Please help me!
Linear Equations with distribution

2(3x + 3) = 18

The distance from point A to point B is 781.5 ft.

Since the angle of elevation from point A to the lighthouse is 15 degrees, use the tangent function to find the height of the lighthouse. Let x be the height of the lighthouse,

tan(15°) = x / 862

Solve for x.

x = 862 (tan(15°))

Similarly, let y be the distance from point B to the lighthouse,

tan(8°) = x / y

Solve for y.

tan(8°) = 862 (tan(15°)) / y

y = 862 (tan(15°)) / tan(8°)

y = 1643.45 feet

Subtract 862 from 1643.45 to get the distance from point A to point B.

distance from point A to point B = 1643.45 - 862 = 781.45 ft = 781.5 ft

Therefore, the distance from point A to point B is 781.5 ft.

Learn more about tangent function here: https://brainly.com/question/10454111

#SPJ4

A quarterback throws an incomplete pass. The height of the football at time t is modeled by the equation h(t) = –16t² + 40t + 7. Rounded to the nearest tenth, the solutions to the equation when h(t) = 0 feet are –0.2 s and 2.7 s.

the solution to be eliminated is -0.2s this is because time do not have negative values

ax² + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a.

It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be real or complex.

Considering the given function, the answer is both real one is negative the other is positive.

The solution in this case represents time, and time of negative value do not apply in real life

Learn more about quadratic equation at:

https://brainly.com/question/1214333

#SPJ1

Answer:Gotta Be G tbh

Step-by-step explanation: Calculator on brainly

Answer:

x=2.4

y=2.5

z=3.3

Step-by-step explanation:

6/5=1.2

1.2 = scale factor

x=2x1.2=2.4

y=3/1.2=2.5

z=4/1.2=3.3

Answer:

x = -5

Step-by-step explanation:

Answer:

4w-8

Step-by-step explanation:

4(w-2)

(4*w)-(4*2)

4w-8

Answer:

4w-8

Step-by-step explanation:

4(w - 2)

Distribute

4*w - 4*2

4w-8

Answer:

C

Step-by-step explanation:

cross multiply

Answer:

2(x + 4)

Step-by-step explanation:

This is because when you open up the brackets and multiply....

2 × x = 2x

and 2 × 4 = +8

So 2(x + 4) = 2x + 8

Ndidi rides y km at 10 km/hr, then walks 0.5y km at 3 km/hr. She is away from. home less than 4hours.Range of the values of Y is =24/7

Let's call the total time spent riding and walking t hours. We know that t is less than 4 hours, so:

t = time spent riding + time spent walking < 4 hours

The time spent riding is given by y / 10 km/hr and the time spent walking is given by 0.5y / 3 km/hr. So, we can write the inequality as:

t = y / 10 + 0.5y / 3 < 4

Expanding and simplifying the expression on the left side gives:

7/6y < 4 * 6/7

Multiplying both sides by 6/7 gives:

y < 4 * 6/7 * 6/7 = 24/7

So, the range of values of y is 0 < y < 24/7 km. This means that Ndidi rode less than 24/7 km, but more than 0 km.

TO know more about values visit:

https://brainly.com/question/26352252

#SPJ4

The qualified student loan interest deduction in 2021 is $37500.

Adjusted gross income is an individual's total gross income less specific deductions in the United States income tax system. It is used to compute taxable income, which is AGI minus personal exemption and itemized deduction allowances. AGI is more important than gross income for most individual tax purposes.

AGI is calculated by taking your gross income and subtracting certain "above the line" deductions. 401(k) contributions, health savings account contributions, and educator expenses are common examples of deductions

As per Law, a maximum of $2,500 will be allowed to be deducted from the Income. Thus the following would be the solution.

Income of Sally Morris = $40,000

Less: Qualified student loan interest $2,500

Modified Adjusted Gross Income $37,500

The deduction is $37500.

Learn more about loan on:

https://brainly.com/question/26011426

#SPJ1

Answer:

$8000

Step-by-step explanation:

profit = selling price - Cost Price

P = 35000-27500

P= 8000

\(-4x (x - 26) = 200 <=> -4x^2+104x -200 = 0\\<=> x= 13+\sqrt{119} /or/ x= 13-\sqrt{119}\)

ok done. Thank to me :>

Answer:

10 miles long

Step-by-step explanation:

The length of the circular trail is calculated as: 10 miles.

