A commercial aircraft gets the best fuel efficiency if it operates at a minimum altitude of 29,000 feet and a maximum altitude of 41,000 feet. Model the most fuel-efficient altitudes using a compound inequality.

x ≥ 29,000 and x ≤ 41,000
x ≤ 29,000 and x ≥ 41,000
x ≥ 41,000 and x ≥ 29,000
x ≤ 41,000 and x ≤ 29,000

Makes no sense.

He scored the lowest in History and Science. Compare the numbers to help you prepare the obvious chart.

Sam scored the lowest in Language Arts with 84% and Math with 88%.

To determine this, We need to calculate Sam's percentage scores for each subject:

Based on these calculations, the two subjects where Sam scored the lowest are Language Arts (84%) and Math (88%).

complete question:

Sam recorded the number of points she scored on each weekly test out of the number of points possible for the test.In which two subjects did Sam score the lowest?Choose exactly two answers that are correct. Sam's Test Scores in Math  22/25 ,in Science 19/20 ,in Language Arts 84/100 ,in History 9/10.

A reflection is a transformation where the mirror image of a figure is shown directly opposite its line of reflection.

To find an image that has been reflected across the line y = x, switch the x- and y-coordinates.

Therefore, the rule for reflecting an image across the line y = x can be described as (x, y) → (y, x).

Now, apply rule to coordinates ABC:

A': (2, 3)

B': (1, -4)

C': (-2, -3)

Answer:

got it right on odyssey

A'(2,3)

B'(1,-4)

C'(-2,-3)

Step-by-step explanation:

Answer:

Choice #2

Step-by-step explanation:

Your linear function is in the slope-intercept form of a line, y = mx + b, where m is the value of the slope, and b is the value of the y-intercept.  The number in the m position in your equation is 1/6, and thee number in the b position in your equation is 7.  So the second choice is the one you want.

Answer:

Formula of standard deviation = √Variance

Standard deviation = 1

Step-by-step explanation:

X-bar is the variance

Therefore, the answer would be

√X-bar

√1 = 1

!!

Answer:

C

Step-by-step explanation:

Answer:

[tex] -4 \sqrt{5} [/tex]

Step-by-step explanation:

Quadrant 2 means cosine is negative.

So [tex] \sin(\theta)=\frac{2}{3} =\frac{\text{ opp }}{\text{ hyp }} [/tex]

So the adjacent side is [tex] \sqrt{3^2-2^2}=\sqrt{9-4}=\sqrt{5} [/tex]

So [tex] \cos(\theta)=-\frac{\sqrt{5}}{3} [/tex]

Now to find [tex] \tan(2 \theta) [/tex]

[tex] \tan(2 \theta) =\frac{2\tan(\theta)}{1-\tan^2(\theta)}[/tex]

We will need [tex] \tan(\theta) [/tex] before proceeding.

[tex] \tan(\theta) =\frac{\sin(\theta)}{\cos(\theta)}=\frac{\frac{2}{3}}{\frac{-\sqrt{5}}{3}}=\frac{-2}{\sqrt{5} } [/tex]

Now plug it in and the rest is algebra.

[tex] \tan(2 \theta) =\frac{2\tan(\theta)}{1-\tan^2(\theta)} =\frac{2 (\frac{-2}{\sqrt{5}}}{1-\frac{4}{5}} [/tex]

Now the algebra, the simplifying.... We need to get rid of the compound fraction.  We will multiply top and bottom by [tex] 5 \sqrt{5} [/tex]

This will give us

[tex] \frac{-4(5)}{5 \sqrt{5}-4 \sqrt{5}} [/tex]

[tex] \frac{-20}{\sqrt{5}} [/tex]

Multiply top and bottom by [tex] \sqrt{5} [/tex]

[tex] \frac{-20 \sqrt{5}}{5} [/tex]

The answer reduces to

[tex] -4 \sqrt{5} [/tex]

Final answer:

To find tan2θ when sinθ = 2/3 and θ is in Quadrant II, we use the Pythagorean identity to find cosθ and the double angle identity for tangent. After calculation, tan2θ = -4√5.

Explanation:

If sinθ = 2/3 and θ is located in Quadrant II, we first have to find cosθ and then use the double angle identity for tangent to find tan2θ. Since sinθ is positive in Quadrant II and cosθ must be negative (as the x-values are negative in Quadrant II), we can use the Pythagorean identity sin2θ + cos2θ = 1 to find cosθ. Thus, cosθ = -√(1 - sin2θ) = -√(1 - (2/3)2) = -√(1 - 4/9) = -√(5/9) = -√5/3.

The double angle identity for tangent is tan2θ = 2tanθ / (1 - tan2θ). But first, we find tanθ = sinθ/cosθ = (2/3) / (-√5/3) = -2/√5. Then, tan2θ = 2(-2/√5) / (1 - (-2/√5)2) = -4/√5 / (1 - 4/5) = -4/√5 / (1/5) = -20/√5. Simplifying further, we multiply by √5/√5 to rationalize the denominator, which gives us tan2θ = -20√5/5 = -4√5.

Answer:

[tex]6\ polyphonic\ ringtones[/tex]  and [tex]1\ standard\ ringtone[/tex]

Step-by-step explanation:

Let

x -----> the number of polyphonic ringtones

y ----> the number of standard ringtones

we know that

[tex]x+y=7[/tex]

[tex]x=7-y[/tex] -----> equation A

[tex]3.25x+1.50y=21[/tex] -----> equation B

Solve the system of equations by substitution

Substitute equation A in equation B and solve for y

[tex]3.25(7-y)+1.50y=21[/tex]

[tex]22.75-3.25y+1.50y=21[/tex]

[tex]3.25y-1.50y=22.75-21[/tex]

[tex]1.75y=1.75[/tex]

[tex]y=1\ standard\ ringtones[/tex]

Find the value of x

[tex]x=7-1=6\ polyphonic\ ringtones[/tex]

Answer:

6 polyphonic, 1 standard

Step-by-step explanation:

Answer:

Divide both sides by -4.

Step-by-step explanation:

If you divide both sides by -4, you'll get the answer n=−174.

Please mark brainliest!

Answer:

D

Step-by-step explanation:

-4n = 696

What must be done to each side of the equation to find the value of n?

Divide both sides by -4 to find the value of n

∴ -4n/-4 = 696/-4

n = -174

Answer: [tex]\dfrac{15}{32}[/tex]

Step-by-step explanation:

Given : The number of cherry lollipop = 5

The total number of lollipop = 8

the number of lollipops other than grape =6

The probability of selecting a cherry lollipop is given by :_

[tex]\text{P(Cherry)}=\dfrac{5}{8}[/tex]

The probability of selecting a lollipop other than grape is given by :_

[tex]\text{P(Other than grape)}=\dfrac{6}{8}[/tex]

Since, there is replacement , then the events are independent of each other.

Now, the probability that Julie will select a cherry lollipop and then a lollipop other than grape is given by :-

[tex]\text{P(Cherry and other than grape)}=\dfrac{5}{8}\times\dfrac{6}{8}=\dfrac{15}{32}[/tex]

Hence, the required probability =[tex]\dfrac{15}{32}[/tex]

Answer:

  The series is divergent

Step-by-step explanation:

An infinite geometric series with a common ratio greater than 1 does not converge to a sum. The series is divergent.

Answer:

5.75t=p

Step-by-step explanation:

22p=126.50/22

p=5.75 per hour

5.75t=p

The $5.75 is earned for every hour worked.

Answer:

[tex]y=10(2)^x[/tex]

Step-by-step explanation:

This is an exponential function.  Peter is not simply adding $10 a week to his savings, he's doubling each value each week.  The first case of adding $10 a week is linear.  

The standard form of an exponential equation is

[tex]y=a(b)^x[/tex]

where a is the initial amount and b is the growth or decay factor.  We know a = 10 because we are told he started with $10.  After the first week he would have $20 then because $10 doubled is $20.  That coordinate is (1, 20).  We will use that in place of x and y and solve for b:

[tex]20=10(b)^1[/tex]

b to the first is just b, so what we have essentially is 10b = 20, so b = 2.  The equation then is:

[tex]y=10(2)^x[/tex]

Answer:

x = -1

Step-by-step explanation:

[tex]\sqrt{1-3x}=x+3\\\\1-3x=x^2+6x+9 \qquad\text{square both sides}\\\\x^2+9x+8=0 \qquad\text{put in standard form}\\\\(x+8)(x+1)=0 \qquad\text{factor}\\\\\left \{ {{x=-8} \atop {x=-1}} \right. \qquad\text{values that make the factors zero}[/tex]

Only the solution x = -1 will work for this equation. The other solution is extraneous.

Step-by-step explanation:

y = x^2 - 1  

y = 2x - 2

x^2 - 1 = 2x - 2

x^2 - 2x + 1 = 0

(x - 1)^2 = 0

x = 1

Because x = 1 the answer must be D (1, 0).

Answer:

(1,0)

Step-by-step explanation:

Replace x values and y values with the answer choices.

[tex]y=(1)^2- 1 = 0[/tex]

[tex]y= 2(1)-2=0[/tex]

Since the coordinate pair [tex](1,0)[/tex] it is safe to assume that D will be the correct answer.

Use the graph to confirm that the solution is (1,0)

The blue line intersects at (1,0), so the solution for the system of equations is (1,0)

Answer:

The Answer is:  -1 and 1

Step-by-step explanation:

Answer:

(1,2) and (2,-1)

Step-by-step explanation:

we have

[tex]y< 5-2x[/tex] ----> inequality A

The solution of the inequality A is the shaded area below the dashed line [tex]y=5-2x[/tex]

[tex]x+5y>-7[/tex] ----> inequality B

The solution of the inequality B is the shaded area above the dashed line [tex]x+5y=-7[/tex]

The solution of the system of inequalities is the shaded area between the two dashed lines

If a ordered pair is a solution of the system of inequalities, then the ordered pair must lie on the shaded area

Two points in the solution are

(1,2) and (2,-1)

see the attached figure

Answer:

Step-by-step explanation:

Alright. Looking at the graph, angle CGE is equal to angle FGD.

FGD = 90-73

FGD = 17

Therefore, as angle CGE is equal to angle FGD, angle CGE is equal to 17.

Answer: 17 degrees.

By applying angle relationships and recognizing the equality of angles, we determined that angle CGE measures 17 degrees, as it is equal to angle FGD in the context of the graph.

In geometry, analyzing angles within shapes and figures is fundamental. Here, we have a graph depicting intersecting lines and angles. Let's break down the steps and reasoning for finding the measurement of angle CGE:

1. Angle CGE and Angle FGD:

First, we observe the graph and notice that angle CGE is mentioned to be equal to angle FGD. This equivalence allows us to focus on finding the measurement of angle FGD, which, in turn, will be the measurement of angle CGE.

2. Calculation of Angle FGD:

We know that angle FGD is related to a right angle, as indicated by the angle symbol "90" next to it. To calculate the measurement of angle FGD, we use the fact that the sum of angles around a point is 360 degrees, and the angle opposite to a right angle is complementary, totaling 90 degrees.

So, we calculate angle FGD as follows:

Angle FGD = 90 degrees (right angle) - 73 degrees (given angle)

Angle FGD = 17 degrees

3. Angle CGE:

Since angle CGE is stated to be equal to angle FGD, we determine that angle CGE is also 17 degrees.

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Answer:

Step-by-step explanation:

Substitute g(x) for x in f(x) and evaluate:

  f(g(x)) = f(x^(1/3) -1)

  = ((x^(1/3) -1) +1)^3 -5

  = (x^(1/3))^3 -5

  = x^(3/3) -5

  f(g(x)) = x -5

This is confirmed by a graphing calculator. (See attached.)

If the functions were inverses, the value of f(g(x)) would be x. It is not, so the functions are not inverses.

Answer:

  A)  The population in the year that she was born.

Step-by-step explanation:

The multiplier of an exponential function is the value that function has when the exponent is zero -- the initial value. The initial value of population in this context is the population in the year Adriana was born.

Answer:

$42,890

Step-by-step explanation:

The standard form for an exponential equation is

[tex]y=a(b)^x[/tex]

where a is the initial amount value and b is the growth rate or decay rate and t is the time in years.  Since we are dealing with money amounts AND this is a decay problem, we can rewrite accordingly:

[tex]A(t)=a(1-r)^t[/tex]

where A(t) is the amount after the depreciation occurs, r is the interest rate in decimal form, and t is the time in years.  We know the initial amount (70,000) and the interest rate (.04), but we need to figure out what t is.  If the car was bought in 2006 and we want its value in 2018, a total o 12 years has gone by.  Therefore, our equation becomes:

[tex]A(t)=70,000(1-.04)^{12}[/tex] or, after some simplification:

[tex]A(t)=70,000(.96)^{12}[/tex]

First rais .96 to the 12th power to get

A(t) = 70,000(.6127097573)

and then multiply.

A(t) = $42,890

Answer:

  5 times as large

Step-by-step explanation:

The ratio of the two numbers tells you how many times as large one is as the other:

[tex]\dfrac{5\cdot 10^5}{1\cdot 10^5}=\dfrac{5}{1}\cdot\dfrac{10^5}{10^5}=5[/tex]

Answer: 5 is the correct answer!

Step-by-step explanation:

Answer:

4280 passes were sold

Step-by-step explanation:

The unknown we are looking for the number of passes that were sold.  We don't know how MANY were sold, but we do know that the cost of ONE is 12.50.  We represent the number of passes at that price per pass as

12.50x

We also know that money earned from the sale of this unknown number of passes came to 53,500.  Our equation then becomes

12.50x = 53,500

Solving for x, we divide both sides by 12.50 to get that

x = 4280

Final answer:

To find the number of annual visitor passes sold at Woodland Mound Park, divide the total sales ($53,500) by the price per pass ($12.50), resulting in 4,280 passes sold.

Explanation:

The question asks how many annual visitor passes were sold at Woodland Mound Park last year if each pass costs $12.50 and the total amount raised from pass sales was $53,500. To find the number of passes sold, you'll need to divide the total sales by the price per pass. Here is the step-by-step calculation:

Answer:

Step-by-step explanation:

A.)Priscilla made a mistake when applying the horizontal shift.  That "x+2" indicates a horiz. shift to the LEFT, not to the right.

Answer:

Option A.

Step-by-step explanation:

Priscilla graphed function g(x), a transformation of the quadratic parent function f (x) = [tex]\frac{1}{2}[/tex] f ( x+2 ) - 1

(1) She graphed the vertical compression correctly

(2) Priscilla graphed the vertical shift of (-1) means 1 unit downwards on y-axis correctly.

(3) In the last she made a mistake because for f(x+2) the parent function should have been shifted left on x-axis by two units f (x) ⇒ f[ x- (-2)]

Therefore Option A will be the answer.

[tex]n,n+1[/tex] - two consecutive integers

[tex]n+n+1=9\\2n=8\\n=4\\n+1=5[/tex]

4 and 5

Answer:

c. 68, 112

Step-by-step explanation:

The angle is our unknown, so we will call it x.  If the angle is x, then its supplement is 180 - x (supplementary angles add up to equal 180).  The word "is" means "equals", so putting the equation together looks like this:

180 - x = 2x - 24.  Add x to both sides and at the same time add 24 to both sides (combining like terms, in other words):

204 = 3x so

x = 68

x is the angle measure, so the angle is 68 and its supplement is 180 - 68 = 112

The angle will be 68 and its supplement will be 112.

It is given that supplement of an angle is 24 less than twice the measure of the angle.

We have to find out the measure of the angle and its supplement.

What are the supplementary angles ?

The supplementary angles are the angles whose sum is equal to 180° i.e., sum of angles 150° and 30° equal to 180°.

The angle is unknown. Let's assume angle be x.  

We know that , supplementary angles add up to equal 180.

If the angle is x, then its supplement will be :

180 - x ----------- Equation 1

Also ;

angle's supplement is equal to ;

2 × x - 24 ----------- Equation 2

Keeping both the equations equal ;

180 - x = 2x - 24.  

180 + 24 = 3x

204 = 3x

x = 68

Supplement will be ;  180-x = 180 - 68 = 112

Thus , x is the angle measure, so the angle is 68 and its supplement is 112.

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Answer:  (f·g)(x) = -5x³ - 31x² + 62x + 18

               (f·g)(-1) = -70

(fog)(x) = 25x² - 130x + 155

(fog)(-1) = 310

Step-by-step explanation:

f(x) = x² + 8x + 2          g(x) = -5x + 9

(f·g)(x) = (x² + 8x + 2)(-5x + 9)

          = -5x³ + 9x²

                    - 40x² + 72x

                               - 10x + 18

          = -5x³ - 31x² + 62x + 18

(f·g)(-1)= -5(-1)³ - 31(-1)² + 62(-1) + 18

         =  -5(-1)  - 31(1)    - 62      + 18

         =    5     -   31      - 62      + 18

         =  -70

****************************************************************************************

(fog)(x) = (-5x + 9)² + 8(-5x + 9) + 2

           = 25x² - 90x + 81

                       - 40x + 72

                                +   2

           = 25x² - 130x + 155

(fog)(-1) = 25(-1)² - 130(-1) + 155

            =   25    +  130    + 155

            = 310

It wasn't clear if you wanted multiplication or composition so I solved both.

The composition (f⋅g)(x) is 50, and the product of functions (f.g)(-1) is -20.

To find the composition of the functions f(x) and g(x), denoted as (f⋅g)(x), we first need to determine g(x). Given g(x) = -5 + 9, we simply add these numbers together to get g(x) = 4. With g(x) found, we can now substitute g(x) into f(x) to find the composition. To do this, wherever there is an x in f(x), we replace it with 4.

So, (f⋅g)(x) = f(g(x)) = f(4) = 4^2 + 8(4) + 2 = 16 + 32 + 2 = 50.

Next, to find (f.g)(-1), which represents the product of the two functions evaluated at x = -1, we evaluate both f(-1) and g(-1). We already know that g(x) is constant at 4, so g(-1) = 4. Now we find f(-1):

f(-1) = (-1)^2 + 8(-1) + 2 = 1 - 8 + 2 = -5.

Thus, the product at x = -1 is:

(f.g)(-1) = f(-1) ⋅ g(-1) = (-5) ⋅ 4 = -20.

Answer:

  A) 255,358.46

  E)  273,353.92

Step-by-step explanation:

The formula for future value of principal P at interest rate r per year compounded n times per year for t years is ...

  FV = P(1 +r/n)^(nt)

Filling in the numbers and doing the arithmetic, we have ...

A) FV = $34,500(1 + 0.069)^30 ≈ $255,358.46

__

E) FV = $34,500(1 + 0.069/365)^(365·30) ≈ $273,352.92

Answer:

  5 days

Step-by-step explanation:

Put the given number in the formula and solve for x.

  2065500 = 8500·3^x

  243 = 3^x . . . . . . . . . . . divide by 8500

  log(243) = x·log(3) . . . take logarithms

  log(243)/log(3) = x = 5 . . . . divide by the coefficient of x

After 5 days, the number of bacteria in culture will be 2,065,500.

Answer:

x-3y-7=0

Step-by-step explanation:

Given

m=1/3

The standard form of point slop form is:

y=mx+b

To find the value of b, we will put the point in the standard form

So,

[tex]-2=\frac{1}{3}(1)+b[/tex]

Solving for b[tex]-2=\frac{1}{3}+b\\-2-\frac{1}{3}=b\\\frac{-6-1}{3}=b\\b=\frac{-7}{3}[/tex]

Putting the values of b and m in standard form:

[tex]y=\frac{1}{3}x+\frac{-7}{3}\\y=\frac{1}{3}x-\frac{7}{3}Multiplying\ both\ sides\ by\ 3\\3y=x-7\\-x+3y+7=0\\Can\ also\ be\ written\ as\\x-3y-7=0[/tex]

Answer:

y = 2x + 20

Step-by-step explanation:

2 * x is the number of minutes from the math problems

20 is the number of minutes for the history homework

Answer:

y= 2x=20

Step-by-step explanation: