curved surface area of a cone = Trl, where r is the
radius and is the slant height.
The cone below has a radius of 3 cm and a slant height
of 7 cm.
Work out the total surface area of the cone.
Give your answer in terms of π.
7 cm
3 cm

Answer:

the answers are B and F since √8 x √8 = √64 which simplifies to 8.

Answer:

:)

Step-by-step explanation:

You don't need help. You got all the answers correct.  :))))) Nice!

Answer:

30%

Step-by-step explanation:

The unemployment rate is 30%

[tex]\left(\frac{-3+1}{2}, \frac{-3+2}{2} \right)=\boxed{\left(-1, -\frac{1}{2} \right)}[/tex]

Answer:

Triangular prisms

Remember the formula for calculating volume is: Volume = Area by height. V = A X h.

For a triangle the area is calculated using the formula: Area = half of base by altitude. A = 0.5 X b X a.

So to calculate the volume of a triangular prism, the formula is: V = 0.5 X b X a X h

Step-by-step explanation:

Answer: Length = 13 ft. , Width = 9 ft.

Step-by-step explanation:

Rectangle area = Length x width

Area = 117 ft.

Length = x + 4

Width = x

To solve

(x)(x + 4) = 117

x^2 + 4x = 117

x^2 + 4x - 117 = 0

(x - 9)(x + 13)

x = 9, -13

x = 9 (measurement cannot be negative)

Length

x + 4

9 + 4 = 13

Answer:

The Mean and Standard deviation for the given data would be as follows:

μ =79.7

б =7.81

Step-by-step explanation:

Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.

Standard deviation is the square root of the arithmetic mean of the squares of deviations of the items from their mean values.

Frequency Distribution

Given that,

Temperature       Lower Limit           Upper Limit             Days([tex]f_{i}[/tex])

50-59                       50                           59                          2

60-69                       60                           69                         313

70-79                         70                           79                          1419

80-89                        80                          89                          1503

90-99                        90                          99                           319

100-109                    100                         109                            9  

Average([tex]x_{i\\}[/tex])    

[tex]\frac{50+59}{2} = 54.5\\ \\\frac{60+69}{2} = 64.5\\ \\\frac{70+79}{2} = 74.5\\\\\frac{80+89}{2} = 84.5\\ \\\frac{90+99}{2} = 94.5\\ \\\frac{100+109}{2} = 104.5[/tex]

As we know,

Mean (μ) =∑ [tex](x_{i}f_{i})[/tex]/∑[tex]f_{i}[/tex]

= { (54.5 * 2) + (64.5 * 313) +(74.5 * 1419)+(84.5*1503)+(94.5*319) + (104.5*9)/ (2+313+1419+1503+319)

∵ μ = 79.7

As we know,

Standard Deviation:-

[tex]\sigma={\sqrt {\frac {\sum(x_{i}-{\mu})^{2}}{N}}}[/tex]

by putting the values, we get

∵ б = 7.81

Hence, μ = 79.7 and б=7.81  are the correct answers.

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Answer:

150 ounces

Step-by-step explanation:

Answer:

x greater than equal to (-1)

x less than 2

all no. greater than -1 = -1,1, 0 , 1 ,2 ......

no. less than2 = 1, 0, -1,.......

-1,0, 1

The total number of tea received in three years is 192.

The total number of coffee received in three years is 128.

The total number of biscuits received in three years is 64.

The total quantity of tea, coffee and biscuits received in the first year = (6 x 2) , (4 x 2) ,  (2 x 2) = 12, 8, 4 respectively

The total quantity of tea, coffee and biscuits distributed in the second year = (6 x 12) , (4 x 12) ,  (2 x 12) = 72, 48, 24 respectively

The total quantity of tea, coffee and biscuits distributed in the third year = (6 x 18) , (4 x 18) ,  (2 x 18) = 108, 72, 36 respectively

Total number of tea received in three years = 108 + 72 + 12 = 192

Total number of coffee received in three years = 8 + 48 + 72 = 128

Total number of biscuits received in three years = 4 + 24 + 36 = 64

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Answer:

404 cm³ Anyway... Look down here for my explanation.

