Answer:
The median is 22.
Step-by-step explanation:
can someone please figure this out for me or at least explain this because im lost here
Let f(x)=3x+2, g(x)=x3−3x2+2x+11, and h(x)=x2−3. Perform the following operations.
a) g(-2)=
b) h(-1)=
c) g(x) - h(x)=__x^3 +__x^2+__x+__
d) -2f(x) * h(x)= __x^3+__x^2+__x+__
e) f(h(x)) = __x^2+__x+__
f) f(g(x)) =__x^3+__x^2+__x+__
Answer:
Step-by-step explanation:
the concepts are confusing of what a function is. f(x) seems mysterious , huh
it's just a way to give a label to some set of terms. Just think of it as a name of a person, but in a generic sense, like hey "guy" or hey "gal" you can address many people that way. f(x) is doing that same thing addressing by a name, a set of math terms.
a)
in a) we are addressing the g(x) function and we are also sending that function the number -2 as an input. so find the g(x) function and put in (-2) everywhere that there is an "x" , so
g(x)=[tex]x^{3}[/tex]-3[tex]x^{2}[/tex]+2x + 11
g(-2) = [tex](-2)^{3}[/tex]-3[tex](-2)^{2}[/tex]+2(-2)+11
g(-2) = -8 -3(4) - 4 +11
g(-2) = -8 -12 -4 + 11
g(-2) = -24 + 11
g(-2) = -13
b)
h(-1) find the h(x) function and input a negative 1 where ever there is an x
h(x) =
h(-1) = [tex](-1)^{2}[/tex] - 3
h(-1) = 1 - 3
h(-1) = -2
c)
for c) just combine like terms of the two given functions
g(x) - h(x) = [tex]x^{3}[/tex]-3[tex]x^{2}[/tex]+2x + 11 - ([tex]x^{2}[/tex] - 3)
g(x) - h(x) = [tex]x^{3}[/tex]-3[tex]x^{2}[/tex]+2x + 11 - [tex]x^{2}[/tex] + 3
g(x) - h(x) = [tex]x^{3}[/tex]-4[tex]x^{2}[/tex]+2x + 14
d)
-2f(x) - h(x) = -2(3x + 2) - ([tex]x^{2}[/tex] - 3)
-2f(x) - h(x) = -6x - 4 - [tex]x^{2}[/tex] + 3
-2f(x) - h(x) = -6x - 1 - [tex]x^{2}[/tex]
-2f(x) - h(x) = - [tex]x^{2}[/tex] - 6x - 1
e)
f(h(x)) this gets a bit more confusing b/c it's a composition of functions, that's just a fancy way of saying the functions are nested. one inside the other.
f(x) = 3x + 2
h(x) = [tex]x^{2}[/tex] - 3
plug h(x) in to f(x) where ever there is an x in f(x) , luckily there is only one x in f(x) :)
f(h(x)) = 3([tex]x^{2}[/tex] - 3) + 2
f(h(x)) = 3[tex]x^{2}[/tex] - 9 + 2
f(h(x)) = 3[tex]x^{2}[/tex] - 7
f(h(x)) = 3[tex]x^{2}[/tex] + 0x + (-7)
f)
f(x) = 3x + 2
g(x) = [tex]x^{3}[/tex]-3[tex]x^{2}[/tex]+2x + 11
f(g(x)) = 3([tex]x^{3}[/tex]-3[tex]x^{2}[/tex]+2x + 11) + 2
f(g(x)) = 3[tex]x^{3}[/tex]-9[tex]x^{2}[/tex]+6x + 33 + 2
f(g(x)) = 3[tex]x^{3}[/tex]-9[tex]x^{2}[/tex]+6x + 35
Hope that helps :)
Suppose that prior to conducting a coin-flipping experiment, we suspect that the coin is fair. How many times would we have to flip the coin in order to obtain a 96.5% confidence interval of width of at most .12 for the probability of flipping a head
Answer:
We have to flip the coin 78 times.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
We suspect that the coin is fair.
This means that [tex]\pi = 0.5[/tex]
96.5% confidence level
So [tex]\alpha = 0.035[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.035}{2} = 0.9825[/tex], so [tex]Z = 2.108[/tex].
How many times would we have to flip the coin in order to obtain a 96.5% confidence interval of width of at most .12 for the probability of flipping a head?
n times, and n is found when M = 0.12. So
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.12 = 2.108\sqrt{\frac{0.5*0.5}{n}}[/tex]
[tex]0.12\sqrt{n} = 2.108*0.5[/tex]
[tex]\sqrt{n} = \frac{2.108*0.5}{0.12}[/tex]
[tex](\sqrt{n})^2 = (\frac{2.108*0.5}{0.12})^2[/tex]
[tex]n = 77.1[/tex]
Rounding up
We have to flip the coin 78 times.
A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation. Using this equation, find out what price the widgets should be sold for, to the nearest cent, for the company to make the maximum profit.
y=-15x^2+801x-5900
Answer:
In order to maximize profit, each widget should sell for $26.70.
Step-by-step explanation:
The total amount of profit y given by the selling price of each widget x is given by:
[tex]y=-15x^2+801x-5900[/tex]
And we want to determine the price of each widget such that is yields the maximum profit.
Since the equation is a quadratic, the maximum profit will occur at the vertex of our parabola.
The vertex of a quadratic is given by:
[tex]\displaystyle \left(-\frac{b}{2a},f\left(-\frac{b}{2a}\right)\right)[/tex]
So, let's find the vertex. In our equation, a = -15, b = 801, and c = -5900.
Therefore, the price that maximizes profit is:
[tex]\displaystyle x=-\frac{801}{2(-15)}=\$26.70[/tex]
Therefore, in order to maximize profit, each widget should sell for $26.70.
Notes:
Then substituting this back into the equation, the maximum profit is:
[tex]y_{\text{max}}=-15(26.7)^2+801(26.7)-5900=\$ 4793.35[/tex]
5. Simplify
(7x2+ 8) - (x2 - 2)
Answer:
[tex](7 \times 2 + 8) - ( {x}^{2} - 2) \\ (14 + 8) - ( {x}^{2} - 2) \\ 14 + 8 - {x}^{2} + 2 \\ 22 + {x}^{2} + 2 \\ 24 + {x}^{2} [/tex]
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
Plz guys help me plz
i hope this helps- im not sure if its correct or not
Which expression is equivalent to
Answer:
The first one.
Step-by-step explanation:
You are ordering a cake for your brother's birthday. You must choose between vanilla, chocolate or marble cake. You must choose between
buttercream or chocolate frosting. Finally you must choose between a cake with a 4-inch radius, 6-inch radius, 9-inch radius, or 12-inch radius. How
many difference cake options are there?
Answer:
24 different options
Step-by-step explanation:
3 cake type options
2 frosting options
4 radius sizes
3 * 2 * 4 = 24 different options
Samuel buys a two-quart bottle of juice for $12.16. What is the unit rate of the cost of the juice per fluid ounce? \text{1 gallon}= 1 gallon= \,\,\text{4 quarts} 4 quarts \text{1 quart}= 1 quart= \,\,\text{2 pints} 2 pints \text{1 pint}= 1 pint= \,\,\text{2 cups} 2 cups \text{1 cup}= 1 cup= \,\,\text{8 fluid ounces} 8 fluid ounces Before you try that problem, answer the question below. How many fluid ounces of juice did Samuel buy?
5. Kurt has a rectangular garden in his backyard with an area of 40 square feet. He wants to
increase the size of the garden by doubling each dimension. What will the area of the garden be
after he doubles the length and width?
a. 180 square feet
b. 160 square feet
c. 120 square feet
d. 80 square feet
The area of the garden be after he doubles the length and width is 160 square feet.
Given that,
Kurt has a rectangular garden in his backyard with an area of 40 square feet. He wants to increase the size of the garden by doubling each dimension.Based on the above information, the calculation is as follows:
We know that
Area = (length) (width)
Now if the area is doubled
So,
= (2) (length) (2) (width)
= 4(length) (width)
= 4 (40)
= 160
Therefore, we can conclude that option b is correct.
Learn more: brainly.com/question/24169758
7. Solve the story problem.
Bailey has collected 9 shells from the
Atlantic Ocean and 3 times as many
shells from the Gulf of Mexico. How
many shells does she have altogether?
shells
She has 36 shells
9+(9*3)
9+27
=36
Please mark as brainliest. :)
What is the area of the hexagon below? 6CM
X+4y<4 linear inequalities
Answer:
See Explanation
Step-by-step explanation:
Given
[tex]x + 4y < 4[/tex]
The question is incomplete, as what is to be done is not stated.
However, possible sub-questions could be to determine the slope and the y-intercept for the boundary line.
To calculate slope, we have:
[tex]x + 4y < 4[/tex]
Solve for 4y
[tex]4y < - x + 4[/tex]
Solve for y
[tex]y < -\frac{x}{4} + \frac{4}{4}[/tex]
[tex]y < -\frac{1}{4}x + 1[/tex]
A linear inequality is represented as:
[tex]y <mx + b[/tex]
Where [tex]m =slope[/tex] and [tex]b = y\ intercept[/tex]
So:
By comparison:
[tex]mx = -\frac{1}{4}x[/tex]
[tex]m = -\frac{1}{4}[/tex]
and
[tex]b = 1[/tex]
So:
[tex]Slope = -\frac{1}{4}[/tex]
[tex]y\ intercept = 1[/tex]
Also, see attachment for graph
What is the constant rate of change shown in the table?
2
4
6
8
Answer:
2
Step-by-step explanation:
Since with every 10 seconds, the distance increase by 20 meters
hence, 20/10 = 2
The figure shows a 1300-yard-long sand beach and an oil platform in the ocean. The angle made with the platform from one end of the beach is 84 degrees and from the other end is 76 degrees . Find the distance of the oil platform, to the nearest tenth of a yard, from each end of the beach.
Answer:
y = 3,254.3 yd
Step-by-step explanation:
Lets denote with 'x' and 'y' the distances we need to find.
Using the Law of Sines we can write:
x/(sin 76) = 1175/(sin(180 - (83 + 76))
x/(sin 76) = 1175/(sin 21)
x = 3,181.4 yd
y/(sin 83) = 1175/(sin(180 - (83 + 76))
y/(sin 83) = 1175/(sin 21)
y = 3,254.3 yd
The platform is 3,181.4 yards far from one end of the beach and 3,254.3 yd far from the other.
The distance of the oil platform is 3708.82 yards, from each end of the beach.
Given that,
The figure shows a 1300-yard-long sand beach and an oil platform in the ocean.
The angle made with the platform from one end of the beach is 84 degrees and from the other end is 76 degrees.
We have to determine,
The distance of the oil platform, to the nearest tenth of a yard, from each end of the beach.
According to the question,
Let x be the distance of the sand beach,
And y be the distance of oil platform.
The distance of the oil platform of a yard, from each end of the beach, is determined by using the sin rule,
[tex]\rm \dfrac{x}{sina} = \dfrac{y}{sinb}\\\\ \dfrac{x}{sin76} = \dfrac{1300}{sin(180-(84+76))}\\\\ \dfrac{x}{0.97} = \dfrac{1300}{sin(180-160)}\\\\\dfrac{x}{0.97} = \dfrac{1300}{sin20}\\\\\dfrac{x}{0.97} = \dfrac{1300}{0.34}\\\\ \dfrac{x}{0.97}= 3823.52 \\\\ x = 3823.52 \times 0.97\\\\x = 3708.82[/tex]
Hence, The distance of the oil platform is 3708.82 yards, from each end of the beach.
For more details refer to the link given below.
https://brainly.com/question/18188038
What is the total weight of Dorothys apples
Weight: Number of apples:
1/4. 3
3/8. 6
1/2. 5
5/8. 4
3/4. 2
Work does not have to be included if you decide to do it! I’ll give anyone who does it a lot of points!
1. In the diagram below, the length of the legs AC and BC of right triangle ABC are 6 cm and 8 cm,
respectively. Altitude CD is drawn to the hypotenuse of AABC. What is the length of AD to the nearest tenth
of a centimeter?
Answer:
Note that ABC is a 6 - 8 -10 right triangle with AB = 10
Also note that triangle ADC is similar to triangle ACB
Therefore
AD/ AC = AC / AB so
AD / 6 = 6/ 10 cross-multiply
10*AD = 6 * 6
810*AD = 36
AD = 36 / 10 = 3.6 = x
I hope this helps a little bit.
Vhat is the domain of the function y = In {-x+3/2}
Answer:
(-∞,3/2),{xIx<3/2}
Step-by-step explanation:
Using inverse function concepts, the correct option is:
B. Domain: x < -2 Range: y> 3
What is domain?The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in
here, we have,
we know that,
The domain of a function is the set that contains all possible input values.
The range of a function is the set that contains all possible output values.
In the inverse function, input and output are exchanged, thus, domain and range are also exchanged.
For the original function, the domain is x > 3 and the range is y < -2.
Thus, for the inverse function, the domain is x < -2 and the range is y > 3, which means that option B is correct.
learn more on domain at :
brainly.com/question/24603090
#SPJ7
Complete question:
The domain of a function h(x) is x > 3, and the range is y2 -2. What are the domain and range of its inverse function, h-1(x)?
A. Domain: x>3 Range: y2 -2
B. Domain: x2 -2 Range: y> 3
C. Domain: x>-2 Range: y> 3
D. Domain: x2 3 Range: y> -2
The International Air Transport Association surveys business travelers to develop quality ratings for transatlantic gateway airports. The maximum possible rating is 10. Suppose a simple random sample of business travelers is selected and each traveler is asked to provide a rating for the Miami International Airport. The ratings obtained from the sample of business travelers follow. 6 10 2 6 3 3 3 6 6 6 6 5 8 9 10 10 7 9 3 6 5 10 9 9 10 3 8 6 6 3 3 6 6 5 4 10 9 3 5 7 10 6 3 8 6 8 3 3 5 5 Develop a confidence interval estimate of the population mean rating for Miami. Round your answers to two decimal places.
Answer:
(5.4582 ; 6.8618)
Step-by-step explanation:
Given the data:
6 10 2 6 3 3 3 6 6 6 6 5 8 9 10 10 7 9 3 6 5 10 9 9 10 3 8 6 6 3 3 6 6 5 4 10 9 3 5 7 10 6 3 8 6 8 3 3 5 5
Sample mean, xbar = Σx / n
n = sample size = 50
ΣX = 308
xbar = 308 / 50 = 6.16
Using a Calculator :
The sample standard deviation, s = 2.469
Confidence interval = xbar ± margin of error
Margin of Error = Tcritical * s/sqrt(n)
Tcritical at 95% ; df = 50 - 1 = 49
Tcritical = 2.010
Hence,
Margin of Error= 2.010 * (2.469/sqrt(50)) = 0.7018
Lower boundary : (6.16 - 0.7018) = 5.4582
Upper boundary : (6.16 + 0.7018) = 6.8618
(5.4582 ; 6.8618)
Which angles are vertical angles and, therefore, congruent?
ILL MARK BRAINIEST
Answer: <A and <F
Step-by-step explanation: Verticle angles are angles that are on opposite sides of each other therefore having the same angle.
tomen puntos y doy corona al primero que comente hola
Answer:
hewo nice to meet ya
Step-by-step explanation:
hi hello
Answer:
Hola!
*Spanish*
Gracias por los puntos!
What is the length of the hypotenuse of the triangle 26 34 68 74
Answer:Answer: 26 ft.
Step-by-step explanation:
Please I’ll give BRAINLY just help
Answer:
24 square units is the answer
Answer:
the area is 32.5
Step-by-step explanation:
The product is 2 2/3 + 4 4/5
Answer:
[tex]7\frac{7}{15}[/tex]
Step-by-step explanation:
Mark as Brainllest plz
Please help immediately!!
Answer:
x=7° y=4°
Step-by-step explanation:
7x+131=180
7x=180-131=49
x=49/7=7°
11x+y+99=180
77+y+99=180
y=180-99-77
y=4°
Does this picture show the diameter or radius of a circle?
Answer:
the diameter is 18 inches
What is the absolute value of point J on the number line?
_------_-----_-----_-----_-----_-----_-----_-----_-----_-----_-----_----J
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
A -6
B 0
C 3
D 6
Answer:
D (6)
Step-by-step explanation:
you must place a number on a number line starting from the smallest (negative number ) to the bigger number (positive number ).
the number that is represented by J is 6
(07.01, 07.02 LC) Factor the greatest common factor: −5k2 + 20k − 30.
−1(5k2 − 20k + 30)
−5(k2 − 4k + 6)
−5k(k2 − 4k + 6)
−5(k2 + 4k − 6)
Answer:
-5(k2-4k+6)
Step-by-step explanation:
I think is -5(k2-4k+6)
I think that it's 5(k2 − 4k + 6)
How do I do this and what is the answer please help??
Answer:
log3x
Step-by-step explanation:
i think it would be y=log3x
Yasmin designed a square table using a scale drawing. The actual length of each side was 4 feet and the scale facto
was 1 inch : 2 feet. Choose the figure with the correct side length if Yasmin changed the scale factor to 1 inch: 3 2/3 feet.
A. X = 2ft
B. X = 6 2/3
C. X = 7 1/3
D. X = 14 2/3
Note: please explain how to get the answer because I kept getting D as my answer. Is there a mistake I made? And please do not answer with links.
Answer:
It is x = 7 1/3
Step-by-step explanation:
2 feet is being used in the scale factor and 2 x 3 2/3 is 7 1/3.
Please mark as brainliest
Answer:
The scale factor is a measure for similar figures, who look the same but have different scales or measures. Suppose, two circle looks similar but they could have varying radii. The scale factor states the scale by which a figure is bigger or smaller than the original figure.
we have:
[tex]scale \: factor = \frac{smaller \: length}{larger \: length} [/tex]
let the length be x.
we have
[tex]2 = \frac{x}{3 \frac{2}{3} } [/tex]
[tex]x = 2 \times \frac{11}{3} [/tex]
[tex]x = 7 \frac{1}{3} [/tex]
so.
C .[tex]x = 7 \frac{1}{3} [/tex] is your answer
In the figure below, what is the value of xº?
A. 430
B. 620
C. 180°
D. 75°
Answer:
b is the answer
Step-by-step explanation:
a triangle equals up to 180 degrees and 75+43+62 equals 180