How many total circles will be used if there are 20 rows of circles? Show all calculations.

Answer:  a) A = 3

               b) P = 4

               c) [tex]\bold{3\ cos\dfrac{\pi}{2}x}[/tex]

Step-by-step explanation:

[tex]Amplitude (A) = \dfrac{max-min}{2}\\\\\\.\qquad \qquad \qquad =\dfrac{6}{2}\\\\\\.\qquad \qquad \qquad =\boxed{3}[/tex]

Period (P) is the reciprocal of the frequency (f)

f = [tex]\frac{1}{4}[/tex]   →    P = [tex]\frac{4}{1}\quad =\boxed{4}[/tex]

y = A cos (Bx - C) + D

[tex]\large{\boxed{y=3\ cos\dfrac{\pi}{2}x}}[/tex]

Answer:

c. [tex]\displaystyle y = 3cos\:\frac{\pi}{2}x[/tex]

b. [tex]\displaystyle 4[/tex]

a. [tex]\displaystyle 3[/tex]

Explanation:

[tex]\displaystyle \boxed{y = 3sin\:(\frac{\pi}{2}x + \frac{\pi}{2})} \\ y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{-1} \hookrightarrow \frac{-\frac{\pi}{2}}{\frac{\pi}{2}} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{4} \hookrightarrow \frac{2}{\frac{\pi}{2}}\pi \\ Amplitude \hookrightarrow 3[/tex]

OR

[tex]\displaystyle y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 0 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{4} \hookrightarrow \frac{2}{\frac{\pi}{2}}\pi \\ Amplitude \hookrightarrow 3[/tex]

Keep in mind that although you are told write a cosine equation, if you plan on writing your equation as a function of sine, then there WILL be a horisontal shift, meaning that a C-term will be involved. As you can see, the photograph on the right displays the trigonometric graph of [tex]\displaystyle y = 3sin\:\frac{\pi}{2}x,[/tex] in which you need to replase "cosine" with "sine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the cosine graph [photograph on the left], accourding to the horisontal shift formula above. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY REALLY ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the sine graph [photograph on the right] is shifted [tex]\displaystyle 1\:unit[/tex]to the right, which means that in order to match the cosine graph [photograph on the left], we need to shift the graph BACKWARD [tex]\displaystyle 1\:unit,[/tex]which means the C-term will be negative, and by perfourming your calculations, you will arrive at [tex]\displaystyle \boxed{-1} = \frac{-\frac{\pi}{2}}{\frac{\pi}{2}}.[/tex]So, the sine graph of the cosine graph, accourding to the horisontal shift, is [tex]\displaystyle y = 3sin\:(\frac{\pi}{2}x + \frac{\pi}{2}).[/tex]Now, with all that being said, in this case, sinse you ONLY have a wourd problem to wourk with, you MUST use the above formula for how to calculate the period. Onse you figure this out, the rest should be simple. Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the midline. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at [tex]\displaystyle y = 0,[/tex]in which each crest is extended three units beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.

b. To find the period [units of time], simply take the multiplicative inverce of the frequency, or use the formula below:

[tex]\displaystyle F^{-1} = T[/tex]

a. To find the amplitude, simply split the height in half.

I am delighted to assist you at any time.

√(3x+4)≥0 (otherwise it becomes imaginary)

3x+4≥0

3x≥-4

x≥-4/3

Y=2(0)-5 (it's the lowest x value, and that means it will limit y)

Y=-5

As x can be > -4/3, let's try for another Y value

Y=2√(3(5/3)+4)-5

Y=2√9-5

Y=6-5

Y=1

1>-5

So, Y≥-5

Answer is A

Replace x with the value in the answers and solve for Y to see which ones match.

y = 1-4 = -3

y = -1-4 = -5

(1,-3), (-1,-5) is the answer.

Answer:

a) 11.51%; b) 13 minutes

Step-by-step explanation:

We will use a z score to answer these questions.  The formula for a z score is

[tex]z=\frac{X-\mu}{\sigma}[/tex]

For part a, X is 20, the mean is 17 and the standard deviation is 2.5:

z = (20-17)/2.5 = 3/2.5 = 1.2

Using a z table, we see the area to the left of, or less than, this value is 0.8849; this means the area to the right of, or greater than, is 1-0.8849 = 0.1151.  This means 11.51% of people have a time greater than 20 minutes and get half off.

For part b, we start out in the z table finding values as close to 5%, or 0.05, as possible.  There are two possibilities, 0.0505 (z=-1.64) and 0.0495 (z=-1.65). Since they are equally distant from the desired value, we will use -1.645 for z.  Our values for the mean and standard deviation are the same:

-1.645 = (X-17)/2.5

Multiply both sides by 2.5:

2.5(-1.645) = ((X-17)/2.5)(2.5)

-4.1125 = X-17

Add 17 to each side:

-4.1125+17 = X-17+17

12.8875 = X

This means the garage should make the guaranteed time no more than 13 minutes.

Answer:

your answer is 10! please mark brainliest :))))))

Step-by-step explanation:

Answer:

Step-by-step explanation:

XYZ

The first one

I hope I helped you.

Answer:

In London it cost $ 6.017 while in Newyork it cost $2.831

so NewYork is cheaper

Step-by-step explanation:

As we know, 1 US gallon = 3.785 liters

so,converting liters into gallon = 1.089 * 3.785

                                                   = 4.121 per gallon

Cost of 4.121 gallon petrol in dollars = 4.121 * 1.46

                                                            = $ 6.017

In London it cost $ 6.017 while in Newyork it cost $2.831

so NewYork is cheaper

Final answer:

Petrol is better value for money in New York, where it costs approximately £0.512 per litre after converting from USD to GBP and gallons to litres, compared to £1.089 per litre in London.

Explanation:

To determine where petrol is better value for money, we need to compare the cost per litre in both London and New York, taking into account the exchange rate and units of measure. First, let's convert the cost of petrol in New York from gallons to litres:

Now, let's compare it to the cost in London:

Comparing the two:

Therefore, the petrol is better value for money in New York as £0.512 per litre is less than £1.089 per litre.

Answer:

The larger pizza is less expensive per square inch

Step-by-step explanation:

we know that

The area of a circle (pizza) is equal to

[tex]A=\pi r^{2}[/tex]

step 1

Find the area of the smaller pizza

we have

[tex]r=10/2=5\ in[/tex] ----> the radius is half the diameter

substitute

[tex]A=(3.14)(5)^{2}=78.5\ in^{2}[/tex]

Find the price per square unit

Remember that

The price of one smaller pizza is [tex]\$15/2=\$7.5[/tex]

so

[tex]\frac{7.5}{78.5}\frac{\$}{in^{2}}=0.10\frac{\$}{in^{2}}[/tex]

step 2

Find the area of the larger pizza

we have

[tex]r=16/2=8\ in[/tex] ----> the radius is half the diameter

substitute

[tex]A=(3.14)(8)^{2}=200.96\ in^{2}[/tex]

Find the price per square unit

so

[tex]\frac{17}{200.96}\frac{\$}{in^{2}}=0.08\frac{\$}{in^{2}}[/tex]

Therefore

The larger pizza is less expensive per square inch

Answer:

You would save $18

Step-by-step explanation:

(27/3)*2 = $18

Leslie needs to divide 48 ounces by the conversion factor of 16 ounces per pound to find out she needs 3 pounds of charcoal for her grill.

Leslie is seeking to understand how much charcoal she should purchase in pounds if she needs 48 ounces for her grill. Since the question involves converting ounces to pounds, we can use the conversion factor that 1 pound is equal to 16 ounces. To find out how many pounds are in 48 ounces, we divide 48 by 16.

48 ounces divided by 16 ounces per pound equals 3. Therefore, Leslie will need to buy 3 pounds of charcoal for her grill.

Team A is the correct answer

Answer:

Team A has 12 points , Team B has 3

Step-by-step explanation:

Answer:

The length of TU is [tex]8\ in[/tex]

Step-by-step explanation:

we know that

The Intersecting Secant-Tangent Theorem states that, if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment

so

in this problem

[tex]TU^{2}=RT*ST[/tex]

we have

[tex]RT=16\ in[/tex]

[tex]ST=4\ in[/tex]

[tex]TU^{2}=(16)(4)[/tex]

[tex]TU^{2}=64[/tex]

[tex]TU=8\ in[/tex]

Answer: Option a.

Step-by-step explanation:

To solve the given exercise, you must keep on mind the law of logarithms shown below:

 [tex]log(a)-log(b)=log(\frac{a}{b})[/tex]

Therefore, by applying the law , you can rewrite the expression given, as following:

[tex]log(\frac{5}{7})=log(5)-log(7)[/tex]

You know that:

[tex]log5=0.6990\\log7=0.8451[/tex]

Then, when you substitute values, you obtain:

[tex]0.6990-0.8451=-0.1461[/tex]

Use the quotient rule [ [tex]\text{log}_a\frac{x}{y} = \text{log}_ax-\text{log}_ay[/tex] ] to simplify.

[tex]\text{log}\frac{5}{7} = \text{log}(5)-\text{log}(7)[/tex]

Simplify using the given values.

0.6990 - 0.8451

-0.1461

Therefore, [tex]\text{log}\frac{5}{7}=-0.1461[/tex]

Best of Luck!

180-124=56

56/2=28

Ans 28

Answer:

  3 m, 7 m, 3 m, 7 m

Step-by-step explanation:

The perimeter is the sum of the side lengths, so the perimeters of your quadrilaterals are ...

6 m + 5 m + 4 m + 6 m = 21 m . . . . ≠ 20 m

7 m + 4 m + 4 m + 6 m = 21 m . . . . ≠ 20 m

3 m + 7 m + 3 m + 7 m = 20 m . . . . . This is it!

6 m + 3 m + 5 m + 5 m = 19 m . . . . ≠ 20 m

The quadrilateral with side lengths of 3 m, 7 m, 3 m, and 7 m will have a perimeter of exactly 20 meters, as the sum of these side lengths is 20 meters.

To determine which quadrilateral with the given side lengths will have a perimeter of 20 meters, we need to add the lengths of all the sides for each option and see which one totals 20 meters.

For the first option (6 m, 5 m, 4 m, 6 m), the sum is 6 + 5 + 4 + 6 = 21 meters.

The second option (7 m, 4 m, 4 m, 6 m), the sum is 7 + 4 + 4 + 6 = 21 meters.

The third option (3 m, 7 m, 3 m, 7 m), the sum is 3 + 7 + 3 + 7 = 20 meters.

The fourth option (6 m, 3 m, 5 m, 5 m), the sum is 6 + 3 + 5 + 5 = 19 meters.

Therefore, the quadrilateral with sides measuring 3 m, 7 m, 3 m, and 7 m will have a perimeter of 20 meters.

Answer:

y=10.33333333333

Step-by-step explanation:

52-3y=20

52-20=3y

3y=32

y=10.3333

Answer:

9

Step-by-step explanation:

Orders of operation tells us we have to multiply or divide first, whichever one comes first from left to right; then we add or subtract from left to right.  It looks like we have a 2*3 which is 6.  That changes our expression to

5 + 10 - 6,

which is 15 - 6 which is 9

Answer: the answer is 7

Step-by-step explanation: 42/3=14 14/2=7 hope this helps

The value of the height will be 7 units.

What is mean by Rectangle?

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

The volume of a rectangular prism = 42 cubic units

And, The length is 3 units ,the width is 2 units.

Now,

Since, We know that;

⇒ Volume of rectangle = Length x Width x Height

Let height of a rectangular prism = x

Hence, we get;

⇒ Volume of rectangle = Length x Width x Height

⇒ Volume of rectangle = 3 × 2 × x

⇒ 42 = 6x

⇒ x = 42 / 6

⇒ x = 7 units

Thus, The value of the height will be 7 units.

Learn more about the rectangle visit:

https://brainly.com/question/25292087

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Answer:

[tex](x+4)^2+(y-6)^2=81[/tex]

Step-by-step explanation:

We want to find equation of a circle with center (-4,6) and radius 9cm.

The equation of a circle with center (h,k) and radius [tex]r[/tex] units is given by;

[tex](x-h)^2+(y-k)^2=r^2[/tex]

We substitute the radius and the center to obtain;

[tex](x+4)^2+(y-6)^2=9^2[/tex]

The required equation is:

[tex](x+4)^2+(y-6)^2=81[/tex]

Answer:

v/4

Step-by-step explanation:

Volume of cylinder a = v

Let the height of cylinder a is h and its radius is r. The volume of cylinder a will be:

[tex]v=\pi r^{2}h[/tex]

Height of cylinder b is same as cylinder a. So height of cylinder b is h.

Radius of cylinder b is half of radius(width) of cylinder a. So radius of cylinder b will be r/2

The volume of cylinder b will be:

[tex]v^{'}=\pi (\frac{r}{2} )^{2}h\\\\ v^{'}=\pi(\frac{r^{2}}{4})h \\\\ v^{'}=\frac{\pi r^{2}h}{4} \\\\ v^{'} = \frac{v}{4}[/tex]

Thus the volume of cylinder b will be v/4

Answer:

The volume of cylinder A is four times the volume of cylinder B.

Step-by-step explanation:

count me brainliest

set up an equation for the perimeter

l = length w = width

2l + 2w = 64

set up another equation as you know the length is 3 times the width

w = 3l

subsitute w = 3l into the 2l + 2w = 64

2l + 2(3l) = 64

solve for l

2l + 6l = 64

8l = 64

length = 8

subsitute into w = 3l

w = 3(8)

width = 24

Answer:

[tex]x=\frac{13\sqrt{2} }{2}[/tex]

Step-by-step explanation:

We can use the sine ratio to find the value of [tex]x[/tex].

Recall the mnemonics SOH; which  means sine is Opposite over Hypotenuse.

[tex]\sin(45\degree)=\frac{x}{13}[/tex]

This implies that;

[tex]x=13\sin(45\degree)[/tex]

[tex]x=\frac{13\sqrt{2} }{2}[/tex]

Answer:   b. 3

Step-by-step explanation:

The limit of the function as it approaches -3 from the left is 3.

The limit of the function as it approaches -3 from the right is 3.

Since the limit from the left equals limit from the right, then the limit of the function exists and is 3.

Answer: 3, or b

Step-by-step explanation:

The rule that it comes from both the right and the left and meets at a common point verifies this.

Answer:

The answer is √3/4 ⇒ answer (d)

Step-by-step explanation:

∵ [tex]\lim_{n \to \infty} \frac{\sqrt{3x^{2}+2} }{4x+1}[/tex]

* By using the limit theorem: divide up and down by x

∵ x = √x²

∴ [tex]\sqrt{\frac{3x^{2} }{x^{2}}+\frac{2}{x^{2}}[/tex] =

  [tex]\sqrt{3+\frac{2}{x^{2}}[/tex] ⇒ numerator

∵ [tex]\frac{4x}{x}+\frac{1}{x}=4+\frac{1}{x}[/tex] ⇒ denominator

∵ x →∞ ⇒ ∴ 2/x² = 2/∞ = 0 and 1/x = 1/∞ = 0

∴ [tex]\lim_{x \to \infty}\frac{\sqrt{3+\frac{2}{x^{2}}}}{4+\frac{1}{x}}=\frac{\sqrt{3}}{4}[/tex]

∴ The answer is √3/4 ⇒ (d)

The answer is: [tex]d.\frac{\sqrt{3} }{4}[/tex]

Since the degree of both numerator and denominator are the same, the result will be a number different of zero, so the first given option (a) it's incorrect.

We need to "break" the indeterminate form of the limit in order to find the correct answer.

To solve this limit, we must divide each term by the largest degree term, for this case is "x" since the numerator is inside of a square root.

So, doing it we can solve the limit:

[tex]\lim_{x \to \infty}\frac{\sqrt{\frac{3x^{2} }{x^{2} }+\frac{2}{x^{2}}}}{\frac{4x}{x}+\frac{1}{x}}\\\\ \lim_{x \to \infty} \frac{\sqrt{3+\frac{2}{x^{2}}}}{4+\frac{1}{x}}[/tex]

Then, before evaluating the limit, we must remember that any number divided by infinity will give as result zero (0), so:

[tex]\lim_{x \to \infty} \frac{\sqrt{3+\frac{2}{(infinity)^{2}}}}{4+\frac{1}{infinity}}\\\\\lim_{x \to \infty} \frac{\sqrt{3+0}}{4+0}=\frac{\sqrt{3} }{4}[/tex]

So, the correct option is: [tex]d.\frac{\sqrt{3} }{4}[/tex]

Have a nice day!

No it’s not a Pythagorean triple

Answer:

a: no the sample size is too small

b:  Yes, the distribution is normal with a mean of 40 and standard deviation of 12

Step-by-step explanation:

a:  If n < 30, we need to know that the sample is normally distributed or else we can't determine anything.  When sample sized get very large, they usually resemble normally distributed data sets so we can still make conjectures even if the data isn't officially normally distributed

b: The question tells us that the sample is normally distributed, so even though n < 30, we can still make conjectures about the population

Answer:

The distance is 10.24 feet ( to the nearest hundredth).

Step-by-step explanation:

Use trigonometry of a right angled triangle:

The angle = 38 degrees, opposite side = 8 ft, we require the adjacent side:  We have  opposite / adjacent side so we need the tangent.

tan 38 = 8 / a

a = 8 / tan 38

= 10.24 feet.

Answer:

There are total 12 outfit combinations.

Step-by-step explanation:

Number of hat are: 2

1 red hat and 1 black hat

Number of shirt are: 3

1 white shirt , 1 black shirt , 1 black-and-white striped shirt.

Number of pants are: 2

1 black and 1 blue

Now, the total number of combinations could be seen with the help of a tree diagram.

We observe that total 12 combinations are possible.

Answer:

  AB = 21

Step-by-step explanation:

The midpoint divides the segment into two congruent parts, so you have ...

  AB = BC

  x +5 = 2x -11 . . . substitute the given expressions for AB and BC

  16 = x . . . . . . . . add 11-x

Then the measure of AB is ...

  AB = x +5 = 16 +5 = 21