When traveling with the wind, it takes an airplane 3 hours to travel 1800 miles. It takes the same airplane 3.6 hours to travel the same 1800 miles when traveling against the wind. Assuming the airplane travels at a constant speed during both trips, what is the speed of the airplane and the speed of the wind?

Answer:

D = 240 - 30t

Step-by-step explanation:

If the equation represents her distance from City A, we need to include 240 in the equation to represent the distance to the city.

Then, we need to subtract 30t from 240 in the equation because 30t represents how far she will have traveled in t hours.

So, D = 240 - 30t is the equation that will represent Layla's distance from the city.

Answer:

  2/5

Step-by-step explanation:

  f(x) = 2(5/2)^-x = 2(2/5)^x

The multiplicative rate of change is the base of the positive exponent, 2/5.

Answer:

5 miles away

Step-by-step explanation:

If you walked north 8 miles, then west 4 miles, then south 5 miles, you have, in total, travelled 4 miles west and [tex]8-5=3[/tex] miles north.

This creates a triangle, in which we can find the the length of the hypotenuse to find how far away you are now.

We can use the Pythagorean theorem since this is a right triangle.

[tex]a^2+b^2=c^2\\3^2+4^2=c^2\\9+16=c^2\\25=c^2\\c=5[/tex]

Hope this helped!

Answer:

5 miles away

Step-by-step explanation:

Answer:

  x = 1.00995066776

  x = 2.52925492433

Step-by-step explanation:

This sort of equation is best solved using a graphing calculator. For that purpose, I like to rewrite the equation as a function whose zeros we're seeking. Here, that becomes ...

  [tex]f(x)=\log{(x)}-\log{(x-1)}^2-2\log{(x-1)}[/tex]

The attached graph shows zeros at

  x = 1.00995066776 and 2.52925492433

_____

Comment on the equation

Note that we have taken the middle term to be the square of the log, rather than the log of a square. For the latter interpretation, see mberisso's answer at https://brainly.com/question/17210068

Comment on the answer refinement

We have used Newton's method iteration to refine the solutions to this equation. The solution near 1.00995 requires the initial guess be very close for that method to work properly. Fortunately, the 1.01 value shown on the graph is sufficient for the purpose.

We want to maximize [tex]x^3y^4z[/tex] subject to the constraint [tex]x+y+z=30[/tex].

The Lagrangian is

[tex]L(x,y,z,\lambda)=x^3y^4z-\lambda(x+y+z-30)[/tex]

with critical points where the derivatives vanish:

[tex]L_x=3x^2y^4z-\lambda=0[/tex]

[tex]L_y=4x^3y^3z-\lambda=0[/tex]

[tex]L_z=x^3y^4-\lambda=0[/tex]

[tex]L_\lambda=x+y+z-30=0[/tex]

[tex]\implies\lambda=3x^2y^4z=4x^3y^3z=x^3y^4[/tex]

We have

[tex]3x^2y^4z-4x^3y^3z=x^2y^3z(3y-4x)=0\implies\begin{cases}x=0,\text{ or}\\y=0,\text{ or}\\z=0,\text{ or}\\3y=4x\end{cases}[/tex]

[tex]3x^2y^4z-x^3y^4=x^2y^4(3z-x)=0\implies\begin{cases}x=0,\text{ or}\\y=0,\text{ or}\\3z=x\end{cases}[/tex]

[tex]4x^3y^3z-x^3y^4=x^3y^3(4z-y)=0\implies\begin{cases}x=0,\text{ or}\\y=0,\text{ or}4z=y\end{cases}[/tex]

Let's work with [tex]x=3z[/tex] and [tex]y=4z[/tex], for which we have

[tex]x+y+z=8z=30\implies z=\dfrac{15}4\implies\begin{cases}x=\frac{45}4\\y=15\end{cases}[/tex]

The smallest of these is C. 15/4.

