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If the equation is r = 3 +4cos(θ) then because b/a>1 the curve is a limacon with an inner loop.

Given limacon with equation r=3+4cos(θ) and we have to answer how the quotient of a and b relate to the existence of an inner loop.

Equation is like a relationship between two or more variables expressed in equal to form and it is solved to find the value of variables.

formula of polar graph is similar to r= a+ b cos (θ).

Case 1. If a<b or b/a>1

then the curve is a limacon with inner loop.

Case 2. If a>b or b/a<1

Then the limacon does not have an inner loop.

Here given that [tex]r=3+4cos[/tex] (θ)

It is observed that , a<b or b/a>1

Therefore the curve is limacon with an inner loop.

Hence because b/a>1 the curve is a limacon with an inner loop.

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Answer:

The answer is B

Step-by-step explanation:

Using a calculator, the correlation coefficient is of 0.7649. Since the correlation is greater than 0.6, there is strong correlation.

Using a calculator, we insert the points (x,y) to find the coefficient. In this problem, the points are given as follows:

(1, 5), (4, 8), (8, 3), (13, 10), (19, 13)

The coefficient is of 0.7649. Since the correlation is greater than 0.6, there is strong correlation.

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The value of x in the equation is x=-44.

The given equation is [tex]\frac{3}{4}\left(\frac{1}{4}x+8\right)-\left(\frac{1}{2}x+2\right)=\frac{3}{8}(4-x)-\frac{1}{4}[/tex].

An algebraic expression in mathematics is an expression that's made from variables and constants, together with algebraic operations (addition, subtraction, etc.). Expressions are made of terms.

Firstly, apply the distributive property as a(b+c)=ab+ac and get

[tex]\begin{aligned}\frac{3}{4}\times \frac{1}{4}x+\frac{3}{4}\times 8-\frac{1}{2}x-2&=\frac{3}{8}\times 4-\frac{3}{8}\times x-\frac{1}{4}\\ \frac{3x}{16}+6-\frac{x}{2}-2&=\frac{3}{2}-\frac{3x}{8}-\frac{1}{4} \end[/tex]

Now, rearrange the terms by taking variable terms on the left-hand side and constant terms on the right-hand side as

[tex]\frac{3x}{16}-\frac{x}{2}+\frac{3x}{8}=\frac{3}{2}-\frac{1}{4}-6+2[/tex]

Further, simplify the above expression by taking L.C.M as

[tex]\begin{aligned}\frac{3x-8x+6x}{16}&=\frac{6-1}{4}-4\\ \frac{x}{16}&=\frac{5-16}{4}\\ \frac{x}{16}&=\frac{-11}{4}\end[/tex]

Then, multiply both sides with 4 and get

[tex]\begin{aligned}4\times \frac{x}{16}&=4\times \frac{-11}{4}\\ \frac{x}{4}&=\frac{-11}{1}\end[/tex]

Furthermore, cross multiply both sides and get

[tex]x=-44[/tex]

Hence, the value of x in the equation which is given [tex]\frac{3}{4}\left(\frac{1}{4}x+8\right)-\left(\frac{1}{2}x+2\right)=\frac{3}{8}(4-x)-\frac{1}{4}[/tex] is x=-44.

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Answer: Addition property of equality

Step-by-step explanation:

Assuming you meant 3x-9=2x+5, it would be the addition property of equality since you are adding 9 to both sides.

Answer: 3

Step-by-step explanation:

Answer:

no

Step-by-step explanation:

the y coordinate 9 repeats twice

Answer:

D. all real numbers greater than or equal to 0

Step-by-step explanation:

The range is the set of y-values.

If one finalist is randomly selected for a prize then the probability that person will be selected is 6.25%.

Given A person is one of 16 finalists and one finalist is randomly selected for a prize.

Probability is the likeliness of happening an event among all the events possible. The formula of calculating probability is number of events possible/total outcomes.

The value of probability lies between 0 and 1. It cannot be negative because there might be chances of something and sometimes not so the value be 0.

Total finalists=16

Probability=1/16

When we convert it in percentage it will be 1*100/16

=6.25%

Hence the probability that person  will be selected is 6.25%.

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Answer:

The scale factor would be 1/2.

Step-by-step explanation:

2 of the sides both are 4 units.

If you go to figure B, it got smaller.

So in this case, you would divide.

On figure B, 2 of the sides are 2 units.

If you did it in reverse, you would get 2 because 2 times 2 is 4.

But we divide, so 4/2 is 2, so the scale factor would be:

1/2

Hope this helped!

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The population of Charlotte is 661,000.

Percentage can be described as a fraction out of an amount that is usually expressed as a number out of hundred.

The population of Charlotte = number of unemployed people / percentage of unemployed

26,440 / 0.04 = 661,000

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The given trig equation is obtained by solving for the critical points of [tex]f[/tex], which is done by differentiating [tex]f[/tex] and setting the derivative equal to zero.

We have

[tex]18 \sin(x) \cos(x) - 9 \sin(x) = 0[/tex]

[tex]9 \sin(x) (2 \cos(x) - 1) = 0[/tex]

[tex]9 \sin(x) = 0 \text{ or } 2 \cos(x)  - 1 = 0[/tex]

[tex]\sin(x) = 0 \text{ or } \cos(x) = \dfrac12[/tex]

In the interval [tex]0\le x< 2\pi[/tex], we have

[tex]\sin(x) = 0 \implies x = 0 \text{ or } x = \pi[/tex]

and

[tex]\cos(x) = \dfrac12 \implies x = \dfrac\pi3 \text{ or } x = \dfrac{5\pi}3[/tex]

In order from smallest to largest, that's

[tex]x = 0 \text{ or } x = \dfrac\pi3 \text{ or } x = \pi \text{ or } x = \dfrac{5\pi}3[/tex]

The solution to the Trigonometric equation is given as below.

A trigonometric equation is one that involves one or more unknown trigonometric ratios. It is represented in terms of sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (cosec) angles.

The provided trigonometric equation is produced by determining the critical points of f by differentiating and setting the derivative to zero.

Thus,

18 sin (x) cos (x) - 9 sin (x) = 0

8 sin(x) = 0 or 2 cos (x) - 1 = 0

Sin (x) = 0 or Cos (x) = 1/2

Given the interval of 0 ≤ x ≤ 2π

→ Sin (x) = 0 → x = 0 or x = π

and

Cos (x) = 1/2

→ x = π/3 or x = 5π/3

Arranging the values from the smallest to the largest, we have:

x = 0 or x = π/3

x = π or x = 5π/3

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(a) The arc length of each of the two smaller semicircles is [tex]4\pi[/tex], and the arc length of each of the two larger semicircles is [tex]15\pi[/tex]. Therefore, the perimeter is [tex]2(4\pi)+2(15\pi)=38\pi[/tex].

(b) The area of each of the smaller semicircles is [tex]\frac{1}{2}(\pi)(4^2)=8\pi[/tex], and the areaof each of the larger semicircles is [tex]\frac{1}{2}(\pi)(15^2)}=\frac{225\pi}{2}[/tex].

So, the combined areas of the four semicircles is [tex]241\pi[/tex].

The area of the rectangle is 60, so the total area is [tex]241\pi+60[/tex].

Answer:

x<3−√11 /2 or x > 3 +√11/2

Step-by-step explanation:

Solve the inequality for x by finding a, b, and c of the quadratic then applying the quadratic formula.

Answer:

  [8, 44]

Step-by-step explanation:

The average of equally-weighted values is their sum divided by their number.

For some fourth test score x, Paul wants an average between 70 and 79. This gives rise to the inequality ...

  70 ≤ (91 +88 +93 +x)/4 ≤ 79

Multiplying by 4, we have ...

  280 ≤ 272 +x ≤ 316

  8 ≤ x ≤ 44 . . . . . . . . . . subtract 272

Paul will get a C if his fourth test score is in the interval [8, 44].

Answer:

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

A) We know any number with power of zero equals 1, therefore the sequence can be expressed as powers of 4:

The number of terms from zero to 99 is:

B) This is a AP with the first term of 11 and common difference of 4.

The nth term equation is:

Substitute the values and solve for n:

C) Same as above, the sequence is AP, with the first term 44 and common difference 1.

Applying the nth term formula:

Answer: B. The lines will intersect once.

Step-by-step explanation:

Multiplying the bottom equation by 2, we get 6y+4x=14.

Adding this to the first equation, this gives 9x=18, and thus x=2.

Therefore, since this means there will be 1 solution, the lines will intersect once.

The probability of an event is the measurement of the chance of that event's occurrence. The probabilities of considered events are:

Binomial distributions consist of n independent Bernoulli trials. Bernoulli trials are those trials that end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))

Suppose we have random variable X pertaining to a binomial distribution with parameters n and p, then it is written as

X = B(n,p)

The probability that out of n trials, there'd be x successes is given by

P(X=x)  = [tex]^nC_xp^x(1-p)^{n-x}[/tex]

Since 10 people can be either diseased or not and they be so independent of each other (assuming them to be selected randomly) , thus, we can take them being diseased or not as outputs of 10 independent Bernoulli trials.

Let we say

Success= Probability of a diseased person tagged as diseased by the clinic

Failure = Probability of a diseased person tagged as not diseased by the clinic.

Then,

P(Success) = p = 72% = 0.72 (of a single person)

P(Failure) = q = 1-p = 0.28

Let X be the number of people diagnosed diseased by the clinic out of 10 diseased people. Then we have: X ≈ B(n+10,P=0.73)

Calculating the needed probabilities, we get:

a) P(At leased 8 have disease) = P(X≥8) =P(X=8) + P(X=9) + P(X=10)

P(X≥8) = [tex]^{10}C_8(0.73)^8(0.28)^2+^{10}C_9(0.73)^9(0.27)^1+^{10}C_{10}(0.73)^{10}(0.27)^0[/tex]

P(X≥8) ≈ 0.2548 + 0.1456 + 0.0374 ≈ 0.4378

b)  P(At most 4 have the disease) = P(X≤4) = P(X=0) + P(X=1)+P(X=2)+P(X=3)+P(X=4)

P (X ≤ 4) =

[tex]^{10}C_0(0.73)^0(0.27)^{10}+^{10}{C_1(0.73)^1(0.27)^9+^{10}{C_2(0.73)^2(0.27)^8+^{10}C_3(0.73)&^3(0.27)^7 \\[/tex]

[tex]+^{10}C_4(0.73)^4(0.27)^6[/tex]

P (X ≤ 4) = 0.000003 + 0.000076+0.00088+0.00604+0.02719

P (X ≤ 4) =  0.0342

Thus,

The probabilities of considered events are:

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Answer: 123/32 or 3 27/32 sticks

Step-by-step explanation:

41/8*3/4 =

41*3/8*4 =

123/32 =

3 27/32

Answer and Explanation:

First, solve for x in both inequalities:

4x − 1 > 7                         5x − 1 < −6

4x > 8                             5x < −5

x > 2                               x < −1

Because this is an OR problem, determine if there is any overlap. (See the attached image for details.) There is not, so the answer is no solution or Ø.

Answer:

B

Step-by-step explanation:

Convert everything to inches first

The floor is 120 inches by 144 inches

The floor can be covered with (120/6) * (144/8) tiles

(120/6) * (144/8) = 20*18=360 tiles, hence b.

Using proportions, it is found that 78 students would prefer long jump.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

Out of 300 students, 26% would prefer long jump, hence the amount is given by:

n = 0.26 x 300 = 78 students.

