What is the surface area of the cylinder? Express the answer in terms of Pi?
Cylinder. Diameter 8 centimeters. Height 18 centimeters

a
304π cm2

b
792π cm2

c
152π cm2

d
176π cm2

The Length of the rod is 3/5 meters.

The civil engineer wants to find the length of a rod that stretches for 1 meter and can be given by the function x=2y^(3/2).

To find the length of the rod, we need to integrate the function x=2y^(3/2) with respect to y. Integrating both sides of the equation,

we have:'int dx = int 2y^(3/2) evaluating the left-hand side gives x = 2/5 y^(5/2) + C, where C is the constant of integration. To find the value of C,

we use the given information that the rod stretches for 1 meter. At y = 0, x = 0 since the rod has no length when it is not stretched. At y = 1, x = 1 since the rod stretches for 1 meter.

Therefore, we have:1 = 2/5 (1)^(5/2) + C1 = 2/5 + CC = 3/5 Substituting C = 3/5 back into the equation for x,

we have:x = 2/5 y^(5/2) + 3/5

The length of the rod is given by the value of x when y = 1. Substituting y = 1,

we have:x = 2/5 (1)^(5/2) + 3/5 = 3/5

The length of the rod is 3/5 meters.

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Answer:

A  -(27x + 7)

B -(15x + 8 )

C -9(2x + 1 )

Step-by-step explanation:

-1/2 (30x + 16) = -15x-8

Answer:

The critical region is t ≥ t(0.025, 7) = 2.365

Since the calculated value of t= 18.50249 falls in the critical region we reject the null hypothesis and conclude that there is sufficient reason to support the claim of a linear relationship between the two variables.

Step-by-step explanation:

We set up our hypotheses as

H0: β= 0   the two variable X and Y are not related

Ha: β  ≠ 0. the two variables X and Y are related.

The significance level is set at α =0.05

The test statistic if, H0 is true, is  t= b/s_b

Where   Sb =S_yx/√(∑(X-X`)^2 )

Syx = √((∑(Y-Y`)^2 )/(n-2))

In the given question we have the estimated regression line as y= 0.449x - 30.27

X Y X2         Y2      XY

72 3 5184 9    216

85 7 7225 49    595

91 10 8281 100      910

90 10 8100 100      900

88 8 7744 64       704

98 15 9604 225      1470

75 4 5625 16       300

100 15 10000 225       1500

80 5 6400 25        400        

∑779 77 68163 813 6995

Now finding the variances

∑(Y-Y`)^2  = ∑〖Y^2- a〗 ∑Y- b∑XY

                      = 813 – (- 30.27)77 - 0.449(6995)

                       = 813+2330.79 – 3140.755

                       = 3.035

∑(X-X`)^2 =  ∑X^2  – (∑〖X)〗^2 /n

                   = 68163 – (779)2/9

                    = 736.22

Syx = √((∑(Y-Y`)^2 )/(n-2))  = √(3.035/7) = 0.65846 and

Sb =S_yx/√(∑(X-X`)^2 ) = (0.65846  )/27.13337 = 0.024267

t= b/s_b  = 0.449/ 0.024267 = 18.50249

The critical region is t ≥ t(0.025, 7) = 2.365

Since the calculated value of t= 18.50249 falls in the critical region we reject the null hypothesis and conclude that there is sufficient reason to support the claim of a linear relationship between the two variables.

From the figure we can obtain 2 equations:

and

first lets simplify both equations:

for the first;

and for the second one:

Now we have that x=15 and we can substitute x for 15 in the first equation to find y:

so the final answe is: x=15 and y=63

The dimensions of the rug would be 27 feet long and 19 feet wide with a 6 foot space around the carpet uniformly.

She wants to buy a rug for a room that is 25 ft wide and 33 ft long.

She wants  to leave a uniform strip of floor around the rug.

she can afford to buy 513 square feet of carpeting.

Cynthia room area = lw

where

Therefore,

Cynthia room area = 25 × 33

Cynthia room area = 825 ft²

She wants to leave a uniform strip of floor all around the rug and has affordability to buy 513 square feet of carpet.

Therefore, the dimension the rug should have is as follows:

(25 - 6) (33 - 6) = 513

19 × 27 = 513 ft²

Therefore, the dimensions of the rug would be 27 feet long and 19 feet wide with a 6 foot space around the carpet uniformly.

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Answer:

$1,200 and $409

Step-by-step explanation:

The ratio of the music to news broadcasted by the WMTH and WILM radio stations of 20:2 (10:1) and 25:4, indicates that the WMTH radio station that have to be on air for 15 minutes to longer than the WMTH radio station.

A ratio is an indication of the number of times a quantity is contained in another quantity.

The possible details of the question includes;

The duration of the news the WMTH station schedules for every 20 minutes music = 2 minutes

The duration of the news broadcasted by the WILM station for every 25 minutes music = 4 minutes

The time after which the WMTH station has broadcasted 4 minutes of news is found as follows;

Sum of the duration = 20 minutes of music + 2 minutes news + 20 minutes music + 2 minutes of news

Sum of the duration for WMTH = 20 + 2 + 20 + 2 = 44

The time after which WILM has broadcasted 4 minutes news can be found as follows;

Sum of broadcast duration = 25 minutes + 4 minutes = 29 minutes

Therefore, the station remains on air longer to broadcast 4 minutes news is WMTH

Part of the question obtained from a similar question indicates that the two radio stations WMTH and WILM broadcast music and news in the ratio of 20 minutes per 2 minutes news and 25 minutes per 4 minutes news respectively.

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Answer:

1) 2160000000

2) 3.24 * 10^14

Step-by-step explanation:

30*8000(5-)1800

240000 * 5 * 1800

1200000 * 1800

2160000000

1500(800-)15000*18000

1200000 * 15000 * 18000

18000000000 * 18000

3.24 * 10^14

not d

Step-by-step explanation:

d is not the anser cus it is to small or a purshes

Aircraft A has 312 seats.

Let's assume that Aircraft B has x seats.

According to the given information, Aircraft A has 105 more seats than Aircraft B. So, the number of seats in Aircraft A can be expressed as x + 105.

The total number of seats in both aircraft is 519, which can be represented by the equation:

x + (x + 105) = 519

Simplifying this equation, we have:

2x + 105 = 519

Subtracting 105 from both sides, we get:

2x = 414

Dividing both sides by 2, we find:

x = 207

Therefore, Aircraft B has 207 seats.

To find the number of seats in Aircraft A, we substitute the value of x back into the expression x + 105:

Aircraft A = 207 + 105 = 312

Hence, Aircraft A has 312 seats.

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Answer:

Step-by-step explanation:

Answer:

Is Mary a guy?  :|  

Step-by-step explanation:

I did this by just a good guess  , not really the right way

2000*.45=900  ( 900 is the old savings)

2000*.2 =400   ( how much her salary went down by )

2000-400=1600 ( new salary )

1600*.45 = 720    ( 45% of new salary is new savings

900-720=180      ( change in savings is 180 , the amount the question asks for)

Mary's old salary was 2,000

The complex numbers graphed on the plane are given as follows:

Complex numbers are number that are divided into a real part and an imaginary part, according to the definition given as follows:

z = a + bi.

In which:

On the complex plane, we have that:

As the number z1 has a horizontal coordinate of 3 and a vertical coordinate of 0, it is given as follows:

z1 = 3 + 0i.

As the number z2 has a horizontal coordinate of 0 and a vertical coordinate of -2, it is given as follows:

z2 = 0 - 2i.

As the number z3 has a horizontal coordinate of -2 and a vertical coordinate of 1, it is given as follows:

z3 = -2 + i.

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Answer:

Direction: Opens Down

Vertex:

(

−

2

,

−

1

)

Focus:

(

−

2

,

−

17

16

)

Axis of Symmetry:

x

=

−

2

Directrix:

y

=

−

15

16

x

y

−

4

−

17

−

3

−

5

−

2

−

1

−

1

−

5

0

−

17

Step-by-step explanation:

Answer:

25✓

Step-by-step explanation:

sorry not really true just need more loints

Answer:

speed of current = 2.1 mph

Step-by-step explanation:

Let the speed of the current be "c" and the speed of the motorboat in still water be "b".

We know that the boat can maintain a constant speed of 41 miles per hour relative to the water. Therefore, the speed of the boat upstream would be:

b - c = 41 mph

Similarly, the speed of the boat downstream would be:

b + c = 41 mph (since the boat maintains the same speed relative to the water)

Now, we need to use the given times to form equations that relate the distance traveled and the speed. Let the distance to the point be "d".

Upstream:

distance = speed x time

d = (b - c) x (43/60)

Downstream:

distance = speed x time

d = (b + c) x (39/60)

Since the distance traveled in both cases is the same, we can equate the two expressions:

(b - c) x (43/60) = (b + c) x (39/60)

Multiplying both sides by 60/3 gives:

(b - c) x 43 = (b + c) x 39

Expanding both sides gives:

43b - 43c = 39b + 39c

Simplifying:

4b = 82c

b = 20.5c

Substituting this into the first equation we obtained:

b - c = 41

20.5c - c = 41

19.5c = 41

c = 2.1 mph (rounded to one decimal place)

Therefore, the speed of the current is 2.1 mph.

The length of AE¯¯¯¯¯ is 5√2 cm.

Since quadrilateral ABCD is a square, all four sides are congruent. Let's denote the length of one side as s. Therefore, the length of BD¯¯¯¯¯ is equal to s.

Given that the length of BD¯¯¯¯¯ is 10 cm, we can conclude that s = 10 cm.

Now, we need to find the length of AE¯¯¯¯¯. Looking at the square, AE¯¯¯¯¯ is the diagonal connecting opposite corners.

In a square, the diagonal divides the square into two congruent right triangles. We can use the Pythagorean theorem to find the length of the diagonal.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this case, the diagonal (the hypotenuse) is the same as the side length, s.

