Work out the area of a circle with radius of 10cm take pi to be 3.142 and give your answer to 1 decimal place​

The answer is 0.471 radians.

FORMULA:

Just do 27° × π/180 = 0.4712rad but then cut off the two.

By calculating , The value of x we get is  5 as a final resultant.

What is trapezoid ?

A trapezoid is a quadrilateral with two parallel sides, called the "bases," and two non-parallel sides, called the "legs." The parallel sides can have different lengths, and the trapezoid can be either right-angled or oblique. In other words, a trapezoid is a geometric shape that has two parallel sides, two non-parallel sides and four angles.

Since a Trapezoid has 360 Degrees total and since the sides are equal we can say that

180=110+17x-15

70=17x-15

85=17x

x=5

Therefore, By calculating , The value of x we get is 5 as a final resultant.

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a. Expenses: Books and supplies, Housing and food, Tuition and fees, Transportation and Personal expenses. Funding: Savings,

Scholarships, Grants and Student loans.

b. Total estimated expenses are $29,400

(a) Below is an estimate of all her expenses and sources of funding for her 2-year college education.

Expense:

Books and supplies: $1700

Housing and food: $14,020

Tuition and fees: $11,660

Transportation: $2040

Personal expenses: $2980

Funding:

Savings: $7800

Scholarships: $10,240

Grants: $11,600

Student loans: $6200

(b) What is the total of her estimated expenses?

To find the total estimated expenses, we need to add up all the expenses mentioned:

$1700 + $14,020 + $11,660 + $2040 + $2980 = $29,400

Therefore, the total estimated expenses for Nicole's 2-year college education is $29,400.

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Answer:

The suspect possesses 0.4 ounces of cocaine.

Step-by-step explanation:

Mass Units Conversion

The mass can be expressed in several units like grams, kilograms, ounces, pounds, etc. Each unit can be converted to any other multiplying by a fixed number.

The international conventions state that 1 gr = 0.035274 ounces.

If a suspect is in possession of 10 grams of cocaine, its equivalent to ounces can be calculated as 10*0.035274=0.35 oz. Rounding to the nearest tenth it would be 0.4 oz.

Since 1/8 = 0.125 and 1/2 is 0.5, our subject should be charged as a Class C felony

The equation for the line of best fit is: C. y = 0.894x + 0.535.

In order to determine the equation for the line of best fit, we would create a table of values based on the given x-values and y-values as follows;

x          y            x²        y²          xy__

5          4          25        16       20

6          6           36       36       36

9          9           81        81        81

10         11          100       121       110

14          12        196       144      168  

Sum                  438       398     415

Next, we would calculate the mean of the x and y variables as follows;

Mean = [∑(x)]/n

Mean = 44/5

Mean, \(\bar{x}\) = 8.8

Mean = [∑(y)]/n

Mean = 42/5

Mean, \(\bar{y}\) = 8.4

∑(x - \(\bar{x}\))(x - \(\bar{y}\)) = (5-8.8)(4-8.4) + (6-8.8)(6-8.4)+(9-8.8)(9-8.4)+(10-8.8)(11-8.4)+(14-8.8)(12-8.4)

∑(x - \(\bar{x}\))(x - \(\bar{y}\)) =45.4

∑(x - \(\bar{x}\))² = (5-8.8)²+(6-8.8)²+(9-8.8)²+(10-8.8)²+(14-8.8)²

∑(x - \(\bar{x}\))² = 50.8

Now, we can determine the slope coefficient for the line of best fit:

Slope (b) = 45.4/50.8

Slope (b) = 0.894.

Lastly, we would determine the intercept (a) as follows;

\(a = \bar{y} - b\bar{x}\)

a = 8.4 - (0.894)8.8

a = 0.535

Therefore, the required equation is y = 0.894x + 0.535.

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The maximum revenue is $4,000 and 100 units should be manufactured to obtain the maximum revenue.

How to calculate a maximum of a function?

The maximums of a function are detected when the derivative becomes null and changes its sign (passing through 0 from the positive side to the negative side).

According to the given question:

Given function is

r(x) = 80x - 0.4x²

where the revenue r(x) is in dollar and no. unit is x.

We know that if function

y = ax²+bx+c.

Then we get the maximum value of y when x = -b/2a

Here a= -0.4 , b = 80 and c = 0.

Therefore,

x = -80/(2*-0.4)

x = 100

Therefore we get maximum revenue when x = 100.

∴ r(100) = 80.100- 0.4(100)²

             =$4000

Therefore the maximum revenue is $4,000 and 100 units should be manufactured to obtain the maximum revenue.

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Answer:

Option 3

Step-by-step explanation:

Each value of x maps onto one value of y and vice versa.

Answer:

a)73

b)27

c)58

d)70

Answer:

x = 1

y = 9

Step-by-step explanation:

The diagonals of the parallelogram bisect each other. Therefore:

✔️2x + 13 = 15

2x + 13 - 13 = 15 - 13

2x = 2

2x/2 = 2/2

x = 1

✔️5y - 36 = y

5y - 36 - 5y = y - 5y

-36 = -4y

-36/-4 = -4y/-4

9 = y

y = 9

Answer:

57

Step-by-step explanation:

90 - 40% = 57

Answer:

The shoes would be $57

Step-by-step explanation:

To calculate percentage you use the equation:

P% x N = A

Before we use it we convert the number 40 into the tenths place of a decimal, 0.40.

Now we use it!

.40 x 95 = 38

38 would be 40%, so we remove it from the last total aka 95

95 - 38 = 57

Answer:

Where is it?

Step-by-step explanation:

Answer:

Whats the Answer?????????

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The table shows that more Republicans and Democrats do not support the law than do support the law

Answer:

see explanation

Step-by-step explanation:

the sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

a hexagon has 6 sides , then

sum = 180° × (6 - 2) = 180° × 4 = 720°

12

the polygon has 5 sides , so

sum = 180° × (5 - 2) = 180° × 3 = 540°

sum the interior angles and equate to 540

y + 90 + 120 + 90 + 110 = 540

y + 410 = 540 ( subtract 410 from both sides )

y = 130

13

the polygon has 7 sides , so

sum = 180° × (7 - 2) = 180° × 5 = 900°

sum the interior angles and equate to 900

p + 90 + 141 + 130 + 136 + 123 + 140 = 900

p + 760 = 900 ( subtract 760 from both sides )

p = 140

The domain of a quadratic function is (-∞, +∞), and the range depends on the coefficient a and can be [c, +∞) or (-∞, c] depending on the direction of the parabola.

To determine the domain and range of a quadratic function, we consider the characteristics of the function and its graph.

The domain of a quadratic function, represented by the variable x, is the set of all possible input values for which the function is defined. Since quadratic functions are defined for all real numbers, the domain of a quadratic function is (-∞, +∞) or the set of all real numbers.

The range of a quadratic function, represented by the variable y or f(x), is the set of all possible output values that the function can take. For a quadratic function in the form f(x) = ax^2 + bx + c, where a ≠ 0, the range depends on the coefficient a. If a > 0, the parabola opens upward, and the range is [c, +∞). If a < 0, the parabola opens downward, and the range is (-∞, c].

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Answer:

∠ GJK = 102°

Step-by-step explanation:

(2x + 92) and (3x + 63) are same- side interior angles and sum to 180° , so

2x + 92 + 3x + 63 = 180

5x + 155 = 180 ( subtract 155 from both sides )

5x = 25 ( divide both sides by 5 )

x = 5

Then

∠ GJK = 2x + 92 = 2(5) + 92 = 10 + 92 = 102°

The power of 0.95 shows that there is a 95% chance of rejecting the alternative hypothesis of p = 0.16 where the true proportion is actually 0.08. That is if the proportion of users who experience abdominal pain is actually 0.08, then there is a 8% chance of supporting the claim that the proportion of users who experience abdominal pain is more than 0.08.

Given that the alternative value of p is 0.16, it means that the power of the test is 0.95.

This means that if the true proportion of drug users experiencing abdominal pain is indeed 0.16, then by conducting the hypothesis test with a significance level of 0.05, we will correctly reject the null hypothesis and support the claim that more than 8% (0.08) of the drug's users experience abdominal pain with a probability of 0.95.

In other words, the power of 0.95 indicates that the test has a high chance (95%) of correctly detecting a true difference and correctly concluding that the proportion of drug users experiencing abdominal pain is greater than 8% when the true proportion is actually 16%. It demonstrates the test's ability to identify and support the alternative hypothesis when it is true.

It's important to note that the power of the test is influenced by factors such as sample size, significance level, effect size, and variability. In this case, with a power of 0.95, there is a high probability of detecting the claimed difference if it truly exists.

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Flint is starting a business. Before starting to sell anything, he bought fixtures for £1,200, a van for £6,000 and an inventory of goods for £2,800. Although he has paid in full for the fixtures and the van, he still owes £1,600 for some of the inventory. B. Rub lent him £2,500. After the above, Flint has £200 in the business bank account and £175 cash in hand. Total capital is £10,375

What do you mean by capital?

Any employed financial asset might be considered capital. A company's capital is represented on its balance sheet as the earnings from its ongoing operations. The money in a bank account, the proceeds from the sale of stock shares, and the proceeds from the sale of bonds are a few examples.

A factory and its equipment, intellectual property like patents, or the financial assets of a company or a person are all examples of things that provide value or benefit to their owners and fall within the broad definition of capital.

Fixtures= £1,200, van= £6,000, inventory of goods= £2,800, cash =£375

So, Total assets= £10,375

Payable=  £1,600, loan from Rub= £2,500, Balancing figure= £6,275

Total liabilities= £10,375

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Answer:

Step-by-step explanation:

i am working on the assumption that nobody does all three of them

i got 4 because including the people that do swimming and park, the total number of people that do swimming is 22.

the same logic goes for cycling: including the people that do swimming and visit the national park, the total is 23.

so that means that find how many people do swimming and cycling, we have to add the people doing only swimming, with the people doing both swimming and park and then subtract that answer from 22 which gives you 4

Answer: s = 3.7 (rounded 3.67 to the nearest tenth)

Step-by-step explanation:

Surface Area = 81 cm^2

Surface Area of the cube = 6s^2

A = 6s^2

81 = 6s^2

S^2 = 81/6

S = 3.67

Answer:

(1.75,0)

Step-by-step explanation:

The surface area of the vase is 168.4 square inches.

What is a cylinder?

A cylinder is a three-dimensional geometric shape that has two congruent circular bases connected by a curved surface.

The surface area of the cylindrical vase can be found using the formula SA = B + Ph, where B is the area of the base, P is the perimeter of the base, and h is the height of the vase. Since the vase has a circular base, the area of the base can be found using the formula for the area of a circle: B = πr², where r is the radius of the base.

The diameter of the vase is 4.3 inches, so the radius is half of that, or 2.15 inches. The area of the base is therefore:

B = πr² = 3.14 * (2.15)² ≈ 14.46 square inches.

The perimeter of the base is the circumference of the circle, which can be found using the formula C = 2πr:

P = 2πr = 2 * 3.14 * 2.15 ≈ 13.53 inches.

Now we can use the formula SA = B + Ph to find the surface area of the vase:

SA = B + Ph = 14.46 + 13.53 * 11 ≈ 168.39 square inches.

Rounding to the nearest tenth of a square inch, the surface area of the vase is approximately 168.4 square inches.

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Answer:

The total cost of the copies will be $ 15.14.

Step-by-step explanation:

Given that a long year-end status report for work is 134 pages long, and I need to print 16 copies for a meeting next week, to determine how much is the paper going to cost for those reports if paper is sold in reams (500 pages) for $ 3.53 each the following calculation must be performed:

(134 x 16) / 500 = X

2,144 / 500 = X

4.288 = X

500 = 100

144 = X

144 x 100/500 = X

14,400 / 500 = X

28.8 = X

100 = 3.53

28.8 = X

28.8 x 3.53 / 100 = X

101.664 / 100 = X

1.016 = X

1.016 + (3.53 x 4) = X

1.016 + 14.12 = X

15,136 = X

Therefore, the total cost of the copies will be $ 15.14.

Answer:

a= true

b=never

c=true

d=never

e=true

Answer:

c. equal to 80

Step-by-step explanation:

Given that:

The population mean = 80

The standard deviation is = 6

The sample mean = 85

The objective is to find the probability that is less than 85

\(P(X < 85) = P( Z < \dfrac{x-\mu}{\sigma})\)

\(P(X < 85) = P( Z < \dfrac{85-80}{6})\)

\(P(X < 85) = P( Z < \dfrac{5}{6})\)

\(P(X < 85) = P( Z < 0.833)\)

From the standard normal table

P(X <85) = 0.7977

P(X< 85) = 79.77%

P(X< 85) = 80%

Therefore, The adjusted value of the true mean in population S that would result in approximately 80% of parts from that population being given a passing score is:  equal to 80    .

Answer:

its 15

Step-by-step explanation:

Levy is painting a miniature model of a World War II tank. His figure uses a 1:72 scale and is 22.5 cm long. The actual tank is 1620 cm long.

To determine the length of the actual tank, we need to scale up the length of the miniature model using the given scale of 1:72.