Find the powers [tex]a=\sqrt{2}+\sqrt{3}[/tex]

$a^{2}=5+2 \sqrt{6}$

$a^{3}=11 \sqrt{2}+9 \sqrt{3}$

The cubic term gives us a clue, we can use a linear combination to eliminate the root 3 term $a^{3}-9 a=2 \sqrt{2}$ Square $\left(a^{3}-9 a\right)^{2}=8$ which gives one solution. Expand we have $a^{6}-18 a^{4}-81 a^{2}=8$ Hence the polynomial $x^{6}-18 x^{4}-81 x^{2}-8$ will have a as a solution.

Note this is not the simplest solution as $x^{6}-18 x^{4}-81 x^{2}-8=\left(x^{2}-8\right)\left(x^{4}-10 x^{2}+1\right)$

so fits with the other answers.

Answer:

[tex]y^3 -6y-6[/tex]

Answer:

The upper bound of the confidence interval is 0.34

Step-by-step explanation:

Here in this question, we want to calculate the upper bound of the confidence interval.

We start by calculating the margin of error.

Mathematically, the margin of error = 0.29 -0.24 = 0.05

So to get the upper bound of the confidence interval, we simply add this margin of error to the mean

That would be 0.05 + 0.29 = 0.34

Answer:

Step-by-step explanation:

This is best read on the number line.

Look at the picture.

[tex]-\dfrac{17}{2}=-8\dfrac{1}{2}=-8.5[/tex]

Answer:

The 3 years investment earns more interest

Step-by-step explanation:

Given

Principal, P = $5,000

Required

Determine which earns more interest

When Rate = 1.75% and Year = 2

Interest is as follows;

[tex]I = \frac{PRT}{100}[/tex]

Substitute 1.75 for R, 5000 for P and 2 for T

[tex]I = \frac{5000 * 1.75 * 2}{100}[/tex]

[tex]I = \frac{17500}{100}[/tex]

[tex]I = \$175[/tex]

When Rate = 1.25% and Year = 3

Interest is as follows;

[tex]I = \frac{PRT}{100}[/tex]

Substitute 1.25 for R, 5000 for P and 3 for T

[tex]I = \frac{5000 * 1.25 * 3}{100}[/tex]

[tex]I = \frac{18750}{100}[/tex]

[tex]I = \$187.5[/tex]

Comparing the interest of both investments, the 3 years investment earns more interest

Answer: $2750

Step-by-step explanation:

Formula to calculate interest : I = Prt , where P = Principal amount , r = rate of interest ( in decimal) , t= time.

Given:  I= $495

t= 3 years

r= 6% = 0.06

Then, according to the above formula:

[tex]495 = P (0.06\times3)\\\\\Rightarrow\ P=\dfrac{495}{0.18}\\\\\Rightarrow\ P=2750[/tex]

Hence, the principal invested = $2750

it was all about equating some values

to bake the required number of cakes during the available 3-hour time period, 7 cooks are required.

Let's determine the number of cooks required to bake the required number of cakes during the available time.

We have the following information:

- Each cook can bake either 5 large cakes or 14 small cakes per hour.

- The kitchen is available for 3 hours.

- We need to bake 29 large cakes and 260 cakes in total.

First, let's calculate the number of large cakes that can be baked by one cook in 3 hours:

1 cook can bake 5 large cakes/hour × 3 hours = 15 large cakes.

Next, let's calculate the number of small cakes that can be baked by one cook in 3 hours:

1 cook can bake 14 small cakes/hour × 3 hours = 42 small cakes.

Now, let's calculate the number of large cakes that can be baked by all the cooks in 3 hours:

Total number of large cakes = Number of cooks × Large cakes per cook per 3 hours

We need to bake 29 large cakes, so:

29 = Number of cooks × 15

Number of cooks = 29 / 15 ≈ 1.93

Since we can't have a fraction of a cook, we need to round up to the nearest whole number. Therefore, we need at least 2 cooks to bake the required number of large cakes.

Similarly, let's calculate the number of small cakes that can be baked by all the cooks in 3 hours:

Total number of small cakes = Number of cooks × Small cakes per cook per 3 hours

We need to bake 260 small cakes, so:

260 = Number of cooks × 42

Number of cooks = 260 / 42 ≈ 6.19

Again, rounding up to the nearest whole number, we need at least 7 cooks to bake the required number of small cakes.

