? Work out the total surface area of this solid cone. Give your answer rounded to 1 DP. 10m 7m​

Answer:

Step-by-step explanation:

a. To find the area of the sector, we can use the formula:

A = (θ/360)πr^2

where A is the area of the sector, θ is the central angle in degrees, r is the radius of the circle, and π is the constant pi.

In this case, the radius is 4 cm and the central angle is 45 degrees. Substituting these values into the formula, we get:

A = (45/360)π(4^2)

A = (1/8)π(16)

A = 2π

Therefore, the area of the sector is 2π square cm.

b. To find the area of the segment of a circle, we need to subtract the area of the triangle formed by the two radii and the chord from the area of the sector.

The central angle of the sector is 45 degrees, so the angle between the chord and one of the radii is 22.5 degrees. We can use trigonometry to find the length of the chord:

cos(22.5) = adjacent/hypotenuse

cos(22.5) = x/4

x = 4cos(22.5)

So the length of the chord is approximately 3.54 cm (rounded to two decimal places).

The area of the triangle can be found using the formula:

A = (1/2)bh

where b is the length of the base (which is the chord) and h is the height (which is the distance from the midpoint of the chord to the center of the circle). The height is equal to the radius minus half the length of the chord:

h = 4 - (3.54/2)

h = 1.23 (rounded to two decimal places)

Substituting the values of b and h, we get:

A = (1/2)(3.54)(1.23)

A = 2.17 (rounded to two decimal places)

So the area of the triangle is approximately 2.17 square cm.

Finally, we can find the area of the segment by subtracting the area of the triangle from the area of the sector:

Area of segment = Area of sector - Area of triangle

Area of segment = 2π - 2.17

Area of segment = 0.85 (rounded to two decimal places)

Therefore, the area of the segment of the circle is approximately 0.85 square cm.

The product shown below in simplest form (x+5) (x-5) and we can use this product to determine that (15) (5)= 75.

First, we need to find the product shown below in simplest form:

we have = (x+5) (x-5)

we need to explain how you can use this product to determine that,

(15) (5) = 75

for us to get the solution we will let x = 10

Then (x + 5) (x - 6) will be:

(10 + 5) (10 - 5), or we can also say that: (15)(5) = 75

Also, this could be calculated as:

10(10 - 5) + 5(10 - 5) = 100 - 50 + 50 - 25 = 75

Therefore we can say that the product shown below in simplest form (x+5) (x-5) and we can use this product to determine that (15) (5)= 75

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Full question: Find the product shown below in simplest form: (x+5) (x-5) explain how you can use this product to determine that (15) (5) = 75

Solving a system of equations we can see that the correct option is A.

Here we can define the variables:

g = snacks in one pack of granola bars.

f = snacks in one pack of fruit rolls.

And we can write a system of equations like:

10g + 6f = 152

7g + 12f = 200

If we take the difference between two times the first equation and the second, we will get:

2*(10g + 6f) - (7g + 12f) = 2*152 - 200

13g = 104

g = 104/13 = 8

There are 8 snacks in a pack of granola, and with that value we can find f.

10g + 6f = 152

6f = 152 -10g

f = (152 - 10*8)/6 = 12

We conclude that the correct option is A.

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The probability of two people on the same team having the same birthday is: P(A) = 1 / 16

The probability of two people having the same birthday in a group of 32 people is 1/365. This is because there are 365 possible days that a person can have a birthday, and the probability of two people having the same birthday is 1/365.

In this case, there are 16 teams of 2 students each, and the probability of two people on the same team having the same birthday is 1/365.

To calculate the probability of this event occurring, we can use the formula:

P(A) = n(A) / n(S)

Where P(A) is the probability of the event occurring, n(A) is the number of favorable outcomes, and n(S) is the total number of possible outcomes.

In this case, the number of favorable outcomes is 1, since there is only one team that has two people with the same birthday. The total number of possible outcomes is 16, since there are 16 teams.

Therefore, the probability of two people on the same team having the same birthday is:

P(A) = 1 / 16

So, the probability of this event occurring is 1/16.

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The required  value of the third side of the triangle is x = 11.78.

We can use the law of cosines to find the value of the third side of the triangle. The law of cosines states that for any triangle with sides a, b, and c and angle C opposite side c,

[tex]$c^2 = a^2 + b^2 - 2ab\cos(C)$[/tex]

In this case, we have sides a = 2 and b = 10 and angle C = 120 degrees. Therefore, we can plug in these values to get:

[tex]$x^2 = 3^2 + 10^2 - 2(3)(10)\cos(120^\circ)$[/tex]

Simplifying the expression inside the parentheses gives:

[tex]$\cos(120^\circ) = -\frac{1}{2}$[/tex]

Plugging this in and simplifying further gives:

[tex]$x^2 = 9 + 100 + 30 = 139$[/tex]

Taking the square root of both sides gives:

[tex]$x = \sqrt{144} = 12$[/tex][tex]$x = \sqrt{139} = 11.78$[/tex]

Therefore, the value of the third side of the triangle is x = 11.78.

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Answer: Please correct me if I'm wrong and I will remove my answer

1:The system of linear equations can be rewritten as:

4x + y = 4 ...(1)

y = -4a + 4 ...(2)

To determine the classification of the system, we can use the method of substitution:

Substituting equation (2) into equation (1) to eliminate y:

4x + (-4a + 4) = 4

4x - 4a = 0

x - a = 0

x = a

Substituting x = a into equation (2) to find the value of y:

y = -4a + 4

So the solution of the system is (x,y) = (a, -4a+4).

Since the system has a unique solution for any value of 'a', it is a consistent independent system of equations.

2:To find the solution to the equation f(x) = g(x), we need to find the value of x that makes the two functions equal.

f(x) = 2^x + 1

g(x) = -x + 7

Setting them equal to each other:

2^x + 1 = -x + 7

Subtracting 1 from both sides:

2^x = -x + 6

Taking the logarithm of both sides (base 2):

x = log2(-x + 6)

Since log2(-x + 6) is only defined when -x + 6 is positive, we need to check if -x + 6 > 0.

-x + 6 > 0

x < 6

Therefore, the solution to the equation f(x) = g(x) is the intersection point of the two graphs for x < 6.

To graph the two functions, we can use a graphing calculator or plot points. Here are some points for each function:

f(x) = 2^x + 1

(0, 2)

(1, 3)

(2, 5)

(3, 9)

g(x) = -x + 7

(0, 7)

(1, 6)

(2, 5)

(3, 4)

Plotting these points on the same coordinate plane:

We can see that the two functions intersect at approximately (2.6, 4.4) for x < 6. Therefore, the solution to the equation f(x) = g(x) for x < 6 is approximately x = 2.6.

The amounts needed for the dessert for 16 people is given as follows:

The amounts are obtained applying the proportions in the context of the problem.

For 8 people, the amounts of the ingredients are given as follows:

With 16 people, the number of people doubles, hence the amount of ingredients also doubles, thus the needed amounts are given as follows:

Gina is preparing a recipe for 8 people, and the amounts are given as follows:

The problem asks for the necessary amounts for 16 people.

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The solution to the inequality  - 11y -13>42 is y < -5.

An inequality is a mathematical statement that compares two quantities using symbols such as <, >, ≤, or ≥ to indicate whether one is less than, greater than, less than or equal to, or greater or equal to the other.

To solve the inequality -11y - 13 > 42, we need to isolate y on one side of the inequality.

-11y - 13 > 42

First, we can add 13 to both sides:

-11y > 55

Next, we can divide both sides by -11, remembering to reverse the direction of the inequality because we are dividing by a negative number:

y < -5

To graph this on a number line,

Here is a rough sketch of the number line:

<=====(●)------------------------

-5

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The probability that a randomly selected boy in secondary school can run the mile in less than 358 seconds is 0.0107 or 1.07%.

The probability that a randomly selected boy in secondary school can run the mile in less than 358 seconds is 0.0013.

Given data:

Mean (μ) = 450 seconds

Standard deviation (σ) = 40 seconds

We are required to find the probability that a randomly selected boy in secondary school can run the mile in less than 358 seconds.i.e., we need to find P(x < 358)

Let us first calculate the z-score.

z = (x - μ) / σ

Where,x = 358 seconds

μ = 450 seconds

σ = 40 seconds

z = (358 - 450) / 40 z = -2.3

Using a z-table or calculator, we can find the probability that corresponds to the z-score of -2.3P(z < -2.3) = 0.0107

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The sοlutiοn tο the equatiοn is x=7.

An equatiοn is an expressiοn that uses mathematical symbοls tο express the relatiοnship between twο οr mοre variables. Equatiοns are used tο describe physical laws, mοdel real-wοrld prοblems, and sοlve mathematical prοblems. Equatiοns can be written in a variety οf fοrms, frοm simple linear equatiοns tο cοmplex nοnlinear equatiοns. Equatiοns can alsο be used tο determine the prοperties οf certain functiοns and tο evaluate integrals.

Sοlving fοr x,

−10(−x+1)+10+10(x+3)=0

−10x+10−10x+10+100+30=0

−20x+140=0

20x=140

x=7

This equatiοn is an example οf a linear equatiοn. Linear equatiοns are equatiοns that invοlve οnly οne variable and can be represented in the fοrm ax + b = 0, where x is the variable and a and b are cοnstants. Linear equatiοns are useful fοr understanding the relatiοnship between different variables and can be used tο sοlve real-wοrld prοblems. In this equatiοn, the variable x is the unknοwn value that we are trying tο sοlve fοr. By rearranging the equatiοn and applying the apprοpriate algebraic οperatiοns, we were able tο sοlve fοr x. This is an example οf hοw linear equatiοns can be used tο sοlve real-wοrld prοblems.

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Solve for x in given expression.

10 + 10(x + 3) = −x −10(−x + 1)

Answer:

a. 6 and 2

b. 3 and 8

Step-by-step explanation: Supplementary angles add up to 180 degrees. In this figure angles 6,2 lie on the same line and a straight line has an angle measure of 180 degrees. Vertical angles are opposite to each other and have the same value. 8 and 3 are one example and on that same area, 7 and 4 are too.

Answer:

(x + 3)

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

As I posted ....looks to be 147°

A. [tex]\mu[/tex] ≤ 503

B. [tex]\mu[/tex] > 503

C. t = (505 - 503) / (41 / [tex]\sqrt{70}[/tex]) = 1.38

D. The P-value (0.086) is greater than the level of significance (0.05).

A. Null Hypothesis: The mean SAT score of the students who completed the preparation course is not significantly higher than the mean score of 503.

[tex]\mu[/tex] ≤ 503

B. Alternative Hypothesis: The mean SAT score of the students who completed the preparation course is significantly higher than the mean score of 503.

[tex]\mu[/tex] > 503

C. The Value of the test statistic:

We apply the algorithm below to determine the test statistic:

[tex]t = (\bar x - \mu) / (s / \sqrt{n} )[/tex]

When s is the sample standard deviation, n is the sample size, and x is the sample mean and is the predicted population mean.

In this case,

[tex]\bar x[/tex] = 505,

[tex]\mu[/tex] = 503,

s = 41,

n = 70.

t =  (505 - 503) / (41 / [tex]\sqrt{70}[/tex]) = 1.38

D. The P-Value:

We want to test whether the mean SAT score of the students who completed the preparation course is significantly higher than the mean score of 503 at the 0.05 level of significance.

Using a t-distribution table with 69 degrees of freedom (df = n-1), we find that the area to the right of 1.38 is 0.086.

Since this is a one-tailed test (we are testing for[tex]\mu[/tex] > 503), the P-value is 0.086.

Since the P-value (0.086) is greater than the level of significance (0.05), we fail to reject the null hypothesis. Therefore, we do not have sufficient evidence to conclude that the preparation course does what it claims, i.e., the mean SAT score of the students who completed the preparation course is not significantly higher than the mean score of 503.

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Answer:

It will have a rise of 20.

Step-by-step explanation:

We can use ratios:

Rise : Run = 16 : 4 = 4 : 1 = 20 : 5

Hope this helps!

The set o rates that Frank could use to finish the events within 7.5 hours is (0.75 km/h, 25 km/h, 12.5 km/h).

To determine the rates at which Frank must complete each event to finish the triathlon within 7.5 hours, we can use the formula:

time = distance / rate

where;

Let x be the rate at which Frank completes the swim,

y be the rate at which he completes the bike ride, and

z be the rate at which he completes the run.

Then, we have the following three equations:

2.25 / x + 65 / y + 20 / z = 7.5

x > 0, y > 0, z > 0

We want to find the set of rates (x, y, z) that satisfy these equations and inequalities.

Here is one possible set of rates that would allow Frank to complete the triathlon within 7.5 hours:

x = 0.5 km/hour

y = 20 km/hour

z = 10 km/hour

Using these rates, we can calculate the time it would take Frank to complete each event:

Swim: 2.25 km / 0.5 km/hour = 4.5 hours

Bike ride: 65 km / 20 km/hour = 3.25 hours

Run: 20 km / 10 km/hour = 2 hours

The total time would be:

4.5 + 3.25 + 2 = 9.75 hours

This is greater than 7.5 hours, so Frank would need to increase his rates to finish within the time limit.

Here are some possible sets of rates that would allow him to do so:

x = 0.75 km/hour, y = 25 km/hour, z = 12.5 km/hour

x = 1 km/hour, y = 30 km/hour, z = 15 km/hour

x = 1.25 km/hour, y = 35 km/hour, z = 17.5 km/hour

Using any of these sets of rates, Frank would be able to complete the triathlon within 7.5 hours.

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Singular Savings Bank received an initial deposit of $3000. By keeping a percentage of this money in reserve based on the reserve rate, the bank loaned out the rest. Over time, the money loaned out was all deposited back into the bank, and with each additional deposit the bank was able to lend out even more money.

This cycle of lending and depositing continued indefinitely until the initial $3000 had increased to $50,000. This increase in money was possible due to the reserve rate, which allowed the bank to lend out a percentage of the money deposited and to keep a percentage in reserve for themselves.

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(x-8)²

(x-8)(x-8)

x(x-8) - 8 (x-8)

x² -8x -8x + 64

x²-16x+64

Answer: just do 30 - 13 which = 17

Step-by-step explanation:

subtraction above

As a result, the total area of the four triangles (PTA, PTB, PTC, and ABC) equation exceeds the size of T, which contradicts the premise that T has the greatest area.

A math equation is a technique that links two assertions and denotes equivalence using the equals sign (=). In algebra, an equation is a mathematical statement that proves the equality of two mathematical expressions. For example, in the equation 3x + 5 = 14, the equal sign separates the numbers 3x + 5 and 14. A mathematical formula may be used to understand the link between the two phrases written on either side of a letter. The logo and the programmed are usually interchangeable. As an example, 2x - 4 equals 2.  

The area of a triangle in hyperbolic geometry is determined by the formula:

Area = K ∙ (α + β + γ - π)

where K is a constant that depends on the curvature of the space and,, and are the triangle's angles.

we want to emphasise the expression + + -.

Consider the following two situations:

Case 1: T has angles that add up to be less than.

Moreover, the total of the areas of triangles PTA, PTB, and PTC is larger than the area of T since their angles add up to more than T's angles. As a result, the total area of the four triangles (PTA, PTB, PTC, and ABC) exceeds the size of T, which contradicts the premise that T has the greatest area.

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Answer:

a= 528 squared centimeters

Step-by-step explanation:

Area of trapezoid is A=[(a+b)/2]*h

Base 1 is 32 cm

height is 12

since the height is also same as the bottom part as told by the line, do 32+12+12 to get...

56 cm for base 2

Sooo put this to use

a=[(32+56)/2]*12

a=[(88)/2]*12

a=[44]*12

a=528 :)

Answer:

Area 528cm²

That's the answer to your question.

Answer:

I believe this what you're asking:

To estimate the sum of 3.456 and 8.79, we can round each number to one decimal place, and then add them:

3.456 ≈ 3.5

8.79 ≈ 8.8

So, 3.456 + 8.79 ≈ 3.5 + 8.8 = 12.3

Therefore, we can estimate that the sum of 3.456 and 8.79 is approximately 12.3.

In equation form, this can be written as:

3.456 + 8.79 ≈ 3.5 + 8.8 = 12.3

Hope this helps! I'm sorry if it doesn't. If you need more help, ask me! :]

a) The probability space is (1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3).

b) The probability that the sum of the numbers drawn is 4 is 2/9.

c) The probability that the sum of the numbers is at least 4 is 2/3.

a) The probability of an event is measured between 0 and 1, and the probability space is a collection of all probable results, hence the probability space is:

P= (1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3)

Hence, the probability space can be written as a set, S = {1,2,3}.

b) If 2 balls are drawn and sum of the numbers is 4, then there could be only one probable way of drawing the balls, which is ball 1 and 3, so probability that the sum of the numbers is 4 is:

P = 2/9

c) If 2 balls are drawn and sum of the numbers is at least 4, then probable ways of drawing the balls are:

(1,3), (2,2), (2,3), (3, 1), (3, 2), and (3, 3)

Hence, the probability that the sum of the numbers is at least 4 = 6/9 = 2/3

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let's move like the crab, backwards.

B)

profit is simply the surplus amount or 3.75 - 2.50 = 1.25.

A)

since the item was bought for $2.50, that's our origin amount, and thus that's our 100%, what's 1.25 off of it in percentage?

[tex]\begin{array}{ccll} Amount&\%\\ \cline{1-2} 2.50 & 100\\ 1.25& x \end{array} \implies \cfrac{2.50}{1.25}~~=~~\cfrac{100}{x} \\\\\\ 2.5x=125\implies x=\cfrac{125}{2.5}\implies x=50[/tex]

Answer:

B.