Step-by-step explanation:

Let's Draw a line from the center of the circle to one of the ends of the chord (water surface) and another to the point at greatest depth on your paper. A right-angled triangle is formed too. The Length of side to the water-surface is 5 cm, the hospot is 7 cm.

We Calculate the angle θ in the corner of the right-angled triangle by: cos θ = 5/7 ⇒ θ = cos ˉ¹ (5/7)

44.4°, so the angle subtended at the center of the circle by the water surface is roughly 88.8°

The area shaded will then be the area of the sector minus the area of the triangle above the water in your diagram.

Shaded area 88.8/360*area of circle - ½*7*788.8°

= 88.8/360*π*7² - 24.5*sin 88.8°

13.5 cm²

(using area of ∆ = ½.a.b.sin C for the triangle)

Volume of water = cross-sectional area * length

13.5 * 30 cm³

404 cm³

Answer:

29/7

Step-by-step explanation:

4 1/7 = 4 + 1/7

4 = 28/7

then:

4 1/7 = 28/7 + 1/7 = (28+1) / 7

= 29/7

Multiplication is the process of multiplying. The number 72 in terms of the product of primes is described as 2³ × 3².

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.

The number 72 in terms of the product of primes can be written as,

72 = 2×2×2×3×3×1 = 2³ × 3²

Hence, the number 72 in terms of the product of primes is described as 2³ × 3².

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Answer:

correct answer is B.

Step-by-step explanation:

for more information see the attachment.

Answer:

no 2/B is the correct answer

Answer:

1/(7^5)=1/16807

Step-by-step explanation:

Assuming 7-key mean zero up to 7,

# of possible codes = 17^5 = 16807

=====

Probability of first try correct = 1/7^5

Answer:

C.6

Step-by-step explanation:

The value of x in the given quadrilateral is; x = 3

The diagonals of a parallelogram bisect each other.

Thus, from the image attached, we can say that;

WC = CY.

Thus;

2x + 5 = 3x + 2

Subtract 2x from each side to get;

5 = x + 2

Subtract 2 from each side to get;

5 - 2 = x + 2 - 2

x = 3

The complete question is;

In quadrilateral WXYZ, WC = 2x + 5 and CY = 3x + 2. What must x equal for quadrilateral WXYZ to be a parallelogram?

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Answer: (-2,0) and (1,0)

Step-by-step explanation:

If y=0, then:

[tex]x+x^2 + 2=4\\\\x^2 + x-2=0\\\\(x+2)(x-1)=0\\\\x=-2, 1[/tex]

So, the points (-2,0) and (1,0) lie on the curve.

The points (-2,0) and (1,0) lie on the curve.

If y=0, then:

[tex]x+(x^2+2)+0=4\\x^2+x+2=4\\[/tex]

A coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.

[tex]x^2+x-2=0[/tex]

[tex]=\left(x^2-x\right)+\left(2x-2\right)[/tex]

[tex]=x\left(x-1\right)+2\left(x-1\right)[/tex]

[tex]=\left(x-1\right)\left(x+2\right)[/tex]

[tex]x=-2,x=1[/tex]

So, the points (-2,0) and (1,0) lie on the curve.

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The expected number of employees working at Sprockets R Us in 2006 will be 8069.45.

The Percentage is defined as representing any number with respect to the 100. It is denoted by the sign %.

Given that:-

The number of employees working for Sprockets R Us in 2005 was 8110, with an expected decrease of 0.5% per year. At the rate of decrease given, what is the expected number of employees working at Sprockets R Us in 2006?

The number of the employees in 2006 will be calculated as:-

Number of employees decreased   = 0.5% x 8110

Number of employees decreased   = (0.5/100) x 8110

Number of employees decreased   = 40.55

The number of the employees in 2006 will be

N = 8110 - 40.55 = 8069.45

Therefore the expected number of employees working at Sprockets R Us in 2006 will be 8069.45.

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Whatever... I'll try to solve the first two problems.

[tex]2^x=4x\\4x=e^{\ln 2^x}\\4x=e^{x\ln 2}\\\dfrac{1}{4x}=e^{-x \ln 2}\\-\dfrac{\ln 2}{4}=-x\ln 2e^{-x \ln 2}\\-x\ln 2=W\left(-\dfrac{\ln 2}{4}\right)\\x=-\dfrac{W\left(-\dfrac{\ln 2}{4}\right)}{\ln 2}[/tex]

1.

[tex]x=\sqrt{13+\sqrt{5+\sqrt{13+\sqrt{5+\sqrt{13+\sqrt{5\ldots}}}}}}\qquad\left( x\geq0\right)\\\\x=\sqrt{13+\sqrt{5+x}}\\\\x^2=13+\sqrt{5+x}\\\sqrt{5+x}=x^2-13\\\\D:5+x\geq0 \wedge x^2-13\geq 0\wedge x\geq 0\\D:x\geq-5 \wedge x^2\geq13\wedge x\geq 0\\D:x\geq \sqrt{13} \vee x\leq-\sqrt{13}\wedge x\geq0 \\D:x\in[\sqrt{13},\infty)\\\\ 5+x=x^4-26x^2+169\\x^4-26x^2-x+164=0\\\vdots\\(x - 4) (x^3 + 4 x^2 - 10 x - 41) = 0\\x-4=0\\x=4[/tex]

One solution is [tex]x=4[/tex], and [tex]4\in D[/tex], therefore[tex]\sqrt{13+\sqrt{5+\sqrt{13+\sqrt{5+\sqrt{13+\sqrt{5\ldots}}}}}}=4[/tex].

We can ignore other possible solutions of the polynomial equation, because the expression can not be equal to two different values simultaneously.

The probabilities are:

a) P = 0.024

b) P = 0.5

a) The probability that the first person grabs a cola is given by the quotient between the number of colas and the total number of drinks.

There are 5 colas, and 16 drinks in total, so the probability is:

P = 5/16

The second person needs to grab a ginger ale, now there are 15 drinks on the cooler (because one cola was taken) so this time the probability is:

Q = 4/15

Finally, the third person grabs (this is incomplete, I will assume that is another cola), this probability is:

Z = 4/14

The joint probability is:

prob = P*Q*Z = (5/16)*(4/15)*(4/14) = 0.024

b) If the two first persons grabed colas, then in the cooler we have:

3 colas, 7 root beers, and 4 ginger ales, for a total of 14 drinks.

Then the probability of grabbing a root beer is:

p = 7/14 = 1/2 = 0.5

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To prove that △DFE ~ △GFH by the SSS similarity theorem, the correct answer is; Option C: HF is 4 units and GH is 2 units

The SSS Similarity theorem states that two triangles are similar If all the three sides of one of the triangles are in same proportion to the three sides of the other triangle.

Since triangle DFE is similar to triangle GHF as seen in the attached diagram, then we can say that;

DF/GF = DE/GH

20/5 = 8/GH

GH = 2 units

Also:

EF/HF = DF/GF

(12 + HF)/HF = 20/5

HF = 4 units

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Hope this helps

Step-by-step explanation:

Answer:

The answer is D

Step-by-step explanation:

I did this already

The expected value of the game is $2.00.

To Find: The fair price to pay to play the game of rolling a colored die with three red sides, two green sides, and one blue side

Now the question arises how to find the Fair Price

We are told that in the game of rolling the colored die;

A roll of a red loses.

A roll of blue pays 5.00 and A roll of green pays 2.00.

Now, the best game to get the fairest price is to play; RRRGGB  i.e (RED, RED, RED, GREEN, GREEN,BLUE)

Fair price = 2(3/6) + 6(1/6) + 0(2/6)

Fair price = $2

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Answer:

B

Step-by-step explanation:

Answer: [tex]\sqrt{(-16)^{2} } =16[/tex]

Step-by-step explanation:

I looked it up on my calculator. I hope this helps!! :)