Since we need to satisfy both requirements for large and small cakes, we choose the larger number of cooks required, which is 7 cooks.

Therefore, to bake the required number of cakes during the available 3-hour time period, 7 cooks are required.

Learn more about work here

https://brainly.com/question/13245573

#SPJ2

Answer: 36 shingles can be placed on the north part of the house.

Step-by-step explanation:

Given: Length of each shingle = [tex]1\dfrac23[/tex] feet = [tex]\dfrac53[/tex] feet.

The north part of the house has a roof line that is 60 feet across.

Then, the number of  shingles can be placed  on the north part of the house = (Length of roof line in north part) ÷ (Length of each shingle)

[tex]=60\div \dfrac{5}{3}\\\\=60\times\dfrac{3}{5}\\\\=12\times3=36[/tex]

Hence, 36 shingles can be placed on the north part of the house.

Answer:

(-∞,-3) and (3,∞)  

Step-by-step explanation:

f(x) = x³ − 27x + 3

1. Find the critical points

(a) Calculate the first derivative of the function.

f'(x) = 3x² -27  

(b) Factor the first derivative

f'(x)= 3(x² - 9) = 3(x + 3) (x - 3)

(c) Find the zeros

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

x + 3 = 0      x - 3 = 0

     x = -3          x = 3

The critical points are at x = -3 and x = 3.

2. Find the local extrema

(a) x = -3

f(x) = x³ − 27x + 3 = (-3)³ - 27(-3) + 3 = -27 +81 + 3 = 57

(b) x = 3

f(x) = x³ − 27x + 3 = 3³ - 27(3) + 3 = 27 - 81 + 3 = -51

The local extrema are at (-3,57) and (3,-51).

3, Identify the local extrema as maxima or minima

Test the first derivative (the slope) over the intervals (-∞, -3), (-3,3), (3,∞)

f'(-4) = 3x² -27 = 3(4)² - 27  = 21

f'(0) = 3(0)² -27 = -27

f'(4) = 3(4)² - 27 = 51

The function is increasing on the intervals (-∞,-3) and (3,∞).

The graph below shows the critical points of your function.

Step-by-step explanation:

Hey, there!!

5(R+2)-6.

Fistly multiply (R+2) by 5.

=5R + 10 - 6

Subtract 6 from 10.

= 5R +4.

Therefore, 5R + 4 is correct answer.

{ While simplifying the expression if there is multiplication or divide do it first and then add or or subtract like terms to get the simplified form of the expressions. }

Hope it helps..

Answer:

Yes it suggest that the actual percentage of type A donations differs from 40%, the percentage of the population having type A blood.

Well if a significance level of 0.05 is used it will not affect the conclusion

Step-by-step explanation:

From the question we are told that

     The  sample size is   [tex]n = 149[/tex]

     The  number that where  type A blood is  k =  76

       The population proportion is   [tex]p = 0.40[/tex]

       The  significance level is  [tex]\alpha = 0.01[/tex]

Generally the sample proportion is mathematically represented as

      [tex]\r p = \frac{k}{n}[/tex]

=>    [tex]\r p = \frac{76}{149}[/tex]

=>    [tex]\r p = 0.51[/tex]

The  Null hypothesis is   [tex]H_o : p = 0.41[/tex]

The  Alternative hypothesis is  [tex]H_a : p \ne 0.40[/tex]

Next we obtain the critical value of [tex]\alpha[/tex] from the z-table.The value is  

       [tex]Z_{\alpha } = Z_{0.01} = 1.28[/tex]

Generally the test statistics is mathematically evaluated as

           [tex]t = \frac{\r p - p }{ \sqrt{ \frac{p(1-p)}{n} } }[/tex]    

substituting values

           [tex]t = \frac{0.51 - 0.40 }{ \sqrt{ \frac{0.40 (1-0.40 )}{149} } }[/tex]    

           [tex]t =2.74[/tex]

So looking at the values for t  and  [tex]Z_{0.01}[/tex] we see that  [tex]t > Z_{0.01}[/tex] so we reject the null hypothesis. Which means that there is no sufficient evidence to support the claim

Now if [tex]\alpha = 0.05[/tex] , the from the z-table the critical value for [tex]\alpha = 0.05[/tex] is  [tex]Z_{0.05} = 1.645[/tex]

So comparing the value of  t and  [tex]Z_{0.05} = 1.645[/tex]  we see that [tex]t > Z_{0.05}[/tex] hence the conclusion would not be different.

Step-by-step explanation:

utilise the formula a+(n-1)d

a is the first number while d is common difference

Answer:

22

Step-by-step explanation:

Using the formular, Un = a + (n - 1)d

Where n = 10; a = -23; d = 5

U10 = -23 + (9)* 5

U10 = -23 + 45 = 22

Answer:

1048576

Step-by-step explanation:

Given the following :

Pizza order :

Size = small, medium, large, or extra large = 4 possible sizes

Toppings = any combination of 8 possible toppings (getting no toppings is allowed, as is getting all 8).

Combination of Toppings = 2^8

Four different sizes of pizza = 4

Number of possibilities in ordering for a single pizza :

(4 * 2^8) = 4 * 256 = 1024

Number of possibilities in ordering two pizzas :

(4 * 2^8)^2

(2^2 * 2^8)^2

From indices :

[2^(2+8)]^2

[2^(10)]^2

2^(10*2)

2^20

= 1048576

Answer:

true

Step-by-step explanation:

there is 100 candies. That means we can easily turn the amount of each type of candy into a percent. there was 30 butterscotch which means that is 30 percent. There was 15 strawberry which means that is 15 percent. add that and you get 45. This is a shortcut and i advise you use the way your teacher taught you.

[tex]|\Omega|=100\\|A|=30+15=45\\\\P(A)=\dfrac{45}{100}=0.45[/tex]

So TRUE

Complete Question

On the uploaded image is a similar question that will explain the given question

Answer:

The value of k is  [tex]k = 214285.7[/tex]

The percentage  of the oil that will be cleaned is [tex]x = 80.77\%[/tex]

Step-by-step explanation:

From the question we are told that

   The  cost of cleaning up the spillage is  [tex]C = \frac{ k x }{100 - x }[/tex]  [tex]x \le x \le 100[/tex]

     The  cost of cleaning x =  70% of the oil is  [tex]C = \$500,000[/tex]

Now at  [tex]C = \$500,000[/tex] we have  

       [tex]\$ 500000 = \frac{ k * 70 }{100 - 70 }[/tex]

       [tex]\$ 500000 = \frac{ k * 70 }{30 }[/tex]

      [tex]\$ 500000 = \frac{ k * 70 }{30 }[/tex]

      [tex]k = 214285.7[/tex]

Now  When  [tex]C = \$900,000[/tex]

       [tex]x = 80.77\%[/tex]

Answer:

[tex]x = \frac{1}{3} [/tex]

Step-by-step explanation:

*Move terms to the left and set equal to zero:

4㏒(√x) - ㏒(3x) - ㏒(x²) = 0

*simplify each term:

㏒(x²) - ㏒(3x) - ㏒(x²)

㏒(x²÷x²) -㏒(3x)

㏒(x²÷x² / 3x)

*cancel common factor x²:

㏒([tex]\frac{1}{3x}[/tex])

*rewrite to solve for x :

10⁰ = [tex]\frac{1}{3x}[/tex]

1 = [tex]\frac{1}{3x}[/tex]

1 · x = [tex]\frac{1}{3x}[/tex] · x

1x = [tex]\frac{1}{3}[/tex]

*that would be our answer, however, the convention is to exclude the "1" in front of variables so we are left with:

x = [tex]\frac{1}{3}[/tex]

Answer:

A.) x=90°

Step-by-step explanation:

Note:

The triangle shown is an isosceles triangle, which means that it has 2 congruent sides (as shown by the small intersecting lines), and this also means that it has two congruent angles.

