Answers
Answer:
11
Step-by-step explanation:
The fraction of students expected to get an A is 5/15 or 1/3
Multiply 1/3 by the number of students
1/3 * 32 = 10.666666
Rounding to the nearest number
11 students
Related Questions
A hiker leaves camp and walks 6 miles east. Then he walks 18 miles south. How far from camp is the hiker? Distance in miles:
Answers
Answer:
18+6=24
Therefore, hiker is 24 miles far away from the camp
Robyn saves up $204 and spends $32.50 on books. She wants to purchase more books from a sale where they cost $8.15 each. Which answer gives the best estimate for the number of books Robyn can buy?
Answers
Answer: 21 books
Step-by-step explanation:
I am estimating $32.50 to $33.
Remaining amount= 204 - 33 = $171
$8.15 = $8
$171 ÷ $8 = 21.375
Estimated answer = 21 books.
By reading the question it feels like there are options to choose from for the final answer. If it is, then choose the one which seems as close as possible to what I have got above.
Hope this helps :)
please help ASAP: Factorise the following:
Answers
Answer:
hope u will understand it....
Answer:
Hello!
___________________
A)Factor x^2 - 12x + 32 using the AC method. ( x - 8 ) ( x - 4)
B) Factor x^2 - 14x + 48 using the AC method. ( x - 8) ( x - 6)
C) Factor x^2 - 3x + 2 using the AC method. ( x - 2) ( x - 1)
Step-by-step explanation: Always factor by x^2 while using the AC method.
Hope this helped you! :D
Ray and Kelsey have summer internships at an engineering firm. As part of their internship, they get to assist in the planning of a brand new roller coaster. For this assignment, you help Ray and Kelsey as they tackle the math behind some simple curves in the coaster's track.
Part A
The first part of Ray and Kelsey's roller coaster is a curved pattern that can be represented by a polynomial function.
Ray and Kelsey are working to graph a third-degree polynomial function that represents the first pattern in the coaster plan. Ray says the third-degree polynomial has 4 intercepts. Kelsey argues the function can have as many as 3 zeros only. Is there a way for the both of them to be correct? Explain your answer.
Kelsey has a list of possible functions. Pick one of the g(x) functions below and then describe to Kelsey the key features of g(x), including the end behavior, y-intercept, and zeros.
g(x) = x3 − x2 − 4x + 4
g(x) = x3 + 2x2 − 9x − 18
g(x) = x3 − 3x2 − 4x + 12
g(x) = x3 + 2x2 − 25x − 50
g(x) = 2x3 + 14x2 − 2x − 14
Create a graph of the polynomial function you selected from Question 2.
Part B
The second part of the new coaster is a parabola.
Ray needs help creating the second part of the coaster. Create a unique parabola in the pattern f(x) = ax2 + bx + c. Describe the direction of the parabola and determine the y-intercept and zeros.
The safety inspector notes that Ray also needs to plan for a vertical ladder through the center of the coaster's parabolic shape for access to the coaster to perform safety repairs. Find the vertex and the equation for the axis of symmetry of the parabola, showing your work, so Ray can include it in his coaster plan.
Create a graph of the polynomial function you created in Question 4.
Part C
Now that the curve pieces are determined, use those pieces as sections of a complete coaster. By hand or by using a drawing program, sketch a design of Ray and Kelsey's coaster that includes the shape of the g(x) and f(x) functions that you chose in the Parts A and B. You do not have to include the coordinate plane. You may arrange the functions in any order you choose, but label each section of the graph with the corresponding function for your instructor to view.
Part D
Create an ad campaign to promote Ray and Kelsey's roller coaster. It can be a 15-second advertisement for television or radio, an interview for a magazine or news report, or a song, poem, or slideshow presentation for a company. These are just examples; you are not limited to how you prepare your advertisement, so be creative. Make sure to include a script of what each of you will say if you are preparing an interview or a report. The purpose of this ad is to get everyone excited about the roller coaster.
Answers
Step-by-step explanation:
Part A
A 3rd degree polynomial can have no more than 3 x-intercepts or zeros. Kelsey is correct. However, Ray stated it had 4 intercepts which can include 3 x-intercept and 1 y-intercept.