Applying the Pythagorean theorem:

s^2 = AE¯¯¯¯¯^2 + AE¯¯¯¯¯^2

10^2 = AE¯¯¯¯¯^2 + AE¯¯¯¯¯^2

100 = 2 * AE¯¯¯¯¯^2

AE¯¯¯¯¯^2 = 50

Taking the square root of both sides:

AE¯¯¯¯¯ = √50

Simplifying the square root:

AE¯¯¯¯¯ = √(25 * 2) = 5√2 cm

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This means that the football’s height when it was kicked 41 yards away was -1.762 yards.

A yard is a unit of length measurement in the imperial and US customary systems of measurement. It is equal to 3 feet or 36 inches.

The equation given is a parabolic equation which models the path of the football. It is a quadratic equation in the form of y = ax² + bx + c, where a, b, and c are coefficients that determine the shape of the path. The coefficient a represents the rate of change in the football’s height as it moves away from the punter. In this equation, a is -0.035, which indicates that the football’s height decreases as it moves away from the punter. The coefficient b indicates the rate of change in the football’s height as it moves back toward the punter, and in this equation, b is 1.4, which means that the football’s height increases as it moves back towards the punter. Finally, the coefficient c is 1, which indicates the height of the football when it is kicked.

In this case, the football was kicked 41 yards, so plugging x = 41 into the equation gives us y = -0.035(41²) + 1.4(41) + 1 = -1.762.

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Answer-

B) 18a3 is the highest common factor

The value of the expression 18 + 4(28) will be 130.

When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.

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.

The expression is given below.

⇒ 18 + 4(28)

Simplify the expression, then the value of the expression will be

⇒ 18 + 4 x (28)

⇒ 18 + 4 x 28

⇒ 18 + 112

⇒ 130

Thus, the value of the expression 18 + 4(28) will be 130.

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Answer:

$2,500 or 25%

Step-by-step explanation:

Let's use the same example:

Cost of Equipment = $10,000

Useful Life = 4 years

Depreciation Rate = (Annual Depreciation / Cost of Equipment) * 100

Annual Depreciation = Cost of Equipment / Useful Life

Annual Depreciation = $10,000 / 4 years

Annual Depreciation = $2,500

Depreciation Rate = ($2,500 / $10,000) * 100

Depreciation Rate = 0.25 * 100

Depreciation Rate = 25%

Answer:

Step-by-step explanation:

acute angle

Answer:

40 degrees

Step-by-step explanation:

The way I did this (and it won't make much sense I know but its just my way of doing it), is to subtract the bigger angle on the tool by the smaller angle. For example, like in the image, one arrow is at 120 degrees and another at 80 degrees, so I would just do 120-80 which equals 40, and because we talk about angles in the hood its 40 degrees, not plain 40

hope you understand

One thing that is not true about equations is A. an equation does not contain an equal sign.

An equation is a mathematical statement that shows the equality of two expressions, and an equal sign (=) is used to connect the two expressions. Without the equal sign, we do not have an equation.

The expressions on each side of the equal sign can contain variables, constants, coefficients, and mathematical operations such as addition, subtraction, multiplication, and division.

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The options are :

Answer: 18.75 lb.ft

Step-by-step explanation:

Given

Force required to stretch spring 8 in. is 18 lb

it can be written

\(\Rightarrow F=kx\\\Rightarrow 18=k(8)\\\\\Rightarrow k=\dfrac{18}{8}=\dfrac{9}{2}\ lb/in.\)

Work done in stretching from its natural length to 10 in.

\(\Rightarrow W=\dfrac{1}{2}kx^2\\\\\Rightarrow W=0.5\times \dfrac{9}{2}\times (10)^2\\\\\Rightarrow W=225\ lb.in.\ or\\\Rightarrow W=18.75\ lb.ft\)

Option (b) correctly represent the graph f(x) = 1/2 (x-3)² -6, we can find by coordinate geometry.

What is Coordinate geometry?

A coordinate system in geometry is a method for    determining the precise location    of points or other    geometrical objects on a manifold, such as Euclidean space, using one (1) or more    numbers, or coordinates.

In coordinate geometry, many geometric figures    are described using graphs and coordinates. The    coordinate plane must be described in a definition of coordinate geometry. The     intersection of 2 number lines, referred to as axes,     yields the coordinate plane, also known as the coordinate graph, which is a grid system.

In option (b), if we    put x = 7 , we get y = 2.

and , if we    put x =4, we get y = -5.5

Hence, the option (b) is correct.

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Answer:

One sample t test

Step-by-step explanation:

A one proportion sample t test is employed when we intend to test the sample mean of a certain sample against a particular or specified population property . In the scenario above, we could use the information given to obtain the one sample proportion test statistic by using the formular :

Test statistic = (xbar - μ) ÷ (σ/sqrt(n))

Where, xbar = sample mean ;

μ = population mean

σ = population standard deviation

n = sample size

Using the test statistic, we can then obtain the Pvalue and compare to the specified α - level

Answer:

The sum of their ages is 29, which we can express as the equation:

P + (P - 11) = 29

Simplifying the equation:

2P - 11 = 29

Adding 11 to both sides:

2P = 40

Dividing both sides by 2:

P = 20

Therefore, Pete's age, represented by "P," is 20 years old.