ECA is a semi equilateral triangle at C,
where EÂC= 30°
B is point on [AC] such that BC = 2cm
and BE = 3cm.
Calculate AE.

The magnitude of an earthquake with an intensity 10,000 times is [㏒10000]

magnitude can be regarded as the size or the weight of destruction that is been experienced as a result of the earthquake.

The magnitude as regards Richter scale is

[㏒(I/I₀]

But we were given l as 10000I₀.

Then if we substitute we have, [㏒(10000I₀./I₀)]

If we simplify we have:

[㏒10000]

Therefore, magnitude of an earthquake with an intensity 10,000 times is [㏒10000]

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Using the t-distribution, it is found that the test statistic for the hypotheses test is given by:

[tex]t = \frac{-1.75 - 0}{\frac{7.12}{\sqrt{35}}}[/tex]

At the null hypotheses, it i tested if the mean difference remains the same, that is:

[tex]H_0: \mu  = 0[/tex]

At the alternative hypotheses, it is tested if it has decreased, hence:

[tex]H_a: \mu < 0[/tex].

The test statistic is given by:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

The parameters are:

The parameters are given as follows:

[tex]\overline{x} = -1.75, s = 7.12, n = 35[/tex].

Hence the test statistic is given by:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{-1.75 - 0}{\frac{7.12}{\sqrt{35}}}[/tex]

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Step-by-step explanation:

we have a right-angled triangle :

the Hypotenuse (baseline opposite of the 90° angle) is the 850 ft cable from the top of the tower down to the point on the ground 360 ft away from the tower.

then the ground distance (360 ft) and the height of the tower are the 2 legs.

so, we can use Pythagoras

c² = a² + b²

with c being the Hypotenuse.

in our case

850² = 360² + height²

height² = 850² - 360² = 592,900

height = 770 ft

the tower is 770 ft tall.

Answer:

770 feet

Step-by-step explanation:

Given

Solving

Answer:

Step-by-step explanation:

The probability of picking a blue counter from the bag is 1 / 13.

The number of counters initially in the bag:

The number of counters now in the bag:

13/26

x = 13 - 5 = 8

Probability of picking a blue counter = number of blue counters / total number of counters

2/26 = 1 / 13

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Answer:

the answer is $31.80

Step-by-step explanation:

6% of $120.00 is $7.20,

75% off of 127.20= $31.80

12.57

Step-by-step explanation:

Area = πr²

40/360 × 22/7 × 36

1/9 × 22/7 × 36

(22 × 4)/7 = 12.57

The factor of the polynomial 18x³ + 6x²y - 9x² - 3xy will be 3x(6x² - 2xy - 3x - y). Then the correct option is C.

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

The polynomial is given below.

⇒ 18x³ + 6x²y - 9x² - 3xy

Then the factor of the polynomial will be

⇒ 18x³ + 6x²y - 9x² - 3xy

⇒ 3x(6x² - 2xy - 3x - y)

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Answer:

See below ~

Step-by-step explanation:

Q1

Q2

Q3

Q4

Q5

Answer:

5 minutes

Step-by-step explanation:

The visitor data is best modeled by a quadratic function, and the state park management should plan for more than 400 visitors next year.

To do this, we simply plot the points on a graph.

See attachment for the graph that represents the table.

From the attached graph, we can see that the points on the graph follows an approximately quadratic path

Hence, the visitor data is best modeled by a quadratic function

Also, the state park management should plan for more than 400 visitors next year.

This is so because the range of a quadratic function is the set of all real numbers.

This means that the table can accept a value of 400 (or greater) as one of its data points

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Step-by-step explanation:

mean =10

sum of no =7+5+0+1+3+4+h=20+h

N=7

now

mean=sum of no/N

10=20+h/7

10×7=20+h

70-20=h

h=50

Answer:

x = 132

Step-by-step explanation:

x = 180 - 48

x = 132

Answer:  $27.5

Step-by-step explanation:

10 percent of 25 is 2.5 (which is the tax). We just add that to the cost of the shirt and we get the final cost of $27.5.

The sales they might anticipate if they raise the price to $40 a bottle is $1,500.

Using this formula

Anticipated sales=(Current selling price÷Increase in price)×Number of bottle sold

Let plug in the formula

Anticipated sales=($30÷$40)×2,000

Anticipated sales=$0.75×2,000

Anticipated sales=$1,500

Therefore the sales they might anticipate if they raise the price to $40 a bottle is $1,500.

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Answer:

as x→+∞, f(x)→+∞   as x→-∞,f(x)→-∞

Step-by-step explanation:

The appropriate inference procedure is the t test for μdiff.

The t test is used to compare the means of two groups. It is a very important tool that can be used in inferential statistics.

Since it shows whether the means of two groups are significantly different, we can say that, the appropriate inference procedure is the t test for μdiff.

