A church rings its bells every 15 minutes, the school rings its bells every 20 minutes and the day care center rings its bells every 25 minutes. If they all ring their bells at noon on the same day, at what time will they next all ring their bells together? (Answer in the form AB:CD without am or pm such as 08:00)

Answer:

The value of given expression is [tex]-\frac{\sqrt{2}-\sqrt{6}}{4}[/tex].

Step-by-step explanation:

The given expression is

[tex]\cos\left(\dfrac{19\pi}{12}\right)[/tex]

The trigonometric ratios are not defined for [tex]\dfrac{19\pi}{12}[/tex].

[tex]\dfrac{19\pi}{12}[/tex] can be split into [tex]\frac{5\pi}{4}+\frac{\pi}{3}[/tex].

[tex]\cos\left(\dfrac{19\pi}{12}\right)=\cos (\frac{5\pi}{4}+\frac{\pi}{3})[/tex]

Using the addition formula

[tex]\cos (A+B)=\cos A\cos B-\sin A\sin B[/tex]

[tex]\cos (\frac{5\pi}{4}+\frac{\pi}{3})=\cos( \frac{\pi}{3})\cdot \cos (\frac{5\pi}{4})-\sin( \frac{\pi}{3})\cdot \sin (\frac{5\pi}{4})[/tex]

We know that, [tex]\cos(\frac{\pi}{3})=\frac{1}{2}[/tex] and [tex]\sin (\frac{\pi}{3})=\frac{\sqrt{3}}{2}[/tex]

[tex]\cos\left(\dfrac{19\pi}{12}\right)=\frac{1}{2}\cdot \cos (\frac{5\pi}{4})-\frac{\sqrt{3}}{2}\cdot \sin (\frac{5\pi}{4})[/tex]

[tex]\frac{5\pi}{4}[/tex] lies in third quadrant, by using reference angle properties,

[tex]\cos(\frac{5\pi}{4})=-\cos(\frac{\pi}{4})=-\frac{\sqrt{2}}{2}[/tex]

[tex]\sin(\frac{5\pi}{4})=-\sin(\frac{\pi}{4})=-\frac{\sqrt{2}}{2}[/tex]

[tex]\cos\left(\dfrac{19\pi}{12}\right)=\frac{1}{2}\cdot (-\frac{\sqrt{2}}{2})-\frac{\sqrt{3}}{2}\cdot (-\frac{\sqrt{2}}{2})[/tex]

[tex]\cos\left(\dfrac{19\pi}{12}\right)=-\frac{\sqrt{2}}{4}+\frac{\sqrt{6}}{4}[/tex]

[tex]\cos\left(\dfrac{19\pi}{12}\right)=-\frac{(\sqrt{2}-\sqrt{6})}{4}[/tex]

Therefore the value of given expression is [tex]-\frac{\sqrt{2}-\sqrt{6}}{4}[/tex].

Final answer:

To find [tex]\(\cos(\frac{19\pi}{12})\),[/tex] we express the angle as the sum of  [tex]\(\frac{4\pi}{3}\) and \(\frac{\pi}{4}\)[/tex] and then use the cosine addition formula. Calculating the values of cosine and sine for these angles gives us the exact value of [tex]\(\cos(\frac{19\pi}{12})\) as \(\frac{\sqrt{6} - \sqrt{2}}{4}\).[/tex]

Explanation:

To find [tex]\(\cos\left(\frac{19\pi}{12}\right)\)[/tex] using an angle addition or subtraction formula, let's break down the angle [tex]\(\frac{19\pi}{12}\)[/tex] into the sum or difference of angles whose cosine values we know. We can express[tex]\(\frac{19\pi}{12}\) as \(\frac{16\pi}{12} + \frac{3\pi}{12}\)[/tex] which simplifies to[tex]\(\frac{4\pi}{3} + \frac{\pi}{4}\).[/tex] Now we use the cosine addition formula [tex], \(\cos(a+b) = \cos a \cos b - \sin a \sin b\)[/tex], to find the answer:

[tex]\(\cos\left(\frac{19\pi}{12}\right) = \cos\left(\frac{4\pi}{3} + \frac{\pi}{4}\right) = \cos\left(\frac{4\pi}{3}\right)\cos\left(\frac{\pi}{4}\right) - \sin\left(\frac{4\pi}{3}\right)\sin\left(\frac{\pi}{4}\right)\)[/tex]

