On a walk through the woods, Mr. Finley saw 16 blue jays and 25 purple finches. Write the ratio of finches to blue jays three different ways.

Answer:

Step-by-step explanation:

The total interest earned will be the sum of the amounts earned by each account. An equation expressing this fact can be solved to find the investment amounts.

__

Let x represent the amount invested at the higher rate. Then 70000-x is the amount invested at the lower rate. The total earnings from the investment will be ...

  0.15x +0.07(70000-x) = 9000

__

Simplifying the equation gives a 2-step linear equation.

  0.08x +4900 = 9000 . . . . simplified

  0.08x = 4100 . . . . . . . . . . subtract 4900

  x = 51,250 . . . . . . . . . . . .divide by 0.08

  70000 -x = 18,750

The woman should invest $51,250 at 15% and $18,750 at 7%.

Answer:

A^32

Step-by-step explanation:

Done

Answer:

Option D:  a³²

Step-by-step explanation:

Powers in this case multiply, 8*4=32

therefore answer D a³² is correct

Answer: A. -3.65

Step-by-step explanation: The best way to figure this out is by using a calculator. One specific rule to remember is the positive/negative rule. When it applies to multiplication, it also applies to division.

[tex](+)*(+)=+\\(+)*(-)=-\\(-)*(+)=-\\(-)*(-)=+\\[/tex]

Knowing this, we can input it into the calculator and find the answer's sign.

[tex]-27.375/7.5=-3.65[/tex]

Therefore, the answer is A. -3.65.

I hope this helps! Pls mark brainliest!! :)

The statement about the sides must respect to represent a triangle is given as follows:

A. a + b > c.

In a triangle, the sum of the lengths of the two smaller sides has to be greater than the length of the greater side.

The smaller sides for the triangle are given as follows:

a and b.

Hence the statement is:

a + b > c.

(as the sum of the lengths of the smaller sides a and b must be greater than the length of the larger side, which is of c).

Hence the correct statement is given by option A.

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The solution of the system of linear equation by substitution method is (3,1).

The method of substitution is the method for solving the linear equation where the value of one variable of one equation is placed in the place of that variable in another equation.

Given here the linear equations are

Equation 1: 6x+2y=20

Equation 2: 2x-3y=3

in equation 1 the value of y will be

6x+2y=20

⇒2y=20-6x

⇒y=(20-6x)/2

⇒y=10-3x

substituting the value of y in the equation 2, we will get

2x-3y=3

⇒2x-3(10-3x)=3

⇒2x-30+9x=3

⇒11x-30=3

⇒11x=30+3

⇒11x=33

⇒x=33/11

⇒x=3

putting the value of x in value of y in equation 1

y=10-3x

⇒y=10-3(3)

⇒y=10-9

⇒y=1

The solution of the system of linear equation by substitution method is (3,1).

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By working with percentages we will see that the down payment is of $11,010 and the first monthly payment is of $275.25

First, the total cost is $110,100.

And we know that you initially pay the 10% of that, so the amount that you pay initially is:

P = 0.10* $110,100 = $11,010

So the down payment is of $11,010

The rest is financed over 30 years, so the rest is:

$110,100 - $11,010 = $99,090

Dividing by the number of months:

N = ( $99,090)/(30*12)  = $275.25

And there is an interest of the 9%, then the amount that you pay on month x is given by:

[tex]P(x) = $275.25*(1.09)^{x-1}[/tex]

Currently (on the first month, so x = 1)

Your pay will be of $275.25

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The length of the chord AB will be 6.08 cm

A chord of a circle is a section of a straight line whose ends both fall on an arc of a circle. A secant line, often known as secant, is a chord's infinite line extension. A chord is, more broadly speaking, a line segment connecting two points on any curve, such as an ellipse.

Given two concentric circles have radii 7cm and 4cm respectively. PQ, a chord to the larger circle, is 13cm

We have to find the length of chord AB drawn to smaller circle

Given:

PQ = 13 cm

R = 7 cm

r = 4 cm

The formula to find length of chord is as follow:

Length of chord = 2 x √(R²-d²)

Where,

R = radius of circle

D = Perpendicular distance from center of circle to chord

So,

PQ = 2 x √(R²-d²)

13 = 2 x √(7²-d²)

d = 2.59 cm

Now,

AB = 2 x √(r²-d²)

AB = 2 x √(4²-2.59²)

AB = 6.08 cm

Hence the length of chord AB will be 6.08 cm

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Answer:

y = -2

(first option listed)

Step-by-step explanation:

a y-intercept is a point where the line crosses over the y-axis, which happens when x = 0.

