Factor completely, use any method (MUST SHOW ALL WORK!!)x^4+6x^2−7

a) There are 2400 animals on the farm.

b) The number of sheep on the farm is 700.

c) The percentage of rabbits in relation to the total number of animals is 37.5%.

d) The angle that represents the number of pigs is 75 degrees.

a) To determine the total number of animals on the farm, we add up the number of rabbits, sheep, cattle, and pigs:

Total number of animals = 900 (rabbits) + 700 (sheep) + 300 (cattle) + 500 (pigs) = 2400 animals.

b) The number of sheep on the farm is given as 700.

c) To calculate the percentage of rabbits in relation to the total number of animals, we divide the number of rabbits by the total number of animals and multiply by 100:

Percentage of rabbits = (900 / 2400) * 100 = 37.5%.

d) To calculate the angle that represents the number of pigs, we need to find the proportion of the total number of animals that pigs make up, and then convert it to an angle on the pie chart.

Proportion of pigs = 500 / 2400 = 0.2083.

To find the angle in degrees, we multiply the proportion by 360 degrees:

Angle representing pigs = 0.2083 * 360 = 75 degrees.

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Answer:

\( 5.62 + 3.65 + 5.62 + x = 23.59 \)

\( x = 8.7 ft \)

Step-by-step explanation:

Perimeter of the trapezoid-shaped window = sum of all the sides of the window frame

Thus, the equation to find the unknown side length, x, would be:

✔️\( 5.62 + 3.65 + 5.62 + x = 23.59 \)

Solve for x

\( 14.89 + x = 23.59 \)

Subtract 14.89 from each side

\( 14.89 + x - 14.89 = 23.59 - 14.89 \)

✔️\( x = 8.7 ft \)

Answer:

w = 5

Step-by-step explanation:

The perimeter of a rectangle is given by

P = 2(l+w)

28 = 2(2w-1 + w)

Combine like terms

28 =2(3w-1)

Divide each side by 2

28/2 = 2/2(3w-1)

14 = 3w-1

Add 1 to each side

14+1 = 3w-1+1

15 = 3w

Divide each side by 3

15/3 =3w/3

5 =w

Functions, f[g(1)] = 0.5 and g(g(1)) = g(-7) by using the details of question.

What are the Functions?

Given that the graphs of y = f(x) and y = g(x) intersect at (-2.5, 0.5), we know that f(-2.5) = g(-2.5) = 0.5.

To find g(1), we can use the equation of the line passing through the points (-3, 3) and (-2.5, 0.5). The slope of this line is:

m = (0.5 - 3) / (-2.5 + 3) = -2.5

So the equation of the line is:

y - 3 = -2.5(x + 3)

Simplifying this equation, we get:

y = -2.5x - 4.5

Therefore, g(1) = -2.5(1) - 4.5 = -7.

To find f[g(1)], we need to evaluate f(x) at x = g(1). Since we don't have an equation for f(x), we need to use the fact that the graphs of f(x) and g(x) intersect at (-2.5, 0.5). This means that:

f(g(1)) = f(-7) = 0.5

Therefore, f[g(1)] = 0.5.

Finally, to find g[g(1)], we need to evaluate g(x) at x = g(1). Since we know that g(1) = -7, we can write:

g(g(1)) = g(-7)

We don't know the equation of the function g(x), so we can't determine g(-7) without additional information.

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Complete question is: f[g(1)] = 0.5 and g(g(1)) = g(-7)

Answer:

Option (A)

Step-by-step explanation:

From the given triangle in the picture,

∠y and the angle measuring 81° is a pair of supplementary angles (linear pair angles).

m∠y + 81° = 180°

m∠y  = 180° - 81°

        = 99°

By the property of a triangle,

x° + y° + 47° = 180°

x° + y° = 180° - 47°

x° + y° = 133°

For y = 99°

x° + 99° = 133°

x° = 133° - 99°

   = 34°

Similarly, z° + 58° + 81° = 180°

z° + 139° = 180°

z° = 180° - 139°

z° = 41°

Therefore, Option (A) will be the correct option.

