A plane is flying within sight of the Gateway Arch in St. Louis, Missouri, at an elevation of 30000 feet. The pilot would like to estimate her distance from Gateway Arch. She finds that the angle of depression to a point on the ground at the arch is 23°. Find the distance between the plane and the arch. Round your answer to the nearest foot. (Do not include ft in your answer)

Answer:

B. 22.5m^2

Step-by-step explanation:

To find the area of a trapezoid, you must use the formula:

1/2 × height × (base 1+ base 2)

1. 1/2 × 5m × (8+1)

2. 1/2 x 5m x (9)

3. Switch it around to make it easier to solve

5m × 9× 1/2 (We can do this because of the commutative property.)

4. 45m × 1/2 = 45 ÷ 2 = 22.5m^2

In the context of the problem, this means that the area of the trapezoid is 22.5m^2.

Answer:The principal for the first account is $5000

The principal for second account is $4600

Step-by-step explanation:

The formula for simple interest is expressed as

I = PRT/100

Where

P = principal

T = time in years

R = interest rate on the principal.

Let x represent the amount invested in the first account

Let y represent the amount invested in the second account

Gabriel invests $9600 in two different accounts. This means that

x + y = 9600 - - - - - - - -1

For first account, The interest rate is 13%. The duration is one year.

Therefore

P = x

T = 1 year

R = 13%

Therefore

I = (x × 13 × 1)/100

I = 0.13x

For second account, he interest rate is 6%. The duration is one year.

Let y represent the principal for the second account. Therefore

P = y

T = 1 year

R = 6

Therefore

I = (y × 6 × 1)/100

I = 0.06y

At the end of the first year he had earned $926 in interest. This means that

0.13x + 0.06y = 926 - - - - - - - -2

Substituting x = 9600 - y into equation 2, it becomes

0.13(9600 - y) + 0.06y = 926

1248 - 0.13y + 0.06y = 926

- 0.13y + 0.06y = 926 - 1248

- 0.07y = -322

y = - 322/- 0.07 = 4600

x = 9600 - y

x = 9600 - 4600

x = 5000

Answer:

  200 students were in the program

Step-by-step explanation:

The parent should know how to figure ...

  170/85% = total/100%

This is the same as ...

  total = 170/0.85 = 200

200 students were in the program.

_____

Critical Thinking

There are three declarative statements here. There is no question. We have made up a question to answer.

Another possible answer to the non-question could be, "The parent can ask his student how many students were in the program."

Answer:

Step-by-step explanation:

20

cause i said so

Answer:

Step-by-step explanation:

The triangle given is aright angle triangle. This is because one if its angles is 90 degrees. The other two angles add up to give 180 degrees. Looking at the right angle triangle, taking the 8 degree angle as the reference angle, the length of the adjacent side is 82, the length of the opposite side is t. Applying trigonometric ratio,

Tan # = opposite side / adjacent side.

# = 8 degrees

Tan 8 = t/82

t = 82 tan8

t = 82 × 0.1405

t = 11.521

Answer:

Their intercepts are unique.

Explanation:

[tex]\displaystyle x^3 - 24x^2 + 192x - 508 = (x - 8)^3 + 4[/tex]

This graph's x-intercept is located at approximately [6,41259894, 0], and the y-intercept located at [0, −508].

[tex]\displaystyle g(x) = x^3[/tex]

The parent graph here, has both an x-intercept and y-intercept located at the origin.

I am joyous to assist you anytime.

Answer:

C) The mean is 22 and the standard deviation is 100.

Step-by-step explanation:

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The expected value of a random variable X is the n-th moment about zero of a probability density function f(x) if X is continuous, or the weighted average for a discrete probability distribution, if X is discrete.

The variance of a random variable X represent the spread of the possible values of the variable. The variance of X is written as Var(X).

If [tex] X\ sim N(\mu_x =5, \sigma_x =25)[/tex]

And the random variable Y =2+4X.

If we are interested in find the mean and the standard deviation for this new variable we need to apply the concepts of expected value and Variance of random variables.

Using the concept of expected value we have:

[tex]E(Y) =E(2+4X) = E(2) +E(4X)= 2+ 4E(X) =2+4(5) =2+20=22[/tex]

So on this case the [tex]E(Y) =\mu_Y =22[/tex]

Using the concept of variance we have:

[tex]Var(Y)=Var(2+4x)=Var(2)+Var(4X)+2Cov(2,4X)[/tex]

But since 2 is a constant we don't have variance for this and the [tex]Cov(2,4x)=0[/tex] because the covariance of a random variable with a constant is zero. So applying these concepts we have:

[tex]Var(Y)= Var(4x)=4^2 Var (X)= 16 \sigma^2_x =16(25^2)=10000[/tex]

And then if we need the standard deviation we just need to take the square root:

[tex]sd(Y) = \sqrt{10000}=100[/tex]

So the best option for this case would be:

C) The mean is 22 and the standard deviation is 100.

Answer:

Option c) is correct.

Step-by-step explanation:

Given :

[tex]\mu_x = 5[/tex]  and  [tex]\sigma_x = 25[/tex]

Y = 2 + 4X

Calculation:

This problem can be solved by using concept of expected value and variance of random variables.

By expected value concept,

[tex]\rm E(Y) = E(2 + 4X)= E(2) + E(4X)= 2 + 4E(X)=2+4(5)=22[/tex]

Therefore, [tex]\mu_y = 22[/tex]

By variance concept,

[tex]\rm Var(Y)= Var(2+4X)=Var(2)+Var(4X)+2Cov(2,4X)[/tex]

[tex]\rm Cov(2,4X)=0[/tex]

Var(2) = 0

Therefore,

[tex]\rm Var(Y) = Var(4X)= 4^2Var(X)= 16\sigma_x^2=16(25^2)=10000[/tex]

Therefore,

Standard deviation(Y) = [tex]\sqrt{10000}[/tex] = 100

Hence, option c) is correct.

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Answer:

$6

Step-by-step explanation:

so you add 16 15 and 20 to see how much you earned in total, to get 51 dollars. we subtract 12 because we used it at the movies and get 39 dollars in total. now we subtract this from 45 to see how much more we need to get 6.

equation: 45-(15+16+20-12)........this equals 6 as well

You need to earn more money to buy a $45 video game and it is equal to $6.

What is algebra ?

Algebra is a branch of mathematics that deals with various symbols and the arithmetic operations such as addition , subtraction , etc.

It is given that , you earn some money by doing different works. The earn money from different works is given.

By mowing the lawn money earned = $16

For babysitting money earned = $15

Money earned for the allowance = $20

So , the total money earned is :

= $16 + $15 + $20

= $51

Now , you have spend $12 at the movie theatre. That meant the money now left is :

= $51 - $12

= $39

You need to buy a video game which costs $45. So , you need to earn some more money which is :

= $45 - $39

= $6

Therefore , you need to earn more money to buy a $45 video game and it is equal to $6.

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Answer: 12 trillion dollars

Step-by-step explanation: The government started with 10 trillion than collected 8 trillion in taxes, reducing their debt to 2 trillion dollars. Then the government spent 10 trillion dollars and now their debt is 12 trillion dollars.

Answer:

12

Step-by-step explanation:

The price of fish this week is $3.15 per pound

Step-by-step explanation:

We have to find the total price of 3 pound fish for last week

So,

Price of fish per pound = $2.75

Price of 3 pound fish = 2.75 * 3 = $8.25

As she made $1.20 more in total for 3 pound fish this week

Price of 3 pound fish this week = 8.25+1.20 = $9.45

$9.45 is the total price for 3 pound fish this week.

So,

Price per pound this week will be:

[tex]=\frac{9.45}{3}\\=3.15[/tex]

Hence,

The price of fish this week is $3.15 per pound

Keywords: Measurements, Unit price

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Answer:

Factory made 4 batches of granola bars yesterday.

Step-by-step explanation:

Given:

1 batch of granola bar is made of 1/8 barrel of raisins.

1/8 barrels can be rewritten as 0.125 barrels.

Hence we can say 1 batch of granola bar is made of 0.125 barrels.

Also Given:

Yesterday Factory used 1/2 barrel of raisins.

1/2 barrels can be rewritten as 0.5 barrels.

Hence we need to find how much batches of granola bars were made using 0.5 barrels of raisins.

Now,

For 0.125 barrels raisins = 1 batch of granola bar

for 0.5 barrels of raisins = Batches of granola bar for 0.5 barrels of raisins

By Using Unitary method we get;

Batches of granola bar for 0.5 barrels of raisins = [tex]\frac{1\times 0.5}{0.125}=4[/tex]

Hence Factory made 4 batches of granola bars yesterday.

Answer: tangent of A = 2.4

Cotangent of B = 0.4167

Step-by-step explanation:

Answer:

[tex]\displaystyle \frac{5}{12} = cot∠B \\ 2\frac{2}{5} = cot∠A[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{OPPOSITE}{HYPOTENUSE} = sin\:θ \\ \frac{ADJACENT}{HYPOTENUSE} = cos\:θ \\ \frac{OPPOSITE}{ADJACENT} = tan\:θ \\ \frac{HYPOTENUSE}{ADJACENT} = sec\:θ \\ \frac{HYPOTENUSE}{OPPOSITE} = csc\:θ \\ \frac{ADJACENT}{OPPOSITE} = cot\:θ \\ \\ \frac{10}{24} = cot∠B → \frac{5}{12} = cot∠B \\ \\ \frac{24}{10} = cot∠A → 2\frac{2}{5} = cot∠A[/tex]

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Answer:x+y=58

Step-by-step explanation:

Sum means addition

Answer:

4 out of 10 or 4/10 is my answer

Answer:

The fraction will be 4/10, or 2/5.

The percentage will be 40%.

Step-by-step explanation:

The fraction and percentage will be the number of black pens divided by the total number of pens.

We can find the total number of pens by adding all the pens in each color together.

2 + 4 + 3 + 1 = 10

The total number of pens is 10. The number of black pens is 4.

The fraction will be 4/10, or 2/5.

The percentage will be 40%.

I hope this helps. Happy studying. :)

Answer:

$ 8300 (Approximately)

Step-by-step explanation:

Given:

Initial price of the trailer is, [tex]P_0=\$35000[/tex]

Rate of decrease per year is, [tex]r=0.25[/tex]

The time in years is, [tex]t=5[/tex]

The exponential expression for the decrease in price after 't' years is given as:

[tex]P=P_0(1-r)^t[/tex]

Plug in all the given values and solve for 'P'. This gives,

[tex]P=35000(1-0.25)^5\\P=35000(0.75)^5\\P=35000(0.2373)\\P=\$8305.5\approx \$8300[/tex]

Rounding it to the nearest whole number, the price of the travel trailer after 5 years is $ 8,300.

Answer:

x = 18 or x = -12.

Step-by-step explanation:

||x-3|-5| = 10 only if |x-3|-5 = 10 or |x-3|-5 = -10, i.e., if |x-3|=15 or |x-3|=-5; but |x-3| cannot be equal to -5, because |x-3| should be a non-negative value. Therefore, the first equation is true only if |x-3|=15. |x-3| = 15 only if x-3 = 15 or x-3 = -15, i.e., x = 18 or x = -12.  We can verify this in the following way: ||18-3|-5|=||15|-5|=|10|=10 and ||-12-3|-5|=||-15|-5|=|15-5|=|10|=10. This verify that our solution is correct.

Answer:

A is the answer

Step-by-step explanation:

If you fail to agree on the actual cash value, amount of loss, or cost of repair or replacement, either can make a written demand for appraisal. ... The two appraisers will then set the amount of loss, stating separately the actual cash value and loss to each item.

When the insured tenant and the insurance company fail to agree on the amount of loss; Choice A is what happens: Either the tenant or the company can request an appraisal, so that an impartial third party determines the amount of loss.

Discussion:

Situations such as in the question may arise when quantifying the amount of loss in an insurance situation.

