What is the height of the prism if there is 30 square centimeters and the volume is 90 cubic centimeters

Answer:

560cm

Step-by-step explanation:

Volume = Length × Breadth × Height

= 10 × 8 × 7

= 560 cm³

Answer:

Step-by-step explanation:

Volume =length x breadth x height

10 x 8 x 7=560cm^3

Answer:

x = 138

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the opposite interior angles

x = B+ C

x = 68+ 70

x =138

Answer:

138 degrees

Step-by-step explanation:

A triangle is made up of 180 degrees, it lists 2 values already, 68&70. when added that equals 138.

So 180-138 is 42 degrees, which would be the last angle within the triangle.

Since a line is also 180 degrees, its 180-42, which makes x 138 degrees

Answer:

x^5

Step-by-step explanation:

x^2 . x^3

x^(2+3)

x^5

Answer:

Step-by-step explanation:

In a right triangle, the sides forming the right angle also determine the angle opposite one of the sides.

Tan(29) =26/x                Multiply both sides by x

x tan(29) = 26                 Divide by tan(29)

x = 26/tan(29)                Find tan(29)

x = 26/0.5543                Divide

x= 46.9

Answer: 4π cm^2/minute

Step-by-step explanation:

Rate of change :

Change with respect to time (dr/dt)

dr/dt = 0.4cm^2/s

r = 5cm

The rate of change when the Radius is 5cm

Area / Circumference of a circle (A) = πr^2

From chain rule of differentiation:

dA/dt = (dr/dt) * (dA/dr)

If A = πr^2

dA/dr = 2πr

dA/dr = 2π * 5 = 10π

However,

dA/dt = (dr/dt) * (dA/dr)

dA/dt = (0.4) * (10π)

dA/dt = 4π cm^2/minute

Answer:

48

Step-by-step explanation:

The formula for the area of a square is A = s².  Plug in each value and see if is in between 2200 and 2400.

A = s²

A = (46)²

A = 2116

A = s²

A = (48)²

A = 2304

A = s²

A = (50)²

A = 2500

A = s²

A = (44)²

A = 1936

The only value that fits in between 220 and 2400 is 48.

Answer:

Step-by-step explanation:

put (x+2)/(x-2)=a

a-1/a=5/6

[tex]multiply~by~6a \\6a^2-6=5a\\6a^2-5a-6=0\\6a^2-9a+4a-6=0\\3a(2a-3)+2(2a-3)=0\\(2a-3)(3a+2)=0\\either 2a-3=0,a=3/2 \\\frac{x+2}{x-2} =\frac{3}{2} \\cross~multiply\\3x-6=2x+4\\3x-2x=4+6\\x=10\\[/tex]

[tex]or~3a+2=0\\a=-2/3\\\frac{x+2}{x-2} =-\frac{2}{3} \\3x+6=-2x+4\\3x+2x=4-6\\5x=-2\\x=-2/5[/tex]

2.

put (x+3)/x=a

a+1/a=4  1/4

[tex]a+\frac{1}{a} =\frac{17}{4} \\multiply~by~4a\\4a^2+4=17a\\4a^2-17a+4=0\\4a^2-16a-a+4=0\\4a(a-4)-1(a-4)=0\\(a-4)(4a-1)=0\\either~a-4=0,a=4\\\frac{x+3}{x} =4\\4x=x+3\\4x-x=3\\3x=3\\x=3/3=1\\or\\4a-1=0\\a=1/4\\\\\frac{x+4}{x} =\frac{1}{4} \\4x+16=x\\3x=-16\\x=-16/3[/tex]

Complete question is;

A mechanic sells a brand of automobile tire that has a life expectancy that is normally​ distributed, with a mean life of 34,000 miles and a standard deviation of 2500 miles. He wants to give a guarantee for free replacement of tires that​ don't wear well. How should he word his guarantee if he is willing to replace approximately​ 10% of the​ tires?

Answer:

The mechanics worded guarantee that the tyre will be replaced if it lasts less than or equal to 30796 miles.

Step-by-step explanation:

Let X = Life expectancy of the automobile tire

For the normal distribution, we are given;

μ = 34000

σ = 2700

Let y miles be the minimum miles of the tyres which the mechanic guarantees that he will replace if it's last less than that.

