8. f^7 • f^1 (1 point)
A. f^8
B. f^7
C. (2f)^8
D. (2f)^7

Answer:

The number of walnut pounds we need to add is 10

Step-by-step explanation:

We need to make a mixture that costs $1 per pound.

That means that the total cost of our mixture, divided by the number of pounds must be equal to 1.

[tex]\frac{MixtureCost}{NumberOfPounds} = 1[/tex]

Well, we know that the total cost of our mixture is equal to the cost of the cashews + cost of walnuts.

[tex]MixtureCost = CashewsCost + WalnutsCost[/tex]

We also know that we'll buy 8 pounds of cashews that cost $1.25 each and some amount of pounds (which we'll call x) of walnuts that cost $0.80.

Knowing all of that, we can write this:

[tex]MixtureCost=8*1.25 + x*0.8[/tex]

If we make that multiplication, we have that

[tex]MixtureCost=10+x*0.8[/tex]

Now that we know the cost of our mixture, we just need to know the total number of pounds... But we already know that, don't we?

We know that there are 8 pounds of cashews and x pounds of walnuts, so here's what we can write:

[tex]NumberOfPounds=8+x[/tex]

Now, if we plug in the values we found in the first equation, here's what we have:

[tex]\frac{10+x*0.8}{8+x}=1[/tex]

The 8+x is dividing, so i'll pass it to the other side multiplying:

       [tex]10+0.8*x=x+8[/tex]

The 10 in the left side will go to the right side with a negative sign:

[tex]0.8x=x-2[/tex]

Now, if I pass the x from the right side to the left one changing signs:

[tex]0.8x-x=-2\\\\-0.2x=-2[/tex]

By changing signs from both sides, we have that:

[tex]0.2x = 2\\\\x = 10[/tex]

Therefore, the number of walnut pounds we need to add is 10

Answer:

111

Step-by-step explanation:

Answer:

They are consistent and independent

Step-by-step explanation:

Consistency

If two lines have an intersection point, they are said to be consistent. For example, two parallel lines do not have an intersection and therefore they are inconsistent.

In the problem, the two lines intersect at (1, -2) so they have a unique solution and therefore consistent.

Dependency

Two lines are said to be independent if one of them cannot be written as an integer multiple of the other. Or, in other words, if the slope-intercept form of both equations have different slope and y intercept

Note: slope-intercept form of an equation is y = mx + c where m is the slope and c the y intercept

Line 1: 5x - y = 7 can be written as y = 5x - 7 which has slope +5 and y intercept -7

Line2 : 5x + 6y = -7 can be re-written as y = (-5/6)x - (7/6). This has slope -5/6 and y intercept -7/6

Since slope and intercepts of both lines are different they form a system of independent equations

Please put a picture next time :)

Answer:

Area = 657 ft^2

Step-by-step explanation:

Heron's Formula: [tex]S=\frac{a+b+c}{2}[/tex] ,

Area = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]

[tex]s=\frac{20+21+29}{2}=\frac{70}{2} =45 ft[/tex]

[tex]Area=\sqrt{45(45-20)(45-21)(45-29)}\\\\=\sqrt{45(25)(24)(16)}\\\\=\sqrt{432000}[/tex]

= 657.267069

Area = 657 ft^2

Answer:

210 ft²

Step-by-step explanation:

Take the base and height of the triangle.

Solving for area :

Answer:

44

Step-by-step explanation:

Parenthesis

Exponents

Multiplication/Division (left to right)

Addition/Subtraction (left to right)

42 + (9 ÷ 3 x 2) - 4 <== divide first (left to right)
42 + ((9 ÷ 3) x 2) - 4

42 + (3 x 2) - 4 <== multiply

42 + 6 - 4 <== add

48 - 4 <== subtract

44

Final answer: 44

Hope this helps!

Answer:

1.75

Explanation:

Take two points: (0, -3), (4,4)

[tex]\sf rate \ of \ change: \dfrac{y_2- y_1}{x_2 - x_1} = \dfrac{rise}{run}[/tex]

Here rate of change:

[tex]\sf \rightarrow \dfrac{4-(-3)}{4-0}[/tex]  (insert values)

[tex]\sf \rightarrow \dfrac{7}{4}[/tex]             (in fraction)

[tex]\sf \rightarrow 1.75[/tex]         (in decimals)

Answer:

1.75

Step-by-step explanation:

Rate of change = slope of the line

Taking two points (4,4) and (0, -3) :

The population of the country by an exponential function which is used to describe the population of a country in millions t years after the 2003 is, 645.4.

Exponential function is the function in which the function growth or decay with the power of the independent variable. The curve of the exponential function depends on the value of its variable.

The population model, which describes the population of a country in millions t years after the 2003 is,

[tex]A=645.4 e^{0.001t}[/tex]

For the year 2003 the value of t will be 0 as no year is passed after 20036. Thus,

[tex]A=645.4 e^{0.001\times0}\\A=645.4 e^{0}\\A=645.4(1)\\A=645.4[/tex]

Thus, the population of the country by an exponential function which is used to describe the population of a country in millions t years after the 2003 is, 645.4.

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Answer:

Step-by-step explanation:

[tex]f(x) = \dfrac{2}{3}x-4\\[/tex]

When x = 0  ;   f(x) = 0-4 = -4

When x = 3  ;

       [tex]\sf f(3) =\dfrac{2}{3}*3-4\\\\ = 2-4\\\\ f(3) = -2[/tex]

When x = 6,

           [tex]\sf f(6) = \dfrac{2}{3}*6-4\\\\ f(6) =2*2-4 = 4-4\\\\ f(6)= 0[/tex]

When x = -6;

         [tex]\sf f(-6) =\dfrac{2}{3}*(-6)-4\\\\[/tex]

                   = 2*(-2)-4

                   = -4 - 4

          f(-6) = -8

Answer:

Below.

Step-by-step explanation:

The 2 triangles are congruent ( By 2 angles and corresponding side).

The  2 marked angle are congruent so

5y - 30 = 2y + 6

3y = 36

y - 12.

So m < O = 5(12) - 30 = 30 degrees.

and m <N = 180 - 30 - 90 = 60 degrees,   (as there are 180degrees in triangle)

EN = IV = 14.

It is possible to find the measure of OE and ON by using trigonometry of a right triangle.

tan 30 = EN / OE

OE = EN / tan30

= 14/tan30

= 24.3.

sin 30 = 14/ON

ON = 14 / sin 30

= 28.

Answer:

1 / 10000

Step-by-step explanation:

10^3 / 10^7

apply exponent rule: x^a / x^b = x^(a-b)

10^3 / 10^7 where a = 3 and b = 7

10^(3 - 7) = 10^(-4)

apply exponent rule: a^-b = 1 / a^b

1 / 10^(4)

10^4 = 10000

1 / 10000

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Answer:

10^-4

Step-by-step explanation:

In division of powers (when the numbers are the same), you subtract both the powers. In this case, it would be 3 - 7 = -4, resulting in a power of -4

Answer:

Hello,

11.2 is your answer!

Let's Beginnn.... READ EXPLANATION!!! ITS ALWAYS HELPS... TRUST MEEEEEEEEEEE!!!!

Step-by-step explanation:

Okay so this is clearly a pythagorean theorem question....

Imagine a ladder on a wall..... its kinda like a triangle.....

with that said... lets begin the math... A^2 + B^2 = C^2

The problem itself gives us c and a.

We have to solve for b.

33^2 - 8^2= b^2

1089 - 64 = 1025 = b^2

notice that we found b^2 but we are looking for b

so we have to take the square root....

√1025= 11.18

it says round to nearest tenth.... sooooo

11.2 is your answer!

Answer: x = 0

Step-by-step explanation:

Given:

(x + 7)² = 49

Distribute:

x² + 7² = 49

Square:

x² + 49 = 49

Subtract 49 from both sides of the equation:

x² = 0

x = 0

  The only solution to this equation is 0.

-> We can also see this with graphing. See attached.

answer:

x=0

Step-by-step explanation:

(x+7)^2=49

take the square root of both sides

√(x+7)^2=√49

x+7=7

x=0

Answer:

2/3

Step-by-step explanation:

2/15 of 5

Of means multiply

2/15 * 5

Multiply the numerators

2*5 = 10

Put over the denominator

10/15

We can divide the top and bottom by 5

10/5 =2

15/5 =3

2/3

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

f(n - 4)= n - 4 + 2 = n - 2

The true statement about the coordinate plane is C. Figures 1 and 2 are not congruent because figure 1 cannot be mapped into figure 2.

A coordinate plane simply means a two dimensional plane that's is formed by the intersection of a vertical line.

In this case, the true statement about the coordinate plane is that Figures 1 and 2 are not congruent because figure 1 cannot be mapped into figure 2 using a sequence of rigid transformation.

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Answer:

Step-by-step explanation:

The year in which the two quantities will be equal is 2133.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

Here we have the following data.

y=0.221x-368.264 For men

y=0.168x-255.196 for women

So when we will equate these two equation we will get the year in which two quantities will be same.

0.221x-368.264=0.168x-255.196

0.221x-0.168x=368.264-255.196

0.053x = 1123.068

x= 2133 year

Hence the year in which the two quantities will be equal is 2133.

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Answer:

The perimeter of the rhombus is 20 units

Step-by-step explanation:

One important fact about a rhombus is that all four of its sides are equal, so we only need to solve for one side in order to find the perimeter. We can use the Pythagorean Theorem to solve the side length of the rhombus. Using line AD as a reference, we know that the length of AD is the square root of the change in x squared plus the change in y squared, or [tex]\sqrt{3^{2}+4^{2} } =\sqrt{9+16} =\sqrt{25}=5[/tex] units. Multiply the length of AD by 4 and you'll get that the perimeter of rhombus ABCD is 5 × 4 = 20 un.

The perimeter of the rhombus ABCD is 20 units.

Option B is the correct answer.

A rhombus is a quadrilateral that has four equal sides.

Some of the properties we need to know are:

- The opposite sides are parallel to each other.

- The opposite angles are equal.

- The adjacent angles add upto 180 degrees.

We have,

We can use the distance formula to find the length of each side of the rhombus, and then add them up to find the perimeter.

The distance between points A and B is:

[tex]AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\\= \sqrt{(-2 - 1)^2 + (-3 - 1)^2}\\ = \sqrt{9 + 16}\\= \sqrt(25) \\= 5[/tex]

The distance between points B and C is:

[tex]BC = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}\\= \sqrt{(-5 - (-2))^2 + (1 - (-3))^2}\\ = \sqrt{9 + 16}\\= \sqrt{25}\\= 5[/tex]

The distance between points C and D is:

[tex]CD = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}\\ = \sqrt{(-2 - (-5))^2 + (5 - 1)^2}\\ = \sqrt{9 + 16}\\ = \sqrt{25}\\ = 5[/tex]

The distance between points D and A is:

[tex]DA = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}\\ = \sqrt{(1 - (-2))^2 + (1 - 5)^2}\\ = \sqrt{9 + 16}\\= \sqrt{25}\\ = 5[/tex]

Since a rhombus has all sides of equal length, we can add up the lengths of the sides to find the perimeter:

P = AB + BC + CD + DA = 5 + 5 + 5 + 5 = 20

Therefore,

The perimeter of the rhombus ABCD is 20 units.

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Answer:

I do not know. sorry I couldn't help

Answer:

One of the practical situation of geometric series is : A ball bouncing is an example of a finite geometric sequence. Each time the ball bounces it’s height gets cut down by half. If the ball’s first height is 4 feet, the next time it bounces it’s highest bounce will be at 2 feet, then 1, then 6 inches and so on, until the ball stops bouncing

Answer:

Geometric series are seen in practical situations, most notably in those involving geometric growth or decay. If a series of numbers are formed by percentages, then it can result in a geometric sequence. Ex. compound interest (see below).

Step-by-step explanation:

A geometric series is the result of adding the terms of a geometric sequence. These sequences have a common ratio, r, which is used to find missing terms. The common ratio is found with [tex]r=\frac{a_n}{a_{n-1}}[/tex]. For example, [tex]a_1(r)=a_2, \mbox{ and } a_2(r)=a_3... \mbox{ etc.}[/tex]

Geometric sequences can be used to model practical situations, and such situation could involve geometric growth or decay.

A geometric sequence can be used to model compound interest. An example of this is [tex]A = P (1 + \frac{r}{100})^n[/tex] where the common ratio, r, of the series is equal to 1 + r/100 in the compound interest formula above.

Answer:

23 players.

Step-by-step explanation:

5 x 4 + 3 = 23

Answer:

The slope is 0

Step-by-step explanation:

Solve the equation for y

y+3=0

y = -3

The slope intercept form is

y = mx+b

where m is the slope and b is the y intercept

y = 0x-3

The slope is 0 and the y intercept is -3

Answer: The Slope Is 3

Step-by-step explanation:

You are missing the x after the 3.

considering the linear equation y=mx+b, the coefficient of x is ALWAYS the slope (rate of change)

Answer:

Hope it help

Step-by-step explanation:

1. B
2. A
3. C
4. C

5. D

Answer:

Minimum: 0

Quartile Q1: 22.5

Median: 50

Quartile Q3: 77.5

Maximum: 100

Step-by-step explanation:

Using it's concept, it is found that there is a 0.3 = 30% experimental probability of drawing green color.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

For an experimental probability, these numbers of outcomes are taken from previous trials.

Researching the problem on the internet, it is found that 15 out of 12 + 10 + 15 + 13 = 50 trials resulted in a green marble, hence the probability is given by:

p = 15/50 = 0.3.

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Step-by-step explanation:

In figure:

∠PRT+∠RTP+∠TPR=180

O

(angle sum property of triangle)

⇒x+(180

O

−∠RTQ)+60

O

=180

O

(linear pair)

⇒x+(180

O

−97

0

)+60

o

=180

O

⇒x=31

o

Now, ∠PRT+∠TRQ+∠QRS=180

O

(angle of straight line)

⇒x+48

o

+y=180

O

⇒31

o

+48

o

+y=180

O

⇒y=101

0

Answer:

See below

Step-by-step explanation:

[tex]\csc\theta=1.2711\\\\\frac{1}{\csc\theta}=\frac{1}{1.2711}\\ \\\sin\theta=\frac{1}{1.2711}\\ \\\theta=\sin^{-1}(\frac{1}{1.2711})\\\\\theta\approx51.88^\circ\approx52^\circ[/tex]

Remember the identity [tex]\csc\theta=\frac{1}{\sin\theta}[/tex], so [tex]\sin\theta=\frac{1}{\csc\theta}[/tex] and it makes the problem easier. Just remember to take the inverse sine (let me know if you are not sure what that means).

The value of the θ in csc θ = 1.2711 is 51.88°.

A trigonometric ratio is a ratio of the length of sides of a right-angle triangle. It relates the ratio of sides to the respective angle. The most common trigonometric ratios are sine, cosine, and tangent.

Given csc θ = 1.2711, we need to find the value of θ,

So, csc θ = 1.2711

θ = csc⁻¹(1.2711)

θ = 51.88°

Hence, the value of the θ in csc θ = 1.2711 is 51.88°.

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