Solve completely (all missing sides and all missing angles) using trig ratios or laws. Round to the nearest tenth.

Answer:

False

Step-by-step explanation:

There are some quadratic equations that cannot be solved using the factoring technique. That is why the quadratic formula exists, to solve equations that cannot be factored.

Step-by-step explanation:

171 km/h

travel distance = 855 km

855 / 171 = 5 hours

it took him 5 hours to fly the 855 km (theoretically to the hospital).

normally, with a plane, you can't land on or at a hospital. you would need a helicopter to be able to do that.

so, he could only fly to a nearby airport, and then travel from there to the hospital. but we have no information about that.

Proof -

So, in the first part we'll verify by taking n = 1.

[tex] \implies \: 1 = {1}^{2} = \frac{1(1 + 1)(2 + 1)}{6} [/tex]

[tex] \implies{ \frac{1(2)(3)}{6} }[/tex]

[tex]\implies{ 1}[/tex]

Therefore, it is true for the first part.

In the second part we will assume that,

[tex] \: { {1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} = \frac{k(k + 1)(2k + 1)}{6} }[/tex]

and we will prove that,

[tex]\sf{ \: { {1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k + 1)(k + 1 + 1) \{2(k + 1) + 1\}}{6}}}[/tex]

[tex] \: {{1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k + 1)(k + 2) (2k + 3)}{6}}[/tex]

[tex]{1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{k (k + 1) (2k + 1) }{6} + \frac{(k + 1) ^{2} }{6} [/tex]

[tex]{1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{k(k+1)(2k+1)+6(k+1)^ 2 }{6} [/tex]

[tex]{1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k+1)\{k(2k+1)+6(k+1)\} }{6}[/tex]

[tex]{1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k+1)(2k^2 +k+6k+6) }{6} [/tex]

[tex]{1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k+1)(2k^2+7k+6) }{6} [/tex]

[tex]{1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k+1)(k+2)(2k+3) }{6} [/tex]

Henceforth, by using the principle of mathematical induction 1²+2² +3²+....+n² = n(n+1)(2n+1)/ 6 for all positive integers n.

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Please scroll left - right to view the full solution.

If the data is not skewed, then the mean is the best measure of center.

This then also includes the standard deviation because the standard deviation relies on the mean.

To get the mean, add up the data values:

5+6+7+7+7+8+8+9+9+9+9+9+10+10+11 = 124

Then divide by the sample size n = 15

124/n = 124/15 = 8.267 approximately

Once you determine the mean, you can then determine the standard deviation which involves a bit more complicated steps. The rough outline is:

Once again, step 1 shows how critical the mean is to finding the standard deviation. The standard deviation measures how far each value is from the mean on average. In other words, it's like a measure of the average distance from the mean.

Use of spreadsheet software is strongly recommended to keep track of everything. You can also use a standard calculator to compute the standard deviation. There are also tons of free online calculators that can help out with that as well.

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If the data was skewed to one side, then the median is the better measure of center because it is not affected by outliers. The IQR (interquartile range) is used instead of the standard deviation for skewed distributions.

Answer 19.35 km

Step-by-step explanation:

We are looking for the Distance that Apostle Paul walked in 4.5 Hours!

I will be using the formula Distance=rate*time 1)

We DONT know the distance so I'll leave it as variable "D".

We know his rate of walking is 4.3 km/h, and we know he walked for a total of 4.5 hours.

Set up the following equation. D=4.3*4.5 2)

Simplify the equation above: D=19.35

Answer:

31/10

Step-by-step explanation:

Answer:

65.62

Step-by-step explanation:

Given:

After eating a meal at a restaurant, we decided to tip 25%, building a grand total of $87.50.

To find:

Price before tip

Solution:

87.50 × 25% = 21.875

~Round~: 21.875 to 21.88

87.50 - 21 .88 = 65.62

Thus the price before the tip is 65.62

Check Answer:

Formula: Higher number - Lower number ÷ original number × 100

Solve:

87.50 - 65.62 = 21.88

21.88 ÷ 87.50=0.25005714285

0.25005714285 × 100 = 25.0057142857

Round - 25%

~lenvy~

Answer:

0.75mg

Step-by-step explanation:

6 years is its half life, meaning that half of it will have iradiated by that point. 1.5 / 2 = 0.75

Answer:

Option 3 is the correct answer.

Answer: The number of tickets sold is the independent variable because it affects the amount of money earned.

Step-by-step explanation: I just took test got 100%

The number of tickets sold is the independent variable because it affects the amount of money earned.

Answer:

1. a = 1

2. See explanation below.

Step-by-step explanation:

First Question

Given:

[tex]\displaystyle \large{\log_b a = 0}[/tex]

Convert to exponential:

[tex]\displaystyle \large{\log_b a = c \to b^c = a}[/tex]

Thus [tex]\displaystyle \large{\log_b a = 0 \to b^0 = a}[/tex]

Evaluate:

[tex]\displaystyle \large{b^0 = a}[/tex]

We know that for every values to power of 0 will always result in 1, excluding 0 to power of 0 itself.

Solution:

[tex]\displaystyle \large{a = 1}[/tex]

__________________________________________________________

Second Question

Given:

[tex]\displaystyle \large{log_0 3}[/tex] and [tex]\displaystyle \large{\log_1 3}[/tex]

Let’s convert to an equation:

[tex]\displaystyle \large{\log_0 3 = x}[/tex] and [tex]\displaystyle \large{\log_1 3 = y}[/tex]

The variables represent unknown values of logarithm.

Convert to exponential:

[tex]\displaystyle \large{0^x = 3}[/tex] and [tex]\displaystyle \large{1^y = 3}[/tex]

Notice that none of x-values and y-values will satisfy the equations. No matter what real numbers you put in, these equations will always be false.

Hence, no solutions for x and y.

Answer: 22.44$

Step-by-step explanation:

1. 30 x 0.20 = 6

2. 30 - 6 = 24

3. 24 x 0.065 = 1.56

24 - 1.56 = 22.44$

Answer:

First one: 27

Second one: 1/8

Step-by-step explanation:

Hope this helps! :)

Total number of tickets sold = 250

Number of prizes = 5

Number of favorable outcomes = 5

[tex]P(A)= \frac{no. of possible outcomes}{No. of total outcomes} [/tex]

[tex]P (getting \: a \: prize) = \frac{5}{250} =\frac{1}{150}[/tex]

Answer:

its 23

Step-by-step explanation:

Answer:

You didnt give the chart so there for I can not give you a good answer

Step-by-step explanation:

Given:

[tex]\frac{3}{9}[/tex] and [tex]\frac{1}{2}[/tex]

Finding a common denominator:

9 * 2 = 18

       -> If you need to stop here, a common denominator is 18.

Converting [tex]\frac{3}{9}[/tex]:

[tex]\frac{3}{9}[/tex] = [tex]\frac{3*2}{9*2}[/tex] = [tex]\frac{6}{18}[/tex]

Converting [tex]\frac{1}{2}[/tex]:

[tex]\frac{1}{2}[/tex] = [tex]\frac{1*9}{2*9}[/tex] = [tex]\frac{9}{18}[/tex]

       ->  [tex]\frac{6}{18}[/tex] and  [tex]\frac{9}{18}[/tex]

Answer:

water level is h=6.5 m, compute the time required to drain the tank to a level of h= 0.5m. Use the fourth-order Runge-Kutta method.

Step-by-step explanation:

water level is h=6.5 m, compute the time required to drain the tank to a level of h= 0.5m. Use the fourth-order Runge-Kutta method.

Answer:

5400

Step-by-step explanation:

8% of 5000 is 400. 5000 + 400 - 5400.

Answer:

$5400

Step-by-step explanation:

We need to find the amount of tax in $

So, if 100% = $5000

           8%   =  ?

cross multiply to be :  8 × 5000

                                        100

to get $400

Add it to the $5000 to get $5400

Answer:

wow that is a tough one             the answer is 438654

Step-by-step explanation:

all that is to it

[tex]- 10(2) + y = 4[/tex]

[tex] - 20 + y = 4[/tex]

[tex]y = 24[/tex]

[tex] - 10( 1) + y = 4[/tex]

[tex] - 10 + y = 4[/tex]

[tex]y = 14[/tex]

[tex] - 10(0) + y = 4[/tex]

[tex]0 + y = 4[/tex]

[tex]y = 4[/tex]

[tex] - 10( - 1) + y = 4[/tex]

[tex]10 + y = 4[/tex]

[tex]y = - 6[/tex]

[tex] - 10( - 2) + y = 4[/tex]

[tex]20 + y = 4[/tex]

[tex]y = - 16[/tex]

Answer:

-2 = -16

-1 = -6

0 = 4

1 = 6

2 = 16

Step-by-step explanation:

Answer:

9.852

Step-by-step explanation:

First, Graph all three functions and find where they intersect and the shape that they make through their intersection. Note that since the shape does not touch the y= -1 line, we will use the "washer" method (where the volume equals  [tex]\pi\int\limits^a_b {R(x)\x^{2} - r(x)^{2} } \, dx[/tex].

The next step is to find a and b. Since the function that the area is going to be rotated about is a " y =" equations, the boundaries will be the x coordinates where the three functions intersect, b=1 for (1,1) and a=3 for (3,1).

Next we have to find R(x) and r(x). In this case, R(x) is the difference between the function furthest away from the axis of rotation and the function of the axis of rotation (or visa versa depending on which is on top), and r(x) is the difference between the function closest to the axis of rotation and the function of the axis of rotation (or visa versa depending on which is on top.

For this problem R(x) = 1 - (-1) and r(x) = 1/x - (-1) since when you look at the graph, Y = 1  is further from y = -1 than y = 1/x is, and both functions are on top of y = -1.

Finally plug in R(x) and r(x) and solve either using a calculator or through integration. If you solve through integration you should get [tex]\pi (-2ln(3) + \frac{16}{3} )[/tex].

Answer:

65

Step-by-step explanation:

angle 2 is equal to angle 4, so that means angle 4 is also 130⁰.

130=2y

130/2=2y/2

65=y

Answer:

y = 65°

Step-by-step explanation:

Vertical Angle Theorem:  When two straight lines intersect, the opposite vertical angles are always equal (congruent) to each other.

⇒ m∠2 = m∠4

⇒ 130° = 2y

⇒ y = 130° ÷ 2

⇒ y = 65°

Answer:

should be 66% of children and 1650 children in the town

Step-by-step explanation:

[tex]\rightarrow[/tex] Side(a) of the cube = [tex]\sf{\frac{1}{3}ft}[/tex].

[tex]\rightarrow[/tex] Surface Area of the cube with side [tex]\sf{\frac{1}{3}ft.}[/tex]

[tex]\rightarrow[/tex] Surface area of cube = [tex]\sf{6a^2}[/tex]

[tex]\rightarrow[/tex] Surface area of cube = [tex]\sf{6a^2}[/tex] (putting the value of a from the above given)

[tex]\rightarrow[/tex] [tex]\sf{=\:6×(\frac{1}{3})^2}[/tex]

[tex]\rightarrow[/tex] [tex]\sf{=\:6×\frac{1}{9}}[/tex]

[tex]\rightarrow[/tex] [tex]\sf{=\:\frac{6}{9}}[/tex]

[tex]\rightarrow[/tex] [tex]\sf{=\:\frac{2}{3}ft^2}[/tex]

Therefore, surface area of the given square = [tex]\sf{=\:\frac{2}{3}ft^2}[/tex]

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Hope it helps you:)

Answer:

Step-by-step explanation:

there are 6 square faces of a cube.

if side=x

surface area=6x²

=6(1/3)²

=6/9

=2/3 square foot

Answer:

Step-by-step explanation:

Use law of cosine to calculate the other side.

c² = a² + b² -2ab Cos C

Here, c  is the length of the side which is  opposite side to ∠E

a = 29   ; b = 25  and C = 109

c² = 29² + 25² - 2*29*25*Cos 107

    = 841 + 625 - 1450* (-0.2923)

     = 1466 + 423.835

     = 1889.835

c =√1889.835

c = 43.47 ≈ 43

No, find ∠D using again use law of cosine

[tex]Cos \ \beta = \dfra{a^{2}+c^{2}}-b^{2}{2ac}\\\\\\ = \dfrac{29^{2}+43^{2}-25^{2}}{2*29*43}\\\\\\Cos \ \beta =\dfrac{841+1849-625}{2494}=\dfrac{2065}{2494}\\\\Cos \ \beta = 0.828\\\\\beta =Cos^{-1} \ 0.828\\\\[/tex]

β = ∠C = 34°

α = 180 - (34 +107)

α = ∠D = 39

Other angles are

∠C = 34°     and  ∠D°39

Answer:

The first one is 11x=16, the second one is 4x=16, and the next one is 7x=12, and the last one is 3=1x hope this helps

Step-by-step explanation:

Answer:

he can buy 8 of lilies and 12 of rose and 48 of daisies

Ali can buy 3 flowers of lilies, 3 flowers of roses, and 18 flowers of daisies.

Suppose Ali buys x flowers of lilies, y flowers of roses, and z flowers of daisies.

According to the question

x+y+z = 24......(1)

3x+2y+0.5z = 24.......(2)

Here, we have three variables but only two equations.

2(2)-(1) gives, 5x+3y = 24......(3)

Since, x, y and z can take only integer values.

Numbers that are not fractions called integers.

So, from (3) only x=3 and y=3 is possible

So, z= 24-x-y

z=24-3-3 = 18

So, Ali can buy 3 flowers of lilies, 3 flowers of roses, and 18 flowers of daisies.

Therefore, Ali can buy 3 flowers of lilies, 3 flowers of roses, and 18 flowers of daisies.

To get more about linear equations visit:

https://brainly.com/question/14323743

Answer:

Step-by-step explanation:

Inscribed angle of diameter is 90°

⇒ ∠ACB = 90°

In ΔACB,

∠A + ∠ B + ∠ACB = 180°   {Angle sum property of triangle}

a + 4a + 90 = 180

      5a + 90 = 180

           5a    = 180 - 90

            5a = 90

              a = 90 ÷ 5

a = 19 -----------(I)

In ΔCOB,

OC = OB   {Radius}

⇒ΔCOB is an isosceles triangle.

c = 4a    {angles opposite to equal angles are conguent}

c = 4*19    {From (I)}

c= 76