Graph the function g(x) = x3 − x2 − 4x + 4. See attached picture.
It has x-intercepts at (-2,0), (1,0) and (2,0). The y-intercept is (0,4). As x-> -∞ then y -> -∞. As x->∞, y->∞.
Part B
Use the quadratic function f(x) = -x^2 - 6x. The parabola faces downward with y -intercept (-3,9) and zeros (-6,0) and (0,0). See the attached graph.
The axis of symmetry will serve as a ladder through the coaster at x = -3.
Part C and D will use the math above to create the coaster and ad campaign.
You are given a choice of taking the simple interest on $100,000 invested for 2 years at a rate of 3% or the interest on $100,000 invested for 2 years at an interest rate of 3% compounded quarterly
Which investment as the greater amount of interest? Give the difference between the amounts of interest earned by the two investments
the investment with simple? or compound?
interest earns $___ more in interest.
(Round to the nearest cant as needed.)
Answers
Answer:
Step-by-step explanation:
the simple interest formula= principal* interest rate*time
simple interest : 100000*%2*2 years
simple interest= 4000 dollars
compound quarterly : A=principal(1+r/4)^t
since it is quarterly and have 4 quarters in a year, and 8 in two years.
compound quarterly: 100000(1+0.03/4)^8=106159.88
it is better to invest with compound interest because it add 6159 dollars in two years to the investment of 100000 dollars.
the difference between the interest: 6159.88-4000=2159.88
The equations of four lines are given. Identfy which lines are parallel. Line 1: y = -9x + 6 Line 2: x + (1/3)y = -6 Line 3: y = -3x - 8 Line 4: y + 7 = (-1/9)(x + 4)
Answers
Answer:
line 2 and line 3
Step-by-step explanation:
line1=y=-9x+6. gradient 1= -9
line2=x+⅓y=-6
⅓y=-6-x. gradient2= -3
y=-18-3x
line3=y=-3x-8. gradient3= -3
line4=y+7=-1/9x-4/9
y=-1/9x-4/9-7. gradient4= -1/9
y=-1/9x-7⁴/9
parallel lines have the same gradient
please help me out with these questions. It's trigonometry
Answers
Step-by-step explanation:
LOOK AT THE PICTURE
In ΔABC:
[tex]\sin\alpha=\dfrac{x}{y+p}\\\\\cos\alpha=\dfrac{q}{y+p}\\\\\tan\alpha=\dfrac{x}{q}[/tex]
In ΔADC
[tex]\sin\alpha=\dfrac{y}{x}\\\\\cos\alpha=\dfrac{z}{x}\\\\\tan\alpha=\dfrac{y}{z}[/tex]
In ΔBCD
[tex]\sin\alpha=\dfrac{z}{q}\\\\\cos\alpha=\dfrac{p}{q}\\\\\tan\alpha=\dfrac{z}{p}[/tex]
A student wants to estimate the mean score of all college students for a particular exam. First use the range rule of thumb to make a rough estimate of the standard deviation of those scores. Possible scores range from 300 to 2200. Use technology and the estimated standard deviation to determine the sample size corresponding to a 90% confidence level and a margin of error of 100 points. What isn't quite right with this exercise? The range. rule of thumb.estimate for the standard deviation. nothing.
Answers
Answer:
See explanation below
Step-by-step explanation:
range = 2200 - 300 = 1900
To find standard deviation, we have:
standard deviation = range/4 = [tex] \frac{1900}{4} [/tex] = 475
The range rule of thumb estimate for the standard deviation is 475
Given:
Standard deviation,[tex] \sigma[/tex] = 475
Margin of Error, ME = 100
[tex] \alpha [/tex] = 1 - 0.90 = 0.10
Za/2 = Z0.05 = 1.64
Find sample size, n:
n ≥ [tex] [Z_\alpha_/_2 * (\frac{\sigma}{ME})]^2 [/tex]
n ≥ [tex][1.64 * (\frac{475}{100})]^2[/tex]
n ≥ 60.68
≈ 61
Minimun sample size,n = 61
solve the following: x+5=11 x-6=8 3+x=7 12=x+5
Answers
Answer:
1) x = 6
2) x = 14
3) x = 4
4) x = 7
Step-by-step explanation:
1) x+5=11
x = 11-5
x =6
2) x-6=8
x = 8+6
x = 14
3) 3+x=7
x = 7-3
x = 4
4) 12=x+5
12-5 = x
7 = x
Write an equation that could be used to find the value of e.
