How to solve these questions?
(with work)

Answer:

4, 6, 4

6, 12, 8

8, 12, 6

Step-by-step explanation:

Tetrahedron:

4 faces, 6 edges, 4 vertices

Cube:

6 faces, 12 edges, 8 vertices

Octahedron:

8 faces, 12 edges, 6 vertices

you can also use the v - e + f = 2 to check

Answer: 10,204 feet

Step-by-step explanation: i would assume you would add the two together, seeing as if the mountain is 10,093 above sea level and the valley is 111 below, the difference in elevation is also the distance between each other.

Answer:

2 and 1/16th inch

Step-by-step explanation:

the half inch mark would be 2 and 1/2 and you know half of half is 1/4 so the best answer is A.

46) True

47) False

These are true by definition.

Answer: x = 50

Concept:

Here, we need to know the idea of alternative interior angles and the angle sum theorem.

Alternative interior angles are angles that are formed inside the two parallel lines, and the values are equal.

The angle sum theorem implies that the sum of interior angles of a triangle is 180°

If you are still confused, please refer to the attachment below or let me know.

Step-by-step explanation:

Given information:

AC ║ DE

∠ABC = 85°

∠A = 135°

Find the value of ∠BAC

∠A + ∠BAC = 180° (Supplementary angle)

(135°) + ∠BAC = 180°

∠BAC = 45°

Find the value of ∠BCA

∠ABC + ∠BAC + ∠BCA = 180° (Angle sum theorem)

(85°) + (45°) + ∠BCA = 180°

∠BCA = 50°

Find the value of x (∠EBC)

∠EBC ≅ ∠BCA (Alternative interior angles)

Since, ∠BCA = 50°

Therefore, ∠EBC = 50°

[tex]\Large\boxed{x=50}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

In calculating the factor A variation, there are two degrees of freedom. In determining the variation of factor B, there are two degrees of freedom.

A two-factor factorial design is an experiment that collects data for all potential values of the two factors of the study. The design is a balanced two-factor factorial design if equivalent sample sizes are used for every of the possible factor combinations.

Suppose we have two components, A and B, each of which has a high number of levels of interest. We will select a random level of component A and a random level of factor B, and n observations will be taken for each experimental combination.

From the data given:

a.

In calculating the factor A variation, there are two degrees of freedom.

In determining the variation of factor B, there are two degrees of freedom.

b.

Finding the degree of freedom using the interaction variation, there are four degrees of freedom.

c.

In finding the random variable, there are 9(4-1) = 27 degrees of freedom.

d.

In calculating the total variable, there are 9*4-1 =35 degrees of freedom.

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Answer:

10x

Step-by-step explanation:

g(x)=5x

f(x)=2x

f(g(x))=f(5x)

f(g(x))=2*5x=10x

The total cost to run Val’s AC costs for a summer month of 30 days is $94.5.

Quantity of electricity used in kilowatts

1000 watts = 1 kilowatts

2,500 watts = 2.5 kilowatts

Cost of Val’s AC to run for a summer month of 30 days = Quantity of electricity used × Number of hours Val runs AC per day × Number of days × Cost of electricity

= 2.5 × 7 × 30 × 0.18

= $94.5

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Answer:

53 mph   and  71 mph

Step-by-step explanation:

bus 1 rate = x

bus 2 rate = x + 18

rate times time = distance

( x    +    x+18) * 6 = 744

(2x+18) * 6 = 744

2x + 18 = 124

2x = 106

x = 53       the other bus is  53 + 18 =  71  mph

The solution to the equation is 0.07, 0.17, 0.27, 0.38........

The trigonometry equation is given as:

tan(30x - 90°) = -x³

We start by splitting the trigonometry equation as follows, by creating two different equations

y = tan(30x - 90°)

y = -x³

Next, we plot the graph of the trigonometry equations y = tan(30x - 90°) and y = -x³

From the graph of the trigonometry equations y = tan(30x - 90°) and y = -x³, we have the x coordinate of the point of intersection to be:

x = 0.07, 0.17, 0.27, 0.38........

Hence, the solution to the trigonometry equation is 0.07, 0.17, 0.27, 0.38........ .

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Answer:

x = 4

Step-by-step explanation:

You can solve for "x" by rearranging the equation and getting the "x" by itself on one side. Remember, whatever you do to one side of the equation, you must do to the other side.

-6 + x = -2                         <----- Original equation
+6         +6                        <----- Add 6 to both sides to isolate "x"

0 + x = 4                           <----- After the addition

x = 4                                 <----- Rewrite

Answer:

None of the above (x = 4) [tex] \sf {} [/tex]

Step-by-step explanation:

Now we have to,

→ find the required value of x.

The equation is,

→ -6 + x = -2

Then the value of x will be,

→ -6 + x = -2

→ x = -2 + 6

→ [ x = 4 ]

Hence, the value of x is 4.

Answer: 25 in³

Step-by-step explanation:

We can calculate the volume of the pyramid by first calculating the volume of a prism with the same dimensions, and then dividing by 3 (all pyramids a volume that's [tex]\frac{1}{3}[/tex] of the volume of a prism with the same dimensions).

The volume of a prism is its base area times its height. The base would be a square, so its area is 5², which is 25. The height is 3 inches, making the prism's volume 75 in³.

The volume of the pyramid would be one-third of this value, which is 75[tex]75\div3[/tex] which is 25 in³.

Answer:

  log(0.0003) = -3.5229

Step-by-step explanation:

The rules of logarithms tell you ...

  log(ab) = log(a) +log(b)

  log(0.0003) = log(3×10^-4) = log(3) +log(10^-4)

  = log(3) -4 = 0.4771 -4

  log(0.0003) = -3.5229

__

Additional comment

If you do much work with logarithms, you find that negative logarithms are generally expressed using a positive mantissa with a negative add-on. Often, that negative add-on is -9, so this would be ...

  5.4771-9

This helps when taking antilogs, as you look up 0.4771 in the table to see that the multiplier is 3.

If you were to look up 0.5229, you would find 3.333, meaning the multiplier is 1/3.333 and the antilog of -3.5229 is (10^-3)/3.333. This may not be a convenient value to work with.

According to the graph, the ships’ paths do not meet at any point.

Linear equations are equations that have constant average rates of change, slope or gradient

A system of linear equations is a collection of at least two linear equations.

In this case, the system of equations is given as

2x = 5y - 40

-4x + 10y = 20

Make y the subject in the second equation, by adding 4x to both sides of the equation

4x -4x + 10y = 20 + 4x

This gives

10y = 20 + 4x

Divide both sides by 10

y = 2 + 0.4x

Substitute y = 2 + 0.4x in 2x = 5y - 40

2x = 5(2 + 0.4x) - 40

Expand

2x = 10 + 2x - 40

Subtract 2x from both sides of the equation.

2x - 2x = 10 + 2x - 2x - 40

Evaluate the like terms

0 = 10 - 40

Evaluate the like terms

0 = -30

The above equation is not true.

This means that the ships’ paths do not meet at any point.

This can be confirmed using the attached graph.

From the graph, we can see that the lines of 2x = 5y - 40 and -4x + 10y = 20 do not intersect

Hence, we can conclude that the ships’ paths do not meet at any point.

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5 and 6 thousandths in standard form is 5.006

The number is given as:

5 and 6 thousandths

This can be rewritten as

5 +  6 thousandths

Express as numbers

5 +  0.006

Evaluate the sum

5.006

Hence, 5 and 6 thousandths in standard form is 5.006

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Answer:

47°

Step-by-step explanation:

If angles are complementary, that means those angles are added up to 90°.

Therefore,

43 + x = 90

Take 43 to the right side to make x as the subject.

x = 90 - 43

x = 47°

Note that a complementary angle adds up to 90 degrees.

In this problem, we get the equation:

43° + x = 90°

So, we need to find the value of x by doing:

90° – 43° = 47°

x = 47°

43° + 47° = 90°

We get the final result as:

x = 47°

Hope this helps :)

Due to the higher z-score, the correct option regarding the highest relative score is:

A score of 4730 on a test with a mean of 3960 and a standard deviation of 555.5.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The z-score measures how many standard deviations the measure is above or below the mean, hence the higher the z-score, the higher the score X is relative to other scores.

The respective z-scores for this problem are given by:

Hence the correct option is:

A score of 4730 on a test with a mean of 3960 and a standard deviation of 555.5.

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The scouts eat 51 bags of chips on their trip

The given parameters are:

Boxes = 9

Bag = 10 chips

2 full boxes of potato chips and 3 bags left over.

This represents:

Potato chips = 2 * 10 + 3

Potato chips = 23 i.e. 23 bags potato chips are left over

1 fewer box of nacho chips than potato chips, with no bags left over

This represents

Nacho chips = (2 - 1) * 10

Nacho chips = 10 i.e. 10 bags of nacho chips are left over

The loose bags of potato chips is 3.

So, we have:

Barbecue chips = 2 * 3 bags

Barbecue chips = 6 bags

At this point, we have:

The total number of bags left over is

Total = 23 + 10 + 6

Total = 39

The number of bags eaten is:

Eaten = 9 * 10 - 39

Evaluate

Eaten = 51

Hence, the scouts eat 51 bags of chips on their trip

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Answer:

A., B.

Step-by-step explanation:

Opposite angles of a quadrilateral inscribed in a circle are supplementary, so their sum must equal 180°.

A. 72° + 108° = 180° Answer: yes

B. 66° + 114° = 180° Answer: yes

C. 80° + 90° = 170° Answer: no

D. 64° + 106° = 170° Answer: no

Answer: A., B.

The particle will stop at D.

If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

In pentagon ABCDE shown above, each side is 1 cm. If a particle starts at point A and travels clockwise 723 cm along ABCDE, then

Number of sides = 5

Let x be the one complete revolution.

5 x = 725

x = 145

Now, 145 - 2 = 143

Hence, it will stop at D which is 2 less than A.

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The measure of angle a is 70 degrees

The angle in a semicircle is a right angle.

This means that:

a + d = 90

Where O is the center of the circle

From the figure, we have:

Angle d and the angle with a measure of 20 degrees are corresponding angles

This means that

d = 20

Substitute d = 20 in a + d = 90

a + 20 = 90

Subtract 20 from both sides of the equation

a = 70

Hence, the measure of angle a is 70 degrees

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The value of surface integral using the Divergence Theorem is [tex]729\pi[/tex] .

Divergence Theorem states that the surface integral of a vector field over a closed surface, is equal to the volume integral of the divergence over the region inside the surface. Mathematically the it can be calculated using the formula:[tex]\int\int\int\limit{ }_V(\delta \cdot F)=\int\int(F \cdot n)dS[/tex]

The divergence of F is

[tex]div F=\frac{d}{dx}(2x^{3}+y^{3})+\frac{d}{dy}( y^{3} +z^{3})+\frac{d}{dz}3y^{3} z[/tex]

[tex]div F=6x^{2}+3y^{2}+3y^{2}[/tex]

Let E be the region [tex]{(x,y,z):0\leq z\leq 9-x^{2} -y^{2}[/tex] then by divergence theorem we have [tex]\int \int\limits^{}_s {F\cdot n\times dS} =\int\int\int\limits^{}_E divFdV=\int\int\int\limits^{}_E(6x^2+6y^2)dV[/tex]

Now we find the value of the integral:

[tex]=\int\limits^{2\pi}_0\int\limits^3_0\int\limits^{9-r^2}_0(6r^2)rdzdrd{\theta}\\=\int\limits^{2\pi}_0 \int\limits^3_0(9-r^2)6r^3drd{\theta}\\=2\pi\int\limits^3_0 {(54r^3-6r^5)} dr\\[/tex]

[tex]=2\pi\times \frac{729}{2}\\=729\pi[/tex]

Thus we can say that the value of the integral for the surface around the paraboloid is given by [tex]729\pi[/tex].

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Question 13

Part (a)

[tex]\frac{3840-3905}{110}=\boxed{0.5\overline{90}}[/tex]

By similar logic, the other answers are

(b) 2.6818181....

(c) 3.5909090...

(d) 1.1363636...

Question 14

Part (a)

[tex]\frac{46800-41400}{4700} \approx \boxed{1.15}[/tex]

Part (b)

[tex]-2.57=\frac{x-41400}{4700} \\ \\ -2.57(4700)=x-41400 \\ \\ x=41400-2.57(4700) \\ \\ x \approx \boxed{29300}[/tex]

The level of significance on 0.05 exists at 83%.

The sample size (n) specified by the local cable company exists 300 which exists quite large.

According to the Central limit theorem, the sampling distribution of sample proportion observes a normal distribution with mean p and standard deviation

[tex]$\sqrt{\frac{p(1-p)}{n}}$[/tex]

Since the sampling distribution of sample proportions observes a normal distribution utilize the z-test for one proportion to execute the test.

The hypothesis is:

[tex]$H_{0}$[/tex]: The proportion of U.S. households that owned two or more televisions exists at 83 %, i.e. p = 0.83

[tex]$H_{1}$[/tex]: The proportion of U.S. households that owned two or more televisions exists less than 83 %, i.e. p < 0.83

Decision Rule:

At the level of significance [tex]$\alpha=0.05$[/tex] the critical region for a one-tailed z-test is:

[tex]$Z \leq-1.645[/tex]

By using the z table for the critical values.

So, if [tex]$Z \leq-1.645$[/tex]  the null hypothesis will be rejected.

Test statistic value:

[tex]$z=\frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

Here [tex]$\hat{p}$[/tex] exists the sample proportion.

Compute the value of [tex]$\hat{p}$[/tex] as follows:

[tex]$&\hat{p}=\frac{X}{n} \\[/tex] [tex]$&=\frac{240}{300} \\[/tex]

= 0.80

To compute the value of the test statistic as follows:

[tex]$z=\frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}}$[/tex]

[tex]$=\frac{0.80-0.83}{\sqrt{\frac{0.83 \cdot(1-0.83)}{3000}}}$[/tex]

The test statistic exists at -1.383 which exists more than -1.645.

Therefore, the test statistic lies in the acceptance region.

Thus we fail to reject the null hypothesis.

At a 0.05 level of significance, we fail to reject the null hypothesis noting that the proportion of U.S. households that owned two or more televisions exists at 83%.

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The equation that is equivalent to 8x - 6y = 12 is: B. y = 4x/3 - 2.

Equations that are equivalent to each other have the same value when evaluated or simplified.

Given the equation, 8x - 6y = 12, to determine which of the given equations in the options is equivalent to, rewrite the equation in slope-intercept form, as y = mx + b.

8x - 6y = 12

Subtract 8x from both sides of the equation

8x - 8x - 6y = -8x + 12

-6y = -8x + 12

Divide both sides of the equation by -6

-6y/-6 = -8x/-6 + 12/-6

y = 4x/3 + (-2)

y = 4x/3 - 2

Therefore, the equation that is equivalent to 8x - 6y = 12 is: B. y = 4x/3 - 2.

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The wholesale cost for the pianos that Tim pays the manufacturer, wages and utility bills that Tim pays are counted as explicit cost. On the other hand, the salary that Tim could earn if he worked as an accountant and the rental income that Tim could earn from renting his showroom fall under implicit cost.

Difference between Implicit Cost and Explicit Cost:

These two expenses, implicit cost and explicit cost, both represent company activity. The connection between cost and business is what distinguishes these two.

An explicit cost is one that the owner bears directly; an implicit cost is one that the owner bears indirectly without paying or utilizing its own resources. However, the organization or corporation takes into account both expenses while making management decisions.

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Answer:

1.

Step-by-step explanation:

10C0 = 1.

The best estimate for the correlation coefficient of the data is: C. 0.5.

Correlation can be defined as a quantitative measure that describes the relationship between variables. Correlation coefficient, r, is a number that ranges from -1 to 1.

The farther the correlation coefficient from 0, the stronger the relationship between two variables, and also, the more closer the data points are on a plotted graph. Also, a negative correlation value will show a trendline on a plot that slopes downward, while positive correlation value will show a trendline that slopes upwards.

In the graph given, the points are moderately closer to each other. Also, the trendline slopes upward, which suggest a positive correlation.

Since the points are moderately spaced from each other, the correlation coefficient would positive and be approximately 0.5.

Therefore, the best estimate for the correlation coefficient of the data is: C. 0.5.

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Answer:

2583000000000

Step-by-step explanation:

[tex]2.583*10^{12} = 2583000000000[/tex]