The diagram shows a circle inside a square.

Work out the area of the circle.
16 cm
Optional working

The 90% confidence interval for the population proportion of adults who made a New Year's resolution is approximately 0.523 to 0.554, while the 95% confidence interval is approximately 0.517 to 0.559.

To construct 90% and 95% confidence intervals for the population proportion based on the survey results of 1220 adults who made a New Year's resolution out of a total of 2267 adults, we can use the formula for confidence intervals for a proportion.

Calculate the sample proportion:

The sample proportion is the number of individuals who made a New Year's resolution divided by the total sample size.

Sample proportion [tex]\hat{p}[/tex]  = 1220 / 2267 = 0.5386

Determine the standard error:

The standard error measures the variability of the sample proportion and is calculated using the formula:

Standard error[tex](SE) = \sqrt{((\hat{p } \times (1 - \hat{p})) / n) }[/tex]

where n is the sample size.

Calculate the margin of error:

The margin of error represents the range within which the true population proportion is likely to fall.

It depends on the desired level of confidence and is calculated by multiplying the standard error by the appropriate critical value from the standard normal distribution.

For a 90% confidence interval, the critical value is 1.645.

For a 95% confidence interval, the critical value is 1.96.

Margin of error = Critical value [tex]\times[/tex] Standard error

Construct the confidence intervals:

The confidence interval is calculated by adding and subtracting the margin of error from the sample proportion.

For the 90% confidence interval: [tex]\hat{p}[/tex] ± Margin of error

For the 95% confidence interval: [tex]\hat{p}[/tex]  ± Margin of error

Using these steps and the provided information, we can construct the confidence intervals for the population proportion.

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A. The function f is injective.

B. The function f is not surjective, as there are values in Q (e.g., y = 1) for which there is no corresponding x ∈ N.

To prove that the function f is injective, we need to show that if f(x) = f(y), then x = y.

Let f(x) = f(y). Then we have:

x / (1 + x) = y / (1 + y)

Cross-multiplying, we get:

x(1 + y) = y(1 + x)

x + xy = y + xy

Now, subtract xy from both sides:

x = y

Since x = y when f(x) = f(y), we can conclude that the function f is injective.

(b) To prove or disprove that the function f is surjective, we need to determine whether for every y ∈ Q, there exists an x ∈ N such that f(x) = y.

Consider the case where y = 1/2. We need to find x ∈ N such that:

f(x) = x / (1 + x) = 1/2

Cross-multiplying, we get:

2x = 1 + x

Subtract x from both sides:

x = 1

In this case, there exists an x ∈ N (x = 1) such that f(x) = 1/2. However, we need to consider all y ∈ Q. Let's try another case.

Consider the case where y = 1. There is no x ∈ N that satisfies the following equation:

f(x) = x / (1 + x) = 1

Cross-multiplying, we get:

x = 1 + x

Subtract x from both sides:

0 = 1

This is a contradiction, so there is no x ∈ N such that f(x) = 1. Therefore, the function f is not surjective, as there are values in Q (e.g., y = 1) for which there is no corresponding x ∈ N.

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The test statistic is given as follows:

t = 2.52.

We have the standard deviation for the sample, thus, the t-distribution is used. The test statistic is given by the equation presented as follows:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

In which:

The parameters for this problem are given as follows:

[tex]\overline{x} = 0.3, \mu = 0, s = 0.8, n = 45[/tex]

Hence the test statistic is given as follows:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{0.3 - 0}{\frac{0.8}{\sqrt{45}}}[/tex]

t = 2.52.

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Using a t-distribution with 21 degrees of freedom (since n-1 = 22-1 = 21), and a 95% confidence level, we can find the critical value from a t-table or calculator.

The critical value is ±2.080.

Rounded to three decimal places, the critical value is 2.080.

Sorry for bad handwriting

if i was helpful Brainliests my answer ^_^

259.25π in² is the surface area of the cone

The surface area of a cone can be calculated using the formula SA = πr² + πrl

where r is the radius and l is the slant height.

