Find the fifth term in the sequence that is defined as follows:

Answer:

7.9km

Step-by-step explanation:

(a)See attached for the diagram representing this situation.

(b)

In Triangle ABC

[tex]\text{Using Law of Sines}\\\dfrac{\sin A}{a}=\dfrac{\sin C}{c} \\\dfrac{\sin A}{5.2}=\dfrac{\sin 58^\circ}{6.8} \\\sin A=5.2 \times \dfrac{\sin 58^\circ}{6.8}\\A=\arcsin (5.2 \times \dfrac{\sin 58^\circ}{6.8})\\A=40.43^\circ[/tex]

Next, we determine the value of Angle B.

[tex]\angle A+\angle B+\angle C=180^\circ\\40.43+58+\angle B=180^\circ\\\angle B=180^\circ-(40.43+58)\\\angle B=81.57^\circ[/tex]

Finally, we find b.

[tex]\text{Using Law of SInes}\\\dfrac{b}{\sin B}=\dfrac{c}{\sin C} \\\dfrac{b}{\sin 81.57^\circ}=\dfrac{6.8}{\sin 58^\circ} \\b=\dfrac{6.8}{\sin 58^\circ} \times \sin 81.57^\circ\\b=7.9km $ (to the nearest tenth of a kilometer)[/tex]

The distance between the small plane and the observation tower is 7.9km.

Answer:

-2²

Explanation:

Doing -k² is the same thing as -(k²), so the answer will be negative. However, (-k)² will still be positive. -2² will equal -4.

Answer:

see below

Step-by-step explanation:

2/3y + 15 = 9

Subtract 15 from each side

2/3y + 15-15 = 9-15

2/3y = -6

Multiply each side by 3/2 to isolate y

3/2 * 2/3y = -6 *3/2

y = -9

Answer:

y = - 9

Step-by-step explanation:

2/3y + 15 = 9

Subtract 15 on both sides.

2/3y = 9 - 15

2/3y = - 6

Multiply both sides by 3/2.

y = - 6 × 3/2

y = -18/2

y = -9

Answer:

the inverse is :10^x/2

Step-by-step explanation:

f(x)= log2x.

f^-1(x)=10^x/2

Answer:

0.00054

Step-by-step explanation:

Gold ball: we have one chance of choosing the correct ball from 1 to 48, so the probability is 1/48

White balls: we will pick 4 numbers from 1 to 51, so the total possibilities of groups of numbers we can choose is a combination of 51 choose 4:

C(51, 4) = 51! / (4! * 47!) = 51*50*49*48/(4*3*2)

If we want to correctly guess two numbers, we have groups of 2 winning numbers in the 4 numbers we guess, so a combination of 4 choose 2, and we also have to incorrectly guess the other 2 winning numbers in the 47 remaining numbers we didn't choose, so a combination of 47 choose 2:

C(4, 2) = 4! / (2! * 2!) = 4*3/2 = 6

C(47, 2) = 47! / (2! * 45!) = 47*46/2

The probability of the white balls case is the two combinations above over the total number of cases (the first combination we calculated):

P = C(4, 2) * C(47, 2) / C(51, 4)

P = (6 * 47 * 46/2) / (51 * 50 * 49 * 48/(4*3*2))

P = (3 * 47 * 46 * 4 * 3 * 2) / (51 * 50 * 49 * 48) = 0.026

Then the final probability is the probability in the gold ball case times the probability in the white balls case:

P = (1/48) * (3 * 47 * 46 * 4 * 3 * 2) / (51 * 50 * 49 * 48) = 0.00054

Answer:

250

Step-by-step explanation:

1000/4000

Answer:

768

Step-by-step explanation:

let C represent cost and w weight, then the equation relating them is

C = kw² ← k is the constant of variation

To find k use the condition w = 20, C = 4800, that is

4800 = k × 20² = 400k ( divide both sides by 400 )

12 = k

C = 12w² ← equation of variation

When w = 8, then

C = 12 × 8² = 12 × 64 = 768

Answer:

its 10 am I think

Step-by-step explanation:

it says 2 hours until midnight. 12 - 2 = 10

Answer:

its 10 am

Step-by-step explanation:

12 - 2 = 10

Answer:

-1/3

Step-by-step explanation:

the slope is always run over rise.

In this case we ran 1 spot to the right from where the line crosses the y axis and then 3 down.

so that gives us 1/3 but since the line is negative, the slope is also negative

Answer:

-0.84

Step-by-step explanation:

hope ths helps i did the test btw :)

Answer:

-6,6

Step-by-step explanation:

x^2=36

6*6=36

-6*-6=36

Answer:

x = 60 and y = 100

Step-by-step explanation:

As shown in the table, you have: x + y = 160

Otherwise, you have x:y = 3:5 or x = 3y/5

=> 3y/5 + y = 160

or 8y/5 = 160

or y/5 = 20

or y = 20*5 = 100

=> x = 160 - y = 160 - 100 = 60

=> x = 60 and y = 100

Answer:

Square each side

Subtract 1  from each side

Divide by 3

Step-by-step explanation:

sqrt(3x+1) = 4

Square each side

(sqrt(3x+1))^2 = 4^2

3x+1 = 16

Subtract 1  from each side

3x+1-1 = 16-1

3x= 15

Divide by 3

3x/3 = 15/3

x = 5

Answer:

3 acute angles.

Step-by-step explanation:

Triangles have three angles. If any one angle is obtuse or right-angle, then the remaining two angles must be acute. Or else, all the 3 angles can be acute.

An example can be an equilateral triangle because it has 3 acute angles. Each angle is 60 degrees.

Answer: 22%

Step-by-step explanation: First, you have to add the percetages of the white and blue towels.

20+58=78

Now, you can simply subtract 78% from 100% to get your answer, 22%

Answer:

A, a rhombus has all the properties of a square.

Step-by-step explanation:

Not all quadrilaterals will be the same

Answer:

There are 8 quarters and 2 nickels

Step-by-step explanation:

4 quarters for every 1 nickel

This means that for every 1 dollar, there are 5 cents

Double the statement above

1.05 x 2 = 2.10

There are 8 quarters and 2 nickels

Answer: The answer would be A.

The coordinates of the line are (0, 3) and (3, 0) hence, the line will pass through these points so, option A is correct.

A graph is a structure made up of a collection of things, where some object pairs are conceptually "connected." The items are represented by mathematical abstractions known as vertices, and each pair of connected vertices is referred to as an edge.

Given:

y = negative x + 3

The above phrase can be written as,

y = -x + 3

Calculate the slope as shown below,

Slope = -1

The x-intercept can be calculated as,

0 = -x + 3  (y is zero at the x-axis)

x = 3

The x-intercept can be calculated as,

y = 0 + 3 (y is zero at the x-axis)

y = 3

Mark the coordinates (0, 3) and (3, 0) on the graph and join the points you will get the graph.

The graph is attached below.

To know more about Graph:

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Answer:

The variance rounded to the nearest tenth is 691.8

Step-by-step explanation:

Xavier's bowling scores:

135, 140, 130, 190, 112, 200, 185, 172, 163, 151, 149

No. of observations n = 11

[tex]Mean = \frac{\text{Sum of all observations}}{\text{No. of observations}}\\Mean = \frac{135+140+130+190+112+200+185+172+ 163+ 151+149}{11}\\Mean =157[/tex]

Formula of variance : [tex]\sigma^2=\frac{\sum(x_i-\bar{x})^2}{n}[/tex]

[tex]\sigma^2=\frac{(135-157)^2+(140-157)^2+(130-157)^2+(190-157)^2+(112-157)^2+(200-157)^2+(185-157)^2+(172-157)^2+(163-157)^2+(151-157)^2+(149-157)^2}{11}[/tex]

[tex]\sigma^2=\frac{7610}{11}[/tex]

[tex]\sigma^2=691.81[/tex]

Hence the variance rounded to the nearest tenth is 691.8

Answer:

12000 liters.

Step-by-step explanation:

The depth of the oil in the tank is 1.2 m.

The height of the oil is 1.2 m.

Length is 5 m and width is 2 m.

The volume of a rectangular prism is l×w×h.

5×2×1.2

= 12

The volume of the oil in the tank is 12 m³.

1 m³ = 1000 liters

12×1000 = 12000 liters.

The quantity of oil in the tank is 12000 liters.

Answer:

The estimated number of times the spinner will land on 3 is 20.

Step-by-step explanation:

The complete question is:

A four-sided spinner is provided. If Tom spins the spinner 80 times then work out an estimate for the number of times the spinner will land on 3.

Solution:

Assume that the four-sided spinner is unbiased.

That is all the four outcomes are equally likely to be selected.

The probability that the spinner lands on any of the four numbers is:

P(1) = P (2) = P (3) = P (4) = 0.25

It is provided that Tom spins the spinner n = 80 times.

The spinner can land on any of the four numbers independently.

The random variable X, defined as the number of times the spinner lands on 3, follows a Binomial distribution with parameters n = 80 and p = 0.25.

The expected value of X is:

[tex]E(X)=np[/tex]

        [tex]=80\times 0.25\\=20[/tex]

Thus, the estimated number of times the spinner will land on 3 is 20.

Answer:

d.

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

just did it

Answer:

A.) It is not in standard form because the degree of the first term is not greater than six.

Step-by-step explanation:

Answer:

Step-by-step explanation:

D is the answer

Answer:

no, janet could not have won 10 games because 3x is not equal to 24

Step-by-step explanation:

if janet won twice as many as nadia that means nadia times 2

so it would be 20 to add both nadia and janet it would be over 24 therefore the answer is d

hope this helps

Answer: No; Janet could not have won 10 games because 3x ≠ 24

Step-by-step explanation:

Janet and Nadia won 30 games together. 10x2(10)=30

! !

—

Answer:

∛50 cm, 2∛50 cm, 3∛50 cm

Step-by-step explanation:

V= wlh

V=300 cm³

w= 1/3l

h= 2/3l

---------

Answer:

Length is 11.052cm

Width is 3.684cm

Height is 7.386cm

Step-by-step explanation:

Let length be x, width y and height Z

Width (y) = X/3 , height (z) = 2x /3

volume =xyz

volume = x(x/3)(2/3)x

Volume = (2/9)x³

But Volume =300

300= (2/9)x³

300/(2/9) = x³ (make x³ the subject to find x )

1350 = x³

x=3√(1350)

x=11.052cm

Length is 11.052cm

Width = x/3 =11.052 /3

= 3.684cm

Height = 2x/3 = 2(11.052) /3

= 7.368cm

You can check it by multiplying LWH to see if you get 300 (the volume)

Answer:

My friend's mower will take approximately 0.75 h to mow the lawn alone.

Step-by-step explanation:

To solve this problem we can use the idea of average speed and apply to this problem, using the appropriate formula shown below:

[tex]speed = \frac{distance}{time}[/tex]

Where each lawn mower has a speed at which they can mown, the distance is the lawn they're mowing and the time is how long they will take to do it. In the case where my equipment is working alone, its speed "x" can be modeled as below:

[tex]x = \frac{lawn}{1.5}[/tex]

When my friend's mower does the job, its speed "y" can be seen as:

[tex]y = \frac{lawn}{time}[/tex]

When both work together the speed can be seen as:

[tex]x + y = \frac{lawn}{0.5}[/tex]

Applying the first two equations on the second, gives us:

[tex]\frac{lawn}{1.5} + \frac{lawn}{time} = \frac{lawn}{0.5}\\\frac{1}{time} = \frac{1}{0.5} - \frac{1}{1.5}\\\frac{1}{time} = 2 - 0.667\\\frac{1}{time} = 1.333\\1.333*time = 1\\time = \frac{1}{1.333} = 0.75[/tex]

My friend's mower will take approximately 0.75 h to mow the lawn alone.

Answer:

25.5x

Step-by-step explanation:

Simply convert the fraction into a decimal and add.

21/2x = 10.5x

10.5x + 15x = 25.5x

If you want to keep it in fraction form, 15 is 30/2, so,

30x/2 + 21x/2 = 51x/2

Answer:

51x/2

Step-by-step explanation:

Add it like a normal fraction equation

Have them both with the same denominator of 2

30/2 + 21/2

Add the numerators

51/2

Now put the x into the numerator since it started as in the numerator

Answer: 51x/2

Hope this helps!

Answer:

Step-by-step explanation:

After one year

A=p(1+r/n)^nt

=2000(1+0.03/12)^12*1

=2000(1+0.0025)^12

=2000(1.0025)^12

=2000(1.0304)

=$2060.8

After two-years

A=p(1+r/n)^nt

=2060.8(1+0.03/12)^12*2

=2060.8(1+0.0025)^24

=2060.8(1.0025)^24

=2060.8(1.0618)

=$2188.157

After three years

A=p(1+r/n)^nt

=2188.157(1+0.03/12)^12*3

=2188.157(1+0.0025)^36

=2188.157(1.0025)^36

=2188.157(1.0941)

=$2394.063

Amount in account after one year, two and three years are respectively  $2,060 , $2,121.8 and $2,185.45

Given:

Principal amount = $2,000

Rate of interest = 3% = 0.03

Amount in account after one year

A = P(1+r)ⁿ

A = 2,000(1+0.03)¹

A = 2,000(1.03)¹

A = 2,000(1.03)

A = $2,060

Amount in account after two year

A = P(1+r)ⁿ

A = 2,000(1+0.03)²

A = 2,000(1.03)²

A = 2,000(1.0609)

A = $2,121.8

Amount in account after three year

A = P(1+r)ⁿ

A = 2,000(1+0.03)³

A = 2,000(1.03)³

A = 2,000(1.092727)

A = $2,185.45

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