Let's denote the length of the actual tank as "x".

According to the scale, 1 cm on the miniature model represents 72 cm on the actual tank.

So, we can set up the following proportion:

1 cm (miniature model) / 72 cm (actual tank) = 22.5 cm (miniature model) / x cm (actual tank)

Cross-multiplying and solving for x, we get:

x = (72 cm * 22.5 cm) / 1 cmx = 1620 cm

The actual tank is 1620 cm long.

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Answer:

Step-by-step explanation:

From the information given:

The joint density of \(y_1\)  and  \(y_2\) is given by:

\(f_{(y_1,y_2)} \left \{ {{y_1+y_2, \ \ 0\ \le \ y_1 \ \le 1 , \ \ 0 \ \ \le y_2 \ \ \le 1} \atop {0, \ \ \ elsewhere \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ } \right.\)

a)To find the marginal density of \(y_1\).

\(f_{y_1} (y_1) = \int \limits ^{\infty}_{-\infty} f_{y_1,y_2} (y_1 >y_2) \ dy_2\)

\(=\int \limits ^{1}_{0}(y_1+y_2)\ dy_2\)

\(=\int \limits ^{1}_{0} \ \ y_1dy_2+ \int \limits ^{1}_{0} \ y_2 dy_2\)

\(= y_1 \ \int \limits ^{1}_{0} dy_2+ \int \limits ^{1}_{0} \ y_2 dy_2\)

\(= y_1[y_2]^1_0 + \bigg [ \dfrac{y_2^2}{2}\bigg]^1_0\)

\(= y_1 [1] + [\dfrac{1}{2}]\)

\(= y_1 + \dfrac{1}{2}\)

i.e.

\(f_{(y_1}(y_1)}= \left \{ {{y_1+\dfrac{1}{2}, \ \ 0\ \ \le \ y_1 \ \le , \ 1} \atop {0, \ \ \ elsewhere \ \\ \ \ \ \ \ \ \ \ } \right.\)

The marginal density of \(y_2\) is:

\(f_{y_1} (y_2) = \int \limits ^{\infty}_{-\infty} fy_1y_1(y_1-y_2) dy_1\)

\(= \int \limits ^1_0 \ y_1 dy_1 + y_2 \int \limits ^1_0 dy_1\)

\(=\bigg[ \dfrac{y_1^2}{2} \bigg]^1_0 + y_2 [y_1]^1_0\)

\(= [ \dfrac{1}{2}] + y_2 [1]\)

\(= y_2 + \dfrac{1}{2}\)

i.e.

\(f_{(y_1}(y_2)}= \left \{ {{y_2+\dfrac{1}{2}, \ \ 0\ \ \le \ y_1 \ \le , \ 1} \atop {0, \ \ \ elsewhere \ \\ \ \ \ \ \ \ \ \ } \right.\)

b)

\(P\bigg[y_1 \ge \dfrac{1}{2}\bigg |y_2 \ge \dfrac{1}{2} \bigg] = \dfrac{P\bigg [y_1 \ge \dfrac{1}{2} . y_2 \ge\dfrac{1}{2} \bigg]}{P\bigg[ y_2 \ge \dfrac{1}{2}\bigg]}\)

\(= \dfrac{\int \limits ^1_{\frac{1}{2}} \int \limits ^1_{\frac{1}{2}} f_{y_1,y_1(y_1-y_2) dy_1dy_2}}{\int \limits ^1_{\frac{1}{2}} fy_1 (y_2) \ dy_2}\)

\(= \dfrac{\int \limits ^1_{\frac{1}{2}} \int \limits ^1_{\frac{1}{2}} (y_1+y_2) \ dy_1 dy_2}{\int \limits ^1_{\frac{1}{2}} (y_2 + \dfrac{1}{2}) \ dy_2}\)

\(= \dfrac{\dfrac{3}{8}}{\dfrac{5}{8}}\)

\(= \dfrac{3}{8}}\times {\dfrac{8}{5}}\)

\(= \dfrac{3}{5}}\)

= 0.6

(c) The required probability is:

\(P(y_2 \ge 0.75 \ y_1 = 0.50) = \dfrac{P(y_2 \ge 0.75 . y_1 =0.50)}{P(y_1 = 0.50)}\)

\(= \dfrac{\int \limits ^1_{0.75} (y_2 +0.50) \ dy_2}{(0.50 + \dfrac{1}{2})}\)

\(= \dfrac{0.34375}{1}\)

= 0.34375