What should you substitute for y in the second equation (bottom equation) in order to solve the system by the substitution method?​

The speed of the wind and the speed of the dragon in still air are respectively;  142.5 mph and 7.5 mph

The dragon flew 300 miles with the wind in two hours.

After flying against the wind for two hours, he had made 270 miles of the return trip.

Let s be the speed in still air

Let w be the speed of the wind

Thus;

(s - w) = effective speed against the wind

and

(s + w) = effective speed with the wind

We know that;

distance = time * effective speed

Thus;

2(s + w) = 300

2(s - w) = 270

This can be simplified to get;

s + w = 150   -----(1)

s - w = 135   -----(2)

Add both equations to get;

2s = 285

s = 285/2

s = 142.5 mph.

Then, plane speed in still air is;

142.5 + w = 150

w = 150 - 142.5

w = 7.5 mph is the speed of the wind

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The 2 colors can be chosen in 6 different ways.

Here we need to identify the selections and the numbers of options for each.

Here the selections are:

And the numbers of options for each are:

The total number of combinations is:

C = 3*2 = 6

The 2 colors can be chosen in 6 different ways.

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Answer:

Cubic expression

Step-by-step explanation:

Polynomials with a degree of 3 are known as cubics.

Answer:

cubic expression

Step-by-step explanation:

it is cubic when raised to the power of 3

Answer:

Step-by-step explanation:

Using the binomial distribution, it is found that there is a 0.9842 = 98.42% probability that 3 or fewer experienced insomnia as a side effect, which means that it is a highly likely event.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

The values of the parameters are given as follows:

n = 20, p = 0.05.

The probability that 3 or fewer experienced insomnia as a side effect is given by:

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

Hence:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{20,0}.(0.05)^{0}.(0.95)^{20} = 0.3585[/tex]

[tex]P(X = 1) = C_{20,1}.(0.05)^{1}.(0.95)^{19} = 0.3774[/tex]

[tex]P(X = 2) = C_{20,2}.(0.05)^{2}.(0.95)^{18} = 0.1887[/tex]

[tex]P(X = 3) = C_{20,3}.(0.05)^{3}.(0.95)^{17} = 0.0596[/tex]

Then:

[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.3585 + 0.3774 + 0.1887 + 0.0596 = 0.9842[/tex]

0.9842 = 98.42% probability that 3 or fewer experienced insomnia as a side effect.

Since this probability is greater than 95%, this is a highly likely event.

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Answer:

etrf4f3dvef3rf3rfr2wrgwrf2rg3rf3rgerferferfef I'm

The statements that are true based on the information are:

1. Last year at least one of their clients made a profit of exactly 10%.

3. Last year some of their clients made a profit of 10% or more.

Options 1 and 3 are the correct answer.

We have,

1. Last year at least one of their clients made a profit of exactly 10%.

- True.

The investment company advertised that, on average, their clients made a profit of 10%.

This means there must be some clients who made exactly 10% profit.

2. Two years ago some of their clients made a profit of at least 10%.

Not enough information is given to determine the accuracy of this statement.

The information provided only refers to last year's profits, not profits from two years ago.

3. Last year some of their clients made a profit of 10% or more.

- True.

The average profit of the clients was 10%, indicating that some clients made a profit of 10% or more.

4. Last year all of their clients made a profit of more than 2%.

- Not necessarily true.

The average profit was 10%, but this does not guarantee that all clients made a profit greater than 2%.

Some clients might have made less than 2% or even incurred losses.

5. Last year, the number of their clients who made a profit of 10% or less was equal to the number of their clients who made a profit of 10% or more.

- Not enough information is given to determine the accuracy of this statement.

The average profit of 10% does not tell us about the distribution of profits among clients to make this comparison.

Thus,

The statements that are true based on the information are:

1. Last year at least one of their clients made a profit of exactly 10%.

3. Last year some of their clients made a profit of 10% or more.

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Answer:

3

Step-by-step explanation:

1: Turn the mixed fraction into improper.

2: Multiply 3/5 to each side

3: The you get x = 3

You need to multiply the fraction instead of division because multiplying by the reciprocal is the same as dividing the normal fraction.

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{5 = 1\dfrac{2}{3}x}[/tex]

[tex]\mathsf{1\dfrac{2}{3}x = 5}[/tex]

[tex]\mathsf{\dfrac{1\times3 + 2}{3}x = 5}[/tex]

[tex]\mathsf{\dfrac{3 + 2}{3}x = 5}[/tex]

[tex]\mathsf{\dfrac{5}{3}x = 5}[/tex]

[tex]\large\textbf{MULTIPLY }\rm{\bf \dfrac{3}{5}}\large\textbf{ to BOTH SIDES}[/tex]

[tex]\mathsf{{\dfrac{3}{5}\times\dfrac{5}{3}x= \dfrac{3}{5}\times 5}}[/tex]

[tex]\large\textbf{SIMPLIFY IT!}[/tex]

[tex]\mathsf{x = \dfrac{3}{5}\times5}[/tex]

[tex]\mathsf{x = \dfrac{3}{5}\times\dfrac{5}{1}}[/tex]

[tex]\mathsf{x = \dfrac{3\times5}{5\times1}}[/tex]

[tex]\mathsf{x = \dfrac{15}{5}}[/tex]

[tex]\mathsf{x = 15\div5}[/tex]

[tex]\mathsf{x = 3}[/tex]

[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{x = 3}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

$16,400

Step-by-step Explanation:

Step 1: We multiply $10,000 by 16%, getting $1,600.

Step 2: We then multiply $1,600 by 4 (which is given). That gives us $6,400.

Step 3: Add that to $10,000. We get $16,400 as the answer!

Answer:

Simple interest = P  x  r  x  t

                         = 10,000  x  16/100  x   4

                         =  $6400

Final amount = P (1 +rt)

                       = 10,000 (1 + 16/100  x  4)

                       = $16400

(or you can just add the simple interest to the principle amount to get the final amount)

Answer:

19 liters 800 milliliters

Step-by-step explanation:

0.33 * 12 * 5 = 19.8 liters

Answer:

The plots are (0,2) (1,-1)

Step-by-step explanation:

a slanted line starting from top left corner ending in the bottom right

Answer:

A. b+2(b+2b)

b + 2b + 4b = 7b

B. 3b + b = 4b

C. 2(2b) = 4b

None of them are equal to 9b

Answer:

[tex]\fbox {None}[/tex]

Step-by-step explanation:

A

B

C

68% of the day's sales will be between 87.23 and 96.57 and on 95% of the days, sales will be between 82.56 and 101.24.

If your distribution follows a normal distribution, the standard deviation and mean can tell you where the majority of the data are.

We have:

The mean number of sandwiches sold per day is 91.9 and the standard deviation is 4.67.

As we know, from the empirical rule, 68% of the data will lie in one standard deviation of the mean, i.e., in the interval with the endpoints x±s

for samples and with endpoints u±б for the population.

x = 91.9

s = 4.67

x - s = 91.9 - 4.67 = 87.23

x + s = 91.9 + 4.67 = 96.57

68% of the day's sales will be between 87.23 and 96.57

95% of the data will lie within two standard deviations of the mean, which means in the interval with the endpoints  x±2s for samples and with endpoints  u±б population.

x - 2s = 82.56

x + 2s = 101.24

On 95% of the days, sales will be between 82.56 and 101.24

Thus, 68% of the day's sales will be between 87.23 and 96.57 and on 95% of the days, sales will be between 82.56 and 101.24.

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For the regions bounded by y = 6cosx and y = one-fourth x squared minus 7, the limits of integration, the expression representing the total area, and the total area are mathematically given as

A=27.03squnit

What are the limits of integration, the expression representing the total area, and the total area.?

Generally, the equation for expression is mathematically given as

y = 6cosx

y=(1/4)x^2-7

therefore

[tex]A=\int^{b}_a (f(x)-g(x))dx[/tex]

The limits are

a=0 b=2\pi

Hence

[tex]A=\int ^{2\pi}_0 (6cosx -((1/4)x^2-7))dx\\\\solving\\\\A=\int^{2\pi}_0 (6cosx -((1/4)x^2-7))dx[/tex]

A=27.03squnit

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Answer:

Step-by-step explanation:

Comment

The angle supplementary to x and 3x are equal.

Supplementary angles = 180

Solution

x + 3x = 180

4x = 180                  Divide by 4

4x/4 = 180/4

x = 45

The angle supplementary to x is 3x

3x = 3*45

3x = 135

This angle is vertically opposite y. Vertically opposite angles are equal. So  y = 135

Answer

x = 45

y = 135

The equation in the vertex form of g(x) is:

[tex]g(x) = (x + 1)^2 - 38[/tex]

We know that g(x) is a translation of 2 units below and 3 units to the left of f(x).

So first, let's rewrite f(x) to its vertex form:

[tex]f(x) = x^2 - 4x - 32[/tex]

The vertex is at:

[tex]x = -(-4)/2*1 = 2[/tex]

The y-value of the vertex is:

[tex]f(2) = 2^2 - 4*2 - 32 = -36[/tex]

Then the vertex form of f(x) is:

[tex]f(x) = (x - 2)^2 - 36[/tex]

If we move this vertex 2 units below, and 3 units to the left, then we have:

[tex]g(x) = f(x +3) - 2\\\\g(x) = (x - 2 + 3)^2 - 36 - 2\\\\g(x) = (x + 1)^2 - 38[/tex]

That is the equation for g(x) in vertex form.

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Answer: 1

Step-by-step explanation:

Substituting in the given values,

3a-5b=3(-3)-5(-2)=-9+10=

Answer:

π(5²)(13)+⅓π(5²)(12)

Step-by-step explanation:

You can find the volume of the cylinder by:

V=πr²h

which is V1=π(5²)(13)

and the volume of the crooked cone by:

⅓πr²h

which is V2=⅓π(5²)(12)

and you need the volume of the whole shape. you can find by adding V1+V2

The formula for the area of the shaded region in the figure.

x² = 4py is mathematically given as

[tex]A=\frac{8}{3} \sqrt{p h} \cdot h[/tex]

Parameters

[tex]$x^{2}=4 p y$[/tex]

[tex]$y=h$[/tex]

[tex]\therefore x^{2}=4 p h \Rightarrow x=2 \sqrt{p h} \\[/tex]

Generally, the equation for the Area is mathematically given as

[tex]& A=2 \int_{0}^{2 \sqrt{p h}}\left(h-\frac{x^{2}}{4 p}\right) d x \\\\& A=2\left(h x-\frac{x^{3}}{12 p}\right]_{0}^{2 \sqrt{p h}} \\\\& A=2\left[\left[h 2 \sqrt{p h}-\frac{1}{12 p} \cdot(2 \sqrt{p h})^{3}-0\right]\right. \\[/tex]

[tex]&A=2\left[2 h^{3 / 2} \sqrt{p}-\frac{8(\sqrt{p})^{3}(\sqrt{h})^{3}}{12 p}-0\right] \\\\&A=2\left[2 h^{k / 2} \sqrt{p}-\frac{2}{3} \sqrt{p} \cdot h^{3 / 2}\right] \\\\&A=2 \times \frac{4 \sqrt{p} \cdot h^{3 / 2}}{3} \\\\&A=\frac{8}{3} \cdot \sqrt{p} \cdot \sqrt{h} \cdot h \\\\&A=\frac{8}{3} \sqrt{p h} \cdot h[/tex]

[tex]A=\frac{8}{3} \sqrt{p h} \cdot h[/tex]

In conclusion,  the equation for the Area is

[tex]A=\frac{8}{3} \sqrt{p h} \cdot h[/tex]

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The interest rate is 36% per year if the value of a savings account can be found using the equation 300(1.03)²⁴ option (c) is correct.

It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.

We can calculate the compound interest using the below formula:

[tex]\rm A = P(1+\dfrac{r}{n})^{nt}[/tex]

Where A = Final amount

          P = Principal amount

          r  = annual rate of interest

          n = how many times interest is compounded per year

          t = How long the money is deposited or borrowed (in years)

We have:

The value of a savings account can be found using the equation =

= 300(1.03)²⁴

From the function:

F(x) = a(1+r)ˣ

On compare:

1 + r = 1.03

r = 0.03

or

r = 3% monthly

r = 3×12 = 36% yearly

Thus, the interest rate is 36% per year if the value of a savings account can be found using the equation 300(1.03)²⁴ option (c) is correct.

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Answer:

A. 5 feet

Step-by-step explanation:

The value could the length of the third side will be 11,12,13,15. Options B, D, E, and F are the correct answers.

A triangle is a three-sided polygon. It is one of the most fundamental geometric forms.

According to the triangle Inequality theorem, any two triangle sides must add up to more than the third side's length.

You may get the potential length of a triangle by multiplying the sum of two sides by the difference between two sides.

Therefore,

Let x is the possible length of the third side of a triangle.

14-4<x<15+4

10<x<19

The values of the third side is lies between the 10 and 19.The value could the length of the third side will be 11,12,13,15

Hence, options B, D, E, and F are the correct answers.

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The formula for the surface area N(t) of the balloon after t seconds is [tex]N(t) = \frac {64}9\pi t^2[/tex]

We have:

[tex]S(r) = 4\pi r^2[/tex]

Also, we have:

[tex]P(t) = \frac 43t[/tex]

The above can be rewritten as:

[tex]r = \frac 43t[/tex]

Substitute [tex]r = \frac 43t[/tex] in S(r) to determine the function N(t)

[tex]S(r) = 4\pi (\frac 43t)^2[/tex]

Express as N(t)

[tex]N(t) = 4\pi (\frac 43t)^2[/tex]

Expand the exponent

[tex]N(t) = 4\pi *\frac {16}9t^2[/tex]

Evaluate the product

[tex]N(t) = \frac {64}9\pi t^2[/tex]

Hence, the formula for the surface area N(t) of the balloon after t seconds is [tex]N(t) = \frac {64}9\pi t^2[/tex]

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The range of the required function f(x)  = -√-x is all real values less than or equal to 0.

The nature of the function is imaginary because of the negative sign present inside the root. Hence the range of the function exists only and only if the function gives real  values in each of its outcomes.

Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in set of y. x is independent variable while Y is dependent variable.

As per question
f(x) = -√-x
clearly, for each positive real number the function becomes imaginary.
So the domain of the given function lies  (-∞, 0).
and for every x in its domain function has its exists in range of all real values less than and equal to zero.

Thus, the range of the function f(x) ≤ 0.

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Answer:

7,500

Step-by-step explanation:

When you round you automatically round up unless told otherwise
so find the hundredth, which is 485 and you round that to 500
then put the 7 back → 7,500

Answer:

Height = 132 mt

Step-by-step explanation:

Shadow lengths are proportional to the height of the object.

So, multiply the length of the tree's shadow by your height.

If you are 5 feet (1.5 meters) tall, and the length of  shadow is 88 meters long,

Multiply them together: 1.5 x 88 = 132 mt.

Hence, Height = 132 mt.

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[tex]\tan x+\frac{\cos x}{1+\sin x}\\\\ =\frac{\sin x}{\cos x}+\frac{\cos x}{1+\sin x}\\\\=\frac{\sin x(1+\sin x)+\cos^{2} x}{\cos x(1+\sin x)}\\\\=\frac{\sin^{2} x+\cos^{2} x+\sin x}{\cos x(1+\sin x)}\\\\=\frac{1+\sin x}{\cos x(1+\sin x)}\\\\=\frac{1}{\cos x}\\\\=\sec x[/tex]