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Answer:

150

Step-by-step explanation:

Knowing that a cube has 6 faces which all are equal.

Thus, Multiply the area of one face by the number of faces to get the total surface area of the cube.

Since, it given that one face is 5 cm

Then, we also must know the formula for area of a cube

Which is:

[tex]Area=6a^2[/tex]

Thus,

[tex]Area=6a^2[/tex]

[tex]Area=6(5)^2[/tex]

[tex]Area=6(25)[/tex]

[tex]Area=150[/tex]

Kavinsky

Answer:

-256

Step-by-step explanation:

The numbers are being multiplied by 2.

( -4 * 2 = -8)

(-8* 2 = -16)

Answer:

There is a total of 200 dollars profit

Answer:

table 1

Step-by-step explanation:

a table represents a proportional relationship between the number of laptop and desktop computers ,if the ratio of the number of desktop computers to laptops is a constant (doesn’t vary)

Table1 : (does not represent a proportional relationship) because :

11÷10=1,1

46÷42=1.09...

and 1.1 ≠ 1.09

Table2 : (represents a proportional relationship) because :

3÷6=0.5

9÷18=0.5

18÷36=0.5

72÷144=0.5

Table3 : (represents a proportional relationship) because :

18÷12=1.5

36÷24=1.5

54÷36=1.5

108÷72=1.5

Table4 : (represents a proportional relationship) because :

2÷3=0.666666666667

18÷27=0.666666666667

22÷33=0.666666666667

200÷300=0.666666666667

Answer:

A. The fewest number of packages of cups and napkins that can be purchased so that they will be the same is 3 packages of cups and 2 packages of napkins.

B. I'm not sure what this part is asking, I hope someone else comes in and helps.

Step-by-step explanation:

Part A Explanation:

3 packages of cups gives you 24 cups total

2 packages of napkins gives you 24 napkins total

Answer:

A parameter is a numerical description of a population characteristic

Step-by-step explanation:

A parameter is a numerical description of a population characteristic

The probability that the student scores a 70 or below is 0.0013

The given parameters are:

The probability that a student scores 70 or below is represented as:

P(x ≤ 70)

Calculate the z score for x = 70 using:

[tex]z =\frac{x - \mu}{\sigma}[/tex]

This gives

[tex]z =\frac{70 - 82}{4}[/tex]

Evaluate

z =-3

The probability becomes

P(x ≤ 70) = P(z ≤ -3)

Using the z tables of probabilities, we have:

P(x ≤ 70) = 0.0013499

Approximate

P(x ≤ 70) = 0.0013

Hence, the probability that the student scores a 70 or below is 0.0013

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Answer:

FOR THE AREA:

Count how many full squares are in the middle, then count how many halves there are on the outer edge. the divide the amount of halves by 2 then add to the amount of full squares.

The domain restrictions on the rational function [tex]\frac{50}{4x - 12} + \frac{x- 4}{x^2 + x - 12} = \frac{x}{2}[/tex] are (b) x = 3 or and (d) x = -4

The function as expressed in the correct format is:

[tex]\frac{50}{4x - 12} + \frac{x- 4}{x^2 + x - 12} = \frac{x}{2}[/tex]

Factorize the denominators of the fractions

[tex]\frac{50}{4(x - 3)} + \frac{x- 4}{x^2 + 4x- 3x - 12} = \frac{x}{2}[/tex]

Factor out x and -3

[tex]\frac{50}{4(x - 3)} + \frac{x- 4}{x(x + 4)- 3(x + 4)} = \frac{x}{2}[/tex]

Factor out x + 4

[tex]\frac{50}{4(x - 3)} + \frac{x- 4}{(x- 3)(x + 4)} = \frac{x}{2}[/tex]

Set the denominators to 0

4(x - 3) = 0

(x - 3)(x + 4) = 0

Solve for x:

4(x - 3) = 0 ⇒ x = 3

(x - 3)(x + 4) = 0 ⇒ x = 3 or x = -4

This means that the domain restrictions on the rational function are (b) x = 3 or and (d) x = -4

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Answer:

17.2

Step-by-step explanation:

23 ⇒ Below 5, round down

20  ⇒ Add to decimal

17. 23 ⇒ 17.2 / 17.20

Answer:

70

Step-by-step explanation:

in parallelograms, the measure of reciprocal angles is equal to 180 because they are supplementary,

m<D = 110 so the measure of m<A which is reciprocal to m<D is equal to 70

Answer:

A. m = 0

Step-by-step explanation:

The slope is 0 as the change in y-value is 0, and change in x-value is infinite.

Graph

Answer:

Step-by-step explanation:

Formula

P = 5 + 1.50n

P is the total Cost

n is the number of Km travelled.

Solution

Substitute n = 25 into the formula

P = 5 + 1.5 * 25

P = 5 + 37.5

P = 42.50

Answer

42.50 dollars for 25 km.