We are told that Arthur walked around a circular trail twice in a total of 4.5 hrs.

Thus, he completed two full loops around the circular trail. Let's call the distance of the trail "d" (in miles) and the time it took for the first loop "t1" hours, and the time it took for the second loop "t2" hours.

So, we have:

t₁ + t₂ = 4.5

He walked the circle at 4 mph the first time and at 5 mph the second time.

The distance traveled is given by the formula:

Distance = Speed × Time.

For the first loop:

d = 4t₁

For the second loop:

d = 5t₂

From Equation 2 and Equation 3, we can set up an equation relating t₁ and t2:

4t₁ = 5t₂

Now, we can solve for t₁ in terms of t₂:

t₁ = (5/4)t₂

Substitute this value of t1 into Equation 1:

(5/4)t₂ + t₂ = 4.5

Combine the terms:

(9/4)t₂ = 4.5

Now, solve for t₂:

t₂ = (4.5 * 4) / 9

t₂ = 2

Now that we have the value of t₂, we can find t₁ using the equation

t₁ = (5/4)t₂

t₁  = (5/4) * 2

t₁  = 2.5

Now we can find the length of the trail using either Equation 2 or Equation 3:

d = 4t₁

d = 4 * 2.5

d = 10

So, the length of the circular trail is 10 miles.

Read more about Algebraic expressions at: https://brainly.com/question/434421

#SPJ3

The probability of time lapsed between two consecutive trades longer than 17 seconds is equal to 0.87 or 87%.

Mean of the normal distribution (μ) = 15 seconds

To find the probability that the time lapsed between two consecutive trades on the New York Stock Exchange will be longer than 17 seconds,

Use the information provided about the normal distribution and probabilities.

Determine the probability of the time lapsed being greater than 17 seconds.

First, the z-scores corresponding to the given probabilities.

To find the z-score for the lower bound, where the time lapsed is below 13 seconds,

P(X < 13) = 0.07

This gives us the area to the left of 13 seconds, and

The z-score corresponding to this probability.

Using a standard normal distribution calculator,

The z-score corresponding to the cumulative probability of 0.07.

Let's denote this z-score as z₁.

Next, the z-score for the upper bound, where the time lapsed is between 16 and 17 seconds,

P(16 < X < 17) = 0.13

This gives us the area between 16 and 17 seconds, and

the z-scores corresponding to these probabilities.

The z-scores corresponding to the cumulative probabilities of 0.13 for both 16 seconds and 17 seconds.

Let's denote these z-scores as z₂ and z₃, respectively.

Now, to find the probability that the time lapsed between two consecutive trades will be longer than 17 seconds,

calculate the area to the right of 17 seconds under the normal distribution curve.

P(X > 17) = 1 - P(X < 17)

Since the z-scores corresponding to the lower bounds (13 seconds) and the upper bounds (16 seconds and 17 seconds),

calculate the probability using the cumulative distribution function (CDF) or the standard normal distribution.

P(X > 17) = 1 - P(X < 17)

P(X > 17) = 1 - P(Z < z3)

Using the z-scores, calculate the probability.

Please use standard normal distribution notation with Z representing the z-score.

Probability (P(Z < z₁)) = 0.07

Probability (P(Z < z₂)) = 0.13

Probability (P(Z < z₃)) = 0.13

Now, let's substitute these probabilities into the equation,

P(X > 17) = 1 - P(Z < z₃)

P(X > 17) = 1 - 0.13

Finally, calculate the probability,

P(X > 17) = 1 - 0.13

P(X > 17) = 0.87

Therefore, probability of time lapsed between two consecutive trades on New York Stock Exchange will be longer than 17 seconds is 0.87 or 87%.

Learn more about probability here

brainly.com/question/13184129

#SPJ4

Answer:

2 ≤ 5

Step-by-step explanation:

-5 ≤ -2 add 7 to both sides

-5+7 ≤ -2+7 calculate

2 ≤ 5

The probability of the range 13.7 < x < 30.7 for a normal random variable with mean μ = 35 and standard deviation σ = 10 is 0.1003.

To find the probability of the range 13.7 < x < 30.7 for a normal random variable with mean μ = 35 and standard deviation σ = 10, we need to first standardize the values using the formula:
z = (x - μ) / σ

For the lower limit of 13.7, we have:
z1 = (13.7 - 35) / 10 = -2.13

For the upper limit of 30.7, we have:
z2 = (30.7 - 35) / 10 = -0.43

Next, we use a standard normal distribution table or calculator to find the area between these two z-scores:
P(-2.13 < z < -0.43) = 0.1003

Therefore, the probability of the range 13.7 < x < 30.7 for a normal random variable with mean μ = 35 and standard deviation σ = 10 is 0.1003.

Know more about probability here:

https://brainly.com/question/251701

#SPJ11

Answer:

1.32cm

Step-by-step explanation:

Step-by-step explanation:

I'm assuming you are saying volume?

But I'll do both volume and surface area.

also note that 0.66 is the diameter, not radius

If 3.41946 is the volume:

V of cylinder = pi*r^2*h

3.41946 = pi*0.33^2*h

h = 3.41946/(pi*0.33^2) = 9.99493043 cm

If 3.41946 is the surface area:

SA of cylinder = pi*r*(r+h)

3.41946 = pi*0.33*(0.33+h)

0.33+h = 3.41946/(pi*0.33) = 3.29832704

h = 3.29832704-0.33 = 2.96832704 cm

The salt will acquire octahedral hole. Thus option B is correct .

Given,

\(r^{+} = 165\\ r^{-} = 297\)

Now,

Find the coordination number ,

Radius ratio = \(r^{+} / r^{-}\)

Substitute the values of radius of salt to get the coordination number .

Radius ratio = 165/297

Radius ratio = 0.556 .

If the radius ratio is between 0.414 and 0.732

Range of radius ratio : 0.414 < r < 0.732

Then coordination number is 6 . If the coordination number is 6 then it will acquire octahedral void .

Know more about coordination number,

https://brainly.com/question/31751524

#SPJ4

Answer: 55

Step-by-step explanation:

Angles 1 and 4 are vertical angles and angles 2 and 3 are vertical angles. Vertical angles are congruent. Therefore, angle 1 is congruent to angle 4 and angle 2 is congruent to angle 3. Angles 1 and 2 form a linear pair, as do angles 3 and 4. Linear pairs must always add up to 180 because they are supplementary and form a line. Angle 2 is 125, so angle 3 is 125. Angle 3 and Angle 4 must equal 180, so you do 125 + x = 180. So, x = 55.

Hope this helps!!! :)

The average velocity from t = 5 to t = 5.1 is -245 m/s.

An equation for the average velocity from 5 seconds to

t seconds is Δt = t - 5.

Required instantaneous velocity at t = 5 is (-50) m/s.

The rock is going down at that moment.

We can tell because the coefficient of the t² term in the equation for d(t) is negative.

The mathematical quantity for instantaneous velocity is a derivative.

How to find the average velocity of the rock from t = 5 to t = 5.1?

To find the average velocity of the rock from t = 5 to t = 5.1, we need to calculate the change in distance and change in time over this interval:

Δd = d(5.1) - d(5) = (35(5.1) - 5(5.1)²) - (35(5) - 5(5)²) ≈ -24.5

Δt = 5.1 - 5 = 0.1

Therefore, the average velocity from t = 5 to t = 5.1 is Δd/Δt ≈ -24.5/0.1 = -245 m/s

To find an equation for the average velocity from 5 seconds to t seconds, we need to calculate the change in distance and change in time over this interval:

Δd = d(t) - d(5) = (35t - 5t²) - (35(5) - 5(5)²) = 35(t - 5) - 5(t² - 25)

Δt = t - 5

Therefore, an equation for average velocity from 5 seconds to t seconds is Δt = t - 5

To find the instantaneous velocity of the rock at t = 5, we need to take the limit of the average velocity expression as Δt approaches 0,

instantaneous velocity at t = 5 = lim(Δt→0) [35 - 5(t + 5)] = 35 - 5(5 + 5) = -50 m/s

Since the instantaneous velocity at t = 5 is negative, the rock is going down at that moment. We can tell because the coefficient of the t² term in the equation for d(t) is negative, which means the parabolic shape of the trajectory is concave downward. The mathematical quantity for instantaneous velocity is a derivative, specifically the derivative of the distance function with respect to time.

Learn more about average velocity here,

https://brainly.com/question/1844960

#SPJ1

The average velocity from t = 5 to t = 5.1 is -245 m/s.

An equation for the average velocity from 5 seconds to

t seconds is Δt = t - 5.

Required instantaneous velocity at t = 5 is (-50) m/s.

The rock is going down at that moment.

We can tell because the coefficient of the t² term in the equation for d(t) is negative.

The mathematical quantity for instantaneous velocity is a derivative.

How to find the average velocity of the rock from t = 5 to t = 5.1?

To find the average velocity of the rock from t = 5 to t = 5.1, we need to calculate the change in distance and change in time over this interval:

Δd = d(5.1) - d(5) = (35(5.1) - 5(5.1)²) - (35(5) - 5(5)²) ≈ -24.5

Δt = 5.1 - 5 = 0.1

Therefore, the average velocity from t = 5 to t = 5.1 is Δd/Δt ≈ -24.5/0.1 = -245 m/s

To find an equation for the average velocity from 5 seconds to t seconds, we need to calculate the change in distance and change in time over this interval:

Δd = d(t) - d(5) = (35t - 5t²) - (35(5) - 5(5)²) = 35(t - 5) - 5(t² - 25)

Δt = t - 5

Therefore, an equation for average velocity from 5 seconds to t seconds is Δt = t - 5

To find the instantaneous velocity of the rock at t = 5, we need to take the limit of the average velocity expression as Δt approaches 0,

instantaneous velocity at t = 5 = lim(Δt→0) [35 - 5(t + 5)] = 35 - 5(5 + 5) = -50 m/s

Since the instantaneous velocity at t = 5 is negative, the rock is going down at that moment. We can tell because the coefficient of the t² term in the equation for d(t) is negative, which means the parabolic shape of the trajectory is concave downward. The mathematical quantity for instantaneous velocity is a derivative, specifically the derivative of the distance function with respect to time.

Learn more about average velocity here,

https://brainly.com/question/1844960

#SPJ1

Answer: 1.905

Step-by-step explanation:

75 percent *2.54

= (75/100)*2.54

= (75*2.54)/100

= 190.5/100 = 1.905

Answer:

i think it is 1.905

Step-by-step explanation:

Answer:

y= -2x +8

Step-by-step explanation:

perpendicular lines have a negative reciprocal gradient so

1/2 becomes -2/1 which is the gradient

sub in the values of x and y

2= -2 (3) +C

2= -6 + C

8=C

y=-2x +8

Answer:

y = -2x + 8

Step-by-step explanation:

for me the easiest way is simply to transform the slope and then just determine the y-intersect.

the slope of the original line is 1/2.

it is always the factor of x and represents the y/x ratio of the function (how many units is y changing when x changes a certain number of units).

a perpendicular line (90 degree angle) simply reverses x and y and the sign of the original slope.

so, the slope of the perpendicular line is -2, and the equation is

y = -2x + c

and c we get by using the point coordinates :

2 = -2×3 + c

2 = -6 + c

c = 8

so, we have

y = -2x + 8

The conditional probability that the size of the family is less than 6 given that it is at least 3 is 1.

To find the conditional probability that the size of the family is less than 6 given that it is at least 3, we need to use the formula for conditional probability.

Let's denote A as the event that the size of the family is less than 6, and B as the event that the size of the family is at least 3.

The conditional probability of A given B, denoted as P(A|B), is calculated as follows:

P(A|B) = P(A and B) / P(B)

First, we need to find P(B), the probability that the size of the family is at least 3. Since the family is selected at random, we can assume that all possible family sizes have an equal chance of being selected.

Let's assume the total number of possible family sizes is n. The probability of selecting a family with at least 3 members is the sum of the probabilities of selecting a family with exactly 3 members, exactly 4 members, and exactly 5 members.

P(B) = P(3) + P(4) + P(5)

Next, we need to find P(A and B), the probability that the size of the family is both less than 6 and at least 3. Since any family size less than 6 is also at least 3, P(A and B) will be the same as P(B).

Finally, we can substitute the values into the formula for conditional probability:

P(A|B) = P(A and B) / P(B) = P(B) / P(B) = 1

Therefore, the conditional probability that the size of the family is less than 6 given that it is at least 3 is 1.

To know more about conditional probability  refer here:

https://brainly.com/question/10567654

#SPJ11

Waterways should retain the old backhoes equipment.

To determine whether it is more favorable to purchase new backhoes or overhaul the old ones, we will evaluate the net present value (NPV), profitability index (PI), and internal rate of return (IRR) for both options.

Net Present Value (NPV):

For the new backhoes:

The initial cost of investment = Purchase cost when new - Salvage value now

= $199,994 - $15,200 = $184,794

The net cash flow generated each year for the new backhoes remains unspecified, so we cannot calculate its NPV.

For the old backhoes:

Initial investment = Cost of the overhaul = $41,400

Net cash flow generated each year = $15,200

Using the provided PV table, we can calculate the NPV for the old backhoes:

NPV = Net cash flow generated each year * PV factor for 8 years - Initial investment

= $15,200 * 5.76162 - $41,400 ≈ $55,689.69

Since the NPV for the old backhoes is positive, retaining the old equipment is favorable.

Profitability Index (PI):

The profitability index is calculated by dividing the present value of cash inflows by the initial investment.

For the new backhoes:

Since the net cash flow generated each year is unspecified, we cannot calculate the PI.

For the old backhoes:

PI = (Net cash flow generated each year * PV factor for 8 years) / Initial investment

= ($15,200 * 5.76162) / $41,400 ≈ 2.11

The profitability index for the old backhoes is 2.11.

Based on the PI, the old backhoes have a higher profitability index than the new backhoes, indicating that retaining the old equipment is more profitable.

Internal Rate of Return (IRR):

The IRR factor for the new and old backhoes is not provided, so we cannot calculate the exact IRR.

In summary, based on the net present value (NPV) and profitability index (PI), it is more favorable for Waterways to retain the old backhoes equipment.

For more questions like Cost click the link below:

https://brainly.com/question/30045916

#SPJ11

Answer:

200.96

Step-by-step explanation:

2(3.14)2^2 + 2(3.14)2*14

8*3.14 = 25.12

56*3.14 = 175.84

175.84 + 25.12 = 200.96

Answer:

40%

Step-by-step explanation:

Discount = 40%

10% = 0.245

40% = 0.98

$2.45 - $0.98 = $1.47

The number of people who know about the celebrity's proposal will continue to grow exponentially each day, starting from 888 and increasing by 50% each day. Let's analyze the growth in the number of people who know about the celebrity's proposal day by day.

Initially, 888 people know about the proposal. On the first day, the number of people who know increases by 50% of 888, which is (50/100) * 888 = 444 people. Therefore, after the first day, the total number of people who know is 888 + 444 = 1332.

On the second day, the number of people who know increases by 50% of 1332, which is (50/100) * 1332 = 666 people. Thus, the total number of people who know after the second day is 1332 + 666 = 1998.

Following this pattern, we can determine the number of people who know on subsequent days:

- On the third day: 1998 + (50/100) * 1998 = 2997 people.

- On the fourth day: 2997 + (50/100) * 2997 = 4495.5 (rounded to 4496) people.

- On the fifth day: 4496 + (50/100) * 4496 = 6744 people.

- And so on...

The growth in the number of people who know follows an exponential pattern since it increases by a certain percentage each day. The formula to calculate the number of people who know after a certain number of days can be written as:

N = 888 * (1 + 0.5)^d

where N is the total number of people who know after d days

In conclusion, the number of people who know about the celebrity's proposal will continue to grow exponentially each day, starting from 888 and increasing by 50% each day.

Learn more about exponents here:

https://brainly.com/question/5497425

#SPJ11

Answer:

1)

Step-by-step explanation:

The opposite angles formed by two intersecting lines are of equal measures.

They are called vertically opposite angles.