In such scenarios; the best option is for either the tenant or the company can request an appraisal, so that an impartial third party determines the amount of loss.

The essence of this, is to ensure fairness in quantification of the amount of loss.

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Answer:

Step-by-step explanation:

The slope is the ratio of the change in y to the change in x:

  m = ((b+3) -b)/((a +3) -a) = 3/3 = 1

The point-slope form of the equation of a line through point (h, k) with slope m is ...

  y -k = m(x -h)

Here, we have (h, k) = (a, b) and m=1, so the equation in point-slope form is ...

  y -b = x -a

Adding b puts this in slope-intercept form:

  y = x + (b-a)

Answer:

Tan33=x/y

y= x/Tan33

Tan40=(10+x)/y

y= (10+x)/Tan40

Therefore

x/Tan33 = (10+x)/Tan40

xTan40-xTan33 =10Tan33

x= 10Tan33/(Tan40-Tan33)

x=34.2m

Step-by-step explanation:

Answer:

A) 4x - 2y + 3z = - 3

B) 2x - 3y + 2z = 1

C) 6x    + 10z = -2

Multiply A) by -1.5

A) -6x  +3y -4.5z = 4.5  Then adding to B)

B) 2x - 3y + 2z = 1

D) -4x -2.5z = 5.5  then we add this to C)

C) 6x + 10z = -2  Now we multiply D) by 1.5

D) -6x -3.75z = 8.25  Adding C) + D)

6.25z = 6.25

z = 1  Then putting z = 1 into A) and B)

A) 4x - 2y + 3 = - 3  equals A) 4x -2y = -6

B) 2x - 3y + 2 = 1  equals B) 2x -3y = -1 we divide A) by -2

A) -2x + y = 3  then adding to B

B) 2x - 3y  = -1

-2y  = 2

y = -1

FINALLY solving for x we'll use equation A)

A) 4x - 2*-1 + 3*1 = - 3

A) 4x +2 + 3 = -3

A) 4x = -8

x = -2

(Yes, it's just that easy. LOL)

Step-by-step explanation:

Answer:

the farmer will need to have 2 pieces of 50 m and one of 100m to maximise the area ( Maximum area=5000 m²)

Step-by-step explanation:

if we assume that the southern fence is not required and if we denote a= length of each lateral side and b= length of the front side , we will have:

Area=A= a*b

Total length of fence=L= 2*a+b

therefore

L= 2*a+b → b= L- 2*a

A= a*(L-2*a) = a*L - 2*a²

therefore

A= a*L - 2*a² → 2*a² - a*L + A = 0

a=  [L ± √((-L)²- 4*2*A)]/(2*2) = L/4  ± √(L²- 8*A) /4

a= L/4  ± √(L²- 8*A) /4

when A goes bigger √(L²- 8*A) diminishes,  but since the minimum possible value √(L²- 8*A) is 0 , then A can not go higher than L²- 8*A=0

therefore

L²- 8*A max=0 → A max = L²/ 8 = (200m)²/8= 5000 m²

and since √(L²- 8*A)=0

a=L/4 = 200m/4 = 50 m

b= L- 2*a = 200m - 2* 50m = 100 m

Answer:

Option B. 8 mi, 9 mi, 2 mi

Step-by-step explanation:

The option A doesn't have a set of numbers which could be the lengths of the sides of a triangle. The numbers 1,9,10 mean that the longest side is exactly the sum of the others. The only possible way is they lie in the same line, no triangle is formed

Option C gives the numbers 1,9,11. It's impossible to have a side of 11 when you have the sum of the others less than 11. The maximum extension of the other sides (forming a line) won't be enough to reach the length of 11

Option D is also infeasible for the same reason as the option A. The three lines must be aligned to be connected in its extremes

Option B is the only one who can provide a set of possible lengths of a triangle since the sum of the shortest sides is greater than the third. If we open wide enough the angle between the 2 mi side and the 8 mi side, we would eventually connect the 9 mi side and form a triangle

Answer: the correct option is A

Step-by-step explanation:

We want to find 95% confidence interval for the mean of the weight of pretzels.

Number of samples. n = 15 bags

Mean, u = 10.2

Standard deviation, s = 0.25

We will use the t- test

Degree of freedom = n - 1 = 15 - 1= 14

Alpha, a = (1-confidence interval )/2

a = (1-0.95)/2 = 0.025

Looking at the t-distribution table, the corresponding z value is 2.131

Confidence interval = z × standard deviation/√n

Confidence interval = 2.131 × 0.25/√15

Confidence interval = 0.13755545851

Approximately 0.138

At 95% confidence interval,

The lower end is 10.2 - 0.138 = 10.062 Approximately 10.06

The upper end is 10.2 - 0.138 = 10.338. Approximately 10.34

Answer: Our required probability is 0.48.

Step-by-step explanation:

Since we have given that

Probability that days are cloudy in January = 51%

Probability that days are cloudy and foggy = 25%

So, we need to find the probability that a randomly selected day in January will be foggy if it is cloudy.

So,P( Foggy|cloudy) is given by

[tex]\dfrac{P(Foggy\cap cloudy)}{P(cloudy)}\\\\=\dfrac{25}{51}\\\\=0.48[/tex]

Hence, our required probability is 0.48.

Answer:

[tex]4.2 kgm^2[/tex]

Step-by-step explanation:

As there's no external force when the disks are attached, the angular momentum of the system should be conserved.

[tex] I_A\omega_A + I_B\omega_B = (I_A + I_B)\omega[/tex]

[tex] 3.2*7.4 + I_B(-9.7) = (3.2 + I_B)(-2.3)[/tex]

[tex] 23.68 - 9.7I_B = -7.36 - 2.3I_B[/tex]

[tex]31.04 = 7.39I_B[/tex]

[tex]I_B = 31.04/7.39 = 4.2 kgm^2[/tex]

The moment of inertia of disk B when it rotates round the axis will be 4.2kgm².

Let the moment of inertia be represented by Ib.

Therefore, the moment of inertia will be calculated thus:

IaWa + IbWb = (Ia + Ib)w

(3.2 × 7.4) + Ib(-9.7) = (3.2 + In)(-2.3)

23.68 - 9.7Ib = -7.36 - 2.3Ib

Collect like terms

23.58 + 7.36 = -2.3Ib + 9.7Ib

31.04 = 7.39Ib

Divide through by 7.39

7.39Ib/7.39 = 31.04/7.39

= 4.2kgm²

Therefore, the moment of inertia of disk B when it rotates round the axis will be 4.2kgm².

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Answers:

1a) The next four terms are: 513, -728, 1001, -1330

1b) The direct formula is [tex]a_n = (-1)^n*n^3+1[/tex]

================================================

Explanation:

It helps to start with part B first. The direct formula will help us find the next four terms in a very efficient manner.

Start with the sequence {0, 9, -26, 65, -124, 217, -342}

Subtract 1 from each term to get this new sequence {-1, 8, -27, 64, -125, 216, -343}, which closely resembles the sequence {1, 8, 27, 64, 125, 216, 343}. This is the sequence of perfect cubes. The only difference is that each term alternates from positive to negative and vice versa.

So we will have an n^3 as part of the equation and also a (-1)^n as part of the equation. The (-1)^n portion allows us to alternate in signs. Put together we have (-1)^n*n^3 so far

The last thing we do is add 1 to this so that we undo the operation "subtract 1" we did earlier to the original list.

Therefore the formula is [tex]a_n = (-1)^n*n^3+1[/tex]

--------------------

To help verify we have the right formula, plug in n = 1 and we get

[tex]a_n = (-1)^n*n^3+1[/tex]

[tex]a_1 = (-1)^1*1^3+1[/tex]

[tex]a_1 = 0[/tex]

and plug in n = 2 to get

[tex]a_n = (-1)^n*n^3+1[/tex]

[tex]a_2 = (-1)^2*2^3+1[/tex]

[tex]a_2 = 9[/tex]

and so on. I'll let you check the other terms

--------------------

Let's find the terms a8,a9,a10,a11

This is simply a matter of plugging n = 8, n = 9, n = 10, and n = 11

Plug in n = 8

[tex]a_n = (-1)^n*n^3+1[/tex]

[tex]a_8 = (-1)^8*8^3+1[/tex]

[tex]a_8 = 513[/tex]

Repeat for n = 9

[tex]a_n = (-1)^n*n^3+1[/tex]

[tex]a_{9} = (-1)^9*9^3+1[/tex]

[tex]a_{9} = -728[/tex]

Repeat for n = 10

[tex]a_n = (-1)^n*n^3+1[/tex]

[tex]a_{10} = (-1)^{10}*10^3+1[/tex]

[tex]a_{10} = 1001[/tex]

Repeat for n = 11

[tex]a_n = (-1)^n*n^3+1[/tex]

[tex]a_{11} = (-1)^{11}*11^3+1[/tex]

[tex]a_{11} = -1330[/tex]

Answer:

The 40% marked up price of refrigerator is  $1260.

Step-by-step explanation:

The cost price of the refrigerator  = $900

Now, the mark up should be 40%

Calculating the markup on the cost price , we get

40 % of $900  =  [tex]\frac{40}{100}  \times 900 = 360[/tex]

or, 40 % mark up = $360

Now, the Marked up cost = Cost Price + Marked up Price

                                          = $900 + $360 = $1260

Hence, the 40% marked up price of refrigerator is $1260.

Answer:

The equation is I = 65 - 15d and it's continuous

Step-by-step explanation:

First, let's discart the options. The last two options cannot be because if you solve for I in those equations, you'll get the following:

65 = I - 15d

I = 65 + 15d

Now, suppose that after 1 day, you want to know the length of the bread:

I = 65 + 15(1) = 80

This is impossible because the bread is being cut and it's not growing each afternoon. Therefore these options, wheter is discrete or continuous are discarted.

The correct equation to use is then

I = 65 - 15d

Now, how do you know if the graph is continuous or discrete?. A graph is continuous when all the points belonging to a set, can take any value within an interval. A discrete graph all the values belonging to a set, are distinct and separate one of another, in other words, the values are unconnected.

In this case, if you graph this equation, you have the following (see attached graph)

As you can see, all the values are connected and continuous.

Answer : B

Step-by-step explanation:

Answer:

56 pentagon.

Step-by-step explanation:

Here is the complete question: Eight point lies on the circle. How many pentagons can you make using five points as vertices?

Given: Five points on vertices.

Using the combination formula to find the number of pentagon.

[tex]_{r}^{n}\textrm{C} = \frac{n!}{r!(n-r)!}[/tex]

⇒ [tex]_{8}^{5}\textrm{C}= \frac{8!}{5!(8-5)!}[/tex]

⇒[tex]_{8}^{5}\textrm{C}= \frac{8!}{5!\times 3!} \\\\_{8}^{5}\textrm{C} = \frac{8\times 7\times 6\times5\times4\times3\times2\times1}{5\times4\times3\times2\times1\times3\times2\times1} = \frac{336}{6}[/tex]

∴ [tex]_{8}^{5}\textrm{C}= 56[/tex]

∴ With eight point lies on circle, we can make 56 pentagons using five points as vertices

[tex](x-5)(x^2-x-4) =x^3-6x^2+x+20[/tex]

Step-by-step explanation:

Given polynomials are:

[tex]x^2-x-4\\and\\x-5[/tex]

Both polynomials have to be multiplied. We will use distributive property for the said purpose

So,

[tex](x-5)(x^2-x-4)\\=x(x^2-x-4)-5(x^2-x-4)\\=x^3-x^2-4x-5x^2+5x+20[/tex]

Combining alike terms

[tex]=x^3-x^2-5x^2-4x+5x+20\\=x^3-6x^2+x+20[/tex]

Hence,

[tex](x-5)(x^2-x-4) =x^3-6x^2+x+20[/tex]

Keywords: Polynomials, Multiplication

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Answer:

6:8

Step-by-step explanation: