10 cows, 26 horses and 4 goats are in a paddock. What is the percentage of animals that are horses?

Answer:

see explanation

Step-by-step explanation:

Given

[tex]tan^{-1}[/tex]x + [tex]tan^{-1}[/tex]y + [tex]tan^{-1}[/tex] z = π

let

[tex]tan^{-1}[/tex]x = A , [tex]tan^{-1}[/tex]y = B , [tex]tan^{-1}[/tex]z = C , so

x = tanA, y = tanB , z = tanC

Substituting values

A + B + C = π  ( subtract C from both sides )

A + B = π - C ( take tan of both sides )

tan(A + B) = tan(π - C) = - tanC ( expand left side using addition identity for tan )

[tex]\frac{tanA+tanB}{1-tanAtanB}[/tex] = - tanC ( multiply both sides by 1 - tanAtanB )

tanA + tanB = - tanC( 1 - tanAtanB) ← distribute

tanA+ tanB = - tanC + tanAtanBtanC ( add tanC to both sides )

tanA + tanB + tanC = tanAtanBtanC , that is

x + y + z = xyz

1st rectangle:

width: 2.48cm

length: 4.96

2nd rectangle:

width: 4.96 (equals to the length of the 1st rectangle)

area: 9.92

length: 9.92/4.96 = 2

Answer:

4%

Step-by-step explanation:

item cost x sales tax rate = sales tax

460 x sales tax rate = 18.40

sales tax rate = 18.40/460

sales tax rate = .04 or 4%

Explanation:

The jump from 13 to 39 is "times 3" when comparing the diagonal segments. So the jump from 5 to 'a' must also be "times 3" to keep the sides in the same proportion. Therefore, a = 3*5 = 15.

Or we could solve it like so

13/39 = 5/a

13a = 39*5 ... cross multiplying

13a = 195

a = 195/13 .... dividing both sides by 13

a = 15

9514 1404 393

Answer:

   $40,615.20

Step-by-step explanation:

The amortization formula will tell you Michelle's monthly payment.

  A = P(r/12)/(1 -(1 +r/12)^(-12t)) . . . . loan value P at interest rate r for t years

  A = $124,500(0.059/12)/(1 -(1 +0.059/12)^(-12·10)) ≈ $1375.96

__

The total of Michelle's 120 monthly payments is ...

  12 × $1375.96 = $165,115.20

This amount pays both principal and interest, so the amount of interest she pays is ...

  $165,115.20 -124,500 = $40,615.20

Michelle will pay $40,615.20 in interest over the course of the loan.

__

A calculator or spreadsheet can figure this quickly.

Answer:

[tex]\pi = \frac{22}{7} [/tex]

Use this OK bro.

The shortest length (circumference) of the string is 18.84cm.

The circumference is that certain length that requires to enclose a  circle with respective of a fixed length known as radius. If radius of cylinder be r, then the circumference will be 2πr.

The required length of the string is the circumference of the base of the cylinder.

The radius of the cylinder is 3cm.

Taking π=3.14, the circumference will be : 2*3.14*3cm

=18.84cm

The shortest length of the string is 18.84cm.

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Answer:

wto

Step-by-step explanation:

Answer:

Z -0.879173965

Step-by-step explanation:

Z -0.879173965

ρ  0.5

π 0.54

n 120

The value of the test statistic is the z-score z = -0.88

The relationship between a value and the mean of a set of values is expressed numerically by a Z-score. The Z-score is computed using the standard deviations from the mean. A Z-score of zero indicates that the data point's score and the mean score are identical.

The Z-score is calculated using the formula:

z = (x - μ)/σ

where z: standard score

x: observed value

μ: mean of the sample

σ: standard deviation of the sample

Given data ,

Let the test statistic value be represented as z

Now , the probability of emergency room visitors are insured is q = 0.54

The total number of patients n = 120

The number of patients that were insured = 60

So , the percentage of people that were insured p = 60/120 = 0.5

Now , test statistic value z = ( p - q ) / [ √ ( q ( 1 - q )/n² ]

The value of z score is

z = [ 0.5 - 0.54 ] / √ 0.54 ( 1 - 0.54 ) / 120²

On simplifying the equation , we get

The value of z score is z = -0.88

Hence , the test statistic is z = -0.88

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Answer:

1 and 5 sevenths of a bag

Step-by-step explanation:

2/7 males half to it takes 4/7 to make a full one multiply 4 by 3 and you get 12/7 so that makes 1 and 5/7

Answer:

Hello,

742/27 (ft)

Step-by-step explanation:

[tex]h_1=14\\\\h_2=\dfrac{14}{3} \\\\h_3=\dfrac{14}{9} \\\\h_4=\dfrac{14}{27} \\\\[/tex]

[tex]d=14+2*\dfrac{14}{3} +2*\dfrac{14}{9} +2*\dfrac{14}{27} \\=14*(1+\dfrac{1}{3}+\dfrac{2}{9} +\dfrac{2}{27} )\\=14*\dfrac{53}{27} \\=\dfrac{742}{27} \\[/tex]

The total distance the ball has traveled at the instant it hits the ground the fourth time [tex]28ft.[/tex]

What is the total distance?

Distance is a numerical measurement of how far apart objects or points are. It is the actual length of the path travelled from one point to another.

Here given that,

A ball is dropped from a height of [tex]14[/tex] ft. The elasticity of the ball is such that it always bounces up one-third the distance it has fallen.

So, after striking with the ground it covers the distance [tex]14[/tex] ft. so it rebounds to the height is [tex]\frac{1}{3}(14)[/tex].

Then again it hits the ground and covers the distance  [tex]\frac{1}{3}(14)[/tex] and again after rebounding it goes to the height is

[tex]\frac{1(1)}{3(3)}.(14)=\frac{(1)^2}{(3)^2}(14)[/tex]

Then it falls the same distance and goes back to the height

[tex]\frac{1}{3}[/tex] ×[tex](\frac{(1)^2}{(3)^2})[/tex] ×[tex]14[/tex] = [tex]\frac{(1)^3}{(3)^3}(14)[/tex]

So, the total distance travelled is

[tex]14+2[\frac{1}{3}(14)+(\frac{1}{3})^2(14)+(\frac{1}{3})^3(14)+...][/tex]

We take the sum is twice because it goes back to the particular height and falls to the same distance.

[tex]S=14+2(\frac{\frac{1}{3}(14)}{1-\frac{1}{3}})\\\\\\S=\frac{a}{1-r}\\\\\\S=14+2(\frac{\frac{14}{3}}{\frac{2}{3}})\\\\S=14+2(\frac{14}{2})\\\\S=14+2(7)\\\\S=14+14\\\\S=28ft[/tex]

Hence, the total distance the ball has traveled at the instant it hits the ground the fourth time [tex]28ft.[/tex]

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let length be x

ATQ

[tex]\\ \sf\longmapsto \dfrac{2}{8}\times x=28[/tex]

[tex]\\ \sf\longmapsto \dfrac{2x}{8}=28[/tex]

[tex]\\ \sf\longmapsto \dfrac{x}{4}=28[/tex]

[tex]\\ \sf\longmapsto x=4(28)[/tex]

[tex]\\ \sf\longmapsto x=112[/tex]

Step-by-step explanation:

there is something wrong with your problem description.

the offered answer options do not fit to the solution as it is described.

2/8th of a rope is 28 meters long. how long is the whole rope ?

as the other answer said : 2/8 = 1/4

and 1/4th of the rope x = 28 m

1/4 × x = 28

x (the length of the whole rope) = 4×28 = 112 meters

but - maybe the original problem said that 7/8th (and not 2/8th) of a rope is 28 m.

7/8 × x = 28

1/8 × x = 4

x = 32 m

then A (32) would be the right answer !

Answer:

X-(-7)

Step-by-step explanation:

If you are subtract by a negative number it turns it into a positive. It would look like this: X+(+7)

The Question is solved with a simple linear equation and is explained as follows:

Simple linear equation is :

Y = 86.784 - 2.67x

The educator wants to see the relationship between no of absences and final grades of the student.

No. of absence of student is independent variable while final grade is dependent variable.

The final grades of the student are dependent on the no. of absence they do.

b = Sxy / Sxx

b =  { 2312 [ 37 * 422 ] / 6 } / 337 - 37^2 / 6 = -2.67

a = -2.67 * 37/6 = 86.784

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Answer:

2x=5y+5

Step-by-step explanation:

Let one number be x, other y

Twice a number(2x) is five more(+5) than 5 times the other number(5y),

It means 2x > 5y

By 5 more, so

2x=5y+5

Answer:

8,15,22,29

Step-by-step explanation:

the interger a is 7,so to find the next term you have to add 7 plus the 8,

8+7=15

15+7=22

22+7=29

8,15,22,29

I hope this helps

Answer:

[tex]l=56m[/tex]

Step-by-step explanation:

From the question we are told that:

Angle from vertical [tex]\theta =5.6[/tex]

Horizontal Distance [tex]d=107m[/tex]

Angle of elevation [tex]\gamma=28.6[/tex]

Generally the Trigonometric equation for exterior angles is mathematically given by

[tex]Exterior\ angles=\sum of\ two\ interior\ angles[/tex]

Where

[tex]Exterior angles=90 \textdegree +5.6 \textdegree[/tex]

Therefore

[tex]90 \textdegree +\theta \textdegree=\omega+\gamma[/tex]

[tex]90 \textdegree +5.6 \textdegree=\omega+28.6 \textdegree[/tex]

[tex]\omega=67 \textdegree[/tex]

Generally the equation for The Sine rule is mathematically given by

[tex]\frac{sin \omega }{d}=\frac{sin \gamma}{l}[/tex]

[tex]l=\frac{107 sin 28.6}{sin 67 \textdegree }[/tex]

[tex]l=56m[/tex]

Answer:

$2884.62

Step-by-step explanation:

A year has 52 weeks

The number of times Charlie will receive a paycheck will be 52w ÷ 2w = 26 times

Charlie's gross income each paycheck will be 7500÷26 = $2884.62 every two weeks

75000 ÷ (52 ÷2)

7500 ÷ 26

$2884.62

Answer:

one half

Step-by-step explanation:

Because the rotation from 12 to 6 is one-half of a complete rotation, it seems reasonable to assume that the hour hand is moving continuously and has therefore moved one-half of the distance between the 2 and the 3. source- ck12.org

Answer:

0.03

Step-by-step explanation:

The Minimum sample size table is attached below

Answer:

[tex]X=173[/tex]

Step-by-step explanation:

From the question we are told that:

Confidence Interval [tex]CI=99\%[/tex]

Variance [tex]\sigma^2=30\%[/tex]

Generally going through the table the

Minimum sample size is

[tex]X=173[/tex]

Answer:

Does the answer help you

Recall that

[tex]\sin(x)=\displaystyle\sum_{n=0}^\infty(-1)^n\frac{x^{2n+1}}{(2n+1)!}[/tex]

Differentiating the power series series for y(x) gives the series for y'(x) :

[tex]y(x)=\displaystyle\sum_{n=0}^\infty a_nx^n \implies y'(x)=\sum_{n=1}^\infty na_nx^{n-1}=\sum_{n=0}^\infty (n+1)a_{n+1}x^n[/tex]

Now, replace everything in the DE with the corresponding power series:

[tex]y'-2xy = 6\sin(3x) \implies[/tex]

[tex]\displaystyle\sum_{n=0}^\infty (n+1)a_{n+1}x^n - 2\sum_{n=0}^\infty a_nx^{n+1} = 6\sum_{n=0}^\infty(-1)^n\frac{(3x)^{2n+1}}{(2n+1)!}[/tex]

The series on the right side has no even-degree terms, so if we split up the even- and odd-indexed terms on the left side, the even-indexed [tex](n=2k)[/tex] series should vanish and only the odd-indexed [tex](n=2k+1)[/tex] terms would remain.

Split up both series on the left into even- and odd-indexed series:

[tex]y'(x) = \displaystyle \sum_{k=0}^\infty (2k+1)a_{2k+1}x^{2k} + \sum_{k=0}^\infty (2k+2)a_{2k+2}x^{2k+1}[/tex]

[tex]-2xy(x) = \displaystyle -2\left(\sum_{k=0}^\infty a_{2k}x^{2k+1} + \sum_{k=0}^\infty a_{2k+1}x^{2k+2}\right)[/tex]

Next, we want to condense the even and odd series:

• Even:

[tex]\displaystyle \sum_{k=0}^\infty (2k+1)a_{2k+1}x^{2k} - 2 \sum_{k=0}^\infty a_{2k+1}x^{2k+2}[/tex]

[tex]=\displaystyle \sum_{k=0}^\infty (2k+1)a_{2k+1}x^{2k} - 2 \sum_{k=0}^\infty a_{2k+1}x^{2(k+1)}[/tex]

[tex]=\displaystyle a_1 + \sum_{k=1}^\infty (2k+1)a_{2k+1}x^{2k} - 2 \sum_{k=0}^\infty a_{2k+1}x^{2(k+1)}[/tex]

[tex]=\displaystyle a_1 + \sum_{k=1}^\infty (2k+1)a_{2k+1}x^{2k} - 2 \sum_{k=1}^\infty a_{2(k-1)+1}x^{2k}[/tex]

[tex]=\displaystyle a_1 + \sum_{k=1}^\infty (2k+1)a_{2k+1}x^{2k} - 2 \sum_{k=1}^\infty a_{2k-1}x^{2k}[/tex]

[tex]=\displaystyle a_1 + \sum_{k=1}^\infty \bigg((2k+1)a_{2k+1} - 2a_{2k-1}\bigg)x^{2k}[/tex]

• Odd:

[tex]\displaystyle \sum_{k=0}^\infty 2(k+1)a_{2(k+1)}x^{2k+1} - 2\sum_{k=0}^\infty a_{2k}x^{2k+1}[/tex]

[tex]=\displaystyle \sum_{k=0}^\infty \bigg(2(k+1)a_{2(k+1)}-2a_{2k}\bigg)x^{2k+1}[/tex]

[tex]=\displaystyle \sum_{k=0}^\infty \bigg(2(k+1)a_{2k+2}-2a_{2k}\bigg)x^{2k+1}[/tex]

Notice that the right side of the DE is odd, so there is no 0-degree term, i.e. no constant term, so it follows that [tex]a_1=0[/tex].

The even series vanishes, so that

[tex](2k+1)a_{2k+1} - 2a_{2k-1} = 0[/tex]

for all integers k ≥ 1. But since [tex]a_1=0[/tex], we find

[tex]k=1 \implies 3a_3 - 2a_1 = 0 \implies a_3 = 0[/tex]

[tex]k=2 \implies 5a_5 - 2a_3 = 0 \implies a_5 = 0[/tex]

and so on, which means the odd-indexed coefficients all vanish, [tex]a_{2k+1}=0[/tex].

This leaves us with the odd series,

[tex]\displaystyle \sum_{k=0}^\infty \bigg(2(k+1)a_{2k+2}-2a_{2k}\bigg)x^{2k+1} = 6\sum_{k=0}^\infty (-1)^k \frac{x^{2k+1}}{(2k+1)!}[/tex]

[tex]\implies 2(k+1)a_{2k+2} - 2a_{2k} = \dfrac{6(-1)^k}{(2k+1)!}[/tex]

We have

[tex]k=0 \implies 2a_2 - 2a_0 = 6[/tex]

[tex]k=1 \implies 4a_4-2a_2 = -1[/tex]

[tex]k=2 \implies 6a_6-2a_4 = \dfrac1{20}[/tex]

[tex]k=3 \implies 8a_8-2a_6 = -\dfrac1{840}[/tex]

So long as you're given an initial condition [tex]y(0)\neq0[/tex] (which corresponds to [tex]a_0[/tex]), you will have a non-zero series solution. Let [tex]a=a_0[/tex] with [tex]a_0\neq0[/tex]. Then

[tex]2a_2-2a_0=6 \implies a_2 = a+3[/tex]

[tex]4a_4-2a_2=-1 \implies a_4 = \dfrac{2a+5}4[/tex]

[tex]6a_6-2a_4=\dfrac1{20} \implies a_6 = \dfrac{20a+51}{120}[/tex]

and so the first four terms of series solution to the DE would be

[tex]\boxed{a + (a+3)x^2 + \dfrac{2a+5}4x^4 + \dfrac{20a+51}{120}x^6}[/tex]

Answer:

Riverbed Cosmetics and Martinez Fashion

March 18, 2020:

Debit Investment in Martinez Fashion $2,580,000

Credit Cash $2,580,000

To record the acquisition of 10% of the 215,000 shares of common stock

June 30, 2020:

Debit Cash $7,400

Credit Dividend Income $7,400

To record dividend income received ($74,000 * 10%).

December 31, 2020:

Debit Investment in Martinez Fashion $215,000

Credit Unrealized Gain $215,000

To record the unrealized gain from the increase in share price.

Situation 2:

Marin, Inc. and Seles Corporation

January 1, 2020:

Debit Investment in Seles Corporation $84,510

Credit Cash $84,510

To record the 30% of Seles's 31,300 shares acquired at a total cost of $9 per share.

June 15, 2020:

Debit Cash $10,980

Credit Investment in Seles Corporation $10,980

To record the 30% of $36,600 dividends paid to all stockholders.

December 31, 2020:

Debit Investment in Seles Corporation $24,030

Credit Retained Earnings $24,030

To record the company's share of the net income.

Step-by-step explanation:

a) Data and Analysis:

Riverbed Cosmetics and Martinez Fashion

March 18, 2020: Investment in Martinez Fashion $2,580,000 Cash $2,580,000 10% of the 215,000 shares of common stock

June 30, 2020: Cash $7,400 Dividend Income $7,400 ($74,000 * 10%)

December 31, 2020: Investment in Martinez Fashion $215,000 Unrealized Gain $215,000

Situation 2:

Marin, Inc. and Seles Corporation

January 1, 2020: Investment in Seles Corporation $84,510 Cash $84,510

30% of Seles's 31,300 outstanding shares of common stock at a total cost of $9 per share

June 15, 2020: Cash $10,980 Investment in Seles Corporation $10,980

30% of $36,600 paid to all stockholders.

December 31, 2020: Investment in Seles Corporation $24,030 Retained Earnings $24,030

Answer:

Check your question again

Step-by-step explanation:

The arithmetic equation of this sequence is an=5+(n-1)*7. Replace 359 with an and solve for n

359=5+(n-1)*7, 354/7=n-1. Wait you got the whole equation wrong, the first term should be 7 so that the common difference be equal to 5

Answer:

1. x = 7

2. 270x+274

Explanation:

see attached filed for step by step reasoning

The area of the patio not taken up by the fountain is 241ft²

Please find attached an image of the patio

Area of the patio not taken up by the fountain = area of patio - area of fountain

The patio is in a shape of a trapezoid. Thus, the area of the patio can be determined by using the formula for the area of a trapezoid

A trapezoid is a convex quadrilateral. A trapezoid has at least on pair of parallel sides. the parallel sides are called bases while the non parallel sides are called legs

Characteristics of a trapezoid

Area of a trapezoid =  0.5 x (sum of the lengths of the parallel sides) x height

Taking a look at the image, we are not provided with the height of the trapezoid, just the parallel sides and the hypotenuse.

Pythagoras theorem can be used to determine the the height of the trapezoid

The Pythagoras theorem : a² + b² = c²

where a = height  

b = base = 20 ft - 12 ft = 8ft

8ft / 2 = 4

c =  hypotenuse

a² + 4² = 25²

a² = 625 - 16

a² = 609

√609 = 24.68 ft

Area of the trapezoid = 0.5 x (20 + 12) x 24.68 = 394.88 ft²

The fountain is in the shape of  a circle.

Area of a circle = πr²

Where : = π = pi = 22/7

R = radius  

The radius would have to determined from the circumference

circumference of a circle = 2πr

14π = 2πr

r = 14π / 2π

r = 7

Area of the circle = [tex]\frac{22}{7}[/tex] × 7²

[tex]\frac{22}{7}[/tex] × 49 = 154 ft²

Area of the patio not taken up by the fountain = 394.88 ft² - 154 ft² = 240.88ft²

To round off to the nearest square, look at the first number after the decimal, if it is less than 5, add zero to the units term, If it is equal or greater than 5, add 1 to the units term.

The tenth digit is greater than 5, so one is added to 0. The number becomes 241ft²

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Answer:

(x - 3/8)^2 = x^2 - 3/4x + 9/64

Step-by-step explanation:

Step-by-step explanation:

divide the number with x by 2 and get the square of that number and add that number to this given equation

number with x = -3/4

= x^2 - 3/4 x + 9/64

= (x -3/8) ^2

Using the z-distribution, it is found that the 99% confidence interval to estimate the treatment effect of buproprion (placebo-treatment) is (-0.234, -0.024).

The confidence interval is:

[tex]\overline{x} \pm zs[/tex]

In which:

In this problem, we are given that z = 2.576, s = 0.0407. The sample mean is the difference of the proportions, hence:

[tex]\overline{x} = \frac{28}{162} - \frac{82}{272} = -0.129[/tex]

Then, the bounds of the interval are given by:

[tex]\overline{x} - zs = -0.129 - 2.576(0.0407) = -0.234[/tex]

[tex]\overline{x} + zs = -0.129 + 2.576(0.0407) = -0.024[/tex]

The 99% confidence interval to estimate the treatment effect of buproprion (placebo-treatment) is (-0.234, -0.024).

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Answer:

C

Step-by-step explanation:

32% of 12 =

32/100 x 12

= 3.84

So, C would be the correct choice

I wasn't sure about my answer so used the Gauthmath App