Applying the definition of the straight line angle and sum of triangle, the values of the variables in the figure are:

Recall:

Thus:

y° + 81° = 180° (angles on a straight line)

y° = 180° - 81°

y° = 99°

x° +  y° + 47° = 180° (sum of triangle)

x° + 99° + 47° = 180°

x° + 146° = 180°

x° = 180° - 146°

x° = 34°

z° + 81° + 58° = 180° (sum of triangle)

z° + 139° = 180°

z° = 180° - 139°

z° = 41°

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The power series of the given function  is 1 + (2x) + (2x)² + (2x)³+ --------------------- + (2x)ⁿ

We know very well that sum of n terms who are in geometric progression their sum of expression is given by  a/1-r where a is first term and r is common ratio between the terms.

Now, we have function f(x)=[1 / (1-2x)]

On comparing with a/1-r with f(x),we get

=>a=1 and r=2x

Now, we know that first term of geometric progression is given by =1

second term of geometric progression is given by=a × r= 1 ×2x

third term of geometric progression is given by =a×r² =1×(2x)²

fourth term of geometric progression is given by=a×r³ =1 × (2x)³

nth term of geometric progression is given by =a×(r)ⁿ = 1 × (2x)ⁿ

Therefore, according to the given formula progression series of given function is=a+ ar +ar² + ar³ + -----------arⁿ

=>progression series = 1+ 2x + (2x)² + (2x)³ + --------- + (2x)ⁿ.

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The weight on the inflation gap has increased from 0.5 to 0.75. The real interest rate is 16.86% and Nominal interest rate is 20%

a. In the base scenario, the real interest rate will be 20%, and the nominal interest rate will be 20%.

b. In scenario B, inflation rate will be higher (4%) compared to the base scenario (3.14%).

Output gap is 0% in both the scenarios, however, in the base scenario inflation gap is 0% (3.14 - 3.14) and in scenario B, inflation gap is 0.86% (4 - 3.14).

Now, let's calculate the real interest rate.

Real interest rate in base scenario = 20% - 3.14%

= 16.86%.

Real interest rate in scenario B = 20% - 3.14% + 1.5 + 0.5 (4-3.14) + 0.5 (0-0/0)

= 19.22%.

The real interest rate has moved in the direction to move inflation rate towards its target.

c. In scenario C, the output gap will be 20% compared to 0% in the base scenario.

Inflation gap is 0% in both the scenarios

Inflation rate is 3.14% and in scenario C, inflation rate is 2%.

Let's calculate the real interest rate. Real interest rate in the base scenario = 20% - 3.14%

= 16.86%.

Real interest rate in scenario C = 20% - 2% + 1.5 + 0.5 (3.14 - 3.14) + 0.5 (20-0/20)

= 20.15%.

Real interest rate in scenario C = 20% - 2% + 1.5 + 0.75 (3.14-3.14) + 0.25 (20-0/20) = 18.78%.

The new policy rule has changed the weight of the output gap in the Taylor Rule from 0.5 to 0.25.

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Answer: A

Step-by-step explanation: The bluebird Inn is more expensive per night because 475 is greater than 350.

Answer:

90% confidence interval is ( -149.114, -62.666   )

Step-by-step explanation:

Given the data in the question;

Sample 1                                Sample 2

x"₁ = 259.23                            x"₂ = 365.12

s₁  = 34.713                              s₂ = 48.297

n₁ = 5                                       n₂ = 10

With 90% confidence interval for μ₁ - μ₂ { using equal variance assumption }

significance level ∝ = 1 - 90% = 1 - 0.90 = 0.1

Since we are to assume that variance are equal and they are know, we will use pooled variance;

Degree of freedom DF = n₁ + n₂ - 2 = 5 + 10 - 2 = 13

Now, pooled estimate of variance will be;

\(S_p^2\) = [ ( n₁ - 1 )s₁² + ( n₂ - 1)s₂² ] / [ ( n₁ - 1 ) + ( n₂ - 1 ) ]

we substitute

\(S_p^2\) = [ ( 5 - 1 )(34.713)² + ( 10 - 1)(48.297)² ] / [ ( 5 - 1 ) + ( 10 - 1 ) ]

\(S_p^2\) = [ ( 4 × 1204.9923) + ( 9 × 2332.6 ) ] / [  4 + 9 ]

\(S_p^2\) = [ 4819.9692 + 20993.4 ] / [  13 ]

\(S_p^2\) = 25813.3692 / 13

\(S_p^2\) = 1985.64378

Now the Standard Error will be;

\(S_{x1-x2\) = √[ ( \(S_p^2\) / n₁ ) + ( \(S_p^2\) / n₂ ) ]

we substitute

\(S_{x1-x2\) = √[ ( 1985.64378 / 5 ) + ( 1985.64378 / 10 ) ]

\(S_{x1-x2\) = √[ 397.128756 + 198.564378 ]

\(S_{x1-x2\) = √595.693134

\(S_{x1-x2\) = 24.4068

Critical Value = \(t_{\frac{\alpha }{2}, df\) = \(t_{0.05, df=13\) = 1.771  { t-table }

So,

Margin of Error E =  \(t_{\frac{\alpha }{2}, df\) × [ ( \(S_p^2\) / n₁ ) + ( \(S_p^2\) / n₂ ) ]

we substitute

Margin of Error E = 1.771 × 24.4068

Margin of Error E = 43.224

Point Estimate = x₁ - x₂ = 259.23 - 365.12 = -105.89

So, Limits of 90% CI will be; x₁ - x₂ ± E

Lower Limit = x₁ - x₂ - E = -105.89 - 43.224 = -149.114

Upper Limit = x₁ - x₂ - E = -105.89 + 43.224 = -62.666

Therefore, 90% confidence interval is ( -149.114, -62.666   )

The biker needs to travel 45 km more to complete his journey.

Given that, a biker traveled 2/5 of the road on the first day, then traveled 5 kilometers less on the next day, which is equal to 3/8 of the road, we need to find how much he need to cover more,

Let the total distance of the road be x,
So,

2x/5 - 5 = 3x/8

2x/5 - 3x/8 = 5

Solving for x,

Multiply by 40 to both sides,

16x-15x = 200

x = 200

Therefore, the total distance of the road is 200 km.

Since, he travelled =

200 (2/5) = 80 km + 200 (3/8) = 75 km = 155 km

Therefore, he needs to travel 200-155 = 45 km more.

Hence, the biker needs to travel 45 km more to complete his journey.

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Note that the coordinates of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4). (Option B)

To rotate a point 90 degrees  clockwise about a given point,we can follow these steps -

Translate the coordinates   of the given point so that the center of rotation is at the origin.   In this case,we subtract the coordinates   of the center (0,1) from the coordinates of point A (5,4) to get (-5, 3).

Perform the rotation by swapping the x and y coordinates and changing the sign of the   new x coordinate. In this case,we  swap the x and y coordinates of (-5, 3)   to  get (3, -5).

Translate the coordinates back to their original position   by adding the coordinates of the center (0,1)  to the result from step 2. In   this case, we add (0,1) to (3, -5) to get (3, -4).

Therefore, the coordinates   of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4).

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we get that, the value of x for the given angles in the diagram is 10°.

We can see that:

∠  NMG + ∠ GML = ∠ NML

Substituting the values of the angles in the equation, we get that:

46 ° + 8 x - 5° = 11 x + 11 °

Combining the like terms:

8 x + 41° = 11 x + 11°

Taking variables on one side:

11 x - 8 x = 41° - 11°

Combining the like terms again:

3 x = 30°

Divide both sides by 3:

x = 30° / 3

x = 10°

Therefore, we get that, the value of x for the given angles in the diagram is 10°.

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Your question was incomplete. Please refer the content below:

∠ NMG = 46°, ∠ NML = 11x + 11, and ∠ GML = 8x-5. Find x.​

Step-by-step explanation:

\( \sf \: {2}^{ \frac{1}{2} } = \sqrt{2} \)

\( \sf \: {2}^{ \frac{2}{3} } = \sqrt{2^3} \)

\( \sf \: {3}^{ \frac{3}{2} } = \sqrt[3]{ {2}^{2} } \)

\( \sf {3}^{ \frac{1}{3} } = \sqrt[3]{3} \)

The radical form of the expression is as follows:

\(2^{1/2} = \sqrt{2}\)

 \(2^{2/3} = \sqrt{2^{3} }\)

\(3^{3/2} = \sqrt{3^{3} }\)

 \(3^{1/2} = \sqrt{3}\)

Radical form simply means to represent in a square root form.

Therefore, the radical form of the expression is as follows;

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The probability of getting a black card and a numbered card is 9/26.

To calculate the probability of getting a black card (E1), we need to determine the number of black cards in a standard deck of 52 cards.

There are 26 black cards in total, which consist of 13 spades (black) and 13 clubs (black).

Therefore, the probability of drawing a black card (P(E1)) is:

P(E1) = Number of favorable outcomes / Total number of possible outcomes

P(E1) = 26 / 52

Simplifying this fraction, we get:

P(E1) = 1/2

So the probability of drawing a black card is 1/2.

To calculate the probability of drawing a numbered card (E2), we need to determine the number of numbered cards (2 through 10) in a standard deck.

Each suit (spades, hearts, diamonds, clubs) contains one card for each numbered value from 2 to 10, totaling 9 numbered cards per suit.

Therefore, the probability of drawing a numbered card (P(E2)) is:

P(E2) = Number of favorable outcomes / Total number of possible outcomes

P(E2) = 36 / 52

Simplifying this fraction, we get:

P(E2) = 9/13

So the probability of drawing a numbered card is 9/13.

To calculate the probability of both events occurring together (getting a black card and a numbered card), we multiply the individual probabilities:

P(E1 ∩ E2) = P(E1) × P(E2)

P(E1 ∩ E2) = (1/2) × (9/13)

Simplifying this fraction, we get:

P(E1 ∩ E2) = 9/26

Therefore, the probability of getting a black card and a numbered card is 9/26.

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The value of cos(7π/6) = -√3/2

Explain values

Values are principles or beliefs that guide our behavior and decision-making. They are deeply ingrained in our personalities and are shaped by our upbringing, culture, and experiences. Values can be ethical, moral, social, or personal and influence how we prioritize our goals and interact with others. Understanding our own values can help us make better choices, build stronger relationships, and lead a more fulfilling life.

According to the given information

The cosine of π/6 is √3/2, so the cosine of 7π/6 is:

cos(7π/6) = -cos(π/6) = -√3/2

Therefore, cos(7π/6) = -√3/2.

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Answer:

-√3/2

Steps:

Rewrite the angle as a sum or difference with its reference angle:cos (\(\pi\) + \(\frac{\pi }{6}\))

Simplify the expression using the general reduction formula: -(\(\frac{\pi }{6}\))

Evaluate the expression: -√3/2

Answer:

a. 105/130

b. 25/130

c. 46/70

d. 24/70

e. 105/200

f. 25/200

Step-by-step explanation:

A.

P(+|condition present)

= Prob(+ and condition present)/condition present

= 105/130

B.

P(-|condition present)

= Prob(- and condition present)/condition present

= 25/130

C.

P(-|condition absent)

= Prob(- and condition absent)/condition absent

= 46/70

D.

P(+ | condition absent)

= Prob(+ and condition absent)/condition absent

= 24/70

E.

P(condition present and +)

= 105/200

F.

P(condition present and -)

= 25/200

Answer:

-0.22222222222222222222222

Step-by-step explanation:

The time Jack left Santa Clara is 1 : 55 pm

A word problem in math is a math question written as one sentence or more. These statements are interpreted into mathematical equation or expression.

The time for Jack to walk to lose Altos is 25 min and he uses another 25mins to work to Palo alto.

Therefore, the total time he spent is

25mins + 25 mins = 50 mins

He arrived Palo at 2 :45 pm, therefore the time he left Santa Clare will be ;

2:45 pm = 14 :45

= 14:45 - 50mins

= 13:55

= 1 : 55pm

Therefore he left at 1:55 pm

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Answer:

I think it's 60 or 64 because u got divided or multiply

Answer:

x = 60

Step-by-step explanation:

This is a proportion..

so basically in proportions you multiply the diagonals.

100x45= 4500

then you divide the product by the other number in this case the other number is 75.

4500/75= 60

The missing value is 60!! I hope this helps!!

Answer:

JL = 78

Step-by-step explanation:

MN is a midsegment. Based on the midsegment theorem,

MN = ½(JL)

MN = 5x - 16

JL = 4x + 34

Plug in the value

5x - 16 = ½(4x + 34)

5x - 16 = ½*4x + ½*34

5x - 16 = 2x + 17

Collect like terms

5x - 2x = 16 + 17

3x = 33

Divide both sides by 3

x = 11

✔️JL = 4x + 34

Plug in the value of x

JL = 4(11) + 34

JL = 44 + 34

JL = 78

Answer:

1. 3:1

2. also 3:1

Step-by-step explanation:

ratio has nothing to do with measurements

Answer:

1.       6:2

2.    12:4

Step-by-step explanation:

3 × 2=6

2 × 1=2

3 × 4=12

4 × 1=4

Answers:

This forms the equation 1x-5y = -15, which is the same as x-5y = -15

=================================================================

Explanation:

Let's find the slope. I'll pick the first two rows to form the two points needed

(x1,y1) = (0,3)

(x2,y2) = (10,5)

These are then plugged into the slope formula.

m = slope

m = (y2-y1)/(x2-x1)

m = (5-3)/(10-0)

m = 2/10

m = 1/5

m = 0.2

The y intercept is b = 3 since this is the y value when x = 0.

With m = 0.2 and b = 3, we go from y = mx+b to y = 0.2x+3

Let's multiply both sides by 5 to turn that decimal value into a whole number. I'm picking 5 since 0.2 = 1/5

So we get

y = 0.2x+3

5y = 5*(0.2x+3)

5y = 5*0.2x+5*3

5y = x+15

Now let's get x and y together, but move that 15 to its own side

5y = x+15

x+15 = 5y

x = 5y-15

x-5y = -15

This is one way to write the equation in standard form.

Standard form is Ax+By = C, where A,B,C are integers. Some math textbooks insist that A > 0. In this case, A = 1, B = -5, and C = -15.

----------------------

As a way to check, we can plug in (x,y) = (15,6) from the third row of the table to see that..

x-5y = -15

15-5(6) = -15

15 - 30 = -15

-15 = -15

This verifies the third row. I'll let you check the first two rows of the table to fully confirm this equation works.

The equation of the line with yellow point in slope intercept form is y = 7 / 6 x + 2.

The equation of a straight line can be represented in different form such as slope intercept form, point slope form, etc.

Therefore, let's represent the line with yellow point in slope intercept form.

Hence,

y = mx + b

where

Therefore, using (0, 2) and (6, 9).

m = 9 - 2 / 6 - 0

m = 7 / 6

Hence, let's find the y-intercept

y = 7 / 6 x + b

2 = 7 / 6(0) + b

b = 2

Therefore,

y = 7 / 6 x + 2.

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The value of the variable is 1. 40

we need to know that algebraic expressions are described as expressions that are made up of term, variables, constants, factors and coefficients.

these algebraic expressions are also made up of arithmetic operations.

These arithmetic operations are listed as;

From the information given, we have that;

7.5x/11=4.8/5

cross multiply the values, we get;

7.5x(5) = 4.8(11)

multiply the values

37. 5x = 52. 8

Divide both sides by the coefficient of x, we get;

x = 1. 40

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The expression that represents the area of the cement walkway is   11 ( 12 + 32x)

The formula for area of a rectangular prism is given as;

Area = 2 ( wl + hw + h )

Where;

Now, let's substitute into the formula for area;

Area = 2 {3(22) + 5x(3) + 22(5x) }

expand the bracket

Area = 2 { 66 + 15x + 110x }

collect like terms

Area = 2{66 + 176x}

Area = 132 + 352x

Area = 11 ( 12 + 32x)

Thus, the expression that represents the area of the cement walkway is   11 ( 12 + 32x)

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\(\huge\boxed{\boxed{\bold{1.5\ \bftext{km/min}}}\ \boxed{\bold{3\ \bftext{km}}}}\)

\(\hrulefill\)

To convert from kilometers per hour to kilometers per minute, we simply divide by \(60\) as there are \(60\) minutes in an hour.

\(\frac{90}{60}=\frac{90\div30}{60\div30}=\frac{3}{2}=\large\boxed{1.5}\)

To find how far the car will travel in a certain time, just multiply the speed by the time.

\(1.5\ \text{km/min}*2\ \text{min}\)

\(\large\boxed{3\ \text{km}}\)

The amount of money that you need to deposit in the account each month is $1388.

Given that,

Suppose you want to have $500,000 for retirement in 30 years.

Your account earns 6% interest.

Final amount = $500,000

Time = 30 years = 360 months

Interest rate = 6% = 6/100 = 0.06

We have to find the amount that needed to be deposited each month.

This is a recurring Deposit.

The formula to calculate this is,

A = nP + [Pn(n+1) /2] × [r/12]

Here n is the number of months, P is the amount each month, A is the final amount and r is the rate of interest.

Substituting,

500,000 = 360P + [360P(361) / 2] [0.06/12]

500,000 = 360P + 324.9

360P = 499,675.1

P = 1387.986 ≈ $1388

Hence the monthly deposit is $1388.

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