Area: Change in Dimensions
A rectangle FGHJ has a width of 3 inches and a length of 7 inches.

Answer:

first tile: X²-55=9

second tile:2x²-32=0

third tile:4x²-100=0

fourth tile:x²-140=-19

Step-by-step explanation:

apply difference of two squares to all i.e (a+b)(a-b)=(a²-b²)=0

x²-55-9=0

x²-64=0

x-8,x+8=0

x=8,x=-8

2x²-32=0

divide through by two

x²-16=0

x=4,x=-4

4x²-100=0

divide through by 4

x²-25=0

x=5 or -5

x²-140=-19

x²-140+19=0

x²-121=0

x=11 or -11

A = πr^2 and d = 2r.

So r = 8/2 = 4 cm.

Now use the first formula

A = π(4 cm)^2 = 50.265 cm^2

Answer:

The area formula is= 1/2(a+b)×height

1/2×20×6=60metres squared

Step-by-step explanation:

kindly correct me if am wrong

Answer: i) [tex]\frac{1}{3}[/tex]

              ii) [tex]\frac{5}{9}[/tex]

Step-by-step explanation:

Total length of film = 45 mins

Fraction of time left after 15 mins = [tex]\frac{15}{45}[/tex]

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

Fraction of time left after 25 mins = [tex]\frac{25}{45}[/tex]

                                                        = [tex]\frac{5}{9}[/tex]

Step-by-step explanation:

question 1

angle DBA=90°, meaning to find m<D you have to add 90+38 then subtract by 180, because ABD is a triangle

90+18+m<D=180

108+m<D=180

m<D=180-108

=72°

question 2

m<D again in this case angle ABD is also 90

m<D=180-(90+48)

=180-138

=42°

I hope this helps

Answer:

y = 3/2x-2

Step-by-step explanation:

slope intercept form is

y = mx+b where m is the slope and b is the y intercept

y = 3/2x+b

Substitute the point in for x and y

1 = 3/2(2)+b

1 = 3+b

1-3 =b

-2=b

y = 3/2x-2

Answer:

4

Step-by-step explanation:

Pick two points on the line

(0,-5)  and (1,-1)

We can find the slope using

m = (y2-y1)/(x2-x1)

   = ( -1 - -5)/(1 - 0)

  (-1+5)/(1-0)

    4/1

  = 4

Solution :

Given :

There are five cities in a network and the cost of [tex]\text{building}[/tex] a road directly between [tex]i[/tex] and [tex]j[/tex]  is the entry [tex]a_{i,j}[/tex]

[tex]a_{i,j}[/tex]  refers to the matrix.

Road cannot be built because there is a mountain.

The given matrix :

[tex]\begin{bmatrix}0 & 3 & 5 & 11 & 9\\ 3 & 0 & 3 & 9 & 8\\ 5 & 3 & 0 & \infty & 10\\ 11 & 9 & \infty & 0 & 7\\ 9 & 8 & 10 & 7 & 0\end{bmatrix}[/tex]

The matrix on the left above corresponds to the weighted graph on the right.

Using the [tex]\text{Kruskal's algorithm}[/tex] we can select the cheapest edge that is not creating a cycle.

Starting with 2 edges of weight 3 and the edge of weight 5 is forbidden but the edge is 7  is available.

The edge of the weight 8 completes a minimum spanning tree and total weight 21.

If the edge of weight 8 had weight 10 then either of the edges of weight 9 could be chosen the complete the tree and in this case there could be 2 spanning trees with minimum value.

If the scale factor is 30, then all you have to do is multiply each measurement by the scale factor. In this case, 4 · 30 = 120.

A stationary point at x = 3 means the derivative dy/dx = 0 at that point. Differentiating, we have

dy/dx = 6x ² + 2ax + b

and so when x = 3,

0 = 54 + 6a + b

or

6a + b = -54 … … … [eq1]

The curve passes through the point (4, 2), which is to say y = 2 when x = 4. So we also have

2 = 128 + 16a + 4b - 30

or

16a + 4b = -96

4a + b = -24 … … … [eq2]

Eliminate b by subtracting [eq2] from [eq1] and solve for a, then for b :

(6a + b) - (4a + b) = -54 - (-24)

2a = -30

a = -15   ===>   b = 96

Answer:

110000/8π

Step-by-step explanation:

Divide 1100000 by 80 and cancel 0. Then divide pi

Answer:

[tex](a)\ f(4) = v[/tex]

(b) There are 7 gallons left in the tank after 4 minuted

Step-by-step explanation:

Given

[tex]f(t) = v[/tex]

[tex]t \to[/tex] time since water began draining

[tex]v \to[/tex] gallons in the tank

Solving (a): Notation for gallons remaining at 4 minutes

This means that [tex]t=4[/tex]

[tex]f(t) = v[/tex] becomes

[tex]f(4) = v[/tex]

Solving (b): Interpret f(4) = 7

We have:

[tex]f(t) = v[/tex]

[tex]t \to[/tex] time since water began draining

[tex]v \to[/tex] gallons in the tank

This means that:

[tex]t =4[/tex]

[tex]v =7[/tex]

It can be interpreted as:

There are 7 gallons left in the tank after 4 minuted

Answer:

0.05x + 0.1(55 - x) = 3.9

Step-by-step explanation:

There are 55 coins.