Now, since the mechanic is willing to replace approximately 10% of the tires, y would be such that:

P(X ≤ y) = 0.1

Using the z formula, we have;

P[(X - μ)/σ) ≤ [(y - μ)/σ] = 0.1

Thus;

P(Z ≤ ([y - μ]/σ) = 0.1

From z-distribution table the Z-score at 0.1 is approximately -1.2816

This is P(Z ≤ -1.2816)

Thus;

[y - μ]/σ = -1.2816

(y - 34000)/2500 = -1.2816

y - 34000 = -1.2816 × 2500

y - 34000 = -3204

y = 34000 – 3204

y = 30796

So, we conclude that the mechanic will guarantee that the tyre will be replaced if it lasts less than or equal to 30796 miles.

Answer:

3 = x

Step-by-step explanation:

5(x+4) = 35

distribute: 5x + 20 = 35

subtract 20 to both sides

15 = 5x

divide by 5 to make x independent

x=3

Answer:

3x^2 + 3/2 x -9

Step-by-step explanation:

f(x) = x/2 -3

g(x) =3x^2 +x -6

(f+g) (x) =  x/2 -3 + 3x^2 +x -6

   Combine like terms

            = 3x^2 + x/2 +x -3-6

              = 3x^2 + 3/2 x -9

Answer:

[tex] Area = 538.5 m^2 [/tex]

Step-by-step Explanation:

Given:

∆XVW

m < X = 50°

m < W = 63°

XV = w = 37 m

Required:

Area of ∆XVW

Solution:

Find side length XW using Law of Sines

[tex] \frac{v}{sin(V)} = \frac{w}{sin(W)} [/tex]

W = 63°

w = XV = 37 m

V = 180 - (50+63) = 67°

v = XW = ?

[tex] \frac{v}{sin(67)} = \frac{37}{sin(63)} [/tex]

Cross multiply

[tex] v*sin(63) = 37*sin(67) [/tex]

Divide both sides by sin(63) to make v the subject of formula

[tex] \frac{v*sin(63)}{sin(63)} = \frac{37*sin(67)}{sin(63)} [/tex]

[tex] v = \frac{37*sin(67)}{sin(63)} [/tex]

[tex] v = 38 [/tex] (approximated to nearest whole number)

[tex] XW = v = 38 m [/tex]

Find the area of ∆XVW

[tex] area = \frac{1}{2}*v*w*sin(X) [/tex]

[tex] = \frac{1}{2}*38*37*sin(50) [/tex]

[tex] = \frac{38*37*sin(50)}{2} [/tex]

[tex] Area = 538.5 m^2 [/tex] (to nearest tenth).

Answer:

Step-by-step explanation:

cosФ=0 then the angle=π/2=90 degrees

sinФ==1     sin 90=1

12) the original price of the console  that Amanda bought :

240+(240*50%)=360 dollars

the price before the tariffs:

360-(360*50^)=180 dollars

Answer:

Option C is the correct option

Step-by-step explanation:

[tex] \frac{ {y}^{2} + 7y + 12}{ {y}^{2} - 2y - 15 } [/tex]

Write 7y as a sum

[tex] \frac{ {y}^{2} + 4y + 3y + 12}{ {y}^{2} - 2y - 15} [/tex]

Write -2y as a difference

[tex] \frac{ {y}^{2} + 4y + 3y + 12}{ {y}^{2} + 3y - 5y - 15} [/tex]

Factor out y from the expression

[tex] \frac{y(y + 4) + 3y + 12}{ {y}^{2} + 3y - 5y - 15 } [/tex]

Factor out 3 from the expression

[tex] \frac{y(y + 4) + 3(y + 4)}{ {y}^{2} + 3y - 5y - 15 } [/tex]

factor out y from the expression

[tex] \frac{y(y + 4) + 3(y + 4)}{y(y + 3) - 5y - 15} [/tex]

Factor out -5 from the expression

[tex] \frac{y(y + 4) + 3(y + 4)}{y(y + 3) - 5( y + 3)} [/tex]

factor out y + 4 from the expression

[tex] \frac{(y + 4)(y + 3)}{y(y + 3) - 5(y + 3)} [/tex]

Factor out y + 3 from the expression

[tex] \frac{(y + 4)(y + 3)}{(y + 3)(y - 5)} [/tex]

Reduce the fraction with y + 3

Hope this helps..

Best regards!!

1 Ampere = 1 Coulomb of charge per second

2.5 A  =  2.5 C of charge per second

Time to deliver 3.5 C of charge = (3.5 C) / (2.5 C / sec)

Time = (3.5 / 2.5) (C / C-sec)

Time = 1.4 sec

A current of 2.5 A delivers 3.5 C of charge in 1.4 seconds.