[tex]\(= (-\frac{1}{2})\cdot(\frac{\sqrt{2}}{2}) - (-\frac{\sqrt{3}}{2})\cdot(\frac{\sqrt{2}}{2})\)[/tex]

[tex]\(= -\frac{\sqrt{2}}{4} + \frac{\sqrt{6}}{4}\)[/tex]

Combining these, we get:

[tex]\(\cos\left(\frac{19\pi}{12}\right) = \frac{\sqrt{6} - \sqrt{2}}{4}\)[/tex]

Answer:

[tex]\frac{2x-20}{x^2+6x-40}[/tex]

Step-by-step explanation:

[tex]f(x)+g(x)[/tex]

[tex]\frac{x-16}{x^2+6x-40}+\frac{1}{x+10}[/tex]

I'm going to factor that quadratic in the first fraction's denominator to figure out what I need to multiply top and bottom of the other fraction or this fraction so that I have a common denominator.

I want a common denominator so I can write as a single fraction.

So since the leading coefficient is 1, all we have to do is find two numbers that multiply to be c and at the same thing add up to be b.

c=-40

b=6

We need to find two numbers that multiply to be -40 and add to be 6.

These numbers are 10 and -4 since (10)(-4)=-40 and 10+-4=6.

So the factored form of [tex]x^2+6x-40[/tex] is [tex](x+10)(x-4)[/tex].

So the way the bottoms will be the same is if I multiply top and bottom of my second fraction by (x-4).

This will give me the following sum so far:

[tex]\frac{x-16}{x^2+6x-40}+\frac{x-4}{x^2+6x-40}[/tex]

Now that the bottoms are the same we just need to add the tops and then we are truly done:

[tex]\frac{(x-16)+(x-4)}{x^2+6x-40}[/tex]

[tex]\frac{x+x-16-4}{x^2+6x-40}[/tex]

[tex]\frac{2x-20}{x^2+6x-40}[/tex]

Answer:

  14a.  an = 149 -6(n -1)

  14b.  Evaluate the formula with n=8.

  15.  (no question content)

Step-by-step explanation:

14. Each week, sales decreases by 6, so the arithmetic sequence for sales has a first term of 149 and common difference of -6. The general formula for the n-th term is ...

  an = a1 + d·(n -1) . . . . . . where a1 is the first term, d is the common difference

Putting the numbers for this sequence into the general formula, we get ...

  an = 149 -6(n -1)

__

To predict the sales for the 8th week, put n=8 into the formula and do the arithmetic.

  a8 = 149 -6(8-1) = 107 . . . . predicted sales for week 8

_____

15. The graph is shown attached. There is no question content.

Answer:

The correct option is A. The graph will be continuous because the amount of gas that she added to the tank does not need to be an integer amount.

Step-by-step explanation:

Consider the given information.

If the value of a function is integer then the graph will be discrete, otherwise it will be a continuous graph.

The amount of gas that Jayne added does not need to be an integer. So, the graph will be continuous.

For example, 16.7 gallons of gas or 19.9 gallons of gas, etc. She can get amounts that are not integers.

This can be represent as:

y = x + 4

Where, y is total amount of gas in tank and x is number of gallons she added.

As it is a linear function which is continuous everywhere.

Thus, the correct option is A. The graph will be continuous because the amount of gas that she added to the tank does not need to be an integer amount.

Answer:

I want yo points

Step-by-step explanation:

Answer:

15 degrees

Step-by-step explanation:

The arc measure of BC is equal to angle created by B, C and the central angle.  The angle created by B,C, and the central angle is 15 degrees so the arc measure is 15 degrees.

Answer: 15°

Step-by-step explanation:

It is important to remember that, by definition:

[tex]Central\ angle = Intercepted\ arc[/tex]

Therefore, in this case, knowing that the angle BAC  (which is the central angle) in the circle provided measures 15 degrees, you can conclude that the measure of arc BC (which is the intercepted arc) is 15 degrees.

Then you get that the answer is:

[tex]BAC=BC[/tex]

[tex]BC=15\°[/tex]

Answer:

Circumference = 25m

Area = 50 m2

Step-by-step explanation:

formula for circumference of a circle is π(d)

when radius is 4m, diameter is 8m

3.14(8)= 25.13

nearest tenth = 25m

formula for area of circle is 2πr or π(r)(r)

when radius is 4m

3.14(4)(4)=50.27 m2

nearest tenth =50m

Answer: circumference of the circle is 25.12 m  and the area of the circle is 50.2 m²

Step-by-step explanation:

To find the circumference of the circle of radius  4 meters, we simply use the formula;

area of a circumference = 2πr

                      π is given to be 3.14 and radius r=4 meter, we will substitute this variable into the formula

area of a circumference = 2πr

                                          = 2 × 3.14 × 4

                                          =25.12

                                           ≈25.1  to the nearest tenth

Therefore, the circumference of the circle is is 25.1 meters

To find the area of the circle, we simply use the formula:

area of circle = π[tex]r^{2}[/tex]

                     =  3.14 × (4)²

                      =3.14 × 16

                        =50.24

                        ≈50.2   to the nearest tenth

Therefore, the area of the circle is 50.2 m²

Answer:

Mean = 51.4.

Mode = 49.

Median = 52.

Range = 6.

Step-by-step explanation:

Mean = Sum of all observations / Number of observations.

Mean = (49+49+54+55+52+49+52)/7

Mean = 360/7

Mean = 51.4 (to the nearest tenth).

Mode = The most repeated values = 49 (repeated 3 times).

Range = Largest Value - Smallest Value = 55 - 49 = 6.

Median = The central value of the data.

First, arrange the data in the ascending order: 49, 49, 49, 52, 54, 55, 55.

It can be seen that the middle value is 52. Therefore, median = 52!!!

Answer:

3.6

Step-by-step explanation:

Divide 6 by 4

You get 1.5

Multiply 1.5 by 2.4

You get 3.6

Answer:

Initial height or what the ball was originally bounced from a height of 9 feet

Step-by-step explanation:

9 represents the height that the ball was originally bounced from.

If you plug in 0 for [tex]n[/tex] into [tex]f(n)=9(0.7)^n[/tex], you get:

[tex]f(0)=9(0.7)^0=9(1)=9[/tex].

9 feet is the initial height since that is what happens at time zero.

Answer:

Initial height or what the ball was originally bounced from a height of 9 feet

Step-by-step explanation:

9 represents the height that the ball was originally bounced from.

If you plug in 0 for  into , you get:

.

9 feet is the initial height since that is what happens at time zero.

Step-by-step explanation:

Rate × time = distance

If x is the rate of the boat and y is the rate of the water:

(x − y) × 4 = 128

(x + y) × 2 = 128

Simplifying:

x − y = 32

x + y = 64

Solve with elimination (add the equations together):

2x = 96

x = 48

y = 16

The speed of the boat is 48 km/hr and the speed of the water is 16 km/hr.

Answer:

Part 1) For x=1 year, [tex]y=\$23,750[/tex]  

Part 2) For x=2 years, [tex]y=\$22,562.50[/tex]  

Part 3) For x=3 years, [tex]y=\$21,434.38[/tex]  

Step-by-step explanation:

we know that

The  formula to calculate the depreciated value  is equal to  

[tex]y=P(1-r)^{x}[/tex]  

where  

y is the depreciated value  

P is the original value  

r is the rate of depreciation  in decimal  

x  is the number of years  

in this problem we have  

[tex]P=\$25,000\\r=5\%=0.05[/tex]

substitute

[tex]y=25,000(1-0.05)^{x}[/tex]  

[tex]y=25,000(0.95)^{x}[/tex]  

Part 1) Find the value of the printer, to the nearest cent, in year 1

so

For x=1 year

substitute in the exponential equation

[tex]y=25,000(0.95)^{1}[/tex]  

[tex]y=\$23,750[/tex]  

Part 2) Find the value of the printer, to the nearest cent, in year 2

so

For x=2 years

substitute in the exponential equation

[tex]y=25,000(0.95)^{2}[/tex]  

[tex]y=\$22,562.50[/tex]  

Part 3) Find the value of the printer, to the nearest cent, in year 3

so

For x=3 years

substitute in the exponential equation

[tex]y=25,000(0.95)^{3}[/tex]  

[tex]y=\$21,434.38[/tex]  

Answer:

Step-by-step explanation:

It is always a good idea to start by defining variables in such a problem. Here, we can let x represent the number of calling minutes, and y represent the number of data minutes. The the total number of minutes used is ...

  x + y = 85

The total of charges is the sum of the products of charge per minute and minutes used:

  7/20x + 2/5y = 31.00

We can eliminate the x-variable in these equations by multiplying the first by -7 and the second by 20, then adding the result.

  -7(x +y) +20(7/20x +2/5y) = -7(85) +20(31)

  -7x -7y +7x +8y = -595 +620 . . . . eliminate parentheses

  y = 25 . . . . . . . . simplify

Then the value of x is

  x = 85 -y = 85 -25

  x = 60

Answer:

The second, fourth and B option are correct.

Step-by-step explanation:

In order to solve this problem, we are going to define the following variables :

[tex]X:[/tex] ''Minutes she used her pay-as-you-go phone for a call''

[tex]Y:[/tex] ''Minutes of data she used''

Then, we are going to make a linear system of equations to find the values of [tex]X[/tex] and [tex]Y[/tex].

''This month, she used a total of 85 minutes'' ⇒

[tex]X+Y=85[/tex]  (I)

(I) is the first equation of the system.

''The bill was $31'' ⇒

[tex](\frac{7}{20})X+(\frac{2}{5})Y=31[/tex] (II)

(II) is the second equation of the system.

The system of equations will be :

[tex]\left \{ {{X+Y=85} \atop {(\frac{7}{20})X+(\frac{2}{5})Y=31}} \right.[/tex]

The second option ''The system of equations is [tex]X+Y=85[/tex] and [tex](\frac{7}{20})X+(\frac{2}{5})Y=31[/tex] .'' is correct

Now, to solve the system, we can eliminate the x-variable from the equations by multiplying the equation with the fractions by 20 and multiplying the other equation by -7. Then, we can sum them to obtain the value of [tex]Y[/tex] :

[tex]X+Y=85[/tex] (I)

[tex](\frac{7}{20})X+(\frac{2}{5})Y=31[/tex] (II) ⇒

[tex](-7)X+(-7)Y=-595[/tex] (I)'

[tex]7X+8Y=620[/tex] (II)'

If we sum (I)' and (II)' ⇒

[tex](-7)X+(-7)Y+7X+8Y=-595+620[/tex] ⇒ [tex]Y=25[/tex]

If we replace this value of [tex]Y[/tex] in (I) ⇒

[tex]X+Y=85\\X+25=85\\X=60[/tex]

The fourth option ''To eliminate the x-varible from the equations, you can multiply the equation with the fractions by 20 and multiply the other equation by -7'' is correct.

With the solution of the system :

[tex]\left \{ {{X=60} \atop {Y=25}} \right.[/tex]

We answer that the option ''B-She used 60 minutes for calling and 25 minutes for data'' is correct.

Answer:  0.4013

Step-by-step explanation:

Given : The volumes of soda in quart soda bottles are normally distributed with : [tex]\mu=32.3\text{ oz}[/tex]

[tex]\sigma=1.2\text{ oz}[/tex]

Let x be the volume of randomly selected quart soda bottle.

z-score : [tex]z=\dfrac{x-\mu}{\sigma}[/tex]

[tex]z=\dfrac{32-32.3}{1.2}=-0.25[/tex]

The probability that the volume of soda in a randomly selected bottle will be less than 32​ oz = [tex]P(x<32)=P(z<-0.25)[/tex]

[tex]=0.4012937\approx0.4013[/tex]

Hence, the probability that the volume of soda in a randomly selected bottle will be less than 32​ oz is 0.4013

The probability that a randomly selected bottle of soda will be less than 32 oz is approximately 40.13%. This is calculated using the z-score and a standard normal distribution.

To find the probability that the volume of soda in a randomly selected bottle will be less than 32 oz, we can use the concept of z-score in statistics. The z-score is a measurement of how many standard deviations a data point is from the mean.

First, we need to calculate the z-score associated with 32 oz. The formula for the z-score is (X - μ) / σ, where X is the data point, μ is the mean, and σ is the standard deviation. Plugging our values in, we get (32 - 32.3) / 1.2 = -0.25.

Next, we consult a standard normal distribution table or use a calculator function to find the probability associated with this z-score. Using a TI-84 calculator, we perform the following steps: Go to the distribution menu ('2nd' then 'VARS'), choose '2: normalcdf(', input the following values: (-1E99, -0.25, 32.3, 1.2). Press 'ENTER' to get the result, which is approximately 0.4013. Thus, the probability that a randomly selected bottle of soda will be less than 32 oz is approximately 0.4013 or 40.13%.

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Answer:

  11.28 in²

Step-by-step explanation:

The area of a Reuleaux triange is given by ...

  A = (1/2)(π -√3)d² . . . . . where d is the diameter of the triangle.

For a triangle of diameter 4 in, the area is ...

  A = (1/2)(π -√3)(4 in)² = (π -√3)8 in² ≈ 11.28 in²

_____

A Reuleaux triangle is the shape of smallest area that has a constant diameter. The diameter of the shape is the radius of each of the arcs between the vertices of the inscribed equilateral triangle.

Answer:

3 pounds of coffee

Step-by-step explanation:

First you have to find how much Jenny spent on coffee.

To find this out subtract 70 by 45.97.

So, 70 - 45.97 = $24.03

Now you have to find how many pounds of coffee she bought, so to find this out you have to divide 24.03 by 8.01.

So, 24.03 divided by 8.01 = 3 pounds of coffee.

Answer:

(- 1, 4 )

Step-by-step explanation:

x = 1 is a vertical line passing through all points with an x- coordinate of 1

The point P(3, 4) is to units to the right of x = 1.

Hence the refection will be 2 units to the left of x = 1

P' = (1 - 2, 4 ) = (- 1, 4 )

Answer:

P(house)+P(interest)-P(both)=probability of P. Both subtracts the double counting.

0.25+0.74-P(Both)=0.89

P=0.10

P(neither) is the complement of P(either), which is OR. That is 1-0.89=0.11

If I can assume independence, which probably is not correct since the two are related, it is P(H)*P(not I)=0.25*0.26=0.065. Not I is 1-P(I)=0.26

Final answer:

The probability that house sales will increase but interest rates will not during the next 6 months is calculated using the addition rule for probabilities and is found to be 0.15 or 15%.

Explanation:

We are given three probabilities:

To find the probability that house sales will increase but interest rates will not during the next 6 months (P(House Sales Increase and Interest Rates Not Increase)), we can use the formula that relates the probability of the union of two events to the probability of each event and the probability of their intersection:

P(House Sales Increase or Interest Rates Increase) = P(House Sales Increase) + P(Interest Rates Increase) - P(House Sales Increase and Interest Rates Increase)

We rearrange the formula to solve for P(House Sales Increase and Interest Rates Not Increase):

P(House Sales Increase and Interest Rates Increase) = P(House Sales Increase) + P(Interest Rates Increase) - P(House Sales Increase or Interest Rates Increase)

Hence, the probability that interest rates will not increase when house sales increase is equal to 1 minus the probability that interest rates will increase. So:

P(House Sales Increase and Interest Rates Not Increase) = P(House Sales Increase) - P(House Sales Increase and Interest Rates Increase)

Plugging in the values we get:

P(House Sales Increase and Interest Rates Not Increase) = 0.25 - (0.25 + 0.74 - 0.89)

This simplifies to:

P(House Sales Increase and Interest Rates Not Increase) = 0.25 - 0.10 = 0.15

The probability that house sales will increase but interest rates will not during the next 6 months is 0.15 or 15%.

Answer:

A. (x + 1, y − 4), reflection over y = x − 4

Step-by-step explanation:

You must perform all the composed transformations to spot the one in which the coordinates of the preimage and the image are not the same.

The coordinates of the preimage are A(0,1), B(3,4), C(5,2) , and D(2,-1)

Option A is a translation (x + 1, y − 4), followed by a reflection over y = x − 4.

[tex]A(0,1)\to(1,-3)\to A'(1,-3)[/tex]

[tex]B(3,4)\to(4,0)\to B'(4,0)[/tex]

[tex]C(5,2)\to(6,-2)\to C'(2,2)[/tex]

[tex]D(2,-1)\to(3,-5)\to D'(-1,-1)[/tex]

Option B is a translation  (x − 4, y − 4), followed by a reflection over y = −x

[tex]A(0,1)\to(-4,-3)\to A'(0,1)[/tex]

[tex]B(3,4)\to(-1,0)\to B'(3,4)[/tex]

[tex]C(5,2)\to(1,-2)\to C'(5,2)[/tex]

[tex]D(2,-1)\to(-2,-5)\to D'(2,-1)[/tex]

Option C is a translation  (x +3, y − 3), followed by a reflection over y = x-4

[tex]A(0,1)\to(3,-2)\to A'(0,1)[/tex]

[tex]B(3,4)\to(6,1)\to B'(3,4)[/tex]

[tex]C(5,2)\to(8,-1)\to C'(5,2)[/tex]

[tex]D(2,-1)\to(5,-4)\to D'(2,-1)[/tex]

Option D is a translation  (x +4, y + 4), followed by a reflection over y = −x+8

[tex]A(0,1)\to(4,5)\to A'(0,1)[/tex]

[tex]B(3,4)\to(7,8)\to B'(3,4)[/tex]

[tex]C(5,2)\to(9,6)\to C'(5,2)[/tex]

[tex]D(2,-1)\to(6,3)\to D'(2,-1)[/tex]

The correct choice is A.

Answer:

A. (x + 1, y − 4), reflection over y = x − 4

Step-by-step explanation:

The answer A. (x + 1, y − 4), reflection over y = x − 4 is right because I got it right on my test!! :)))

Answer:

(25.732,30.868)

Step-by-step explanation:

Given that in a random sample of 42 ​people, the mean body mass index​ (BMI) was 28.3 and the standard deviation was 6.09.

Since only sample std deviation is known we can use only t distribution

Std error = [tex]\frac{s}{\sqrt{n} } =\frac{6.09}{\sqrt{42} } \\=0.9397[/tex]

[tex]df = 42-1 =41[/tex]

t critical for 99% two tailed [tex]= 2.733[/tex]

Margin of error[tex]= 2.733*0.9397=2.568[/tex]

Confidence interval lower bound = [tex]28.3-2.568=25.732[/tex]

Upper bound = [tex]28.3+2.568=30.868[/tex]

Answer:

i think its uh

Step-by-step explanation: carrot

Answer:

21.77 After the donation

Step-by-step explanation:

3.99 Multiplied by 6 is 23.94

So 45.71 - 23.94 = 21.77

Answer:

Given:

POS system = 3,400

useful life = 10 years

salvage value = 400

double declining method means that the depreciation expense is higher in the early years than the later years of the asset.

Straight line depreciation = (3,400 - 400) / 10 yrs = 300 

300 / 3000 = 0.10 or 10%

10% x 2 = 20% double declining rate

Depreciation expense under the double declining method:

Year 1: 3,400 x 20% =  680 depreciation expense.

Year 1 book value = 3,400 - 680 = 2,720

Year 2 : 2,720 x 20% = 544 depreciation expense

Year 2 book value = 2,720 - 544 = 2,176

Answer:

[tex]4x^2-20x+25[/tex]

Step-by-step explanation:

[tex](2x-5)^{2} \\(2x)^2+2(2x)(-5)+(-5)^2\\4x^2-20x+25[/tex]

Answer:

[tex]4x^2-20x+25[/tex]

Step-by-step explanation:

You can use the formula:

[tex](u+v)^2=u^2+2uv+v^2[/tex].

[tex](2x-5)^2=(2x)^2+2(2x)(-5)+(-5)^2[/tex]

[tex](2x-5)^2=4x^2-20x+25[/tex].

You could also use foil:

[tex](2x-5)^2=(2x-5)(2x-5)[/tex]

First: 2x(2x)=4x^2

Outer: 2x(-5)=-10x

Inner: -5(2x)=-10x

Last: -5(-5)=25

--------------------------Add.

[tex]4x^2-20x+25[/tex]

[tex]\bf \boxed{A}\\\\ \stackrel{\textit{3 less than D}}{D-3}~\hspace{5em}A=(D-3)(D-3)\implies A=(D-3)^2 \\\\[-0.35em] ~\dotfill\\\\ \boxed{B}\\\\ \stackrel{\textit{area of rabbits' pen}}{25=(D-3)^2}\implies \stackrel{\stackrel{\textit{same exponents}}{\textit{same base}}}{5^2=(D-3)^2}\implies 5=D-3\implies 8=D \\\\\\ \boxed{C}\\\\ 5+5+5+5=20[/tex]

Final answer:

To find the expression that represents the area of the rabbit cage, use (D - 3)². The side of the rabbit cage, given the area, is 25 square feet, is 5 feet, so the dog pen's side length is 8 feet. The rabbit cage requires 20 feet of fencing to be enclosed.

Explanation:

To solve for the expression that represents the area of the rabbit cage, we'll start by defining the side of the square dog pen as D. Since each side of the rabbit cage is 3 feet less than the dog pen, the side of the rabbit cage would be D - 3. Therefore, the area of the rabbit cage, which is a square, is given by the expression (D - 3)². This tells us that the area is the side length squared. Now, we know that the area of the rabbit cage is 25 square feet.

To find the side length of the rabbit cage, we would take the square root of the area, which gives us 5 feet. Hence, to find the side length of the dog pen, we would add the 3 feet back to the side length of the rabbit cage. This gives us D - 3 = 5, which means D = 5 + 3, so D = 8 feet.

For part c, to find out how many feet of fencing is needed to enclose the rabbit cage, we take the side length of the rabbit cage, which is 5 feet, and multiply it by 4, since a square has four equal sides. This means we would need 5 feet x 4 sides = 20 feet of fencing to enclose the rabbit cage.

Step-by-step explanation:

The coefficient of the x is 3, so it is horizontally shrunk by factor of 3.

The coefficient of the sine is 4, so it is vertically stretched by factor of 4.

The constant inside the sine is -pi, so it is horizontally shifted pi units to the right.

The constant outside the sine is 5, so it is vertically shifted 5 units up.

Answer:

-3x+3

Step-by-step explanation:

The equation to the line shown is formed as follows.

It passes through the points (-6,0) and (-8,6)

The gradient of the line=Δy/Δx

=(y₂-y₁)/(x₂-x₁)

=(6-0)/(-8--6)

=6/-2

=-3

The line parallel to the line shown has the same gradient i.e -3

Therefore the line in question is

-3x+3.

Answer:

No, the triangle is not possible.

Step-by-step explanation:

Given,

A triangle ABC in which C = 38°, a = 19, c = 10,

Where, angles are A, B and C and the sides opposite to these angles are a, b and c respectively,

By the law Sines,

[tex]\frac{sin A}{a}=\frac{sin C}{c}[/tex]

[tex]\implies sin A = \frac{a sin C}{c}[/tex]

By substituting the values,

[tex]sin A = \frac{19\times sin 38^{\circ}}{10}[/tex]

[tex]=1.16975680312[/tex]

[tex]\implies A=sin^{-1}(1.16975680312)[/tex] = undefined

Hence, the triangle is not possible with the given measurement.

Answer:

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

-4  |  3     -10       7

Step-by-step explanation:

Take the coefficients of the numerator inside the division bar

Take the opposite of the number in the denominator

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

-4  |  3     -10       7

Answer:

The correct option is B.

Step-by-step explanation:

The given expression is

[tex]\frac{3x^2-10x+7}{x+4}[/tex]

Here the numerator is

[tex]3x^2-10x+7[/tex]

So, the coefficients of numerator are 3, -10 and 7.

If the denominator of an expression is (x+c), then in synthetic division form -c is written on outside and coefficients of numerator are written under the sign of division(descending order of degree of terms).

The denominator of the expression is (x+4), so -4 is written outside the sign of division.

[tex]-4\overline{|3\quad -10\quad 7}[/tex]

Therefore the correct option is B.

bearing in mind that 4¾ is simply 4.75.

[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$600\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &3 \end{cases} \\\\\\ A=600\left(1+\frac{0.05}{1}\right)^{1\cdot 3}\implies A=600(1.05)^3\implies A=694.575 \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$750\\ r=rate\to 4.75\%\to \frac{4.75}{100}\dotfill &0.0475\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &3 \end{cases} \\\\\\ A=750\left(1+\frac{0.0475}{1}\right)^{1\cdot 3}\implies A=750(1.0475)^3\implies A\approx 862.032[/tex]

well, the interest for each is simply A - P

695.575 - 600 = 95.575.

862.032 - 750 = 112.032.

Answer:

Step-by-step explanation:

The perimeter in each case is double the sum of the side dimensions. Since the perimeters are equal, the sum of side dimensions will be equal:

  2x +x = (x +12) +(x -3)

  3x = 2x +9 . . . . . . . . collect terms

  x = 9 . . . . . . . . . . . . . subtract 2x

Given this value of x, the dimensions of the first rectangle are ...

  {2x, x} = {2·9, 9} = {18, 9}

And the dimensions of the second rectangle are ...

  {x+12, x-3} = {9+12, 9-3} = {21, 6}

Answer:

12.4 calories  / minute to the nearest tenth.

Step-by-step explanation:

That would be 560 / 45

= 12.44...  calories  / minute.