Find the value of x in the figure.

Answer:

172.5

Step-by-step explanation:

mean of men=sum/no of men

177=sum/30

sum=177*30

= 5310

mean of women=sum/no of women

164=sum/16

sum=164*16

= 2624

mean height= (5310+2624)/30+16

=7934/46

=172.5

Answer:

172.48cm is the mean height for both groups put togther

Step-by-step explanation:

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The volume will be 3π + π²/16 if the solid obtained by rotating the region bounded by the given curves about the specified axis. y=0, y= cos(4 x), x = π/8, x = 0 about the axis y= -4f

It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.

We have curves,

[tex]\rm y=0, y= \cos(4 x), x = \frac{\pi}{8}, x = 0[/tex]

Here the axis is y = -4f, but not mentioned the value of f.

We are assuming the f = 3/2

So the axis will be y = -4(3/2) = -6

Inner radius = 6

Outer radius = 6 + cos4x

[tex]\rm A(x) = \pi((6+cos4x)^2-6^2)[/tex]

[tex]\rm A(x) = \pi (cos^24x+12cos4x)[/tex]

[tex]\rm A(x) = \pi( \dfrac{1+cos8x}{2}+12cos4x)[/tex]

For the volume;

[tex]\rm Volume = \int\limits^\dfrac{\pi}{8}}_0 {A(x)} \, dx[/tex]

Put the function A(x) in the above integration and solve we will get:

[tex]\rm Volume = 3\pi + \dfrac{\pi^2}{16}[/tex]

Thus, the volume will be 3π + π²/16 if the solid obtained by rotating the region bounded by the given curves about the specified axis. Y=0, y= \cos(4 x), x = π/8, x = 0 about the axis y= -4f

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The statement that correctly compares the slopes of the linear functions is: the slope of g(x) is less than the slope of f(x).

Slope of a linear function = change in y / change in x = rise/run

Given the linear functions, g(x) and f(x) as shown in the image attached:

Slope of g(x) = 1/2 = 0.5

Slope of f(x) = 2/1 = 2

Therefore, we can conclude that: the slope of g(x) is less than the slope of f(x).

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Answer: $184

Step-by-step explanation:

Step (1)- 1/3 of 120= $40

Step (2)= 3/5 of 40= $24

Step (3)- 40+24+120= $184 (ToTaL)

Hope this helpss!

The parabola y = -16x^2 + 32x opens downward and the y value of the vertex is 16

The equation of the function is given as:

y = -16x^2 + 32x

Factor out -16

y = -16(x^2 - 2x)

In the above equation, the factor -16 is negative,

This means that the parabola opens downward

We have:

y = -16(x^2 - 2x)

Set to 0

-16(x^2 - 2x) = 0

Divide by -16

x^2 - 2x = 0

Factor out x

x(x - 2) = 0

Split

x = 0 or x - 2 = 0

Solve for x

x = 0 or x = 2

Hence, the roots are 0 and 2, and the x-intercepts are (0,0) and (2,0)

We have:

y = -16x^2 + 32x

Differentiate

y' = -32x + 32

Set to 0

-32x + 32= 0

Divide through by -32

x - 1 = 0

Add 1 to both sides

x = 1

Hence, the x value of the vertex is 1

In (c), we have:

x = 1

Substitute x = 1 in y = -16x^2 + 32x

y = -16(1)^2 + 32(1)

Evaluate

y = 16

Hence, the y value of the vertex is 16

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Answer:

The answer is A

Step-by-step explanation:

because the angle in the circle is a central angle the angle is the same value as the arc.
Hope this helps!!

Answer:

The longest ski pole to fit would lie diagonally. The length of the diagonal can be found by the Pythagorean theorem.

d=sqrt(1202+252)

d ~= 122.58 cm

Step-by-step explanation:

Answer:

123 cm (nearest whole number)

Step-by-step explanation:

The orientation of the ski pole to allow it to be its maximum length would be placing it from corner to opposite corner of the base of the box.

Therefore, this can be modeled as the hypotenuse of a right triangle, where the length and width of the box are the legs.

To find the hypotenuse, use Pythagoras' Theorem: a² + b² = c²

(where a and b are the legs, and c is the hypotenuse)

Given:

Substitute given values into the formula and solve for c:

⇒ a² + b² = c²

⇒ 25² + 120² = c²

⇒ c² = 15025

⇒ c = √(15025)

⇒ c = 123 cm (nearest whole number)

Ans

2:47 mins

Step-by-step explanation:

2 1/6 ÷7/8 = 2 10/21

2 10/12 to decimal 2.47

Answer:

a3 = 112

Step-by-step explanation:

a2 + a1 = a4

So

3x + 20 = 4x + 4

x = 16

a4 = 68

180 - 68 = 112

Given the volume of the space in the pot and the volume of the meatballs, the sauce will not spill over.

The first step is to determine the volume of the remaining space that the sauce is yet to fill. A pot usually has the shape of a cylinder, so the formula for the volume of a cylinder would be used.

Volume of a cylinder = πr²h

π x (14/2)³ x 2 = 98 in³

The second step is to determine the volume of the two dozen meatballs.

Volume of a sphere = 4/3πr³

24 x (4/3 x π x (2/2)³) = 32π in³

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The sauce will spill over if the volume of the pot is less than 146π in³ and it will not spill over if the volume of the pot is more than 146π in³.

The volume of sauce in the pot is calculated as follows;

V = πr²h

V = π x (7)² x (2)

V = 98π in³

Area of 1 meatball = πr² = π x (1)² = π in²

Area of the 2 dozen = (2 x 12) x A

                                       = 24 x π in² = 24π in²

the height of each meatball = 2 in,

Volume of the 2 dozens = 2 in x 24π in² = 48π in³

Total volume of the meatball and sauce in the pot = 98π + 48π = 146π in³

Thus, the sauce will spill over if the volume of the pot is less than 146π in³ and it will not spill over if the volume of the pot is more than 146π in³.

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Answer: 2/3 i beleive

Step-by-step explanation:

Answer:

Step-by-step explanation:

Step-by-step explanation:

we can only solve an equation.

but here we only have an expression, which we can simplify :

(-2x - 6x² - 4) + (5x² - 2x)

-2x - 2x - 6x² + 5x² - 4

-4x - x² - 4

Answer:

Circumference= 2πr

For a semi circle, C= 2πr/2

144= (2×22×r)÷(7×2)

144= (44r)÷(14)

cross multiply:

44r= 144×14

44r= 2016

divide both sides by 44

r= 2016÷44

r=45.8cm. But d=2r

d= 2×45.8

d=91.6cm approximately 92cm

Thus, diameter= 92cm

Answer:

[tex]a=12[/tex]

Step-by-step explanation:

Pythagorean Theorem: [tex]a^{2}+b^{2}=c^{2}[/tex]

In this case, a = 9, b = a, and c = 15.

[tex]9^{2}+a^{2}=15^{2}[/tex]

[tex]81+a^{2}=225[/tex]

The, we subtract 81 from both sides getting:

[tex]a^{2}=144[/tex],

Then, [tex]a=12[/tex]

The value of the given expression will be equal to 2060.

Expression in maths is defined as the collection of the numbers variables and functions by using the signs like addition,substraction, multiplication and division.

It is given that:-

=p²(m)-(np+r)

=(-8)²(32)-(2x(-8)+4)

=(64x32)-(-16+4)

=2060

Hence value of the given expression will be equal to 2060.

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720

Answer:

15/9 = 1200/x

15x/ 15 =10800/15

x= 720

Answer:

41.89 cm3

Step-by-step explanation:

Given : Height = 10 cm

Given: Radius = 2 cm

Find the volume,

The formula for volume is,

V = π([tex]r^2[/tex])[tex]\frac{h}{3}[/tex]

Fill in the formula with the given values,

π · [tex]2^2[/tex] · [tex]\frac{10}{3}[/tex]

= 41.8879.....

Round answer to the nearest hundredth,

(The Rule For Rounding: the last digit is less than 5, keep the previous digit the same. If it's 5 or more then you should round the previous digit up.)

41.8879

7 is more than 5 so bring the 8 up to a 9,

41.89

Therefore the answer is 41.89 cm3.

Answer:

41.9 cm³ (nearest tenth)

Step-by-step explanation:

[tex]\textsf{Volume of a cone}=\sf \dfrac{1}{3} \pi r^2h \quad\textsf{(where r is the radius and h is the height)}[/tex]

Given:

[tex]\begin{aligned}\implies \textsf{Volume} &=\sf \dfrac{1}{3} \pi \cdot 2^2 \cdot 10\\\\ & = \sf \dfrac{1}{3}\pi \cdot 40\\\\& = \sf \dfrac{40}{3}\pi\\\\ & = \sf 41.88790205\:cm^3\end{aligned}[/tex]

Therefore, the volume is 41.9 cm³ (nearest tenth)

Answer:

The answer is sh50......

Answer:

y = 4 + 5x

Step-by-step explanation:

You can plug in numbers from the top row (the x's) and times and add to see if you get the corresponding number from the bottom row. This problem is a little mean and tricky because if you check with x=1, all of them work out right. But check with any other x and you will see that only one equation works, the first answer.

You can find "the rule" by looking for a pattern in the rows of numbers. The x goes up by 1, and the y goes up by 5 (if you go left to right on the table) With the 5 on top and 1 on the bottom, y/x, you get 5...that's the 5 that is beside the x in the answer. And if you imagine making one more column on the left side of the table, x=0 and y=4, that's the 4 that stands alone in the answer.

The division equation that satisfies the required parameters where 13 is the quotient is 1/1/13 = 13

The given parameters are:

A division equation is represented as:

Dividend/Divisor = Quotient

Substitute Quotient = 13

Dividend/Divisor = 13

A unit fraction is represented as 1/n, where n is an integer.

So, the divisor can be represented as 1/13

Dividend/1/13 = 13

Divide both sides by 13

Dividend = 1

So, we have:

1/1/13 = 13

Hence, the division equation is 1/1/13 = 13

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Answer:

The expression is repeated multiplication form is 5.

The expression as power is 9.

Step-by-step explanation:

Answer:

The expression as powers is 5^9

Answer:

Ricky drove at a speed of 34 mi/h.

Step-by-step explanation:

Danny = 26 mi/h

26 x 4 = 104

104 - 2 = 102

102/3 = 34

Answer:

0

Step-by-step explanation:

-100+100 = 0

Answer:

the answer would be 0

because if you take 100 away from 100 you have 0 left

Answer:

aₙ = 3n - 5

5th term = a₅ = 3.5 - 5 = 15 - 5 = 10

Answer:

Step-by-step explanation:

aₙ = 3n - 5

Put n = 5:

a₅ = 3 · 5 - 5

a₅ = 15 - 5

a₅ = 10

Answer: A

Step-by-step explanation:

Answer:

well its slop interform

Step-by-step explanation:

Answer:

77 pounds of fudge were sold.

Answer:

I got x=4

Step-by-step explanation: