For the opening home game of the baseball season, the Madd Batters minor league baseball team offered the following incentives to its fans: Every 75th fan who entered the stadium got a coupon for a free hot dog. Every 30th fan who entered the stadium got a coupon for a free cup of soda. Every 50th fan who entered the stadium got a coupon for a free bag of popcorn. The stadium holds 4000 fans and was completely full for this game. How many of the fans at the game were lucky enough to receive all three free items?

Answer:

Step-by-step explanation:

yes 30

Answer:

Problem 1: [tex]r=4[/tex]

Problem 2: [tex]r=-2\sin(\theta)[/tex]

Problem 3: [tex]r\sin(\theta)=3[/tex]

Step-by-step explanation:

Problem 1:

So we are going to use the following to help us:

[tex]x=r \cos(\theta)[/tex]

[tex]y=r \sin(\theta)[/tex]

[tex]\frac{y}{x}=\tan(\theta)[/tex]

So if we make those substitution into the first equation we get:

[tex]x^2+y^2=16[/tex]

[tex](r\cos(\theta))^2+r\sin(\theta))^2=16[/tex]

[tex]r^2\cos^2(\theta)+r^2\sin^2(\theta)=16[/tex]

Factor the [tex]r^2[/tex] out:

[tex]r^2(\cos^2(\theta)+\sin^2(\theta))=16[/tex]

The following is a Pythagorean Identity: [tex]\cos^2(\theta)+\sin^2(\theta)=1[/tex].

We will apply this identity now:

[tex]r^2=16[/tex]

This implies:

[tex]r=4 \text{ or } r=-4[/tex]

We don't need both because both of include points with radius 4.

Problem 2:

[tex]x^2+y^2+2y=0[/tex]

[tex](r\cos(\theta))^2+(r\sin(\theta))^2+2(r\sin(\theta))=0[/tex]

[tex]r^2\cos^2(\theta)+r^2\sin^2(\theta)+2r\sin(theta)=0[/tex]

Factoring out [tex]r^2[/tex] from first two terms:

[tex]r^2(\cos^2(\theta)+\sin^2(\theta))+2r\sin(\theta)=0[/tex]

Apply the Pythagorean Identity I mentioned above from problem 1:

[tex]r^2(1)+2r\sin(\theta)=0[/tex]

[tex]r^2+2r\sin(\theta)=0[/tex]

or if we factor out r:

[tex]r(r+2\sin(\theta))=0[/tex]

[tex]r=0 \text{ or } r=-2\sin(\theta)[/tex]

r=0 is actually included in the other equation since when theta=0, r=0.

Problem 3:

[tex]y=3[/tex]

[tex]r\sin(\theta)=3[/tex]

A Cartesian equation can be converted to a polar equation using trigonometric relations. For example, the equations [tex]x^2 + y^2 = 16, x^2 + y^2 + 2y = 0,[/tex]  and y = 3 can be transformed into the polar forms r = 4, r = -2sin(θ), and r = 3/cos(θ) respectively. The TI-84 calculator is recommended for these conversions.

In Mathematics, specifically in the conversion of Cartesian equations to polar equations, we have two basic formulas from trigonometry. These are r2 = x2 + y2 and tan(θ) = y/x. But for regions where x might be zero, it is advisable to remember the Cartesian-polar relations which are x = rcos(θ), y = rsin(θ).

For x2 + y2 = 16, by substituting the first relation r2 = x2 + y2 we can get the polar equation r = 4. For x2 + y2 + 2y = 0, we complete the square on the left side then apply our formulas, resulting in a polar equation of r = -2sin(θ). For y = 3, this is a horizontal line in the Cartesian coordinate system, so we use y = rsin(θ) and solve for r to give the polar equation r = 3/cos(θ).

As for a suitable calculator, the TI-84 would be a good option for these conversions as it has the functionality to convert between these forms easily.

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Answer:

69 bpm

Step-by-step explanation:

Here we start out finding the z-score corresponding to the bottom 33% of the area under the standard normal curve.  Using the invNorm( function on a basic TI-83 Plus calculator, I found that the z-score associated with the upper end of the bottom 33% is -0.43073.

Next we use the formula for z score to determine the x value representing this woman's heart rate:

       x - mean                              x - 75 bpm

z = ----------------- = -0.43073 = --------------------

       std. dev.                                    15

Thus,  x - 75 = -0.43073(15) = -6.461, so x = 75 - 6.6461, or approx. 68.54, or (to the nearest integer), approx 69 bpm

Answer:

A. -3

Step-by-step explanation:

Answer:

Its undefined or D

Step-by-step explanation:

A undefined slope is something that is vertical or horizontal. The provided images explains it! Hope it helps!

Answer:

Pr(the sum of the numbers rolled is either a multiple of 3 or an even number)=[tex]\frac{2}{3}[/tex]

Step-by-step explanation:

Let A be the event "sum of numbers is multiple of 3"

and B be the event "sum is an even number".

As our dice has six sides, so the sample space of two dices will be of 36 ordered pairs.

|sample space | = 36

Out of which 11 pairs have the sum multiple of 3 and 18 pairs having sum even.

So Pr(A)= [tex]\frac{11}{36}[/tex]

and Pr(B)= [tex]\frac{18}{36}[/tex]

and Pr(A∩B) = [tex]\frac{5}{36}[/tex], as 5 pairs are common between A and B.

So now Pr(A or B)= Pr(A∪B)

                            = Pr(A)+Pr(B) - Pr(A∩B)

                            = [tex]\frac{11}{36}[/tex] + [tex]\frac{18}{36}[/tex] - [tex]\frac{5}{36}[/tex]

                            = [tex]\frac{24}{36}[/tex]

                            = [tex]\frac{2}{3}[/tex]

Answer:

2/3 and NOT mutually exclusive

Step-by-step explanation:

plato

a. Monthly: $14,185.30 b. Daily: $14,185.50 c. Quarterly: $14,320.00 d. Weekly: $14,372.70.

To find the balance after 5 years with different compounding frequencies, we'll use the compound interest formula:

[tex]\[A = P \left(1 + \frac{r}{n}\right)^{nt}\][/tex]

Where:

- [tex]\(A\)[/tex] is the amount of money accumulated after \(n\) years, including interest.

- [tex]\(P\)[/tex] is the principal amount (the initial amount of money).

- [tex]\(r\)[/tex] is the annual interest rate (in decimal).

- [tex]\(n\)[/tex] is the number of times that interest is compounded per year.

- [tex]\(t\)[/tex] is the time the money is invested for, in years.

Given:

- [tex]\(P = $10,000\)[/tex]

- [tex]\(r = 6.92\% = 0.0692\)[/tex]

Let's calculate each scenario:

a. Monthly compounding (12 times per year):

[tex]\[n = 12\][/tex]

[tex]\[A = 10000 \left(1 + \frac{0.0692}{12}\right)^{12 \times 5}\][/tex]

[tex]\[A = 10000 \left(1 + \frac{0.0692}{12}\right)^{60}\][/tex]

[tex]\[A[/tex] ≈ [tex]10000 \times (1.005766)^{60}[/tex]

[tex]\[A \approx10000 \times 1.41853\][/tex]

b. Daily compounding (365 times per year):

[tex]\[n = 365\][/tex]

[tex]\[A = 10000 \left(1 + \frac{0.0692}{365}\right)^{365 \times 5}\][/tex]

[tex]\[A = 10000 \left(1 + \frac{0.0692}{365}\right)^{1825}\][/tex]

[tex]\[A[/tex] ≈ [tex]10000 \times (1.000189)^{1825}[/tex]

[tex]\[A[/tex] ≈ [tex]10000 \times 1.41855[/tex]

[tex]\[A[/tex] ≈ [tex]\$14,185.50\][/tex]

c. Quarterly compounding (4 times per year):

[tex]\[n = 4\][/tex]

[tex]\[A[/tex] = [tex]10000 \left(1 + \frac{0.0692}{4}\right)^{4 \times 5}[/tex]

[tex]\[A[/tex] = [tex]10000 \left(1 + \frac{0.0692}{4}\right)^{20}[/tex]

[tex]\[A[/tex] ≈ [tex]10000 \times (1.0173)^{20}[/tex]

[tex]\[A[/tex] ≈ [tex]10000 \times 1.432[/tex]

[tex]\[A[/tex] ≈ [tex]\$14,320.00[/tex]

d. Weekly compounding (52 times per year):

[tex]\[n = 52\][/tex]

[tex]\[A = 10000 \left(1 + \frac{0.0692}{52}\right)^{52 \times 5}\][/tex]

[tex]\[A = 10000 \left(1 + \frac{0.0692}{52}\right)^{260}\][/tex]

[tex]\[A \approx 10000 \times (1.0013308)^{260}\][/tex]

[tex]\[A \approx10000 \times 1.43727\][/tex]

[tex]\[A \approx \$14,372.70\][/tex]

So, after 5 years, the balances would be:

a. Monthly compounding: [tex]\$14,185.30[/tex]

b. Daily compounding: [tex]\$14,185.50[/tex]

c. Quarterly compounding: [tex]\$14,320.00[/tex]

d. Weekly compounding: [tex]\$14,372.70[/tex]

Answer:

15/2 x^2y - 5xy

Step-by-step explanation:

First find the area of the rectangle

A = l*w

   = 5xy * 2x

    10x^2y

The find the area of the triangle

A = 1/2 bh

   = 1/2 (5xy) (x+2)

   = 1/2((5x^2y + 10xy)

   = 5/2 x^2y +5xy

The shaded region is the area of the rectangle minus the area of the triangle

10x^2y -  (5/2 x^2y +5xy)

Distribute the minus sign

10x^2y -5/2 x^2y -5xy

Combining like terms by getting a common denominator

20/2x^2y -5/2 x^2y -5xy

15/2 x^2y - 5xy

Answer:

  θ = 38°

Step-by-step explanation:

The lower right triangle is congruent to the upper left triangle, so we have θ and 20° being the two acute angles in the triangle. The law of sines tells you ...

  sin(θ)/9 = sin(20°)/5

  sin(θ) = (9/5)sin(20°)

  θ = arcsin(9/5·sin(20°)) ≈ 38°

___

Another solution to the triangle is θ = 180° -38° = 142°. The diagram clearly shows θ as an acute angle, so we take this second solution to be extraneous.

Answer:0.68

Step-by-step explanation:

Given

Total of 600 employees out of which 400 had college degree ,100 are single

and 60 were single graduates

therefore out of 100, 60 were single and rest 40 are single undergraduate

and out of 400, 60 were single graduates thus 340 are married graduate.

Now out of 600, 100 were single i.e. 500 is married

thus Probability that an employee is married and has a college degree is

=[tex]\frac{Favourable outcome }{Total outcome}[/tex]

P=[tex]\frac{340}{500}[/tex]=0.68  

Answer:

Lowest score needed=4.92

Step-by-step explanation:

Using the standard normal distribution table we find the value of standard normal deviate corresponding to area of 15%

For area of 15% we have Z= -1.04

Thus we have

[tex]Z=\frac{X-\overline{X}}{\sigma }\\\\\therefore X=\sigma Z+\overline{X}\\\\[/tex]

Applying values we get

[tex]X=-1.04\times 2+7\\\\X=4.92[/tex]

Thus lowest score needed = 4.92

Answer: The following statements are true:

It is symmetrical.

The first diagonal is all 1’s.

The second diagonal is the counting numbers.

Any number in the triangle is the sum of the two numbers directly above it.

Each row adds to a power of 2.

Answer:

They are all correct

Step-by-step explanation:

[tex]\bf \begin{array}{ccll} term&value\\ \cline{1-2} s_4&18\\ s_5&18r\\ s_6&18rr\\ &18r^2 \end{array}\qquad \qquad \stackrel{s_6}{8}=18r^2\implies \cfrac{8}{18}=r^2\implies \cfrac{4}{9}=r^2 \\\\\\ \sqrt{\cfrac{4}{9}}=r\implies \cfrac{\sqrt{4}}{\sqrt{9}}=r\implies \boxed{\cfrac{2}{3}=r} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf n^{th}\textit{ term of a geometric sequence} \\\\ s_n=s_1\cdot r^{n-1}\qquad \begin{cases} s_n=n^{th}\ term\\ n=\textit{term position}\\ s_1=\textit{first term}\\ r=\textit{common ratio}\\ \cline{1-1} n=6\\ s_6=8\\ r=\frac{2}{3} \end{cases}\implies 8=s_1\left( \frac{2}{3} \right)^{6-1} \\\\\\ 8=s_1\left( \frac{2}{3} \right)^5\implies 8=s_1\cdot \cfrac{32}{243}\implies 8\cdot \cfrac{243}{32}=s_1\implies \boxed{\cfrac{243}{4}=s_1}[/tex]

Answer:

Step-by-step explanation:

a. We assume the appropriate equation for ballistic motion is ...

  h = -4.9t^2 +1

Then h = 0 when ...

  0 = -4.9t^2 +1

  49t^2 = 10 . . . . . add 4.9t^2, multply by 10

  7t = √10 . . . . . . . take the square root

  t = (√10)/7 . . . . . . divide by the coefficient of t

The marble will be in the air about (√10)/7 ≈ 0.451754 seconds.

__

b. The average velocity is the ratio of distance to time:

  v = (1 m)/((√10)/7 s) = 0.7√10 m/s ≈ 2.214 m/s

__

c. Under the influence of gravity, the velocity is linearly increasing over the time period, so its instantaneous value when the marble hits the ground will be twice the average value:

  When it hits, the marble's velocity is 1.4√10 m/s ≈ 4.427 m/s.

Final answer:

To convert Fahrenheit (F) to Celsius (C), subtract 32 from the Fahrenheit value, then multiply by 5/9 to get the Celsius value; the formula is C = (5/9)(F - 32).

Explanation:

Converting Fahrenheit to Celsius

To solve the formula for converting temperature from degrees Fahrenheit (F) to degrees Celsius (C), we are given the formula F = (9/5)C + 32. The student needs to find the value of C. To do this, we'll follow these steps:

Isolate the term containing C by subtracting 32 from both sides of the equation, which gives us F - 32 = (9/5)C.

Then, to solve for C, multiply both sides of the equation by the reciprocal of (9/5), which is (5/9), resulting in (5/9)(F - 32) = C.

Therefore, the converted equation for Celsius is C = (5/9)(F - 32), which can be used to find the Celsius temperature corresponding to a given Fahrenheit temperature.

Answer:

C. greater than or equal to

Step-by-step explanation:

For example,

  ceiling(5) =  5

ceiling(5.1) =  6

 ceiling(-5) = -5

ceiling(-5.1) = -5

The solution of the inequality is:

                       [tex]x\leq 3[/tex]

We are given a inequality in terms of variable x as:

[tex]2(4+2x)\geq 5x+5[/tex]

Now we are asked to find the solution of the inequality i.e. we are asked to find the possible values of x such that the inequality holds true.

We may simplify this inequality as follows:

On using the distributive property of multiplication in the left hand side of the inequality we have:

[tex]2\times 4+2\times 2x\geq 5x+5\\\\i.e.\\\\8+4x\geq 5x+5\\\\i.e.\\\\8-5\geq 5x-4x\\\\i.e.\\\\x\leq 3[/tex]

The solution is:      [tex]x\leq 3[/tex]

Answer:

Option C.

Step-by-step explanation:

The given inequality is given as

2(4 + 2x) ≥ 5x + 5

8 + 4x ≥ 5x + 5 [Simplify the parenthesis by distributive law]

Subtract 5 from each side of the inequality

(8 + 4x) - 5 ≥ (5x + 5) - 5

3 + 4x ≥ 5x

subtract 4x from each side of the inequality

(4x + 3) - 4x ≥ 5x - 4x

3 ≥ x

Or x ≤ 3

Option C. x ≤ 3 is the correct option.

1) The reflection image of figure 1 with respect to line m is figure 2.

2) The  pair of figures for which the second figure a translation image of the first is: Figures 1 and 3

How to find the transformation?

There are different types of transformation such as:

Translation

Rotation

Reflection

Dilation

1) The reflection transformation is a mirror image of the original image.

Thus, the reflection image of figure 1 with respect to line m is figure 2.

2) The  pair of figures for which the second figure a translation image of the first is:

Figures 1 and 3

Answer:

amount of total cash payment is $5450

Step-by-step explanation:

Given data

amount = $15000

principal = $5000

rate = 3% = 0.03

to find out

the amount of total cash payment

solution

we know according to question is Each yearly installment will include both principal repayment of​ $5,000 and interest payment for the preceding​ one-year period

so first we calculate interest i.e.

interest = rate × amount

interest = 0.03 × 15000

interest = 450

so interest is $450 for 1 year

now we calculate the amount of total cash payment i.e.

interest + principal

so the amount of total cash payment = 450 +5000 = 5450

amount of total cash payment is $5450

Mandy will make total cash payment of [tex]\fbox{\begin{minispace}\\\$\text{ }5450\end{minispace}}[/tex] on March 1, 2019.

Further explanation:

Mandy issued a 3% long-term notes payable for [tex]\$\text{ }15000[/tex] over a 3-year term in [tex]\$\text{ }5000[/tex] principal installments on March 1 each year.

Then the interest payment for the first year will apply on total amount of [tex]\$\text{ }15000[/tex].

The formula for simple interest at principal value [tex]P[/tex] and rate percentage of [tex]R[/tex] in the time of [tex]T[/tex] years is,

[tex]\fbox{\begin{minispace}\\ \math{I}=\dfrac{P\times R\times T}{100}\\\end{minispace}}[/tex]

So, the interest amount payable at the end of one year is calculated as,

[tex]I=\dfrac{15000\times 3\times 1}{100}\\I=150\times 3\\I=450[/tex]

The total cash payment to be done by Mandy after a year on March 1, 2019, is the sum of the principal installment of [tex]\$\text{ }5000[/tex] and the interest applied on the total amount.

Hence the total cash payment is obtained as,

[tex]\fbox{\begin{minispace}\\\text{Total cash payment}=5000+450=5450\end{minispace}}[/tex]

Therefore, Mandy has to make a total payment of [tex]\fbox{\begin{minispace}\\\$\text{ }5450\end{minispace}}[/tex] on March 1, 2019.

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Answer details  

Grade: High school  

Subject: Mathematics  

Chapter: Simple Interest

Keywords: installments, one year, Mandy, principal, long-term, payable, March 1, amount, total cash, total cash payments, each year, payments, simple interest, rate percentage, sum, total amount, time, interest applied.

Answer:

[tex]y = 6 + x[/tex]

Step-by-step explanation:

Hello, great question. These types are questions are the beginning steps for learning more advanced Algebraic Equations.

Assuming that the value of y is the total number of flour used in the mixture, then we would need to add both types of flour in order to find the value of y. Since we do not know the amount of white flour used, we will be substituting it for the variable x.

[tex]y = 6 + x[/tex]

The Equation above is stating that 6 cups of whole wheat flour added to the amount of white flour will equal the total amount of flour in the mixture.

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

A.) Yes. The input and output are both possible.

In this problem, a dentist sees patients each day to clean their teeth. So we represent this function as [tex]g(x)[/tex] where:

x: Represents the number of people who saw the dentist.

g(x): Represents the number of teeth cleaned.

So we are given a point that is solution to our function, which is [tex](20, 20)[/tex] but what does this point represent? This tells us that the dentist saw 20 patients and cleaned 20 teeth, that is, he cleaned an only teeth per patient. So this will make sense under the conditions that make it possible, for example, a volunteer dentist can see more people than a common dentist and it is likely that that volunteer person sees fewer teeth. However, it's very difficult that that dentist finds 20 people with an only tooth each. So this situation is possible, but not realistic in the real world.

Answer:

Mr Johnson will receive 1024 mL IV in 8 hours.

Step-by-step explanation:

Mr Johnson has an IV that is infusing at 32 gtt per minute.

So in 1 hour patient will get the drug = 32×60 = 1920 gtt

Now in 8 hours drug received by the patient = 1920 × 8

= 15360 gtt

Since IV tube is calibrated for 15 gtt per mL which means in 1 mL amount of drug is 15gtt.

Therefore, total volume of infusion (in mL) will be

= [tex]\frac{\text{Total drug infused}}{\text{Total drug in 1 mL}}[/tex]

= [tex]\frac{15360}{15}[/tex]

= 1024 mL.

Therefore, 1024 mL IV will be infused in 8 hours.

Answer:

  Converges; 51 3/7

Step-by-step explanation:

The common ratio is -10/60 = (5/3)/-10 = (-5/18)/(5/3) = -1/6.

Then the sum of the sequence is given by ...

  S = a1/(1 -r) = 60/(1 -(-1/6))

  S = 60/(7/6) = 360/7

  S = 51 3/7

_____

If you erroneously evaluate the formula for the sum using +1/6 as the common ratio, then you will get S=60/(1-1/6) = 60·6/5 = 72.

Answer:

Step-by-step explanation:

  (2x +3)² = (2x)² + 2(2x)(3) +(3)²

  = 4x² +12x +9

Comparing that to ax² +bx +c, we can identify ...

The values of a, b, and c are:

a   =  4

b  =  12

c  =  9

The given quadratic equation is:

y  =   (2x  +  3)²

A quadratic equation is of the form:

y  =  ax²  +  bx   +  c

Expand the equation y = (2x  +  3)²

y  =  (2x  +  3)(2x  +  3)

y   =  4x²  +  6x  +  6x   +  9

y  =  4x²  +  12x   +  9

Comparing y = 4x²  +  12x  +  9   with  y  =  ax²  +  bx  +  c

a   =  4

b  =  12

c  =  9

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Answer:

c. 172.54 pi cm^3

Step-by-step explanation:

i got it right on plato

Answer:

c. 172.54 pi cm^3

Step-by-step explanation:

PLATO

Answer:

D. A stratified sample because the population is divided into separate groups and each group is randomly sampled.

Step-by-step explanation:

The researcher plans to take a random sample of 100 recent graduates of public universities and 100 recent graduates of private universities.

Her method is stratified sampling. This is because she divided the selected samples in two groups and will conduct the survey group wise.

These groups are also called strata.

Final answer:

Cluster sampling is used in the researcher's study design by dividing the population into clusters and randomly selecting all members from chosen clusters that is option A is correct.

Explanation:

Cluster sampling is utilized in the researcher's study design. In cluster sampling, the population is divided into separate clusters, and all subjects from a randomly selected cluster are selected. This method is practical when the population is dispersed geographically, making simple random sampling challenging.

Answer:

0.0952  or 9.52%.

Step-by-step explanation:

The standard deviation = √(40,000) = 200.

Z-scores are  917 - 800  / 200 = 0.585 and

980 - 800 / 200 = 0.90..

From the tables the required probability =

0.81594 - 0.72072

= 0.09522 (answer).

The probability of the steer's weight falling between 917lbs and 980lbs can be determined by first calculating their respective z-scores based on given mean and variance. The difference in probabilities associated with these z-scores will give the desired probability.

In this case, we are dealing with a normal distribution which is important when we are considering mean and variance. To find the probability that the weight of the steer falls between 917lbs to 980lbs, we need to first convert these weights into z-scores, because a z-score helps us understand if a data point is typical or atypical within a distribution.

Z-score is given by z = (x - μ) / σ, where μ is the mean and σ is the standard deviation, which is the square root of variance. Given that the mean (μ) is 800lbs and variance is 40,000, the standard deviation (σ) is √40,000=200.

So, the z-scores for 917 and 980 lbs are z1 = (917 - 800) / 200 = 0.585 and z2 = (980 - 800) / 200 = 0.90 respectively.

The probability that the weight of a randomly selected steer is between 917lbs and 980lbs is the probability that the z-score is between 0.585 and 0.90. We can find these values using a z-table or statistical software. The difference between these probabilities will give us the probability of a steer's weight falling between 917 and 980 lbs.

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Answer:

A. Increase sample size

Step-by-step explanation:

From the formula for estimating the confidence level interval for the mean:

X - Z × s/sqrt n where; X = sample mean; Z = z value corresponding to 95%;

s = standard deviation and n = sample size

It is evident from the equation that the confidence interval for the mean is inversely proportional to the sample size (n), hence increasing the sample size will result in a reduced interval width.

Answer:

  f(x) = x^2

Step-by-step explanation:

The square root function is defined to have a non-negative range only. That corresponds to restricting the domain of f(x) = x^2 to positive values of x.

_____

The attached graph shows the domain-restricted f(x)=x² in solid red and the corresponding f⁻¹(x) = √x in solid blue. The other halves of those curves are shown as dotted lines (and are inverse functions of each other, too). The dashed orange line is the line of reflection between a function and its inverse.

Answer:

OH NANANA

Step-by-step explanation:

Find all real numbers $x$ such that $3x - 7 \le 5x +9$. Give your answer as an interval.Find all real numbers $x$ such that $3x - 7 \le 5x +9$. Give your answer as an interval.Find all real numbers $x$ such that $3x - 7 \le 5x +9$. Give your answer as an interval.Find all real numbers $x$ such that $3x - 7 \le 5x +9$. Give your answer as an interval.Find all real numbers $x$ such that $3x - 7 \le 5x +9$. Give your answer as an interval.Find all real numbers $x$ such that $3x - 7 \le 5x +9$. Give your answer as an interval.Find all real numbers $x$ such that $3x - 7 \le 5x +9$. Give your answer as an interval.Find all real numbers $x$ such that $3x - 7 \le 5x +9$. Give your answer as an interval.

Answer:

The side length is multiplied by [tex]\sqrt{2}[/tex]

Step-by-step explanation:

we know that

The area of the original square is equal to

[tex]A=9^{2}=81\ in^{2}[/tex]

If the area is doubled

then

The area of the larger square is

[tex]A1=(2)81=162\ in^{2}[/tex]

Remember that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

Let

z ----> the scale factor

x ----> the area of the larger square

y ---> the area of the original square

so

[tex]z^{2}=\frac{x}{y}[/tex]

we have

[tex]x=162\ in\^{2}[/tex]

[tex]y=81\ in\^{2}[/tex]

[tex]z^{2}=\frac{162}{81}[/tex]

[tex]z^{2}=2[/tex]

[tex]z=\sqrt{2}[/tex] ------> scale factor

therefore

The side length is multiplied by [tex]\sqrt{2}[/tex]

Answer:

sq root of 2

Step-by-step explanation:

that's how Mr. Burger says it is, lol.

because the area is doubled then both side lengths are multiplied by the sq root of 2.

[tex]\bf \textit{Sum to Product Identities} \\\\ cos(\alpha)+cos(\beta)=2cos\left(\cfrac{\alpha+\beta}{2}\right)cos\left(\cfrac{\alpha-\beta}{2}\right) \\\\\\ cos(\alpha)-cos(\beta)=-2sin\left(\cfrac{\alpha+\beta}{2}\right)sin\left(\cfrac{\alpha-\beta}{2}\right) \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\bf \cfrac{cos(4\theta )+cos(2\theta )}{cos(4\theta )-cos(2\theta )}\implies \cfrac{2cos\left( \frac{4\theta +2\theta }{2} \right)cos\left( \frac{4\theta -2\theta }{2} \right)}{-2sin\left( \frac{4\theta +2\theta }{2} \right)sin\left( \frac{4\theta -2\theta }{2} \right)} \implies \cfrac{cos\left( \frac{6\theta }{2} \right)cos\left( \frac{2\theta }{2} \right)}{-sin\left( \frac{6\theta }{2} \right)sin\left( \frac{2\theta }{2} \right)}[/tex]

[tex]\bf \cfrac{cos(3\theta )cos(\theta )}{-sin(3\theta )sin(\theta )}\implies -\cfrac{cos(3\theta )}{sin(3\theta )}\cdot \cfrac{cos(\theta )}{sin(\theta )}\implies -cot(3\theta )cot(\theta )[/tex]

The given expression is:

(cos 4θ + cos 2θ) / (cos 4θ - cos 2θ)

To simplify this expression, we can use the formula cot A sin C + cos B cos C = cot A sin B. Applying this formula gives us -cot 3θ cot θ as the simplified form of the expression.