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Answer:

?=3

Step-by-step explanation:

3=3/1

Flip 3/1 and you get

1/3

Answer:

sin=-3/5
cos=4/5

tan-3/4

csc=5/-3

sec=5/4

cot=4/-3

Step-by-step explanation:

you draw a right triangle in the fourth quadrant and then use pythagoreas theorem to find the length of the hypotenuse(2 sides are -3 and 4, hypotenuse is 5), and then just use the sides to find all 6 trigonometric functions.

The perimeter of the shaded region is 8π cm and the area of the shaded region is 32(π - 2) cm² or 36.53 square cm.

It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)

We have shown a square in which a one-fourth circle is shown and making an ellipse.

The perimeter of the circle = 2πr = 2π(8) = 16π cm

The perimeter of the one-fourth is circle = (16π)/4 = 4π cm

The perimeter of 2 one-fourth circle = 2(4π) = 8π cm

The area of the one-fourth circle = (1/4)πr² = (1/4)π(8)² = 16π square cm

The area of the right-angle triangle = (1/2)(8)(8) = 32 square cm

The area of the shaded region = 2(16π - 32) = 36.53 square cm

or

= 32(π - 2)cm²

Thus, the perimeter of the shaded region is 8π cm and the area of the shaded region is 32(π - 2) cm² or 36.53 square cm.

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Using PEDMAS, the value of each expressions are:

a. 1 + 5 × 2 + (1 + 3)² = 27

b. 0.25 × 4³ - 1 = 15

c. 4 + 8(1/4 + 2) = 22

PEDMAS implies that you solve a problem first following the order, parentheses, exponent, division, multiplication, addition, and subtraction.

Let's evaluate the expressions using PEDMAS:

a. 1 + 5 × 2 + (1 + 3)²

1 + 5 × 2 + (4)²

1 + 5 × 2 + 16

1 + 10 + 16

= 27

b. 0.25 × 4³ - 1

0.25 × 64 - 1

16 - 1

= 15

c. 4 + 8(1/4 + 2)

4 + 8(9/4)

4 + 18

= 22.

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The area of polygon MNOPQR = (Area of a rectangle that is 15 square units + Area of a rectangle that is 2 square units)

From the information about the polygon MNOPQR, side MN is parallel to side RQ and also the side MR is parallel to side PQ

With a perpendicular line drawn from point O on the side RQ, which intersects with line  RQ at point S.

We can then  divide the  polygon into two different rectangles

MNSR  with A₁ as its area

OPQS  with A₂ as its area

For rectangle MNSR, line MN is 5 units and line MR is 3 units

The formula for area of a rectangle is given as;

A₁ = (length)×(width)

Substitute the values

A₁ = 5 × 3

A₁ = 15 square units

For rectangle MNSR, line MN= line RS and line MR = line NS,

We have RS= 5 units and NS= 3 units

So, line SQ= RQ- RS = 7-5 = 2 units

Also,  OS= NS - NO = 3- 2 = 1 unit

Let's substitute the values

A₂ = 2 × 1

A₂ = 2 square units

Therefore, the area of polygon MNOPQR = (Area of a rectangle that is 15 square units + Area of a rectangle that is 2 square units)

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Answer:

100+946=1046

Ao the next no. Is 1046

Answer:

See below

Step-by-step explanation:

Start by subtracting 5.2 from both sides of the equation

  so  "subtraction property of equality "    I suppose ......

then the next step would be divide both sides by 2.5  

  which would be division property of equality  

Answer: Subtraction Property of Equality

Step-by-step explanation:

- the subtraction property of equality is the rule that when you subtract the same number to or from both sides of an equation and get an equivalent equation

__________________________________________________________

- for this equation you would subtract 5.2 from the left-side of the equation and subtract it from 35.2 on the right side of the equation

      - this is to isolate n

- basically 2.5n = 30 since n is a variable and that number multiplied by 2.5 will equal 30

- so the new equation would be 2.5n = 30

- so then:  [tex]\frac{n}{2.5}[/tex] = [tex]\frac{30}{2.5}[/tex]  so n = 12

hope this helps :)