Answer:

c

Step-by-step explanation:

c

Answer:

the answer is C ;D

Step-by-step explanation:

Answer:

The values in the domain where f(x) = 0 are x = -2.5, x = - 0.75 and x = 1.

Step-by-step explanation:

Since we are given the points (-2.5,0), (-0.75, 0), (0, -3) and (1,0) where the coordinates are in ordered pairs of (x, y) where y = f(x).

To find the values in the domain where f(x) = 0, we look at the ordered pairs given.

We look for the pair in which f(x) = 0.

So f(x) = 0 in (-2.5, 0)

f(x) = 0 in (-0.75, 0)

and f(x) = 0 in (1, 0)

The corresponding values of x  in which f(x) = 0 are x = -2.5, x = - 0.75 and x = 1.

So, the values in the domain where f(x) = 0 are x = -2.5, x = - 0.75 and x = 1.

Answer:

C. [tex]x=1[/tex]

Step-by-step explanation:

When x is 1, y is 0.

Hey there! I'm happy to help!

I assume that n is supposed to be π. To find the volume of a cone, you multiply the base by the height and then divide by three.

First, we find the area of the base, which is a circle. To find the area of a circle, you square the radius and multiply by π.

5²=25

And we multiply by π.

25π

Now we multiply by the height.

25π×13=325π

We divide by three.

325π/3≈108π

Therefore, the answer is 108π in.

Have a wonderful day! :D

Answer:

Yes.

Step-by-step explanation:

You are correct except to the nearest hundredth it is 795.54 cm^2.

Answer:

144

Step-by-step explanation:

An angle of a regular pentagon is of 180(5-2)/5=108°

and that all the sides are equal so angle MNL=108/3=36

then MNK=180-MNL=180-36=144

I don't know if you understand this but it's hard to work without more points :)

Answer:

- 1

Step-by-step explanation:

Given

( [tex]\frac{1+i}{1-i}[/tex] )²

= [tex]\frac{(1+i)^2}{(1-i)^2}[/tex]

= [tex]\frac{(1+i)(1+i)}{(1-i)(1-i)}[/tex] ← expand numerator/ denominator using FOIL

= [tex]\frac{1+2i+i^2}{1-2i+i^2}[/tex] ← simplify using i² = - 1

= [tex]\frac{1+2i-1}{1-2i-1}[/tex]

= [tex]\frac{2i}{-2i}[/tex]

= - 1

Answer:

400

Step-by-step explanation:

There are 400.

Assuming the number must be at least 10,000, then:

In a 5 digit palindrome, the first and last digits must be the same, and the second and fourth digits must be the same; and:

For the first and last digit there is a choice of 4 digits {2, 4, 6, 8};

For each of these there is a choice of 10 digits {0, 1, ..., 9} for the second and fourth digits;

For each of the above choices these is a choice of 10 digits {0, 1, ..., 9} for the third digit;

Making 4 x 10 x 10 = 400 possible even 5 digit palindromes.

Answer:

12√5

Step-by-step explanation:

6√5 + 6√5 = (6 + 6) * √5 = 12 * √5 = 12√5.

Answer:

12 [tex]\sqrt{5}[/tex]

Step-by-step explanation:

When you add the surds which are the same type, (both are root 5), just add the integers before them together.

Answer:

Step-by-step explanation:

m1=40

Taking m3

m3=40 ×3

m3= 120

Answer:

The last choice (3,2), because both lines pass through this point.

Step-by-step explanation:

For a point to be a solution to a system of linear equations, both equation's lines have to pass through that same point.

Answer: (3, 2), because both lines pass through this point

Step-by-stepexplanation:

This can be solved by substitution. The graph will show the same result.

Answer:

a = 11.71 ; b = 15.56

Step-by-step explanation:

For this problem, we need two things.  The law of sines, and the sum of the interior angles of a triangle.

The law of sines is simply:

sin(A)/a = sin(B)/b = sin(C)/c

And the sum of interior angles of a triangle is 180.

45 + 110 + <C = 180

<C = 25

We can find the sides by simply applying the law of sines.

length b

7/sin(25) = b/sin(110)

b = 7sin(110)/sin(25)

b = 15.56

length a

7/sin(25) = a/sin(45)

a = 7sin(45)/sin(25)

a = 11.71

Answer:

4.7 feet³ of water

Step-by-step explanation:

Diameter of 4 feet

Radius = 2 feet

Height = 0.75 feet

Formula for Volume = 2·[tex]\pi[/tex]·radius·height

But she only wants to fill half, so divide by 2, cancels the 2 in the formula for volume, giving us: [tex]\pi[/tex]·radius·height

[tex]\pi[/tex]·2·0.75 = 4.71 feet³

Answer:

The correct option is;

0.28

Step-by-step explanation:

The given data values are;

x,      f(x)

8,     12

12,    40

6,      15

20,    20

Where;

x = The number of flowers in the bouquet

f(x) = The total cost (in dollars)

The equation for linear regression is of the form, Y = a + bX

The formula for the intercept, a, and the slope, b, are;

[tex]b = \dfrac{N\sum XY - \left (\sum X \right )\left (\sum Y \right )}{N\sum X^{2} - \left (\sum X \right )^{2}}[/tex]

[tex]a = \dfrac{\sum Y - b\sum X}{N}[/tex]

Where:

N = 4

∑XY = 1066

∑X = 46

∑Y = 87

∑X² = 644

(∑X)² = 2116

b = (4*1066 - 46*87)/(4*644 - 2116) = 0.5696

a = (87 - 0.5696*46)/4 = 15.1996

The standard deviation of the x- values

[tex]S_X = \sqrt{\dfrac{\sum (x_i - \mu)^2}{N} }[/tex]

[tex]\sum (x_i - \mu)^2}[/tex] = 115

N = 4

Sx =√(115/4)

Sx = 5.36

[tex]S_Y = \sqrt{\dfrac{\sum (y_i - \mu_y)^2}{N} }[/tex]

[tex]\sum (y_i - \mu_y)^2}[/tex] = 476.75

N = 4

Sy =√(476.75/4)

Sy= 10.92

b = r × Sy/Sx

Where:

r = The correlation coefficient

r = b × Sx/Sy = 0.5696*5.36/10.92 = 0.2796 ≈ 0.28

The correct option is 0.28.

Answer:

C on edge

Step-by-step explanation:

Answer/Step-by-step explanation:

3. By substitution method, let's substitute [tex] \frac{2}{3}x- 4 [/tex] for y in the first equation.

Thus,

[tex] \frac{1}{3}x + 2(\frac{2}{3}x- 4) = 1 [/tex]

Solve for x

[tex] \frac{x}{3} + \frac{4x}{3} - 4 = 1 [/tex]

Add 4 to both sides

[tex] \frac{x}{3} + \frac{4x}{3} - 4 + 4 = 1 + 4 [/tex]

[tex] \frac{x}{3} + \frac{4x}{3} = 5 [/tex]

[tex] \frac{x + 4x}{3} = 5 [/tex]

[tex] \frac{5x}{3} = 5 [/tex]

Multiply both sides by 3

[tex] \frac{5x}{3}*3 = 5*3 [/tex]

[tex] 5x = 15 [/tex]

Divide both sides by 5

[tex] x = 3 [/tex]

Now, substitute 3 for x in the equation.

[tex] y = \frac{2}{3}x- 4 [/tex]

[tex] y = \frac{2}{3}(3) - 4 [/tex]

[tex] y = 2 - 4 [/tex]

[tex] y = -2 [/tex]

The solution of the equation is x = 3, y = -2

4. Solving by elimination, let's try to eliminate the x-variable by adding both equation together.

[tex] 3x - 2y = 11 [/tex]

[tex]-3x - y = 4[/tex]

            [tex] -3y = 15 [/tex]  => [tex] (-3x +(-3x) = 0; -2y +(-y) = -3y; 11 + 4 = 15) [/tex]

Divide both sides by -3 to solve for y

[tex] \frac{-3y}{-3} = \frac{15}{-3} [/tex]

[tex] y = -5 [/tex]

Substitute -5 for y in the first equation to find x

[tex] 3x - 2(-5) = 11 [/tex]

[tex] 3x + 10 = 11 [/tex]

Subtract 10 from both sides

[tex] 3x + 10 - 10 = 11 - 10 [/tex]

[tex] 3x = 1[/tex]

Divide both sides by 3

[tex] \frac{3x}{3} = \frac{1}{3} [/tex]

[tex] x = \frac{1}{3} [/tex]

The solution is [tex] x = \frac{1}{3}, y = -5 [/tex]