Step-by-step explanation:

The proportions should be exactly the same for each set of questions and correct questions.

Based on Raven's history, she get 5 of 7.

Choice B. shows exactly that with a scalar of 2, 3, and 4. For Row 2, the set is twice as large, so Raven gets exactly twice as many questions correct and exactly twice as many incorrect.

For Option B., the [tex]\frac{correct}{total}[/tex] always simplifies to [tex]\frac{5}{7}[/tex] for every row.

According to the given information, the coordinates of C′ are (-7, 3.5).

What is the scaling of a triangle?

Scaling is a type of transformation in which the size of an object, in this case, a triangle, is changed while its shape and orientation are maintained. In other words, scaling involves multiplying the coordinates of the vertices of the triangle by a factor called the scale factor.

To dilate a triangle using a scale factor of 3.5, we need to multiply the distance between each vertex and the center of dilation by 3.5. The center of dilation can be any point, but for simplicity, we can choose the origin (0,0).

So, the coordinates of the new vertex C′ can be found by multiplying the distance between the old vertex C(-2,1) and the origin (0,0) by 3.5, and then adding this to the coordinates of the origin.

The distance between C and the origin is [tex]\sqrt{(-2-0)^2+(1-0)^2}[/tex] = [tex]\sqrt{5}[/tex] so the distance between C′ and the origin is [tex]3.5*\sqrt{5}[/tex].

Therefore, the coordinates of C′ are (-23.5, 13.5) = (-7, 3.5).

So, the answer is C′(-7, 3.5).

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the direct distance between the airport and Car's grandparents' house in the woods is 63.64 miles

The Pythagorean theorem is a fundamental principle in mathematics that relates to the sides of a right triangle. It is referred that the hypotenuse's square length, which is the side that faces the right angle, is equal to the sum of the squares of the lengths of the other two sides of a right triangle.

Let d be the distance between the airport and Car's grandparents' house in the woods.  Therefore, we can use the Pythagorean theorem to solve for d:

d² = 45² + 45²

d² = 2(45²)

d = sqrt(2)× 45

Therefore, the direct distance between the airport and Car's grandparents' house in the woods is approximately 63.64 miles (since sqrt(2) is approximately 1.414).

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From the listed factor pairs, there are no factor pairs for 36x² that add up to 15x.

A factor pair is a set of two numbers that can be multiplied together to get a specific product.

The factor pairs for 36x² are:

1 x 36x²

2 x 18x²

3 x 12x²

4 x 9x²

6 x 6x²

To identify which pair adds to 15x, we need to look for the factor pair whose two terms add up to 15x. None of the above factor pairs add up to 15x. Therefore, there is no factor pair for 36x² that adds up to 15x.

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Answer:

a = 24

b = 10

c = 26

======================================================

Explanation:

We're given a list of possible b values and they are:

4, 5, 8, 10, 12, 24

Let's make a table to show what each value of 'a' would be based on those b values above.

[tex]\begin{array}{|c|c|} \cline{1-2}b & a\\\cline{1-2}4 & 12\\\cline{1-2}5 & 14\\\cline{1-2}8 & 20\\\cline{1-2}10 & 24\\\cline{1-2}12 & 28\\\cline{1-2}24 & 52\\\cline{1-2}\end{array}[/tex]

Example calculation: If b = 4, then a = 2b+4 = 2*4+4 = 12 (first row)

I recommend using spreadsheet software to quickly compute these values. Also, a spreadsheet is useful to organize the data into a table.

Next we'll add a third column c.

This column will be computed using the formula [tex]c = \sqrt{a^2+b^2}[/tex] which is based from the pythagorean theorem [tex]a^2+b^2 = c^2[/tex]

So,

[tex]\begin{array}{|c|c|c|} \cline{1-3} & & \\b & a & c = \sqrt{a^2+b^2}\\\cline{1-3}4 & 12 & 12.6491\\\cline{1-3}5 & 14 & 14.8661\\\cline{1-3}8 & 20 & 21.5407\\\cline{1-3}10 & 24 & 26\\\cline{1-3}12 & 28 & 30.4631\\\cline{1-3}24 & 52 & 57.2713\\\cline{1-3}\end{array}[/tex]

Each decimal value mentioned is approximate. The only time c is an integer is when a = 24 and b = 10.

So that's how I got a = 24, b = 10, c = 26 as the final answer.