Please answer this correctly

Answer:

1,950 cubic units

Step-by-step explanation:

The computation of the volume of the prism is shown below;

As we know that

[tex]V=B\times h[/tex]

where,

V = Volume of the prism

B = Area of the base

h = height of the prism

But before that,  we need to do the following calculations

a. Area of rectangle is

[tex]= length \times breadth[/tex]

[tex]= 13 \times 10[/tex]

[tex]= 130\ units ^2[/tex]

b. Now the height of the prism which could find out by using the Pythagoras theorem

[tex]17^{2}=8^{2} +h^{2}h^{2}=17^{2}-8^{2}h^{2}=225h = 15\ units[/tex]

So, the volume of the prism is

[tex]= 130 \times 15[/tex]

= 1,950 cubic units

Answer:

3/4

Step-by-step explanation:

Convert the fractions into decimals.

5/8 = 0.625

3/4 = 0.75

0.75 is greater than 0.625.

Answer:

The nearest penny will be £9146.6

Step-by-step explanation:

A = P[1 + (r/n)]^(nt)

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

A = 8300 [ 1 + {1.4 / (7*100)}]^(7*7)

A = 8300 [ 1 + {0.002}]^(49)

A= 8300 [ 1.002 ]^(49)

A = 8300 [ 1.102 ]

A = £9146.6

What is Compound Interest (CI) ?

Compound Interest is all about adding interest to principal amount of loan , deposit .

Focus on Gamble B only. Multiply each winnings with their corresponding probabilities.

5100*0.50 = 2550

200*0.25 = 50

0*0.25 = 0

Add up those results: 2550+50+0 = 2600

The expected value of gamble B is $2600

Answer:

[tex]P(\overline{W})=0.99281[/tex]

Step-by-step explanation:

W denotes the event of screening a driver and getting someone who is intoxicated.

Out of 695 drivers, the man observed that 5 were arrested for driving while intoxicated.

Therefore: [tex]P(W)=\dfrac{5}{695} \approx 0.00719[/tex]

The probability of the complement of event W, [tex]\overline{W}[/tex] denotes the probability of screening a driver and getting someone who is NOT intoxicated.

From probability theory, we know that the sum of the probability of an event and its complement is 1.

[tex]P(W)+P(\overline{W})=1\\P(\overline{W})=1-P(W)\\=1-0.00719\\\\P(\overline{W})=0.99281[/tex]

Answer:

6 times.

Step-by-step explanation:

There is a 1/9 chance you pick the orange one. If you pick 54 times, you can expect to pick the orange marble 6 times.

Answer:

[tex]z=1.64<\frac{a-14.4}{1.1}[/tex]

And if we solve for a we got

[tex]a=14.4 +1.64*1.1=16.204[/tex]

The 95th percentile of the hip breadth of adult men is 16.2 inches.

Step-by-step explanation:

Let X the random variable that represent the hips breadths of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(14.4,1.1)[/tex]  

Where [tex]\mu=14.4[/tex] and [tex]\sigma=1.1[/tex]

For this part we want to find a value a, such that we satisfy this condition:

[tex]P(X>a)=0.05[/tex]   (a)

[tex]P(X<a)=0.95[/tex]   (b)

We can find a quantile in the normal standard distribution who accumulates 0.95 of the area on the left and 0.05 of the area on the right it's z=1.64

Using this value we can set up the following equation:

[tex]P(X<a)=P(\frac{X-\mu}{\sigma}<\frac{a-\mu}{\sigma})=0.95[/tex]  

[tex]P(z<\frac{a-\mu}{\sigma})=0.95[/tex]

And we have:

[tex]z=1.64<\frac{a-14.4}{1.1}[/tex]

And if we solve for a we got

[tex]a=14.4 +1.64*1.1=16.204[/tex]

The 95th percentile of the hip breadth of adult men is 16.2 inches.

Answer:26 2/3 feet

Step-by-step explanation:40/30 = 4/3

(26 2/3) / 20= 4/3

Answer:

495.6 Euros

Step-by-step explanation:

If 1 pound equals 1.77 euros we can set up a proportion that;

[tex] \frac{1 pound}{1.77 euros} [/tex]

This proportion would be equal to the new amount;

[tex] \frac{280 pounds}{x euros} [/tex]

This means that

[tex] \frac{1 pound}{1.77 euros} = \frac{280 pounds}{ x euros} [/tex]

So;

[tex]280 pounds*1.77 euros / 1 pound[/tex]

Pounds cancel out; and so you have

[tex]280 * 1.77 euros[/tex]

giving you as performed on a calculator;

495.6 euros.

Hope this helps

Answer:

495.6 euros.

Step-by-step explanation:

For each pound we get 1.77 euros so:

it  is 280 * 1.77

= 495.6 euros.

Step-by-step explanation:

WX is parallel to YZ and WZ is also parallel to XY

Option C,D and E are correct.

Explanation:

In Euclidean geometry,a parallelogram is a simple quadrilateral with two pairs of parallel sides.The opposite or facing sides of a parallelogram are of equa length and the opposite angles of a parallelogram are of equal measure.

Hope this helps...

Good luck on your assignment..

Answer:

C. [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

You can use the formula to find the slope: [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

(-1.5, 1.5) & (1.5, 0)

[tex]\frac{0-(-1.5)}{1.5-(-1.5)} =\\\\\frac{0+1.5}{1.5+1.5} =\\\\\frac{1.5}{3} =\\\\\frac{1}{2}[/tex]

The slope is [tex]\frac{1}{2}[/tex]

Answer:

2√21

Step-by-step explanation:

√81 is √4 times √21

Since √4 is a perfect square, √4 = 2

We are left with 2 times √21

2√21

Answer:

2√21

Step-by-step explanation:

√84

84 can be written as 4 × 21.

√(4 × 21)

Distribute the square root to both terms.

√4 × √21

4 is a perfect square.

2 × √21

Answer:I believe that it is A but i am not fully sure

Step-by-step explanation:

Answer:

[tex]f(n) = 3f(n - 1) + 2f(n - 2)[/tex], if [tex]n \geq 2[/tex].

[tex]f(0) := 1[/tex],  [tex]f(1) := 3[/tex]

Step-by-step explanation:

Let [tex]f(n)[/tex] be the number of different tiling of [tex]1 \times n[/tex] floor. We can divide all possible tiling of floor [tex]1 \times n[/tex] into five not overlapping groups by color of last cell in the row (Blue, Red, Green, Orange, White).

The number of tiling [tex]1\times n[/tex] floor such that last cell in row is Blue is exactly f(n - 1) because we can throw away last [tex]1\times 1[/tex] tile and cover the rest [tex]1\times (n - 1)[/tex] cells in f(n - 1) ways. Similarly for Red and Green.

The number of tiling [tex]1\times n[/tex] floor such that last cell in row is Orange is exactly f(n - 2) because we can throw away last [tex]1\times 2[/tex] tile and cover the rest [tex]1\times (n - 2)[/tex] cells in f(n - 2) ways. Similarly for White.

So we get recurrent relation:

[tex]f(n) = 3f(n - 1) + 2f(n - 2)[/tex], if [tex]n \geq 2[/tex].

Now we should define the initial conditions.

[tex]f(0) := 1[/tex] because there is only one empty tiling.

[tex]f(1) := 3[/tex] because we can place Blue, Red or Green tile.

This completely define our recurent sequence because the depth of reccurence is 2.

Answer:

A = bh

Step-by-step explanation:

Area = base × height

Area = base · height

A = bh

Answer:

Integers, Terminating Decimals, Recurring Decimals, Proper and Improper Fractions.

Step-by-step explanation:

The following subset of the real number system can be written in the form [tex]\dfrac{a}{b}[/tex], b≠0.

Integers(ℤ): These are positive and negative whole numbers. For example, 5 can be written as [tex]\dfrac{5}{1}[/tex]

Terminating Decimals: These are fractions that when converted to decimal numbers have an end.

e.g. [tex]\dfrac{5}{2}=2.5[/tex]

Recurring Decimals: These are fractions that when converted to decimal numbers do not have an end.

e.g. [tex]\dfrac{8}{11}=0.727272...=0.\overline{72}[/tex]

Proper Fractions: These are fractions of the form [tex]\dfrac{a}{b}[/tex] where a<b. An examples is [tex]\dfrac{4}{5}[/tex]

Improper Fractions: These are fractions of the form [tex]\dfrac{a}{b}[/tex] where a>b. An examples is [tex]\dfrac{5}{4}[/tex]

Answer:

[tex]x=8[/tex]

[tex]y=24[/tex]

Step-by-step explanation:

3x+2y=72

If y=3x, we plug it into our equation and get:

3x+2×3x=72

3x+6x=72

9x=72

Divide both sides by 9

x=8

Answer:

x = 8

Step-by-step explanation:

3x + 2y = 72

Put y as (3x), and solve for x.

3x + 2(3x) = 72

Multiply 2(3x).

3x + 6x = 72

Add like terms 3x and 6x.

9x = 72

Divide 9 into both sides and isolate x.

x = 72/9

x = 8

The value of x is 8.

Answer:

All rhombi are parallelograms.

All squares are rhombi.

No trapezoid is a rectangle.

Answer:

a. 0.00783

b. 0.003876

Step-by-step explanation:

The computation is shown below;

a. The probability for the rivet to be defective is

Let us assume A is the event for seam failure and B would be event for rivets failure

Now

a) [tex]P[A] = 1 - P[B']^{30}[/tex]

[tex]0.21 = 1 - P[B']^{30}[/tex]

[tex]0.79 = P[B']^{30}[/tex]

[tex]P[B'] = 0.79^{\frac{1}{30}}[/tex]

P[B'] = 0.99217

P[B] = 1 - P[B']

= 0.00783

b) Now the Next one is

[tex]0.08 = 1 - P[B']^{25}[/tex]

[tex]0.89 =P[B']^{30}[/tex]

[tex]P[B'] = 0.89^{(\frac{1}{30})}[/tex]

= 0.99612

So,

P[B]  is

= 1 - P[B']

= 0.003876

We simply applied the above formula so that each one part could be calculated i.e the probabilities of the given question

Answer: h = 9

Step-by-step explanation: A system of linear equations is consistent when it has at least one solution.

The matrix given is:

[tex]\left[\begin{array}{ccc}-15&21&h\\5&-7&-3\end{array}\right][/tex]

Transform this matrix in a row-echelon form:

[tex]\left[\begin{array}{ccc}-15&21&h\\5&-7&-3\end{array}\right][/tex]   [tex]R_{2} = 3R_{2}+R_{1}[/tex] [tex]\left[\begin{array}{ccc}-15&21&h\\0&0&-9+h\end{array}\right][/tex]

For this row-echelon form to have solutions:

-9 + h = 0

h = 9

For this system to be consistent: h = 9.

Answer:

X<3

Step-by-step explanation:

4x-7 <5

4x < 5+7

4x < 12

X < 12/4

X < 3

Hope this helps..

Good Luck!

Answer:

1.90.93

2.90.27

Step-by-step explanation:

Answer:

one above correct

Step-by-step explanation:

1st - 90.93

2nd-90.27

Answer:

-6 on both sides

4x < 12

divide by 4

x < 3

if the 18 is negative

4x = -24

x < -6

Step-by-step explanation:

Answer:

The solutions of the equation in the interval [0,2π )

                    ={  [tex]\frac{\pi }{3}[/tex] }

General solution    θ = 2 nπ +α

                                θ =   [tex]2n\pi + \frac{\pi }{3}[/tex]

Step-by-step explanation:

Step(i):-

Given equation

                      cos x + sin x tan x = 2

               ⇒      [tex]cos x + sin x \frac{sin x}{cos x} = 2[/tex]

    On simplification , we get

              ⇒     [tex]\frac{sin^{2} x+ cos^2x}{cos x} = 2[/tex]

we know that trigonometry formula

[tex]sin^{2} x+ cos^2 x = 1[/tex]

now we get

             [tex]\frac{1}{cos x} = 2[/tex]

⇒         [tex]cos x = \frac{1}{2}[/tex]

⇒         cos x = cos 60°

Step(ii):-

General solution of cosθ = cosα

General solution    θ = 2 nπ +α

                               θ = 2 nπ +60°

                                θ =   [tex]2n\pi + \frac{\pi }{3}[/tex]

put n = 0 ⇒ θ = 60°

Put n =1 ⇒  θ = 360°+60°= 420°

.....and so on

The solutions of the equation in the interval  =[tex]\frac{\pi }{3}[/tex]

Final answer:-

The solutions of the equation in the interval [0,2π )

                    ={  [tex]\frac{\pi }{3}[/tex] }

General solution    θ = 2 nπ +α

                                θ =   [tex]2n\pi + \frac{\pi }{3}[/tex]

Answer:

a

The number of linearly independent vectors needed to span M2,4. N =8

b

The dimension of    [tex]M_{2,4}[/tex] is 8

Step-by-step explanation:

 From the question we are told that  

        The  vector space is an [tex]M_{2,4}[/tex] matrix

Now the number of linear linearly independent vectors needed to span M2,4.

is  evaluated as

      [tex]N = 2 * 4 = 8[/tex]

this is due to the fact that each entry of the matrix is independent

Given that there are eight  independent  in the vector space the dimension of

  [tex]M_{2,4}[/tex] is 8

a The number of linearly independent vectors needed to span M2,4. N =8

b The dimension of M2, 4 is 8.

Since there is vector space i.e. M2, 4

So, here n be = 2(4) = 8

Also, each entry of the matrix should be considered independent. Therefore, the dimension should also be 8.

Hence,

a The number of linearly independent vectors needed to span M2,4. N =8

b The dimension of M2, 4 is 8.

Learn more about vector here: https://brainly.com/question/12623333

Answer:

Step-by-step explanation:

Hello!

The variable of interest is:

X: height of seaweed.

X~N(μ;σ²)

μ= 10 cm

σ= 2 cm

You have to find the value of the variable X that separates the bottom 0.30 of the distribution from the top 0.70

P(X≤x)= 0.30

P(X≥x)= 0.70

Using the standard normal distribution you have to find the value of Z that separates the bottom 0.30 from the top 0.70 and then using the formula Z= (X-μ)/σ translate the Z value to the corresponding X value.

P(Z≤z)= 0.30

In the body of the table look for the probability of 0.30 and reach the margins to form the Z value. The mean of the distribution is "0" so below 50% of the distribution you'll find negative values.

z= -0.52

Now you have to clear the value of X:

Z= (X-μ)/σ

Z*σ= X-μ

X= (Z*σ)+μ

X= (-0.52*2)+10= 8.96

The value of seaweed height that divides the bottom 30%  from the top 70% is 8.96 cm

I hope this helps!

Answer:-0.53 and 9.72

Step-by-step explanation:

Answer:

1). [tex]P'(t) = (-9025t).e^{-0.05(53+0.95t^2)}[/tex]

2). (-435.36) dollars per week

Step-by-step explanation:

Weekly price decay of the product is represented by the function,

P(x) = [tex]95000.e^{-0.05x}[/tex]

And the price of the product changes over the period of 't' weeks is represented by,

x(t) = [tex]53+0.95t^2[/tex]

Function representing the rate of change in the profit with respect to the time will be represented by,

1). P'(t) = [tex]\frac{dP}{dx}.\frac{dx}{dt}[/tex]

Since, P(x) = [tex]95000.e^{-0.05x}[/tex]

P'(x) = [tex]95000\times (-0.05).e^{-0.05x}[/tex]

       = [tex](-4750).e^{-0.05x}[/tex]

Since, x(t) = 53 + 0.95t²

x'(t) = 1.9t

[tex]\frac{dP}{dx}.\frac{dx}{dt}=(-4750).e^{-0.05x}\times (1.9t)[/tex]

By substituting x = 53 + 0.95t²

[tex]\frac{dP}{dx}.\frac{dx}{dt}=(-4750).e^{-0.05(53+0.95t^2)}\times (1.9t)[/tex]

   P'(t) = [tex](-9025t).e^{-0.05(53+0.95t^2)}[/tex]

2). For t = 7 weeks,

P'(7) = [tex](-9025\times 7).e^{-0.05(53+0.95(7)^2)}[/tex]

       = [tex](-63175).e^{-4.9775}[/tex]

       = (-63175)(0.006891)

       = (-435.356) dollars per week

       ≈ (-435.36) dollars per week

Answer:

second side = s  first side = s +1  third side = s +2

39 feet = s + (s+1) + (s +2)

39 feet = 3s +3

36 feet = 3s

s = second side = 12 feet

first side = 13 feet

third side = 14 feet

Step-by-step explanation: