A circular cake has radius 12 cm and height 7 cm. The uniform cross-section of a slice of the cake is a sector with angle 22°. The top and the curved surface of the slice, shaded in the diagram, are covered with chocolate. Calculate the area of the slice which is covered with chocolate.

Answer:

f(x)=3x+5

Step-by-step explanation:

just plus 5 when moving up, mines 5 when moving down

Please give brilianst!!!!

Thank you

Answer:

Gradient = 2

Step-by-step explanation:

Gradient of a line = Slope of the line

Since, slope of a line passing through two points \((x_1, y_1)\) and \((x_2,y_2)\) is given by,

Slope = \(\frac{y_2-y_1}{x_2-x_1}\)

Given line in the graph passes through two points (1, 0) and (2, 2)

Therefore, slope or gradient of the line = \(\frac{2-0}{2-1}\)

                                                                  = 2

Gradient = 2 will be the answer.

Answer:

continuous it is continuous

Answer:

1/4

Step-by-step explanation:

Hope this helps.

Answer:

The remaining is 75%, the length of the stick would be 1.2

Step-by-step explanation:

According to the information given,

We know that Brian cut off 25% of a stick which was 1.6 meters long

and 1.6 is the 100% of the stick:

It is fairly easy to calculate this, subtract 25 from 100 ( 100 - 25 ), which is equal to 75.

Hence, the answer is 75% and 1.2 for the remaining length of the stick

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Answer:

3 yards

Step-by-step explanation:

8 1/2 - 2 1/2 = 6

6 - 3 = 3

Your answer is 3.

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(A) The range and IQR for boxplot 1 is 10 and 6 respectively.

(B) The range and IQR for boxplot 2 is 12 and 7 respectively.

The interquartile range defines the difference between the third and the first quartile.

The formula for the interquartile range is given below.

Interquartile range = Upper Quartile – Lower Quartile = Q­3 – Q­1

The range is the difference between the lowest and highest values.

The formula for the interquartile range is given below.

Range = Maximum – Minimum

(A) For boxplot 1, we need to find the range and IQR from the given data set.

So, let 34 be the maximum and 24 be the minimum.

\(\text{Range}=\sf 34-24\)

\(\text{Range}=\sf10\)

Therefore, the range is 10.

Now time to find the IQR.

So, let 33 be Q3 and 27 be Q1.

\(\text{IQR}=\sf 33-27\)

\(\text{IQR}=\sf 6\)

Therefore, the IQR is 6.

(B) Now for boxplot 2, we will do the same thing as from part A.

Let's find the range.

So, let 24 be the maximum and 12 be the minimum.

\(\text{Range}=\sf 24-12\)

\(\text{Range}=\sf12\)

Hence, the range is 12.

Now for the IQR.

So, let 22 be Q3 and 15 be Q1.

\(\text{IQR}=\sf 22-15\)

\(\text{IQR}=\sf 7\)

Hence, the IQR is 7.

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The volume of the cylinder is 113.143 cubic cm

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

Diameter = 6 cm

Height = 4 cm

Using the above as a guide, we have the following:

r = 6/2 = 3

h = 4

So, we have

V = pi r^2h

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

V = 22/7 * 3^2 * 4

Evaluate

V = 113.143

Hence, the volume is 113.143 cubic cm

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The least common multiple LCM of 5/12 and 7/16 is 35/16 or 2 whole number 3/16 expressed as a mixed fraction.

The least common multiple also called LCM of two numbers is the smallest positive integer that is divisible by both numbers.

5/12 = 1/2 × 1/2 × 1/3 × 5 {expressed as product of its prime factors}

7/16 = 1/2 × 1/2 × 1/2 × 1/2 × 7 {expressed as product of its prime factors}

so their least common multiple is calculated as;

LCM = 1/2 × 1/2 × 1/2 × 1/2 × 5 × 7

LCM = 35/16

Therefore, the LCM of 5/12 and 7/16 is the fraction 35/16 or expressed as 2 whole number 3/16.

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9514 1404 393

Answer:

  A, B

Step-by-step explanation:

The equation is equivalent to ...

  cos(x -π/7) = -(√2)/2

  x -π/7 = arccos(-(√2)/2) = {3π/4, 5π/4} . . . . . cosine is negative in QII and QIII

  x = {3π/4 +π/7, 5π/4 +π/7} +2nπ . . . . . matches A and B

The value of angle C in given quadrilateral ABCD is 107⁰.

The measure of angle C is calculated by applying the following rule of geometry for a quadrilateral as shown below.

Angle A + Angle C = 180 (opposite angles of a quadrilateral are supplementary).

We know the value of angle A, and we are to find the value of angle C as shown below.

C + (2x + 3) = 180

C = 180 - 2x - 3 ------- (1)

Using the knowledge of sum of angles in a quadrilateral, we will calculate the value of x:

A + B + C + D = 360

2x + 3 + 2x - 4 + (180 - 2x - 3) + 3x + 9 = 360

5x + 185 = 360

5x = 175

x = 175/5

x = 35

Angle C = 180 - 2x - 3

= 180 - 2(35) - 3

= 180 - 73

= 107⁰

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Answer:

201.088 cubic units

Step-by-step explanation:

Given data

height= 12 units

radius= 4 units

The expression for the volume of a cone is given as

Volume = 1/3*πr^2h

Substitute the given data to find the volume of the cone

Volunme= 1/3* 3.142* 4^2* 12

Volume = 1/3* 3.142* 16*12

Volume= 1/3* 603.264

Volume= 201.088 cubic units

Answer:

slope intercept form: y= -6x+3

point slope form: y-0= -6(x -1/2)

Step-by-step explanation:

point slope form: y - y1 = m(x - x1)

substitute the values  y-0=-6(x-1/2)

slope intercept form:

find the slope using two given points

m = (y2 - y1) / (x2 - x1)

= (3 - 0) / (0 - 1/2)

= 3 / (-1/2)

= -6

substitute into equation

y= -6x+3

Answer:

6 + 3e

Step-by-step explanation:

The expression in the mathematical form will be 6 + 3e.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

Three times the sum of 2 and e. Then the expression in the mathematical form will be

The sum of 2 and e will be

⇒ 2 + e

Then the three times the sum of 2 and e will be

⇒ 3(2 + e)

⇒ 6 + 3e

The expression in the mathematical form will be 6 + 3e.

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Answer: cos4

Step-by-step explanation: 50 meters

B. 50-√3 meters

C. 100 meters

D. 100-√3 meters

40. What expression is used to answer: "A 4-m tall man stands on horizontal ground 43 m from a tree.

The angle of depression from the top of the tree to his eyes is 22°. Estimate the height of the tree."

A. sin 22

B. cos 22

C. tan 22

D. cot 22

Answer:

y=6x-8

Step-by-step explanation:

y=2(x-8)+4x

y=2x+4x-8, y=6x-8

Answer:

Step-by-step explanation:

Observe that \(y^6-64=y^6-2^6.\)

And you factor out using this expression:

\((a^6-b^6)=(a-b)(a^5+a^4b+a^3b^2+a^2b^3+ab^4+b^5)\)

Take a=y and b=2.

Answer:

(y - 2)(y + 2)(\(y^{4}\) + 4y + 16)

Step-by-step explanation:

\(y^{6}\) - 64 ← is a difference of cubes and factors in general as

a³ - b³ = (a - b)(a² + ab + b²) , then

\(y^{6}\) - 64

= (y² )³ - 4³

= (y² - 4)(\(y^{4}\) + 4y + 16) ← note y² - 4 is a difference of squares

= (y - 2)(y + 2)(\(y^{4}\) + 4y + 16)

A study based on a population sample that includes 2000 respondents would be the most reliable out of the given options.

In statistical analysis, the reliability of a study depends on the representativeness and size of the sample.

A larger sample size generally provides more reliable results as it reduces the sampling error and increases the precision of the estimates.

Given that the population contains 20,000 people, we need to consider which number of respondents would yield the most reliable study.

Option A: 200 respondents

This represents only 1% of the population.

While it is better than having just 2 respondents, it may not be sufficient to accurately capture the characteristics of the entire population.

Option B: 20 respondents

This represents only 0.1% of the population.

With such a small sample size, the study would likely suffer from a high sampling error and may not provide reliable results.

Option C: 2000 respondents

This represents 10% of the population.

While it is a larger sample size compared to the previous options, it still only captures a fraction of the population.

The study may provide reasonably reliable results, but there is room for potential sampling error.

Option D: 2 respondents

This represents an extremely small sample size, accounting for only 0.01% of the population.

With such a small sample, the study would be highly susceptible to sampling bias and would likely yield unreliable results.

Based on the options provided, option C with 2000 respondents would be the most reliable study.

Although it does not include the entire population, a sample size of 2000 respondents provides a larger representation of the population and reduces the potential for sampling error.

However, it's important to note that the reliability of a study depends not only on sample size but also on the sampling method, data collection techniques, and other factors that ensure representativeness.

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Answer:

60 miles

Step-by-step explanation:

Since 1 inch on the map equals 20 miles, you just have to multiply 3 by 20.

3x20=60

The solution for all three is mathematically given as

Generally, the equation for students taking only PE and not Bio and Eng is  mathematically given as

P(PBE)= 28 – (5+6+4)

= 28 - 15

= 13

Students taking only Bio and not PE and Eng

P(BP)= 31 – (5+4+2)

= 31 - 11

= 20  

Students who are merely studying English and are not also taking Bio and PE

P(EP)= 42 – (6+4+2)

= 42 - 12

= 30  

Now, students who have taken three different classes

P(3)= 100 - ( 13 + 5 + 4 + 20 + 2 + 30 + 6 )

= 100 - 80

= 20

In conclusion, Students who have taken BIO and PE but not ENG will get a = 5 for their efforts.

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Answer:

After 4 weeks: $45, After w weeks: 5w + 25

Step-by-step explanation:

5 per week is 20 for 4 weeks. $25 + $20 = $45.

5w is 5 times the week. +25 because he had 25 to begin with. 5w+25.

The shape of each PDF will be different due to the different standard deviations, with the PDF with the smallest standard deviation being the narrowest and tallest, and the PDF with the largest standard deviation being the widest and shortest.

For our case, since we want to plot four normal distributions with mean zero, we can simplify the formula as:

f(x) = (1/σ√(2π)) * e^-(x^2/(2σ^2))

where µ = 0.

Now, to plot the four normal distributions, we can use the same formula but with different standard deviations. We can choose any values for the standard deviations, but in this case, let's use 1/4, 1/2, 1, and 2.

Thus, the PDFs for the four normal distributions are:

f1(x) = (1/(1/4)√(2π)) x \(e^{-x^2/(2(1/4)^2)}\)

f2(x) = (1/(1/2)√(2π)) x \(e^{-(x^2/(2(1/2)^2))}\)

f3(x) = (1/1√(2π)) x \(e^{-(x^2/(2(1)^2))}\)

f4(x) = (1/2√(2π)) x \(e^{-(x^2/(2(2)^2))}\)

We can then plot these four PDFs on the same graph, with the x-axis representing the data and the y-axis representing the probability density.

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Answer:

Step-by-step explanation:

-3≤ x = graph 6

-3 > x = graph 3

x≥ 3 = graph 2

x ≤ 3 = graph 4

3 > x = graph 1

x > 3 = graph 5

the closed circles means greater/less than or equal to

the open circle means greater/less than

the direction of the arrow tells you if the number is greater than x or less than x

The coordinates of the point on the directed line segment from (-7, 9) to (3, -1) that partitions the segment into a ratio of 2 to 3 are (-3, 5).

To find the coordinates of the point that divides the directed line segment from (-7, 9) to (3, -1) into a ratio of 2 to 3, we can use the section formula.

Let's label the coordinates of the desired point as (x, y). According to the section formula, the x-coordinate of the point is given by:

x = (2 * 3 + 3 * (-7)) / (2 + 3) = (6 - 21) / 5 = -15 / 5 = -3

Similarly, the y-coordinate of the point is given by:

y = (2 * (-1) + 3 * 9) / (2 + 3) = (-2 + 27) / 5 = 25 / 5 = 5

Therefore, the coordinates of the point that divides the line segment in a ratio of 2 to 3 are (-3, 5).

To understand this conceptually, consider the line segment as a distance from the starting point (-7, 9) to the ending point (3, -1). The ratio of 2 to 3 means that the desired point is two-thirds of the way from the starting point and one-third of the way from the ending point. By calculating the x and y coordinates using the section formula, we find that the desired point is located at (-3, 5).

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The total number of shirts in the dresser is 4y + ×. The correct option is A

We need to add up the number of shirts on each shelf.

The first shelf's shirt count is indicated with the number x.

y indicates how many shirts are present on each of the four remaining shelves.

We may add up the shirts on each rack to determine the overall number of shirts:

Total = x + y + y + y + y

Simplifying the expression, we have:

Total = x + 4y

Therefore, The total number of shirts in the dresser is 4y + ×.

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Step-by-step explanation:

The Circumference is:

\(c = 2\pi \: r\)

Radius r is:

\(r = \frac{d}{2} \)

So,

\(c = \pi \: d \\ d = \frac{c}{\pi} \\ d = \frac{604}{\pi} \: cm\)

Answer:
the interest rate for the savings account is 15%

Step-by-step explanation:

We can use the formula for simple interest to solve this problem:

Simple Interest = Principal x Rate x Time

Where:

Principal is the amount of money invested

Rate is the interest rate (as a decimal)

Time is the length of time the money is invested

We know that Troy placed $40,000 in a savings account with simple interest for 5 years and earned $30,000 in interest. So we can plug these values into the formula to get:

$30,000 = $40,000 x Rate x 5 years

Simplifying this expression, we get:

Rate = $30,000 ÷ ($40,000 x 5 years)

Rate = 0.15 or 15%

Therefore, the interest rate for the savings account is 15%.