We are given an angle measure adjacent to one of the missing angles. These two form supplementary angles, which means that they're sum is equal to 180°, or a straight line. So, to find:

[tex]180=135+y[/tex]

y is the unknown angle. Solve for y:

[tex]180-135=y\\\\y=45[/tex]

y is 45°. Since this and the other angle are congruent, add:

[tex]45+45=90[/tex]

Note:

Triangles angles will always add up to a total of 180°.

To find the missing angle x°, use:

[tex]180=a+b+c[/tex]

These are the angles in a triangle. Substitute any known values and solve:

[tex]180=45+45+x\\\\180=90+x\\\\180-90=x\\\\x=90[/tex]

The missing angle x° is 90°.

:Done

Answer:

We have the magnitude, M, and the angle A.

(The angle is always measured from the +x-axis)

Then we have that:

x = M*cos(A)

y = M*sin(A)

in this case:

M = 9m

A = -80°

x = 9m*cos(-80°) = 1.562

y = 9m*sin(-80) = -8.86m

Now, the component parallel to the x axis is:

x = 9m*cos(-80°) = 1.562 m

And the slope of something parallel to the x-axis is always zero, as this is a constant line.

Answer:

$3

Step-by-step explanation:

Given

Total Cost Price: $12,000

Unit Cost Price= $6

Total Selling Price = $18,000

Required

Determine the profit on each share

First, we need to determine the units of share bought;

Units = Total cost price / Unit Cost Price

[tex]Units = \frac{\$12000}{\$6}[/tex]

[tex]Units = 2000[/tex]

Next is to determine the selling price of each share; This is calculated as follows;

Unit Selling Price = Total Selling Price / Units Sold

[tex]Unit\ Selling\ Price = \frac{\$18000}{\$2000}[/tex]

[tex]Unit\ Selling\ Price = \$9[/tex]

The profit is the difference between the unit cost price and unit selling price

[tex]Profit = Unit\ Selling\ Price - Unit\ Cost\ Price[/tex]

[tex]Profit = \$9 - \$6[/tex]

[tex]Profit = \$3[/tex]

Answer:

[tex]\mathbf{P(X=5) =0.0888}[/tex]    

P(x ≤ 5 ) = 0.9707

P ( x ≥ 6) = 0.0293

Step-by-step explanation:

The probability of a binomial mass distribution can be expressed with the formula:

[tex]\mathtt{P(X=x) =(^{n}_{x} ) \ \pi^x \ (1-\pi)^{n-x}}[/tex]

[tex]\mathtt{P(X=x) =(\dfrac{n!}{x!(n-x)!} ) \ \pi^x \ (1-\pi)^{n-x}}[/tex]

where;

n = 8 and π = 0.36

For x = 5

The probability [tex]\mathtt{P(X=5) =(\dfrac{8!}{5!(8-5)!} ) \ 0.36^5 \ (1-0.36)^{8-5}}[/tex]

[tex]\mathtt{P(X=5) =(\dfrac{8!}{5!(3)!} ) \ 0.36^5 \ (0.64)^{3}}[/tex]

[tex]\mathtt{P(X=5) =(\dfrac{8 \times 7 \times 6 \times 5!}{5!(3)!} ) \times \ 0.0060466 \ \times 0.262144}[/tex]

[tex]\mathtt{P(X=5) =(\dfrac{8 \times 7 \times 6 }{3 \times 2 \times 1} ) \times \ 0.0060466 \ \times 0.262144}[/tex]

[tex]\mathtt{P(X=5) =({8 \times 7 } ) \times \ 0.0060466 \ \times 0.262144}[/tex]

[tex]\mathtt{P(X=5) =0.0887645}[/tex]

[tex]\mathbf{P(X=5) =0.0888}[/tex]     to 4 decimal places

b. x ≤ 5

The probability of P ( x ≤ 5)[tex]\mathtt{P(x \leq 5) = P(x = 0)+ P(x = 1)+ P(x = 2)+ P(x = 3)+ P(x = 4)+ P(x = 5})[/tex]

[tex]{P(x \leq 5) = ( \dfrac{8!}{0!(8!)} \times (0.36)^0 \times (1-0.36)^8 \ ) + \dfrac{8!}{1!(7!)} \times (0.36)^1 \times (1-0.36)^7 \ +[/tex][tex]\dfrac{8!}{2!(6!)} \times (0.36)^2 \times (1-0.36)^6 \ + \dfrac{8!}{3!(5!)} \times (0.36)^3 \times (1-0.36)^5 + \dfrac{8!}{4!(4!)} \times (0.36)^4 \times (1-0.36)^4 \ + \dfrac{8!}{5!(3!)} \times (0.36)^5 \times (1-0.36)^3 \ )[/tex]

P(x ≤ 5 ) = 0.0281+0.1267+0.2494+0.2805+0.1972+0.0888

P(x ≤ 5 ) = 0.9707

c. x ≥ 6

The probability of P ( x ≥ 6) = 1  - P( x  ≤ 5 )

P ( x ≥ 6) = 1  - 0.9707

P ( x ≥ 6) = 0.0293

Answer: 2 years

Step-by-step explanation:

The exponential growth function is given by :-

[tex]y=A(1+r)^x[/tex] (i)

, where A = initial value , r = rate of growth and  x= time period.

As per given ,

A= 242

r= 12% = 0.12

To find : t when y= 300.

Put all the values in (i)

[tex]300=242(1+0.12)^x\\\\\Rightarrow\ \dfrac{300}{242}=(1.12)^x\\\\\Rightarrow\ 1.23967=(1.12)^x[/tex]

Taking log on both sides , we get

[tex]\log (1.2396) = t \log (1.12)\\\\\Rightarrow\ 0.09328=t(0.049218)\\\\\Rightarrow t=\dfrac{0.09328}{0.049218}=\approx2[/tex]

hence, it will take 2 years.

Answer:

It sold 14 cans boxes of food and 12 cans of food.

Step-by-step explanation:

The factor for the food cans depend upon every seven food boxes .So, the same no. of sets of food cans will be sold.

Let the no. of sets of food boxes be x.

According to the question,

6x+7x=26

13x=26

x=26/13

x=2

No. of food cans =6x=6×2=12 cans

No. of food boxes=7x=7×2=14 boxes

Please mark brainliest ,if it is truly the best ! Thank you!

Answer:

The operation:

(a,b) is equal to the rest of the division of a by b.

Now, if we have:

(a + kb,b) = (a,b) + (k*b,b)

But if we have that k and b are integers, then:

(k*b)/b = k

So b divides k*b into a whole number, this means that (k*b,b) = 0

then:

(a + kb,b) = (a,b) + (k*b,b) = (a,b) + 0 = (a,b)

Answer:

k=8

Step-by-step explanation:

Since y and x are in direct proportions, the equation is

y= kx, where k is a constant.

when y= 33.6, x=4.2,

33.6= k(4.2)

k= 33.6 ÷4.2

k=8

Answer:

k=8

Step-by-step explanation:

Answer:

Mean age: 48

Standard deviation: 4

Step-by-step explanation:

a) Mean

The formula for Mean = Sum of terms/ Number of terms

Number of terms

= 42 + 54 + 50 + 54 + 50 + 42 + 46 + 46 + 48+ 48/ 10

= 480/10

= 48

The mean age is 48

b) Standard deviation

The formula for Standard deviation =

√(x - Mean)²/n

Where n = number of terms

Standard deviation =

√[(42 - 48)² + (54 - 48)² + (50 - 48)² +(54 - 48)² + (50 - 48)² +(42 - 48)² + (46 - 48)² + (46 - 48)² + (48 - 48)² + (48 - 48)² / 10]

= √-6² + 6² + 2² + 6² + 2² + -6² + -2² + -2² + 0² + 0²/10

=√36 + 36 + 4 + 36 + 4 + 36 + 4 + 4 + 0 + 0/ 10

=√160/10

= √16

= 4

The standard deviation of the ages is 4