Answers
Answer:
Last option is the correct answer.
Step-by-step explanation:
By sine rule..
[tex] \huge \frac{ \sin \: 45 \degree}{22} = \frac{ \sin \: 63 \degree}{e} \\ [/tex]
Ronnie can paint 8 rocks in 5 minutes. How long will it take him to paint 54 rocks
Answers
54 rocks / 8 rocks = 6.75
6.75 x 5 minutes = 33.75 minutes
Answer:
33 minutes and 45 seconds.
Step-by-step explanation:
We can easily set up a proportion...
He can paint 8 rocks in 5 minutes. He can paint 54 rocks in x minutes.
[tex]\frac{8}{5} =\frac{54}{x}[/tex]
8 * x = 54 * 5
8x = 270
4x = 135
x = 33.75
So, it will take Ronnie 33 minutes and 45 seconds to paint 54 rocks.
Hope this helps!
The length of Sally’s garden is 4 meters greater than 3 times the width. The perimeter of her garden is 72 meters. What are the dimensions of Sally’s garden
Answers
Answer:
Width=8
Length=28
Step-by-step explanation:
Width=x
Length=3x+4
perimeter is 2 lengths and 2 widths
2x + 2(3x+4)=72
2x+6x+8=72
8x=72-8
8x=64
x=8, so the width is 8
the length Is 3(8)+4 = 28
I need to find the derivative. I’m not very good at this so I am answer asap would be sosososo helpful
Answers
Answer:
See below.
Step-by-step explanation:
First, notice that this is a composition of functions. For instance, let's let [tex]f(x)=\sqrt{x}[/tex] and [tex]g(x)=7x^2+4x+1[/tex]. Then, the given equation is essentially [tex]f(g(x))=\sqrt{7x^2+4x+1}[/tex]. Thus, we can use the chain rule.
Recall the chain rule: [tex]\frac{d}{dx}[f(g(x))]=f'(g(x))\cdot g'(x)[/tex]. So, let's find the derivative of each function:
[tex]f(x)=\sqrt{x}=x^\frac{1}{2}[/tex]
We can use the Power Rule here:
[tex]f'(x)=(x^\frac{1}{2})'=\frac{1}{2}(x^{-\frac{1}{2} })=\frac{1}{2\sqrt{x}}[/tex]
Now:
[tex]g(x)=7x^2+4x+1[/tex]
Again, use the Power Rule and Sum Rule
[tex]g'(x)=(7x^2+4x+1)'=(7x^2)'+(4x)'+(1)'=14x+4[/tex]
Now, we can put them together:
[tex]y'=f'(g(x))\cdot g'(x)=\frac{1}{2\sqrt{g(x)}} \cdot (14x+4)[/tex]
[tex]y'=\frac{14x+4}{2\sqrt{7x^2+4x+1} } =\frac{7x+2}{\sqrt{7x^2+4x+1} }[/tex]
(4x + 9)/2 1/3= 3x/0.5
Answers
Answer:
X = 0.9
Step-by-step explanation:
step-by-step.
4x+9
2
1
3
=
3x
0.5
Step 1: Simplify both sides of the equation.
12
7
x+
27
7
=6x
Step 2: Subtract 6x from both sides.
12
7
x+
27
7
−6x=6x−6x
−4.285714x+
27
7
=0
Step 3: Subtract 27/7 from both sides.
−4.285714x+
27
7
−
27
7
=0−
27
7
−4.285714x=
−27
7
Step 4: Divide both sides by -4.285714.
−4.285714x
−4.285714
=
−27
7
−4.285714
x=0.9
A student spends no more than 2 hours on his math and English homework. If math takes about twice as long as English, what is the maximum time that the student can spend on English?
Answers
Answer: I'm pretty sure it's 40 minutes
Step-by-step explanation:
2 hours is 120 minutes and if one subject takes double the time of the other than you basically just have to divide 120 by three. I hope you get what I'm saying cause I'm bad at explaining.
Answer:
40 minutes (or 2/3 hours.)
Step-by-step explanation:
Let the no. of hours the student spend on English be t.
Since math takes twice as long as English, the no. of hours the student takes on math will be 2t.
With the information, we can write this equation:
t + 2t ≤ 2
(≤ symbol is used because the maximum time spent is 2 hours, meaning the student can spend any no. of hours between 0 and 2, including 2 hours exactly.)
Solve the equation like usual (you can take the ≤ sign like =)
t + 2t ≤ 2
3t ≤ 2
t ≤ 2/3 (or 0.666666... hours)
So the maximum amount of time is 2/3 hours.
Multiply 2/3 by 60 to get the time in minutes
2/3 x 60
= 40minutes
So the answer is 40 minutes or 2/3 hours.
If f(x)=-5squared -4 and g(x) = -3x-2find (f+g)(x)
Answers
Answer:
-3x + 19
Step-by-step explanation:
f(x) = -5² - 4
f(x) = 25 - 4
f(x) = 21
(f+g)(x) = f(x) + g(x)
21 + -3x - 2
-3x + 19
Please please please someone help me
Answers
Determine if the coordinate (6, 8) lies on the circle x^2 + y^2 = 100.
Answers
Answer:
x² + y² = 100
6² + 8² = 100
36 + 64 = 100
100 = 100
Because this is a true statement, the answer is yes, it does lie on the circle.
In 2008 a newspaper sold 120 thousand papers, and had 60 thousands people reading online. Their online readership has been increasing by 8 thousand people each year, while their physical paper sales have decreased by 6 thousand papers a year. In what year does online readership exceed physical sales?
Answers
Answer:
t = 5 years
online readership will exceed physical sales in 5 years
Step-by-step explanation:
The number of physical readership can be represented by the equation;
P(t) = 120 - 6t
The number of Online readership can be represented by the equation;
K(t) = 60 + 8t
For online readership to exceed physical sales
K(t) > P(t)
60 + 8t > 120 - 6t
Collecting the like terms;
8t+6t > 120-60
14t>60
t > 60/14
t > 4.29
To the nearest year greater than 4.29.
t = 5 years
online readership will exceed physical sales in 5 years
what are the values of a and b?
Answers
I hope this helps you
Step-by-step explanation:
By using cosine rules:
6/sin45° = b/sin90°
b = 6× sin45°/sin90°
b = 9.124(3d.p)
Also,
using Pythagoras theorm of right-triangle
b² = 6² + a²
9.124² = 6² + a²
83.247376 = 36 + a²
83.247376-36 = a²
47.247376 = a²
√47.247376 = a
6.874 = a
T_T I need big help
Answers
Answer:
D. The volume is the product of the area of the base, (2x - 1)(x - 3), and the height x + 4.
Step-by-step explanation:
Volume of a Rectangular Block: V = lwh
Since we are given variables l, w, and h, we simply plug them in:
V = (2x - 1)(x -3)(x + 4)
We can see that we would need to multiply all 3 to find our volume. Therefore, our answer is D.
MATH HELP ASAP PLSSSS
Answers
Answer:
(30,0)
Step-by-step explanation:
y=0
-2/5 *x +12=0
2x/5=12
2x=12*5
2x=60
x=60/2
x=30
Hey there! :)
Answer:
(30, 0).
Step-by-step explanation:
Solve for the x-intercept, or zero of the equation by setting the equation equal to 0:
y = -2/5x + 12 becomes:
0 = -2/5x + 12
Subtract both sides by 12:
-12 = -2/5x
Divide both sides by -2/5:
-12 (-5/2) = -2/5x (-5/2)
30 = x.
Therefore, the x-intercept is at (30, 0).
It takes me 10 minutes to swim 2 laps. How long will it take
me to swim 5 laps?
Answers
Answer:
25 minutes
Step-by-step explanation:
10 ÷ 2 = 5
1 lap = 5 minutes
5/1 × 5 = 25
25 minutes
Hope this helped! :)
Answer:
25 minutes
Step-by-step explanation:
Let's set up a proportion using the following setup:
minutes/laps=minutes/laps
It takes 10 minutes to swim 2 laps.
10 minutes / 2 laps = minutes/laps
We don't know how long it will take to swim 5 laps. Therefore, we can say it takes x minutes to swim 5 laps.
10 minutes/ 2 laps= x minutes / 5 laps
10/2= x/5
We want to find out what x is. Therefore, we need to get x by itself.
x is being divided by 5. The inverse of division is multiplication. Multiply both sides by 5.
5*(10/2)=(x/5)*5
5*10/2=x
5*5=x
25=x
It takes 25 minutes to swim 5 laps.
simplify -13 + 25 - 36 + -2
Answers
Answer:
-26
Step-by-step explanation:
-13 + 25 - 36 + -2
12 - 36 - 2
-24 - 2
-26
Answer:
-13 + 25 - 36 + -2
12 - 36 + -2
12 - 38
-26
Please answer this - i'm so desperate!
Answers
What do I do next please help
Answers
Answer:
13
Step-by-step explanation:
Since a point on the line is (0, 13) we know that the y-intercept is 13. The answer is already written in slope-intercept form so the answer is 13.
Answer:
13
Step-by-step explanation:
Let the missing value be c.
y = -3x + c
Put x as 0, and y as 13.
13 = -3(0) + c
13 = 0 + c
13 = c
what is the domain represented by the graph
Answers
Answer:
All real numbers.
Step-by-step explanation:
Since the graph is a linear function, and the line doesn't have any holes or asymptotes, the graph can input any x-value and output any y-value. Therefore, our domain is all real numbers (any x-value can work).
Answer: All real numbers
Step-by-step explanation:
It is a infinite line, therefore all x values and all y values can be put in and will read a value :)
The radius of the water well is 9 inches. Find the area of the water well
Answers
Answer:
A=254.34
Step-by-step explanation:
1. A=πr²
2. A=π(9)²
3. A=π(81)
4. A=3.14(81)
5. A=254.34
Answer:
a=254.34 in^2
Step-by-step explanation:
We need to figure out the are of the water well which is a circle with a radius of 9.
This can be represented by the equation
[tex]a=\pi (9)^2[/tex]
Now just simplify.
[tex]a=\pi (81)[/tex]
a=254.34
Which of the following expressions is a factor of the polynomial x 2 +3/2x-1
Answers
Answer:
[tex]\large \boxed{\sf \ \ \ (x+2)(x-\dfrac{1}{2}) \ \ \ }[/tex]
Step-by-step explanation:
Hello,
let's solve
[tex]x^2+\dfrac{3}{2}x-1=0\\\\<=> 2x^2+3x-2=0 \ \text{multiply by 2}\\\\\\[/tex]
[tex]\Delta=b^2-4ac=9+4*2*2=9+16=25[/tex]
There are two solutions
[tex]x_1=\dfrac{-3-\sqrt{25}}{4}\\\\x_1=\dfrac{-3-5}{4}\\\\x_1=\dfrac{-8}{4}\\\\\boxed{x_1=-2}[/tex]
And
[tex]x_2=\dfrac{-3+\sqrt{25}}{4}\\\\x_2=\dfrac{-3+5}{4}\\\\x_2=\dfrac{2}{4}\\\\\boxed{x_2=\dfrac{1}{2}}[/tex]
So we can write
[tex]x^2+\dfrac{3}{2}x-1\\\\=(x-x_1)(x-x_2)\\\\=(x+2)(x-\dfrac{1}{2})[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Which of the following is the equation of a line in slope-intercept form for a
line with slope = 5 and y-intercept at (0, -3)?
O A. y = 5x - 3
O B. y = 5x + 3
O C. y=-3x + 5
D. x = 3y-5
Answers
Answer:
The answer is option A
y = 5x + 3Step-by-step explanation:
Equation of a line is y = mx + c
where m is the slope
c is the y intercept
From the question
Slope or m = 5
y intercept is ( 0 , - 3) which is - 3
So the equation of the line is
y = 5x - 3
Hope this helps you