Could someone remind me how to find the area of a triangle? Thank you.

Answer:

the probability that the mean student loan debt for these people is between $31000 and $33000 is 0.1331

Step-by-step explanation:

Given that:

Mean = 30000

Standard deviation = 9000

sample size = 100

The probability that the mean student loan debt for these people is between $31000 and $33000 can be computed as:

[tex]P(31000 < X < 33000) = P( X \leq 33000) - P (X \leq 31000)[/tex]

[tex]P(31000 < X < 33000) = P( \dfrac{X - 30000}{\dfrac{\sigma}{\sqrt{n}}} \leq \dfrac{33000 - 30000}{\dfrac{9000}{\sqrt{100}}} )- P( \dfrac{X - 30000}{\dfrac{\sigma}{\sqrt{n}}} \leq \dfrac{31000 - 30000}{\dfrac{9000}{\sqrt{100}}} )[/tex]

[tex]P(31000 < X < 33000) = P( Z \leq \dfrac{33000 - 30000}{\dfrac{9000}{\sqrt{100}}} )- P(Z \leq \dfrac{31000 - 30000}{\dfrac{9000}{\sqrt{100}}} )[/tex]

[tex]P(31000 < X < 33000) = P( Z \leq \dfrac{3000}{\dfrac{9000}{10}}}) -P(Z \leq \dfrac{1000}{\dfrac{9000}{10}}})[/tex]

[tex]P(31000 < X < 33000) = P( Z \leq 3.33)-P(Z \leq 1.11})[/tex]

From Z tables:

[tex]P(31000 < X <33000) = 0.9996 -0.8665[/tex]

[tex]P(31000 < X <33000) = 0.1331[/tex]

Therefore; the probability that the mean student loan debt for these people is between $31000 and $33000 is 0.1331

Answer:

a. P= -0.1x + 39.6

b.  R(x) = -0.1x^2 + 39.6x

c. x = -534 units

d. Number of units demand weekly when the revenue is maximized is 198 units

e. Price p = 15.8 units

Step-by-step explanation:

So for the demand equation let price =p

x= number of units sold

m = per unit price

b = initial fix amount

a. p = mx + b

When p = 26.10 $, x = 135 units so equation

26.10 = m(135) + b .......................(1)

When p = 9.10, x = 305 units so equation

9.10 = m(305) + b .......................(2)

subtracting equation (2) from equation (1)

26.10 - 9.10 =135x +b - 305x - b

17.00 = -170m

m= 17/-170

m= -0.1

Lets plug the value of m in the first equation

26.10 = m(135) + b

26.10 = (-0.1)(135) + b

26.10 = -13.5 + b

b= 26.10 + 13.5

b= 39.6

So the equation would be P= -0.1x + 39.6

b. Revenue = price * quantity

R(x) = p * x

R(x) = x (-0.1x + 39.6)

R(x) = -0.1x^2 + 39.6x

c. Here we have p = $ 93.00

P= -0.1x + 39.6

93 = -0.1x + 39.6

93 - 39.6 = -0.1x

-0.1x = 53.4

x = 53.4 / -0.1

x = -534 units

d. R(x) = -0.1x^2 + 39.6x

On differentiating it with respect to x.

R'(x) = -0.1(2)x^2-1 + 39.6x^1-1

R'(x) = -0.2x + 39.6

So for the maximum revenue differentiation of revenue function must be 0.

0 = -0.2x + 39.6

0.2x = 39.6

x = 39.6 / 0.2

x = 198 units

Number of units demand weekly when the revenue is maximized is 198 units

e. Price p = -0.1x + 39.6

on plugging the value x =238

Price p = -0.1(238) + 39.6

Price p = -23.8 + 39.6

Price p = 15.8 units

Answer:

true

Step-by-step explanation:

The test for divisibility by 9 is to add all the digits of the number. If that sum is divisible by 9, then the number is divisible by 9.

Answer:

Yes

Step-by-step explanation:

The Mean Value Theorem states that if f(x) is defined and continuous on the interval [a,b] and differentiable on (a,b), then there is at least one number c in the interval (a,b) (that is a < c < b) such that

[tex]f'(c)=\dfrac{f(b)-f(a)}{b-a}[/tex]

Given [tex]f(x)=x^3+x-9$ in [0,2][/tex]

f(x) is defined, continuous and differentiable.

[tex]f(2)=2^3+2-9=1\\f(0)=0^3+0-9=-9[/tex]

[tex]f'(c)=\dfrac{f(2)-f(0)}{2-0}=\dfrac{1-(-9)}{2}=5[/tex]

[tex]f'(x)=3x^2+1[/tex]

Therefore:

[tex]f'(c)=3c^2+1=5\\3c^2=5-1\\3c^2=4\\c^2=\frac{4}{3} \\c=\sqrt{\frac{4}{3}} =1.15 \in [0,2][/tex]

Since c is in the given interval, the function satisfy the hypotheses of the Mean Value Theorem on the given interval.

Answer:

Subtract 2 and two-thirds from both sides of the equation

8 minus 2 and two-thirds = 5 and one-third

Substitute the value for r to check the solution.

Step-by-step explanation:

2 2/3  + r   = 8

Subtract 2 2/3 from each side

2 2/3  + r  - 2 2/3   = 8 - 2 2/3

r = 5 1/3

Check the solution

2 2/3 +5 1/3 =8

8 =8

Answer:

1, 3, 5

Step-by-step explanation:

edge

Answer:

3x / 2 + 9 = 5

3x / 2 = -4

3x = -8

x = -8/3

(2 + v) / 3 = 9

2 + v = 27

v = 25

32 / (d - 2) = 10

32 = 10 * (d - 2)

3.2 = d - 2

d = 5.2

2p - 4 = 3p / 2

2 * (2p - 4) = 3p

4p - 8 = 3p

p - 8 = 0

p = 8

3b / 2 = 12

3b = 24

b = 8

Answer:

0.3174

Step-by-step explanation:

Z-score:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the area under the normal curve to the left of Z. Subtracting 1 by the pvalue, we find the area under the normal curve to the right of Z.

Left of z = -1

z = -1 has a pvalue of 0.1587

So the area under the standard normal curve to the left of z = -1 is 0.1587

Right of z = 1

z = 1 has a pvalue of 0.8413

1 - 0.8413 = 0.1587

So the area under the standard normal curve to the right of z = 1 is 0.1587

Left of z = -1 or right of z = 1

0.1587 + 0.1587 = 0.3174

The area is 0.3174

Answer:

(-2 ,3)

Step-by-step explanation:

Step 1: Rewrite first equation

x = 4 - 2y

-2x + y = 7

Step 2: Substitution

-2(4 - 2y) + y = 7

Step 3: Solve y

-8 + 4y + y = 7

-8 + 5y = 7

5y = 15

y = 3

Step 3: Plug in y to find x

x + 2(3) = 4

x + 6 = 4

x = -2

Question:

A silver coin is dropped from the top of a building that is 64 feet tall. the position function of the coin at time t seconds is represented by

s(t) = -16t² + v₀t + s₀

Determine the position and velocity functions for the coin.

Answer:

position function: s(t) = (-16t² + 64) ft

velocity function: v(t) = (-32t) ft/s

Step-by-step explanation:

Given position equation;

s(t) = -16t² + v₀t + s₀                ---------(i)

v₀ and s₀ are the initial values of the velocity and position of the coin respectively.

(a) Since the coin is dropped, the initial velocity, v₀, of the coin is 0 at t = 0. i.e

v₀ = 0.  

Also since the drop is from the top of a building that is 64 feet tall, this implies that the initial position, s₀, of the coin is 64 ft at t=0. i.e

s₀ = 64ft

Substitute the values of v₀ = 0 and s₀ = 64 into equation (i) as follows;

s(t) = -16t² + (0)t + 64    

s(t) = -16t² + 64

Therefore, the position function of the coin is;

s(t) = (-16t² + 64) ft

(b) To get the velocity function, v(t), the position function, s(t), calculated above is differentiated with respect to t as follows;

v(t) = [tex]\frac{ds(t)}{dt}[/tex]

v(t) = [tex]\frac{d(-16t^2 + 64)}{dt}[/tex]

v(t) = -32t + 0

v(t) = -32t

Therefore, the velocity function of the coin is;

v(t) = (-32t) ft/s

The correct answer is The line will be less steep because the rate will be slower

Explanation:

The rate of the graph is defined by the number of gallons filled vs the time; this relation is shown through the horizontal axis (time) and the vertical axis (gallons). Additionally, there is a constant rate because each hour 2,500 gallons are filled, which creates a steep constant line.

However, if the rate decreases, fewer gallons would be filled every hour, and the line will be less steep, this is because the number of gallons will not increase as fast as with the original rate. For example, if the rate is 1,250 gallons per hour (half the original rate), after 8 hours the total of gallons would be 1000 gallons (half the amount of gallons); and this would make the line to be less steep or more horizontal.

Answer:

The answer is below

Step-by-step explanation:

First we have that free trade refers to the movement of goods, services, capital and knowledge from one place to another. But in reality, free trade does not exist since there are many tariffs and non-tariff barriers.

However,

- Tariff barriers are taxes imposed on imports into a country according to quantity or quantity. Tariff barriers increase the price of imports in the country, which affects the demand for goods and services. Countries agree to lower these tariff barriers, which make trade reasonable for countries that sign agreements.

- Non-tariff barriers are barriers that do not directly affect import prices. It does not impose a tax directly on imports. It tries to reduce imports by using barriers other than taxes.

Therefore countries try to protect their domestic industries using various tariff and non-tariff barriers. The amount of the barriers cannot be precisely decided, since the barriers are not only to protect national industries, but some barriers are imposed to avoid the economic and political monopoly of a foreign country in the national country.

Government actions:

The government applies various health and safety regulations to domestic and foreign products, since consumers in the country must be protected against any impurities. Still, these restrictions are also more than required, leading to protectionism.

The government uses various tariff and non-tariff barriers not only to protect national industries but also for various social, economic, and political reasons.

Therefore, it is difficult to establish tariff and non-tariff barriers in a country accurately.

Answer:

D. Two-sample chi-square

Step-by-step explanation:

A chi-square test is a test used to compare the data that is observed, from the data that is expected.

In a two-sample chi-square test the observed data should be similar to the expected data if the two data samples are from the same distribution.

The hypotheses of the two-sample chi-square test is given as:

H0: The two samples come from a common distribution.

Ha: The two samples do not come from a common distribution

Therefore, in this case, the best statistical test to utilize is the two-sample chi-square test.

Answer:

  $4,457,391.19

Step-by-step explanation:

The sum of n terms of a geometric sequence with common ratio r and initial value "a" is ...

  S = a(r^n -1)/(r -1)

Here, your growth factor is r = 1 +6% = 1.06. So, the sum of expenses over 35 years will be ...

  S = $40,000(1.06^35 -1)/(1.06 -1) = $4,457,391.19

Answer:

simple really

Step-by-step explanation:

10 gigabytes of data on my computer, x gigabytes are movies and the rest is music.

so it will have to be 10-X= remaining gigabites of music

Answer:

Movies: x gig

pictures: x/2 gig

music:  10 - x - x/2 = 10 - (3/2)x

The probability of picking greens on both occasions will be 5/18.

The probability of picking greens cards will be:

= 5/9 × 4/8

= 5/18

The probability of picking at least one green will be:

= 1 - P(both aren't green)

= 1 - (4/9 × 3/8)

= 1 - 1/6.

= 5/6

From the tree diagram, the probability as a fraction of P(G2 | G1) will be:

= 4/8 = 1/2

Learn more about probability on:

brainly.com/question/24756209

#SPJ1

Answer:

A. 3

Step-by-step explanation:

[tex] log_{4}(64) = y \\ 64 = {4}^{y}(\because if \: log_a b = x \implies b = a^x) \\ {4}^{3} = {4}^{y} \\3 = y..(equal \: bases \: have \: equal \: exponents ) \\ \huge \purple { \boxed{y = 3}}[/tex]

Answer:

Its B

Step-by-step explanation:

Answer:

The answer is B

Step-by-step explanation:

Its B on edge

Answer:

1000

Step-by-step explanation:

=> [tex]\frac{1}{10^{-3}}[/tex]

According to the law of exponents, [tex]\frac{1}{a^{-m}} = a^{m}[/tex]

So, it becomes

=> [tex]10^{3}[/tex]

=> 1000

Answer:

-$3576

Step-by-step explanation:

Depreciation using double declining method=100%/useful life*2

Depreciation using double declining method=100%/10*2=20%

2017 depreciation=$60,000*20%=$12000

2018 depreciation=($60,000-$12000)*20%=$9600

2019 depreciation=($60,000-$12000-$9600 )*20%=$7680

2020 depreciation=($60,000-$12000-$9600-$7680 )*20%=$6144

carrying value in 2021=$60000-$12000-$9600 -$7680-$6144 =$24576

Loss on disposal of machine=$21,000-$24576  =-$3576

Answer:

This question is about:

sin(A/2) and cos(A/2)

First, how we know when we need to use the positive or negative signs?

Ok, this part is kinda intuitive:

First, you need to know the negative/positve regions for the sine and cosine function.

Cos(x) is positive between 270 and 90, and negative between 90 and 270.

sin(x) is positive between  0 and 180, and negative between 180 and 360.

Then we need to see at the half-angle and see in which region it lies.

If the half-angle is larger than 360°, then you subtract 360° enough times such that the angle lies in the range between (0° and 360°)

and: Tan(A/2) = Sin(A/2)/Cos(A/2)

So using that you can infer the sign of the Tan(A/2)

Now, why these relationships use the two signs?

Well... this is because of the square root in the construction of the relationships.

This happens because:

(-√x)*(-√x) = (-1)*(-1)*(√x*√x) = (√x*√x)

For any value of x.

so both -√x and √x are possible solutions of these type of equations, but for the periodic nature of the sine and cosine functions, we can only select one of them.

So we should include the two possible signs, and we select the correct one based on the reasoning above.

Answer:

0.62

Step-by-step explanation:

1. We assume, that the number 62 is 100% - because it's the output value of the task.

2. We assume, that x is the value we are looking for.

3. If 62 is 100%, so we can write it down as 62=100%.

4. We know, that x is 1% of the output value, so we can write it down as x=1%.

5. Now we have two simple equations:

1) 62=100%

2) x=1%

where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:

62/x=100%/1%

6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for what is 1% of 62

62/x=100/1

(62/x)*x=(100/1)*x       - we multiply both sides of the equation by x

62=100*x       - we divide both sides of the equation by (100) to get x

62/100=x

0.62=x

x=0.62

now we have:

1% of 62=0.62

Answer:

A

Step-by-step explanation:

Since we are given BC is congruent to DC and angle b and d are 90. We can prove that <C is congruent to itself by reflexive  property of congruence. We can also you use linear pair theorem to prove <CDA is congruent to <CBE. Since they are right angles, we can prove that they are congruent by rt <s thm. Thus, we cna prove they are congruent by ASA. Hope it helps

Answer:

50%

Step-by-step explanation:

Cost of 3 bananas= Rs. 5 ⇒ cost of 1 banana= Rs. 5/3

Selling price of 2 bananas= Rs. 5 ⇒ selling price of 1 banana= Rs. 5/2

Gain= Rs. (5/2- 5/3)= Rs. (15/6- 10/6)= Rs. 5/6

Gain %= 5/6÷5/3 × 100%= 50%

Answer:

5 pints of milk.

Step-by-step explanation:

Note the unit conversion:

1 quart = 2 pint.

There are 3 quarts of milk. Multiply 3 with 2 to get the amount of pints in the jug:

3 x 2 = 6

The jug of milk has 6 pints of milk. Michael then pours 1 pint of milk. Subtract 1 from 6:

6 - 1 = 5

There are 5 pints of milk left in the jug.

~

Answer:

[tex]2.5[/tex]

Step-by-step explanation:

1 quart = 2 pints

1 pint = 0.5 quarts

[tex]3 - 0.5 = 2.5[/tex]

[tex]=2.5q[/tex]

Hope this helps.

Answer:

-2w - 4

Step-by-step explanation:

What is the simplest form of this expression

2(w - 1) + (-2)(2w + 1) =

= 2w - 2 - 4w - 2

= -2w - 4

Answer: -2w-4

Step-by-step explanation:

subtract 4w of 2w

2w-2-4w-2

subtract 2 of -2

-2w-2-2

final answer

-2w-4

Answer:

1 year

Step-by-step explanation:

1. Convert 10% into a z-score, using a calculator or whateva

2. Z = -1.281551 ( you can find this by doing the following equation: (x - mean) / (standard deviation)

3. Hence -1.281551 = (x - 4) / 2 or, x = 1.436898, ( rounded to the nearest year ) = 1 year

Answer:

B. 120 m²

Step-by-step explanation:

To find the surface area of the composite solid, we would need to calculate the area of each solid (square pyramid and square prism), then subtract the areas of the sides that are not included as surface area. The sides not included as surface area is the side the pyramid and the prism is joint together.

Step 1: find the surface area of the pyramid:

Surface area of pyramid with equal base sides = Base Area (B) + ½ × Perimeter (P) × Slant height (l)

Base area = 4² = 16 m

Perimeter = 4(4) = 16 m

Slant height = 3 m

Total surface area of pyramid = 16 + ½ × 16 × 3

= 16 + 8 × 3 = 16 + 24

= 40 m²

Step 2: find the area of the prism

Area = 2(wl + hl + hw)

Area = 2[(4*4) + (5*4) + (5*4)]

Area = 2[16 + 20 + 20]

Area of prism =  2[56] = 112 m²

Step 3: Find the area of the sides not included

Area of the sides not included = 2 × area of the square base where both solids are joint

Area = 2 × (4²)

Area excluded = 2(16) = 32 m²

Step 4: find the surface area of the composite shape

Surface area of the composite shape = (area of pyramid + area of prism) - excluded areas

= (40m²+112m²) - 32m²

= 152 - 32

Surface area of composite solid = 120 m²

Answer:

  8

Step-by-step explanation:

That total is ...

  (number of possibilities in each location)^(number of locations) = 2^3 = 8

The possible numbers are ...

  444, 449, 494, 499

  944, 949, 994, 999

There are 8 of them.

Answer:

[tex] P(X \geq 3)= 1- P(X<3)= 1-P(X \leq 2)= 1- [P(X=0) +P(X=1) +P(X=2)][/tex]

And we can find the individual probabilites using the probability mass function and we got:

[tex] P(X=0) = (15C0) (0.08)^{0} (1-0.08)^{15-0}=0.286 [/tex]

[tex] P(X=1) = (15C1) (0.08)^{1} (1-0.08)^{15-1}=0.373 [/tex]

[tex] P(X=2) = (15C2) (0.08)^{2} (1-0.08)^{15-2}=0.227 [/tex]

And replacing we got:

[tex] P(X\geq 3) = 1-[0.286+0.373+0.227 ]= 0.114[/tex]

Step-by-step explanation:

For this case we can assume that the variable of interest is "drivers were involved in a car accident last year" and for this case we can model this variable with this distribution:

[tex] X \sim Bin (n =15, p =0.08)[/tex]

And for this case we want to find this probability;

[tex] P(X \geq 3)[/tex]

and we can use the complement rule and we got:

[tex] P(X \geq 3)= 1- P(X<3)= 1-P(X \leq 2)= 1- [P(X=0) +P(X=1) +P(X=2)][/tex]

And we can find the individual probabilites using the probability mass function and we got:

[tex] P(X=0) = (15C0) (0.08)^{0} (1-0.08)^{15-0}=0.286 [/tex]

[tex] P(X=1) = (15C1) (0.08)^{1} (1-0.08)^{15-1}=0.373 [/tex]

[tex] P(X=2) = (15C2) (0.08)^{2} (1-0.08)^{15-2}=0.227 [/tex]

And replacing we got:

[tex] P(X\geq 3) = 1-[0.286+0.373+0.227 ]= 0.114[/tex]