So, the y-intercept is actually pretty each to find.

this is the easier way to find it:    {plug directly into equation given}

2x - 3y = 6

(set x equal to 0)

[0] - 3y = 6

(divide both sides by -3)

y = -2

but you might have seen/ learned to solve the equation like this {to actually find the equation of the line and solve from that}

[this method is helpful to know/practice for when equations for functions get more complex]

  2x - 3y = 6

      + 3y      + 3y           {add 3y to both sides}

  2x = 3y + 6

   -6          -6                {subtract 6 from both sides}

  2x - 6 = 3y

    ÷3      ÷3            {divide both sides by 3 to isolate y}

  [tex]\frac{2}{3}x[/tex] [tex]- 2 = y[/tex]                [flip sides of the equation]

 [tex]y=\frac{2}{3}x-2[/tex]  

set x equal to 0 (x = 0)

y = [tex]\frac{2}{3} (0)[/tex] - 2

y = 0 - 2

y = -2

So, the y-intercept is -2.

Answer:

10π cm

Step-by-step explanation:

c = 2πr

c = (2*5) * π

c = 10π

Answer: 32x+4

Step-by-step explanation:

[tex]f(x) \cdot g(x)=(8x+1)(-5+9)=4(8x+1)=\boxed{32x+4}[/tex]

Answer:

Yes, she passes with 80%

Step-by-step explanation:

4 divided by 5 = 0.8

0.8 multiplied by 100 = 80%

80% is greater than the required 75% needed to pass

Answer:

Yes

Step-by-step explanation:

First lets establish the key points

We know she needs 75% to pass and she gets 4/5 of the marks

Lets make 4/5 a decimal 4/5 X 2/2 is 8/10 better know as .8

.75 = 75%

.8 = 80%

80% > 75%

Meaning She PASSED!!!

Answer:

29, 36, 38

Step-by-step explanation:

The pattern is add 7 then 2, then 7, then 2, then 7, then 2. You should get the hang of it. All you have to do is just do the same thing for the next three numbers.

The amount of winning is more than amount of loosing. Then the amount of winning will be $3738.

Binomial distributions consist of n independent Bernoulli trials.

The expected value will be

E(X) = np

Suppose that you and a friend are playing cards, and you decide to make a friendly wager.

The bet is that you will draw two cards without replacement from a standard deck.

If both cards are spades, your friend will pay you $39.

Otherwise, you have to pay your friend $5.

If this same bet is made 623 times.

The maximum amount of winning will be

E(win) = np

We have

p = 0.25

n = 623

Then we have

E(win) = 0.25 × 623

E(win) = 155.75

Then the winning amount will be

WA = 155.75 × 39

WA = $6074.25

The maximum amount of loosing will be

E(loose) = np

We have

p = 0.75

n = 623

Then we have

E(loose) = 0.75 × 623

E(loose) = 467.25

Then the loosing amount will be

LA = 467.25 × 5

LA = $2336.25

Then the amount of winning will be

⇒ $ 6074.25 - $ 2336.25

⇒ $ 3738

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A 106.7 GPA into weighted form like on the 4.0 scale will be 4.26.

Rounding some number to a specific value is making its value simpler (therefore losing accuracy), mostly done for better readability or accessibility.

As 106.7 out of 100 gives 106.7% calculated below:

Percentage formula = (Obtained value/total value) x 100.......eq(1)

Putting values:

= (106.7/100) x 100

= 106.7%

Now finding 106.7% of 4:

Putting values in eq (1):

106.7% = (Obtained value/4) x 100

106.7/100= (Obtained value/4)    

1.067= (Obtained value/4)

4 x 1.067 = Obtained value

4.268 = Obtained value

Then 106.7% of 4 will be equal to 1.067 x 4  = 4.268

A 106.7 GPA into weighted form like on the 4.0 scale will be 4.26.

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Answer:

3y= 36×9x

3y=324x

y=324÷3

y=108 ans

Answer:

the second option listed

(A = 53 degrees)

(a = 13.3)

(c = 16.6)

Step-by-step explanation:

SOH CAH TOA

(sin = opposite / hypotenuse)

(cos = adjacent / hypotenuse)

(tan = opposite / adjacent)

For this question, you are provided an angle (37), and its opposite (10)

so, we can solve for either sin or tan first.

tan = opposite / adjacent

tan 37 = 0.7535540501

0.7535540501 = 10/a  [multiply by a]

0.7535540501a = 10 [divide by [0.7535540501]

a = 13.2704482163

rounded to the nearest tenth, a = 13.3

we know that the three angles shown here must add up to 180

so,

90 + 37 + A = 180

127 + A = 180

- 127           - 127

A = 53

--this is enough information to answer, but I will also solve side c to prove my answer

c = hypotenuse

a²+ b²=c²

[13.3]² + [10]² = c²

176.89 + 100 = c²

276.89 = c²

√276.89 = √c²

16.6400120192 = c

c = 16.6 (rounded to the nearest tenth)

**I am assuming this is a right triangle, otherwise there wouldn't be a matching answer

Answer:

(2a-b)(3c-d)

I don't even know Brian tanks

Answer:

radius ≈ 15.5

Step-by-step explanation:

the radius is RS

the angle between a tangent and the radius at the point of contact is 90°

then Δ RST is a right triangle

using Pythagoras' identity in the right triangle.

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides , then

RS² + ST² = RT² ( substitute values )

RS² + 7² = 17²

RS² + 49 = 289 ( subtract 49 from both sides )

RS² = 240 ( take square root of both sides )

RS = [tex]\sqrt{240}[/tex] ≈ 15.5 ( to 1 dec. place )

Step-by-step explanation:

easy how thick it is we need a picture

The values of x and y such that AB is perpendicular to CD will be 19 and 14.5.

The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.

AB and CD intersect at point E.

If measure angle AED equals 6x – 24 and measure angle CEB equals 4y + 32.

Then the values of x and y such that AB is perpendicular to CD will be

6x – 24 = 90

        6x = 114

          x = 19

Then we have

4y + 32 = 90

       4y = 58

         y = 14.5

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Answer:

take 1/2 multiply by sin 91°×2×8

According to the given table the line of best fit is

f(x)=4.54x+77.84

The term "line of best fit" describes a line that passes across a scatter plot of data points and best captures their connection. Statisticians often utilise regression analysis software or manual computations to arrive at the geometric equation for the line using the least squares approach. A straightforward linear regression study of two or more independent variables will provide a straight line. 

Hence, as asked by the question we need to find the time at which the tempurature will become 100°C.

To find that let us put f(x)=100 and find out the value of x for which it is satisfied.

4.54x+77.84=100

⇒[tex]x=\frac{100-77.84}{4.54}=4.88[/tex]

⇒x≈5

Therefore the time at which the tempurature is 100°C is 5 minutes.

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The result after rationalizing is [tex]\frac{9\sqrt{x+3} }{x+3}[/tex].

Rationalization can be considered as the process used to eliminate a radical or an imaginary number from the denominator of an algebraic fraction.

Here, given fraction

 [tex]\frac{9}{\sqrt{x+3} }[/tex]

Multiply and divide by [tex]\sqrt{x+3}[/tex], we get

[tex]\frac{9}{\sqrt{x+3} } \frac{\sqrt{x+3} }{\sqrt{x+3} }[/tex]  =  [tex]\frac{9\sqrt{x+3} }{x+3}[/tex]

Thus, the result after rationalizing is [tex]\frac{9\sqrt{x+3} }{x+3}[/tex].

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The transformation of a function may involve any change. The transformation of the function is Right shift by 90 units.

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs) etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units:

y=f(x+c) (same output, but c units earlier)

Right shift by c units:

y=f(x-c)(same output, but c units late)

Vertical shift:

Up by d units: y = f(x) + d

Down by d units: y = f(x) - d

Stretching:

Vertical stretch by a factor k: [tex]y = k \times f(x)[/tex]

Horizontal stretch by a factor k: [tex]y = f\left(\dfrac{x}{k}\right)[/tex]

Since the function is transformed from f(x)=x to g(x)=x-90, therefore, the transformation of the function is Right shift by 90 units.

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Using the combination and the arrangements formula, it is found that the number of possible playlists is given by:

[tex]7.98 \times 10^8[/tex]

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

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

In this problem, we have that:

Hence, without considering the order, the number of playlists is given by:

[tex]C_{7,7}C_{12,3} = \frac{7!}{7!0!} \times \frac{12!}{3!9!} = 220[/tex]

The number of possible arrangements of n elements is given by the factorial of n, that is:

[tex]A_n = n![/tex]

In this problem, the 10 musics are arranged, hence the number of playlists, considering the order, is given by:

[tex]n = 10! \times 220 = 798336000 = 7.98 \times 10^8[/tex]

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Answer:

[tex](x,y) = (5,-6)[/tex]

Step-by-step explanation:

[tex]\underline{\textbf{Determinant of a matrix.}}\\\\\text{For a}~ 2 \times 2 ~ \text{matrix,}\\\\\begin{vmatrix} a_1&a_2\\b_1&b_2 \end{vmatrix} = a_1b_2 - a_2b_1\\\\\\\text{For a}~ 3 \times 3 ~ \text{matrix,}\\\\\begin{vmatrix} a_1&a_2&a_3\\ b_1&b_2&b_3\\ c_1&c_2&c_3 \end{vmatrix} = a_1\begin{vmatrix} b_2&b_3\\c_2&c_3 \end{vmatrix} - a_2 \begin{vmatrix} b_1&b_3\\c_1&c_3 \end{vmatrix}+ a_3 \begin{vmatrix} b_1&b_2\\c_1&c_2 \end{vmatrix}\\\\\\[/tex]

                     [tex]~~~~~~~~~~~~~~~~~~=a_1(b_2c_3-b_3c_2) -a_2(b_1c_3-b_3c_1) +a_3(b_1c_2-b_2c_1)[/tex]

[tex]\underline{\textbf{Cramer's Rule to solve a system of two equations.}}\\\\\text{Consider the system of two equations:}\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~a_1x + b_1 y= c_1\\\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~a_2x +b_2 y = c_2\\\\\text{Here,}\\\\x = \dfrac{D_x}{D}= \dfrac{\begin{vmatrix} c_1&b_1\\c_2&b_2 \end{vmatrix}}{\begin{vmatrix} a_1&b_1\\a_2&b_2 \end{vmatrix}}\\\\\\ y= \dfrac{D_y}{D}= \dfrac{\begin{vmatrix} a_1&c_1\\a_2&c_2 \end{vmatrix}}{\begin{vmatrix} a_1&b_1\\a_2&b_2 \end{vmatrix}}\\\\[/tex]

[tex]\underline{\textbf{Solution:}}\\\\~~~~~~~~~~~~~~~~~~~~~~~8x-5y = 70~~~~~~...(i)\\\\~~~~~~~~~~~~~~~~~~~~~~~9x +7y = 3~~~~~~~...(ii)\\\\\text{Applying Cramer's rule:}\\\\x = \dfrac{D_x}{D}\\\\\\~~=\dfrac{\begin{vmatrix} 70& -5 \\3&7 \end{vmatrix}}{\begin{vmatrix} 8& -5\\ 9& 7\end{vmatrix}}\\\\\\~~=\dfrac{70(7) -(-5)(3)}{(8)(7)-(-5)(9)}\\\\\\~~=\dfrac{490+15}{56+45}\\\\\\~~=\dfrac{505}{101}\\\\\\~~=5[/tex]

[tex]y = \dfrac{D_y}{D}\\\\\\~~=\dfrac{\begin{vmatrix} 8& 70 \\9&3 \end{vmatrix}}{\begin{vmatrix} 8& -5\\ 9& 7\end{vmatrix}}\\\\\\~~=\dfrac{(8)(3) -(70)(9)}{(8)(7)-(-5)(9)}\\\\\\~~=\dfrac{24-630}{56+45}\\\\\\~~=-\dfrac{606}{101}\\\\\\~~=-6[/tex]

[tex]\textbf{Hence, the solution to the system of equation is}~ (x,y) = (5,-6)[/tex]

Solution: Below! ^^

Detailed explanation:

Hii! I'm sorry, I can't graph the line for you, but I'll try to give you the best possible explanation.

First, note that the question provides us with the info that the y intercept is -8. This is a very valuable piece of information!

This means that the line crosses the y axis (since it's the y intercept) at the point (0,-8). Plot it on the co-ordinate plane.

Next, this question also provides us with the fact that the slope of the line is 1/4. This is yet another valuable piece of information!

What this tells us is: from that point (0,-8), you need to go up 1 unit, then over 4, and so forth, until you obtain a line.

_________

Hope I helped, best wishes & happy studies!

Please reach out to me if any queries arise.

_________

Answer:

Image attached below

Step-by-step explanation:

The line should cross y axis as -8 and should have a point of (0,-8)

The line should have a gradient / slope of 1/4

The solution is  x ≈ 0.3 , Option A is the right Answer.

An Equation is a mathematical statement formed when two algebraic expressions are equated using an equal sign.

To find the value of

22x = 5.3

A graph has to be plotted for the line

From the graph it can be clearly seen the point at which the line intersect x axis is  x = 0.24 , which is approx equal to 0.3.

Therefore the solution is  x ≈ 0.3 ,

Option A is the right Answer.

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The function can be best modeled by a linear regression and the values of a, b and c are -6, 100 and 240, respectively

From the table, we can see that as the number of years increases, the population increases.

This implies that the function can be best modeled by a linear regression.

A linear regression equation is represented by

ax + by = c

Next, we enter the data in a statistical calculator.

From the statistical calculator, we have the following summary:

The regression equation is then represented as:

y = bx + a

Where:

b = SP/SSX = 231.49/3937.5 = 0.05879

a = MY - bMX = 4.58 - (0.06*37.5) = 2.37952

So, we have:

y = 0.05879x + 2.37952

Approximate

y = 0.06x + 2.4

Multiply through by 100

100y = 6x + 240

Rewrite as:

-6x + 100y = 240

Hence, the values of a, b and c are -6, 100 and 240, respectively

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Answer:

The data is best modeled by an exponential function.

The value of a is 2.653, the value of b is 1.01, and the value of c is not used

Step-by-step explanation:

EDGE answers