

Step-by-step explanation:

An equivalent expression to 9 1/2k - (7 + 31/4k) is 51k/4 +7

The given expression is 9 1/2k - (7 + 31/4k)

This involves the the simplification of the fraction above following the rule of BOADMAS

⇒19k/2 - 7/1 + 13k/4

Simplifying the right hand side of the fraction with parenthesis,

18k/2 - [(28+13k)/4

This fraction gives

*38k - 28+ 13k)/4

Collecting the like terms

= 25k + 28

Therefore the equivalent expression is 25k/1 + 7

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The perimeter of the rectangle with area 174.8m² and side-length 3.8m is equal to 99.6 meters.

Area of the rectangle is equal to 174.8 m².

Length of the rectangle is equal to 3.8 m

let us consider 'w' be the width of the rectangle.

area of the rectangle = length × width

⇒ 174.8 = 3.8 × w

⇒ w = 174.8 / 3.8

⇒ w = 46 m

Perimeter of the rectangle = 2 ( length + width )

⇒ Perimeter of the rectangle = 2 ( 3.8 + 46 )

⇒ Perimeter of the rectangle = 2 ( 49.8 )

⇒Perimeter of the rectangle = 99.6 meter.

Therefore, the perimeter of the rectangle with length 3.8m and width 46m is equal to 99.6m.

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The grams of potatoes that still need to be peeled is equal to 301 grams.

In this exercise, we would determine the total weight of the bag of potatoes in grams:

Note: 1,000 grams is equal to 1 kilogram.

Total weight of the bag of potatoes = 4 kilograms + 500 grams

Total weight of the bag of potatoes = 4,000 grams + 500 grams

Total weight of the bag of potatoes = 4,500 grams.

For the total weight of peeled potatoes, we have the following:

Total weight of peeled potatoes = 1,841 grams + 2,358 grams

Total weight of peeled potatoes = 1,841 + 2,358

Total weight of peeled potatoes = 4,199 grams.

Now, we can determine the weight of the unpeeled potatoes:

Weight of the unpeeled potatoes = 4,500 grams - 4,199 grams.

Weight of the unpeeled potatoes = 301 grams.

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The length of the strawberry lace Lucy has is 36cm, and she needs a piece 18mm long for her cake decoration.

To calculate how many pieces of the strawberry lace she needs, we must convert the measurements from centimeters to millimeters.

We can do this by multiplying 36 centimeters by 100 to get the length of the lace in millimeters (36 cm x 100 = 3600 mm). We then divide this number by the length of the desired piece (3600 mm / 18 mm = 200). Therefore, Lucy needs 200 pieces of 18mm long strawberry lace to decorate her cake.

To summarize, the formula used to calculate the number of pieces Lucy needs is:

(Length of lace in millimeters) / (Length of desired piece in millimeters) = Number of pieces needed.

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The Probability Distribution of X is P(X = k) = (4 choose k) * (0.75)^k * (0.25)^(4-k) and there is no evidence to suggest that the manager's claim is false.

a. The probability distribution for X can be found using the binomial distribution, since the number of customers who get their meal in less than 7 minutes is a count of the number of successes in a fixed number of independent trials, each with the same probability of success. The probability distribution for X is given by:

P(X = k) = (4 choose k) * (0.75)^k * (0.25)^(4-k)

where k = 0, 1, 2, 3, or 4, and (4 choose k) is the number of combinations of 4 items taken k at a time.

b. The probability of observing exactly 0 customers getting their meal in less than 7 minutes is P(X = 0) = (0.25)^4 = 0.390625. This is a low probability, but it is still possible to observe 0 customers getting their meal in less than 7 minutes, even if the manager's claim is true. Therefore, observing 0 customers getting their meal in less than 7 minutes does not provide any evidence to suggest that the manager's claim is false.

The complete question is:

The Cornbread Cafe in Eugene, Oregon, recently installed a new computer system that allows customers to order their meals electronically from their tables. The manager of the restaurant claims that this new system will decrease the waiting time, and that the probability of getting a meal in less than 7 minutes (with this system in place) is 0.75. Suppose four customers are selected at random. Let the random variable X be the number of customers who get their meal in less than 7 minutes. (a) Find the probability distribution for X. (b) Suppose none of the four customers gets the meal in less than 7 minutes. Is there any evidence to suggest that the manager's claim is false? Justify your answer.

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Answer: t=2

Step-by-step explanation:

-4t+14= -9t+24

+9t     =+9t

5t+14=24

    -14=-14

5t=10

5t/5       10/5

t=2

The plant's growth over 6 weeks is described as the increasing of plant volume and/or mass with or without formation of new structures such as organs, tissues, cells or cell organelles.

The term volume in math is called as a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface.

Here we need to describe the plant's growth over 6 weeks.

As we know that the stages that plants go through are from seed to sprout, then through vegetative, budding, flowering, and ripening stages.

On the other hand the nutritional needs of people and plants change as they grow.

Then the main stages in the life cycle of a plant are seed germination, seedling formation, growth, development and differentiation leading to a mature plant, pollination and fertilizations and the formation of fruit and seeds.

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Answer: h(x) = 3x

Step-by-step explanation:

The height of a toy bunny, h(x), is directly proportional to the length of the carrot, x. The given information is that the height of the bunny is three times the length of the carrot. Therefore, the equation for the function h(x) would be the answer above.

Answer:

h(x) = 3x

I'm so cool w/ my fashionista lipstick! :D

If her average rate was 20 miles per hour faster on the trip home, Amy live 480 miles far from the mountains

Suppose Amy lives x miles from the mountains.

Fill in x as both distances and the times

going and coming 12 hours and 8 hours.  

Distance         |  speed | time

To mountains |    x        |   8

Coming home  |    x      |   5

Use: speed =distance/ time

to fill in the two rate boxes:

                         Distance | Speed | time

To mountains |          x     |  x/12  |  8

Coming home  |    x         |  x/8  |  5

The equation comes from this sentence:

Her average rate was 20 miles per hour faster on the trip home

Her speed coming home late = Her speed going to the mountains + 20 miles per hour

x/8 = x/12+20

20 = x/8-x/12

20 = x/24

x = 24×20

x = 480

So Amy lives 480 miles from the mountains.

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The unknown side of a right-angled triangle can be located using Pythagoras' theorem.Answer is 43.19 cm

The unknown side of a right-angled triangle can be located using Pythagoras' theorem.Using the formula c2 = a2 + b2—where "c" stands for the hypotenuse and "a" and "b" are the two legs—it is possible to determine the third side of a right-angled triangle if the two other sides are provided as 4 and 6 units, respectively.

The sum of the squares on the shorter two sides of a right triangle equals the length of its longest side.

A2 + B2 = C2 is a formula that illustrates this.

Use the phytagorean theorem for this problem:

C= √a²+b²

C = hypotenuse = distance between the centers of the two gears

A = one side of the chain attaching the gears

= 43cm

B = the difference of the radii = (8 - 4) = 4

√43² +(8 - 4) ²

= 43.1856

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Since angle y and angle x form vertical angles, the measure of angle x is equal to 50°.

In Geometry, the vertical angles theorem is also referred to as vertically opposite angles theorem and it states that two (2) opposite vertical angles that are formed whenever two (2) lines intersect each other are always congruent, which simply means being equal to each other.

Furthermore, the sum of the angles on a straight line is equal to 180. Therefore, we would sum up all of the angles as follows;

60° + 70° + y = 180°

130° + y = 180°

y = 180° - 130°

y = 50°

Since both angle x and angle y are vertical angles, we can logically deduce that they are congruent and as such the magnitude of angle x is equal to 50°.

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Liam started with $12 amount in his wallet and ended up with $4 after spending $5 on ice cream, $8 on a movie ticket, and $3 on candy.

Total: $16

Liam has $4 amount left in his wallet.

1. Start by adding up the amount that Liam spent:

Ice Cream: $5

Movie Ticket: $8

Candy: $3

Total Spent: $16

2. Subtract the total amount spent from the amount Liam started with:

Initial Amount: $12

Total Spent: $16

Remaining Amount = Initial Amount - Total Spent

Remaining Amount = $12 - $16

Remaining Amount = -$4

Since the result is negative, this means that Liam has spent more than he started with and now has $4 left in his wallet.

Liam started with $12 in his wallet and ended up with $4 after spending $5 on ice cream, $8 on a movie ticket, and $3 on candy.

The complete question is:

Liam started with $12 in his wallet. He kept track of the amount he gained and pent throughout the day, as shown in The table below.

Expense | Amount

Ice Cream | $5

Movie Ticket | $8

Candy | $3

What is the amount of money Liam has left in his wallet?

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It is recommended to model the data in the tables using a ilnear or exponential function.

The exponential function will be the best model for tigers.

The optimal model for narwhals will be a linear function.

Test for vertical lines:

A vertical line test can be used to determine whether an expression is a function or not. In this test, we look for a single image of x and determine whether we receive one or many images.

It won't be a function if we receive more photographs.

For illustration, use y2 = 4ax.

y = ±√4ax

We receive two values of y for a single value of x.

Consequently, it won't be a function.

Due to that,

There are two data sets for the numbers of tigers and narwhals.

first gather tiger info,

Let's see if it satisfies the requirement for a linear function or not.

y = mx + c

x = 0, y = 1204

1204 = m0 + c

c = 1204

y = mx + 12-04

when y = 1050 and x = 3

1050 = 3m + 1205

m = -155/3

If a linear relationship exists,

Therefore, y should be 902 for x = 6.

However, is not the same as 902.

So, for this dataset exponential function will be best.

Similarly, we can check for the second dataset.

And it will satisfy the all the conditions of linear function.

So, for the Narwhals linear function is best model.

Complete question:

The populations of Siberian tigers and narwhals since 1990 are represented by the following tables:

Determine whether the data described in the tables is best modeled by a linear function or an exponential function.

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Answer: 83000

Step-by-step explanation:

There are 32.1 pounds of meat.

Addition is an operation used in math to add numbers. The result that is obtained after addition is known as the sum of the given numbers. The addition symbol is one of the widely used math symbols. The addition symbol consists of one horizontal line and one vertical line. It is also known as the addition sign or the plus sign (+). The addition formula is the statement that shows an addition fact and is expressed as, addend + addend = sum. This can be understood with the help of the example shown in the figure given below. While adding numbers, if the sum of the addends is greater than 9 in any of the columns, we regroup this sum into tens and ones. Then we carry over the tens digit of the sum to the preceding column and write the ones digit of the sum in that particular column. In other words, we write only the number in 'ones place digit' in that particular column, while taking the 'tens place digit' to the column to the immediate left.

Add up the pounds of meat.

7.75 + 17.85 + 6.5 = 32.1 pounds

Thus, there are 32.1 pounds of meat.

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Using the digits 7,8 and 9, the positive seven-digit integers can be made that are palindromes are 729.

When constructing a seven-digit palindrome out of the digits 7, 8, and 9, the first three digits must be the same as the last three digits in reverse order.

This means that each of the first three digits can be either a 7, 8, or 9. Therefore, the total number of combinations for the first three digits is 3 x 3 x 3 = 27.

Since the last three digits must match the first three, the total number of possible combinations of integers is 27 x 27 = 729.

Thus, the total number of positive seven-digit palindromes that can be created using the digits 7, 8 and 9 is 729.

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