Let x = number of nickels.

The number of dimes is 55 - x.

The value of a nickel is $0.05, and the value of a dime is $0.10.

The value of x nickels is 0.05x

The value of 55 - x dimes is 0.1(55 - x)

The total value of the coins is 0.05x + 0.1(55 - x)

The total value of the coins is $3.90

0.05x + 0.1(55 - x) = 3.9

Answer:

B+A

Step-by-step explanation:

Answer:

1375

Step-by-step explanation:

Answer:

[tex]12a^3d^2-6ad^3[/tex]

To factor an integer, we need to divide it by the ascending sequence of primes 2, 3, 5

In the end, the number of times each prime divides the original integer becomes its exponent.

Prime number 2  to the power of 2 equals 4 .

Prime number 3 to the power of 1 equals 3 .

[tex]2^{2} \times 3\times a^{3} \times b^{2} -(2\times3)ad^{3}[/tex]

Result:-  [tex]6ad^2\left(2a^2-d\right)[/tex]

 OAmalOHopeO

Answer:

the probability that a truck drives less than 159 miles in a day = 0.9374

Step-by-step explanation:

Given;

mean of the truck's speed, (m) = 120 miles per day

standard deviation, d = 23 miles per day

If the mileage per day is normally distributed, we use the following conceptual method to determine the probability of less than 159 miles per day;

1 standard deviation above the mean = m + d, = 120 + 23 = 143

2 standard deviation above the mean = m + 2d, = 120 + 46 = 166

159 is below 2 standard deviation above the mean but greater than 1 standard deviation above the mean.

For normal districution, 1 standard deviation above the mean = 84 percentile

Also, 2 standard deviation above the mean = 98 percentile

143 --------> 84%

159 ---------> x

166 --------- 98%

[tex]\frac{159-143}{166-143} = \frac{x-84}{98-84} \\\\\frac{16}{23} = \frac{x-84}{14} \\\\23(x-84) = 224\\\\x-84 = 9.7391\\\\x = 93.7391\ \%[/tex]

Therefore, the probability that a truck drives less than 159 miles in a day = 0.9374

===========================================================

Explanation:

Any equilateral triangle has all three angles of 60 degrees each. Splitting the triangle in half like this produces two identical copies of 30-60-90 triangles.

Any 30-60-90 triangle will have its hypotenuse twice as long compared to the short leg. The short leg here is 5 (it's opposite the smallest angle), so that doubles to 2*5 = 10 which is the value of x.

Note: the other side of this right triangle is 5*sqrt(3).

Answer:

x=10

Step-by-step explanation:

∵ Δ IS Equilateral.

∴ sides are equal.

perpendicular from vertex bisects it.

x=2×5=10

Answer:

432

Step-by-step explanation:

x=1hr (6x)=6hours x= 72 hours through train so (6x)=72x6=432

Answer:

a) the probability that the defective board was produced during the first hour of operation is [tex]\frac{1}{10}[/tex] or 0.1000

b) the probability that the defective board was produced during the  last hour of operation is [tex]\frac{1}{10}[/tex] or 0.1000

c) the required probability is 0.2000

Step-by-step explanation:

Given the data in the question;

During a specific ten-hour period, one defective circuit board was found.

Lets X represent the number of defective circuit boards coming out of the machine , following Poisson distribution on a particular 10-hours workday which one defective board was found.

Also let Y represent the event of producing one defective circuit board, Y is uniformly distributed over ( 0, 10 ) intervals.

f(y) = [tex]\left \{ {{\frac{1}{b-a} }\\\ }} \right _0[/tex];   ( a ≤ y ≤ b )[tex]_{elsewhere[/tex]

= [tex]\left \{ {{\frac{1}{10-0} }\\\ }} \right _0[/tex];   ( 0 ≤ y ≤ 10 )[tex]_{elsewhere[/tex]

f(y) = [tex]\left \{ {{\frac{1}{10} }\\\ }} \right _0[/tex];   ( 0 ≤ y ≤ 10 )[tex]_{elsewhere[/tex]

Now,

a) the probability that it was produced during the first hour of operation during that period;

P( Y < 1 )   =   [tex]\int\limits^1_0 {f(y)} \, dy[/tex]

we substitute

=    [tex]\int\limits^1_0 {\frac{1}{10} } \, dy[/tex]

= [tex]\frac{1}{10} [y]^1_0[/tex]

= [tex]\frac{1}{10} [ 1 - 0 ][/tex]

= [tex]\frac{1}{10}[/tex] or 0.1000

Therefore, the probability that the defective board was produced during the first hour of operation is [tex]\frac{1}{10}[/tex] or 0.1000

b) The probability that it was produced during the last hour of operation during that period.

P( Y > 9 ) =    [tex]\int\limits^{10}_9 {f(y)} \, dy[/tex]

we substitute

=    [tex]\int\limits^{10}_9 {\frac{1}{10} } \, dy[/tex]

= [tex]\frac{1}{10} [y]^{10}_9[/tex]

= [tex]\frac{1}{10} [ 10 - 9 ][/tex]

= [tex]\frac{1}{10}[/tex] or 0.1000

Therefore, the probability that the defective board was produced during the  last hour of operation is [tex]\frac{1}{10}[/tex] or 0.1000

c)

no defective circuit boards were produced during the first five hours of operation.

probability that the defective board was manufactured during the sixth hour will be;

P( 5 < Y < 6 | Y > 5 ) = P[ ( 5 < Y < 6 ) ∩ ( Y > 5 ) ] / P( Y > 5 )

= P( 5 < Y < 6 ) / P( Y > 5 )

we substitute

 [tex]= (\int\limits^{6}_5 {\frac{1}{10} } \, dy) / (\int\limits^{10}_5 {\frac{1}{10} } \, dy)[/tex]

[tex]= (\frac{1}{10} [y]^{6}_5) / (\frac{1}{10} [y]^{10}_5)[/tex]

= ( 6-5 ) / ( 10 - 5 )

= 0.2000

Therefore, the required probability is 0.2000

Answer:

a = 3√6 in

Step-by-step explanation:

From the question given above, the following data were obtained:

Angle θ = 60°

Adjacent = 3√2 in

Opposite = a =?

The value of 'a' can be obtained by using the tan ratio as illustrated below:

Tan θ = Opposite / Adjacent

Tan 60 = a / 3√2

√3 = a / 3√2

Cross multiply

a = √3 × 3√2

Recall:

c√d × n√m = (c×n) √(d×m)

Thus,

√3 × 3√2 = (1×3)√(3×2)

√3 × 3√2 = 3√6

a = 3√6 in

Answer:

main aapki madad karna chahti hun per Mujhe Ae Jahan question Nahin Aata sorry I don't know

sorry dear friend

Step-by-step explanation:

ok I don't know

Answer:

116 miles

Step-by-step explanation:

We can solve this by first writing an equation for the cost of the car rental. To begin, the base cost is $17.95, so any further costs must be added to that. Next, the car costs 19 cents (0.19 dollars) for each mile driven, so for each mile, we add 19 cents. This can be written as 0.19 *x if x represents the amount of miles driven. Therefore, we can add the two input costs of the car (the base cost and cost per mile) to get

17.95 + 0.19 * x = total cost.

After that, we want to maximize x/the number of miles with only 40 dollars. We can do this by setting this equal to the total cost, as going over the total cost is impossible and going under would be limiting the amount of miles (this because we are adding money for each mile, so more money means more miles). Therefore, we have

17.95 + 0.19 * x = 40

subtract 17.95 from both sides to isolate the x and its coefficient

22.05 = 0.19 * x

divide both sides by 0.19 to isolate x

22.05/0.19 = x = 116.05

The question asked us to round down, and 116.05 rounded down is 116 for our answer

Solution :

[tex]$H_0: p = 0.5$[/tex]

[tex]$H_a: p > 0.5$[/tex]

Alpha, α = 0.01

The sample proportion is :

[tex]$p'=\frac{x}{n}$[/tex]

   [tex]$=\frac{513}{806}$[/tex]

   = 0.636

Test statistics, [tex]$z=\frac{p'-p}{\sqrt{\frac{pq}{n}}}$[/tex]

[tex]$z=\frac{0.636-0.5}{\sqrt{\frac{0.5\times 0.5}{806}}}$[/tex]

[tex]$z=\frac{0.136}{0.0176}$[/tex]

z = 7.727

The p value = 0.00001

Here we observe that p value is less than α, and so we reject the hypothesis [tex]H_0[/tex].

Therefore, there is sufficient evidence,

Answer:

y = - x - 2

Step-by-step explanation:

y=mx+b

m refers to slope

b refers to y intercept

y = (-1)x + (-2)

y = - x - 2

Answer:

y=-1x-2

Step-by-step explanation:

plug in the slop and y intercept to the equation y=mx+b

Answer:

4. 53

5. 66

6. 89

7. 31

Step-by-step explanation:

4.  14 + 18 + 21

     ^      ^

        33 + 21

            53

5.  86 - 20

        66

6.  34 + 55

        89

7.  14 + 11 + 6

     ^     ^

      25 + 6

          31

9514 1404 393

Answer:

Step-by-step explanation:

The given information tells us there is one congruent side in the two right triangles. That is not sufficient to claim congruence of the triangles.

  CNBD

__

The figure shows one congruent angle in addition to one congruent side, so the figures can be shown to be congruent using the ASA theorem.

  ΔLAW ≅ ΔWKL

_____

Additional comment

We don't know which answer is expected. You should discuss this question with your teacher, since it appears to be missing the statement that

  ∠ALW ≅ ∠KWL