Given that the diameter is 17 inches, the radius (r) is half of the diameter, which is 17/2 = 8.5 inches.

The slant height (l) is given as 22 inches.

Substituting these values into the formula:

Surface Area = π(8.5)² + π(8.5)(22)

= 72.25π + 187π

= 259.25π

Therefore, the surface area of the cone is 259.25π in²

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Answer:

5/12

Step-by-step explanation:

Since Julia has 12 different flowers and we know she has 5 roses

we can turn it into a fraction which will be 5/12.'

The simplified form of the expression 3 1/5x + 10 7/9 - 2 2/5x - 10 8/9 is 4/5x - 1/9.

To simplify the expression: 3 1/5x + 10 7/9 - 2 2/5x - 10 8/9, we need to perform the addition and subtraction of the terms.

First, let's focus on the x terms: 3 1/5x - 2 2/5x.

The whole numbers can be treated as fractions with a denominator of 1. Thus, we have:

(3 1/5)x - (2 2/5)x.

To perform the subtraction, we need to find a common denominator for the fractions involved, which is 5.

(3 1/5)x - (2 2/5)x = (16/5)x - (12/5)x.

Now we can subtract the terms:

(16/5)x - (12/5)x = (16 - 12)/5x.

Simplifying further:

4/5x.

Now let's simplify the whole number and fraction terms: 10 7/9 - 10 8/9.

10 - 10 = 0.

The fraction terms can be simplified by finding a common denominator, which is 9:

(7/9) - (8/9) = (-1/9).

Now we can combine all the simplified terms:

3 1/5x + 10 7/9 - 2 2/5x - 10 8/9

= (4/5x) + 0 + (-1/9)

= 4/5x - 1/9.

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The volume of the oblique rectangular prism that is given above would be = 212.4

To calculate the volume of the oblique rectangular prism, the formula for the volume of a prism should be used which is given below. That is;

Volume of prism= L×w×h

where;

Length = 9

width = 4

height = ?

But the height of the oblique rectangular prism can be calculated using the sine formula;

That is;

height = 8× 0.7314

= 5.9

Therefore volume = 9×4×5.9 = 212.4

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The period of the trigonometric function in this problem is given as follows:

A) 540º.

The standard definition of the sine function is given as follows:

y = Asin(B(x - C)) + D.

For the tangent function, we have that it is similar to the sine function, that we use tan() instead of sin().

For which the parameters are given as follows:

The coefficient B for the equation is given as follows:

B = 2/3.

Hence the period of the function is given as follows:

2π/(2/3) = 3π = 540º.

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The bisector of angle RQP is angle PQT and angle RQT, both angles are equal and their sum is equal to angle RQP.

Angle bisector or a bisector angle is a type of angle obtained after dividing the initial angle into two equal parts.

The bisected angle can be obtained using a pair of compass and a pencil attached to it.

To bisect the given angle RQP; we will take the following steps;

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Paul will spend $1,382.4 constructing the patio.

Looking at the design, we can see that the length of the patio is represented by 8 cm, and the width is represented by 6.4 cm. To convert these measurements to feet, we multiply them by the scale factor:

Length = 8 cm * 3 ft/cm = 24 ft

Width = 6.4 cm * 3 ft/cm = 19.2 ft

The area of the patio is calculated by multiplying the length and width:

Area = Length * Width = 24 ft * 19.2 ft = 460.8 ft²

The cost to construct the patio is $3 per square foot. Therefore, Paul will spend:

Cost = Area * Cost per square foot = 460.8 ft² * $3/ft² = $1,382.4

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Answer:

Impossible

Step-by-step explanation: if a cube is number from 1-6 theirs no chance of getting a number less than 1.

The expression  3m³np⁶  is a monomial

A monomial is an algebraic expression that consists of only one term.

In this case, the expression 3m³np⁶ has a single term as it is the product of constants (3), variables (m, n), and their exponents (3, 1, and 6).

Therefore, it meets the criteria of a monomial.

Hence, the expression  3m³np⁶  is a monomial

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The rule for (f - g)(x) is (f - g)(x) = 2x² - 11x - 3 and the value of (f - g)(-2) is 27

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

f(x) = 2x² - 3x + 4

g(x) = 8x + 7

The rule for (f - g)(x) is calculated as

(f - g)(x) = f(x) - g(x)

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

(f - g)(x) = 2x² - 3x + 4 - 8x - 7

So, we have

(f - g)(x) = 2x² - 11x - 3

Here, we have

x = -2

Substitute the known values in the (f - g)(x) = 2x² - 11x - 3, so, we have the following representation

(f - g)(-2) = 2(-2)² - 11(-2) - 3

Evaluate

(f - g)(-2) = 27

Hence, the value of (f - g)(-2) is 27

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The phase shift of the trigonometric function is given as follows:

D) 90º to the left.

The standard definition of the sine function is given as follows:

y = Asin(B(x - C)) + D.

For the cosine function, we have the same definition, we only use cos() instead of sin().

For which the parameters are given as follows:

For this problem, we have that the phase shift is of C = 90. As we are adding inside of the domain of the function, the phase shift is to the left.

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Answer:

$2.25

Step-by-step explanation:

Red: $2

Blue: $6

Green: $6 + $5 (original cost of game) = $11

Yellow: $20

The total number of slots on the spinner is 4, with one slot for each color. Since the spinner can land on any color with equal probability, the probability of it landing on each color is 1/4 or 0.25.

Therefore, the expected value of the game is:

(0.25 x $2) + (0.25 x $6) + (0.25 x $11) + (0.25 x $20) - $5 = $2.25

The width of the rectangle is 13 cm and the dimension is 26 cm x 13 cm

Given data ,

Let the length be L and width be W

Now , the width is 1/2 of the length, so we can write:

W = (1/2)L

The area of a rectangle is given by the formula:

Area = Length x Width

Given that the area is 338 square centimeters, we can write:

338 = L × W

Substituting W with (1/2)L, we have:

338 = L × (1/2)L

To solve this equation, we can multiply both sides by 2 to eliminate the fraction:

676 = L²

Taking the square root of both sides, we find:

L = √676

L = 26

So the length of the rectangle is 26 centimeters.

Substituting this value back into the equation for the width, we have:

W = (1/2)L

W = (1/2)(26)

W = 13

Hence , the dimensions of the rectangle are length = 26 centimeters and width = 13 centimeters

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The experimental probability of the computer generating a 3 or a 5 is given as follows:

20%.

The parameters that are needed to calculate a probability are given as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

The total number of outcomes in the table is given as follows:

90.

The desired number of outcomes is given as follows:

10 + 8 = 18.

Hence the experimental probability is given as follows:

p = 18/90 = 0.2 = 20%.

The problem is given by the image presented at the end of the answer.

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[tex]2x^2=-8\\x^2=-4[/tex]

No real solutions.

Complex solutions:

[tex]x=\sqrt{-4} \vee x=-\sqrt{-4}\\x=2i \vee x=-2i[/tex]

Answer:

4/15 square unit (0.2667 rounded)

Step-by-step explanation:

The whole square is one square as

((1/10) x 10 (columns)) multiplied by ((1/3) x 3 (rows)) = 1 multiplied by 1 = 1.

So, with that, the area of the striped rectangles should be:

(1/10) x 4 (columns in the striped area of rects) multiplied by (1/3) x 2 (rows in the striped area of rects) = 0.4 multiplied by 2/3 = 4/15 square unit.

The maximum error of the midpoint approximation is 0.55.

To estimate the maximum error, we can consider the worst-case scenario by assuming that the second derivative is at its maximum value throughout the interval [11, 31]. In this case, we can use the largest possible value for M.

To find the maximum error of the midpoint approximation, we need to determine the width of the interval and divide it by 2.

Width of the interval = upper bound - lower bound = 10.5 - 9.4 = 1.1

Maximum error (E) = (Width of the interval) / 2 = 1.1 / 2 = 0.55

Therefore, the maximum error of the midpoint approximation is 0.55.

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The pairs of coordinates arranged from least to greatest based on the differences between the points are:

(-1,-2) and (1,-4)

(4,1) and (2,2)

(-5,2) and (-3,-2)

(3,-4) and (-2,1)

(5,-2) and (-1,-1)

Let's calculate the differences and arrange the pairs accordingly:

(4,1) and (2,2):

Difference in x-coordinates: 4 - 2 = 2

Difference in y-coordinates: 1 - 2 = -1

(-5,2) and (-3,-2):

Difference in x-coordinates: -5 - (-3) = -2

Difference in y-coordinates: 2 - (-2) = 4

(3,-4) and (-2,1):

Difference in x-coordinates: 3 - (-2) = 5

Difference in y-coordinates: -4 - 1 = -5

(-1,-2) and (1,-4):

Difference in x-coordinates: -1 - 1 = -2

Difference in y-coordinates: -2 - (-4) = 2

(5,-2) and (-1,-1):

Difference in x-coordinates: 5 - (-1) = 6

Difference in y-coordinates: -2 - (-1) = -1

Now let's arrange them in order from least to greatest based on the differences in the points:

(3,-4) and (-2,1) (difference: 5)

(-1,-2) and (1,-4) (difference: 2)

(4,1) and (2,2) (difference: 2)

(-5,2) and (-3,-2) (difference: 4)

(5,-2) and (-1,-1) (difference: 6)

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The final volume of the gas is 8 litres when the pressure is 55 kilo pascals.

Boyle's law simply states that "the volume of any given quantity of gas is inversely proportional to its pressure as long as temperature remains constant.

Boyle's law is expressed as;

P₁V₁ = P₂V₂

Where P₁ is Initial Pressure, V₁ is Initial volume, P₂ is Final Pressure and V₂ is Final volume.

Given that:

Plug the given values into the above formula and solve for the final volume:

88 kPa × 5L = 55 kPa × V₂

V₂ = 440 / 55

V₂ = 8 L

Therefore, the final volume is 8 litres.

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Answer:

Step-by-step explanation:

x° + 2x° + 9° = 180°

3x° + 9° = 180°

x° + 3° = 60°

x = 57°

Answer: when the value of the dollar decreases, also when demand is high.

Step-by-step explanation: economics

Answer:

hello

the answer is:

Sin B = CA/AB ----> Sin 65° = 5/AB ----> 0.906 = 5/AB

----> AB = 5.51

The slope and y-intercept include the following:

Slope = 2.

y-intercept = -1.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + b

Where:

Based on the information provided above, we have the linear equation:

-6x + 3y =-3

By making y the subject of formula, we have:

3y = 6x - 3

y = 2x - 1

By comparison, the slope and the y-intercept include the following:

Slope, m = 2.

y-intercept, b = -1.

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The three statements about the measures of center that are true include the following:

A. The mean for Group A is less than the mean for Group B.

B. The median for Group A is less than the median for Group B.

C. The mode for Group A is less than the mode for Group B.

In Mathematics and Geometry, the mean for this set of data can be calculated by using the following formula:

Mean = [F(x)]/n

Group A

Mean for Group A = [(1 × 5) + (2 × 4) + (3 × 1)]/(5 + 4 + 1)

Mean for Group A = (5 + 8 + 3)/10

Mean for Group A = 16/10

Mean for Group A = 1.6

Mode for Group A = 1

Median for Group A = (1 + 2)/2

Median for Group A = 3/2

Median for Group A = 1.5

Group B

Mean for Group A = [(1 × 3) + (2 × 2) + (3 × 4) + (5 × 1)]/(3 + 2 + 4 + 1)

Mean for Group A = (3 + 4 + 12 + 5)/10

Mean for Group A = 24/10

Mean for Group A = 2.4

Mode for Group B = 3

Median for Group B = (2 + 3)/2

Median for Group B = 5/2

Median for Group B = 2.5

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer: A,B,C

Step-by-step explanation: