a vertical pole stands on an horizontal ground. a student position due west of the pole observes that the angle of elevation of the top of the pole is 40 degree. when the the students moves 10 m due South. he observes that the angle of elevation of the top of the pole is 35 degrees. what is the height of the pole.​

Answer:

A = 20,000

Step-by-step explanation:

200,000 ÷ 10 = 20,000

The loan amount going to be for a home that cost  $200000 home. You plan to pay 10% as a down payment and take out a 30-year loan for the rest is $180000.

When the loan is given to you, then some amount is charged to you for the principal amount and that is called interest.

Given:

The cost of the house, C = $200000,

The time = 30 years,

If the down payment is 10% then the remaining amount,

Down payment  amount, D = 10% of 2000000 = $20000

Remaining amount = C - D

Remaining amount = $200000 -  $20000 = $180000,

Therefore, the loan amount is $180000.

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Answer:

A. [tex]y = 2.5\cdot x[/tex]

Step-by-step explanation:

Let be [tex]x[/tex] the sold amount of strawberries, measured in pounds, and [tex]y[/tex] the amount of money acquired due to sales, measured in monetary units. According to the statement of the problem, there is a direct proportionality between [tex]x[/tex] and [tex]y[/tex]. That is:

[tex]y\propto x[/tex]

[tex]y = k\cdot x[/tex]

Where [tex]k[/tex] is the proportionality factor, measured in monetary units per pound. This factor is now deducted and tested: ([tex]x = 4\,lb[/tex], [tex]y = \$\,10[/tex])

[tex]k = \frac{y}{x}[/tex]

[tex]k = \frac{\$\,10}{4\,lb}[/tex]

[tex]k = 2.5\,\frac{\$}{lb}[/tex]

The proposed formula is [tex]y = 2.5\cdot x[/tex], and then, let consider that [tex]x = 8\,lb[/tex], the the amount of money acquired due to sales is:

[tex]y = 2.5\cdot (8\,lb)[/tex]

[tex]y = \$\,20[/tex]

Which coincides with the relationship described in the statement of problem. Finally, the right answer is A.

Answer:

y = 2.5x

Step-by-step explanation:

Just did it on Edmentum and got it right

The probability of heads would be 1 - probability of tails.

1-0.4 = 0.6

The probability of getting heads is 0.6

Based on the information given, the probability will be 0.6.

From the question, it was stated that Leon throws a biased coin and that the probability of getting tails is 0.4.

Therefore, the probability of getting heads will be:

= 1 - 0.4

= 0.6.

In conclusion, the correct option is 0.6.

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Answer:

a

Step-by-step explanation:

Answer:

b my man or women

Step-by-step explanation:

no need for one

Answer:

2/3

Step-by-step explanation:

Total sides = 6

Number 5 and all even numbers = 1+3

=> 4

P(5 or even ) = 4/6

=> 2/3

Answer:

[tex] \frac{c}{a + b} [/tex]

Step-by-step explanation:

Point A is on the origin, hence its coordinates would be (0, 0). Coordinates of point C are (a + b, c)

Slope of AC

[tex] = \frac{c - 0}{a + b - 0} \\ \\ = \frac{c}{a + b} \\ [/tex]

Answer:

In the green box of the numerator, enter "c"

In the gray bax in the denominator, there should be "a"

Step-by-step explanation:

Slope is Rise/Run.

Here the rise is "c" because the base is at 0, and the top of the parallelogram is at "c"

Answer:

The value of the 2nd 5 is 50,000 and it is in the ten thousands place

Complete Question:

You are the operations manager for an airline and you are considering a higher fare level for passengers in aisle seats. How many randomly selected air passengers must you​ survey? Assume that you want to be 99% confident that the sample percentage is within 3.5 percentage points of the true population percentage.

Answer:

1,355 air passengers must be surveyed

Step-by-step explanation:

Note that the population proportion is not stated in the question, it will be assumed to be 50%. i.e. p = o.5

Error Margin, E = 3.5% = 0.035

Confidence Level, CL = 90% = 0.99

Therefore, Significance Level, [tex]\alpha = 0.01[/tex]

At [tex]\alpha = 0.01[/tex], [tex]Z_{crit} = Z_{\alpha/2} = Z_{0.005} = 2.576[/tex]

The number of randomly selected air passengers that must be surveyed:

This is the sample size and is given by the equation:

[tex]n = \frac{(Z_{\alpha/2})^2 p(1-p)}{E^2} \\n = \frac{2.576^2 * 0.5 *(1-0.5)}{0.035^2}\\n = 1354.24\\n = 1355[/tex]

Answer:

48x divided by 8= 6p

Step-by-step explanation:

Answer:

All possible rational zeros are given by the rational zeros theorem are 1, -1, 19 and -19.

Step-by-step explanation:

The rational zeros theorem indicates that for a polynomial

f (x) = aₙxⁿ + aₙ₋₁xⁿ⁻ + ⋯ + a₂x² + a₁x + a₀

where aₙ, aₙ₋₁, ⋯ a₀ are integers, the rational roots can be determined from of the factors of aₙ and a₀.

Being p divisor of the independent term a₀ and q divisor of the coefficient  principal aₙ, then all rational factors or possible rational roots will take the form of [tex]\frac{p}{q}[/tex]

In the case of p(x)=x³ -7x² +19, aₙ=1 and a₀=19

So:

Dividers of the independent term (19): p=±1,±19

Divisors of the main coefficient (1): q=±1

Being the possible roots of the polynomial: [tex]\frac{p}{q}=[/tex]±1, ±19

All possible rational zeros are given by the rational zeros theorem are 1, -1, 19 and -19.

Answer:

5 out of 100 adults so not very likely

0.05 or 5% likely that a randomly chosen adult will exercise 30 minutes each day.

Probability is the possibility of occurrence of a particular event.

In other word, Probability is the ratio of number of favorable incident under an event to the Total number of incident under that event.

[tex]\text{Probability}=\frac{\text{Number of Favorable Cases}}{\text{Number of Total cases}}[/tex]

In this problem it is given that 5% of adults participate in at least 30 minutes of exercise each day.

Then it implies 5 adults out of total 100 adults participate in at least 30 minutes of exercise each day.

Here the event is that one adult exercises 30 minutes each day.

Number of adults in favor is 5

Number of total adults is 100

Probability that one randomly chosen adult will exercise 30 minutes each day is [tex]=\frac{5}{100}=0.05[/tex]

Hence 0.05 or 5% likely that a randomly chosen adult will exercise 30 minutes each day.

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Answer:

By either graphing or completing the square

Step-by-step explanation:

The fastest way to find the vertex is to graph the equation and trace the graph to your vertex to find your point.

Alternatively, you can complete the square to get form f(x) = a(bx - h)² + k (vertex form) and find your vertex (-h, k).

Answer:

The correct set of hypotheses is:

[tex]H_0: \pi=0.75\\\\H_a:\pi>0.75[/tex]

Step-by-step explanation:

This should be researched with a hypothesis test on the proportion of tourists visiting Rock City.

The claim that want to be tested is if the proportion has increased from the past proportion (π=0.75).

Then, the alternative hypothesis will state that the proportion is significantly higher than 0.75.

On the contrary, the alternative hypothesis will state that the proportion is not significantly different than 0.75.

This can be written as:

[tex]H_0: \pi=0.75\\\\H_a:\pi>0.75[/tex]

Answer:

D

Step-by-step explanation:

as it indicates whole F in the figure

Venn diagram are used to represent the relationships between sets. The correct notation for the shaded region is (d) F.

Given the attached Venn diagram.

The shaded region highlights

This means that options (a) and (b) are false because set G is not shaded

This also means that option (c) is false because the shaded region is just a part of set M, and not the whole set M.

Hence, we can conclude that option (d) is correct because the whole of set F is shaded.

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Answer:

x=1.2

Step-by-step explanation:

25x^2 -36=0

25x^2 =36

25x^2/25=36/25

x^2 =1.44

x=square root of 1.44

x=1.2

Answer:

-7

Step-by-step explanation:

y−x=9 ⇒ y=x+9

10+2x=−2y

5+x= -y  ====== replacing y with x+9

5+x= -x-9

2x= -14

x= -7

Answer:

-7

Step-by-step explanation:

y - x = 9

10 + 2x = -2y

Solve for y in the first equation.

y = 9 + x

Put y as 9 + x in the second equation and solve for x.

10 + 2x = -2(9 + x)

10 + 2x = -18 - 2x

2x + 2x = -18 - 10

4x = -28

x = -28/4

x = -7

Answer:

1. All real numbers

2. All real numbers except y = 0

3. All real numbers except x = -7

4. All real numbers except b = 10

Step-by-step explanation:

For any function to be defined at a particular value, it should not be approaching to a value [tex]\infty[/tex] or it should not give us the [tex]\frac{0}{0}[/tex] (zero by zero) form when the input is given to the function.

The value of function will depend on the denominator.

Now, let us consider the given functions one by one:

1. 5y+2

Here denominator is 1. So, it can not attain a value [tex]\infty[/tex] or [tex]\frac{0}{0}[/tex] (zero by zero) form

So, for all real numbers, the function is defined.

[tex]2.\ \dfrac{18}{y}[/tex]

At y = 0, the value

[tex]At\ y =0, \dfrac{18}{y} \rightarrow \infty[/tex]

So, the given function is defined for all real numbers except y = 0

[tex]3.\ \dfrac{1}{x+7}[/tex]

Let us consider denominator:

x + 7 can be zero at a value x = -7

[tex]At\ x =-7, \dfrac{1}{x+7} \rightarrow \infty[/tex]

So, the given function is defined for all real numbers except x = -7

[tex]4.\ \dfrac{2b}{10-b}[/tex]

Let us consider denominator:

10-b can be zero at a value b = 10

[tex]At\ b =10, \dfrac{2b}{10-b} \rightarrow \infty[/tex]

So, the given function is defined for all real numbers except b = 10

Answer:

25%

Step-by-step explanation:

Sum the parts of the ratio, 7 + 5 + 4 = 16 parts

Of the 16 parts, 4 parts are blue, thus percentage is

[tex]\frac{4}{16}[/tex] × 100% = [tex]\frac{1}{4}[/tex] × 100% = 25%

Answer:

So C is root 39 I meant and B is 399.99

Step-by-step explanation:

I am correct because of Pythagorean theorem, ok so these are correct!

Answer:

Step-by-step explanation:

1. opp=5,adj=4,hypotenuse=c

[tex]c^{2} =5^{2} +4^{2} \\c^{2} =25+16\\c^{2} =41\\c=\sqrt{41} \\c=6.4\\2.opp=25,hyp=25,adj=b\\hyp^{2} =opp^{2} +adj^{2} \\25^{2} =15^{2} +b^{2} \\625=225+b^{2} \\625 - 225 =b^{2} \\400=b^{2} \\b=\sqrt{400} \\b=20.0[/tex]

Answer:

1,498,454,000 sq. miles

Step-by-step explanation:

Volume of a sphere = 4/3 (3.14) r^3

So since the diameter is 1420 miles, the radius would be half.

V = 4/3 x (3.14) x 710^3

V=4.18666667 x 357,911,000

V = 1,498,454,054.5 but if you want it rounded to the nearest thousand then it'd be 1,498,454,000.

Answer:

$2,385.75

Step-by-step explanation:

The  computation of the balance left that offer the same deal is shown below:

Let us assume the required balance be P

Now the equation for the credit card A is

[tex]P (1 + \frac{0.222}{12}^{12}) + \$50[/tex]

And, the equation for the credit card B is

[tex]P (1 + \frac{0.239}{12})^{12}[/tex]

Now equate these two equations which are as follows

[tex]P (1 + \frac{0.222}{12})^{12} + \$50 = P (1 + \frac{0.239}{12})^{12}[/tex]

1.246041193 P + $50 = 1.266998979 P

After solving this, the P value is $2,385.75

Answer:

A. $2,385.75

Answer: 3 grams

Step-by-step explanation:

[tex]210\bigg(\dfrac{1}{2}\bigg)^6=\dfrac{210}{64}\quad =\large\boxed{3.28125}[/tex]

Answer:

The amount in the account at the end of three years will be $59,861.

Step-by-step explanation:

The formula to compute the amount at the end of t years, compounded continuously is:

[tex]A=P\times e^{t\times i}[/tex]

Here,

A = Amount at the end

P = Principal amount

i = interest rate

t = number of years.

It is provided that:

P = $50,000

i = 6%

t = 3 years

Compute the amount in the account at the end of three years as follows:

[tex]A=P\times e^{t\times i}[/tex]

   [tex]=50000\times e^{(3\times 0.06)}\\=50000\times 1.19722\\=59861[/tex]

Thus, the amount in the account at the end of three years will be $59,861.

Answer:

The answer is below

Step-by-step explanation:

For the first clock that is 20 minutes faster in a day, that means it is [tex]\frac{20\ min}{60\ min/hr}=\frac{1}{3}hr[/tex] faster every day. For it to show the correct time, the clock should be 24 hours faster.

Since 1 day = 1/3 hr faster

x days = 24 hr faster

Let x number of days be required to be 24 hr faster. To find x we use the formula:

[tex]x=\frac{24 \ hr* 1\ day}{\frac{1}{3}hr } \\x=72\ days[/tex]

For the second clock that is 30 minutes slower in a day, that means it is [tex]\frac{30\ min}{60\ min/hr}=\frac{1}{2}hr[/tex] faster every day. For it to show the correct time, the clock should be 24 hours slower.

Since 1 day = 1/2 hr slower

y days = 24 hr faster

Let x number of days be required to be 24 hr slower. To find x we use the formula:

[tex]y=\frac{24 \ hr* 1\ day}{\frac{1}{2}hr } \\y=48\ days[/tex]

Answer:

$24, $30, $36

Step-by-step explanation:

First we need to find the unit rate.

1. 18÷3 = 6

So that means one taco costs $6.

6*4 = 24

6*5 = 30

6*6 = 36

The cost of 4 taco is $24, 5 taco is $30 and 6 taco is $36.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

3 tacos cost $18.

Cost of 1 taco= 18/ 3

= $6

So, cost of 4 taco = 4 x 6 = $24

and, cost of 5 taco = 5 x 6= $30

and, cost of 6 taco = 6x 6= $36

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Answer:

The percentage points within which the obtained results would differ from the real population value.

Step-by-step explanation:

The ideas of the margin of error and confidence interval are borne from the observed truth, which is that there is always room for error in any statistically computed figure such as a survey or poll. For example, the result of a poll could show an 80% confidnce interval with a margin of error of 3%. This simply means that if the poll was repeated, 80% of the real population would fall within an estimate of 3%.

Statistics are not always error proof. Sometimes, the results might even be totally different from the computed results. So, it is very important that room is made for the possibility of an error, and that is why we need the mrgin of error.

Answer:

  1.8 times the cost of labor.

Step-by-step explanation:

At the beginning of the year, the rate for overhead was estimated to be ...

  (overhead $)/(direct labor $) = $396/$220 = 1.8

The overhead rate is 1.8 times the labor cost.

Answer:

Add 3, 144

+3,990

And you wil get your answer

7, 134

Answer:

The probability that there are 2 or more fraudulent online retail orders in the sample is 0.483.

Step-by-step explanation:

We can model this with a binomial random variable, with sample size n=20 and probability of success p=0.08.

The probability of k online retail orders that turn out to be fraudulent in the sample is:

[tex]P(x=k)=\dbinom{n}{k}p^k(1-p)^{n-k}=\dbinom{20}{k}\cdot0.08^k\cdot0.92^{20-k}[/tex]

We have to calculate the probability that 2 or more online retail orders that turn out to be fraudulent. This can be calculated as:

[tex]P(x\geq2)=1-[P(x=0)+P(x=1)]\\\\\\P(x=0)=\dbinom{20}{0}\cdot0.08^{0}\cdot0.92^{20}=1\cdot1\cdot0.189=0.189\\\\\\P(x=1)=\dbinom{20}{1}\cdot0.08^{1}\cdot0.92^{19}=20\cdot0.08\cdot0.205=0.328\\\\\\\\P(x\geq2)=1-[0.189+0.328]\\\\P(x\geq2)=1-0.517=0.483[/tex]

The probability that there are 2 or more fraudulent online retail orders in the sample is 0.483.

Answer:

112.569 ( D )

Step-by-step explanation:

Applying the estimated Regression Equation

y = b1X1 + b2X2 + a

b1 = ((SPX1Y)*(SSX2)-(SPX1X2)*(SPX2Y)) / ((SSX1)*(SSX2)-(SPX1X2)*(SPX1X2)) = 596494.5/635355.88 = 0.93884

b2 = ((SPX2Y)*(SSX1)-(SPX1X2)*(SPX1Y)) / ((SSX1)*(SSX2)-(SPX1X2)*(SPX1X2)) = 196481.5/635355.88 = 0.30925

a = MY - b1MX1 - b2MX2 = 149.25 - (0.94*61.31) - (0.31*193.88) = 31.73252

y = 0.939X1 + 0.309X2 + 31.733

For x1 ( age ) =39, and  x2(weight) =143

y = (0.93884*39) + (0.30925*143) + 31.73252= 112.569

where

Sum of X1 = 981

Sum of X2 = 3102

Sum of Y = 2388

Mean X1 = 61.3125

Mean X2 = 193.875

Mean Y = 149.25

attached is the Tabular calculation of the required values needed for estimated regression equation