Work Shown:
(f+g)(x) = f(x) + g(x)
(f+g)(x) = 2x+6 + 4x^2
(f+g)(x) = 4x^2+2x+6
f(x) = -3x + 7
What is f (0)?
Answer:
f(0) = 7
Step-by-step explanation:
f(x) = -3x + 7
Let x =0
f(0) = -3*0 + 7
f(0) = 7
Marco purchased a large box of comic books for $300. He gave 15 of the comic books to his brother and then sold the rest on an internet website for $330 making a profit , making a profit of $1.50 on each one.how many comic books were in the box? what was the original price of each comic book (assuming they all cost the same amount)?
Answer: There are 75 books.
Price of each book = $4.
Step-by-step explanation:
Let x = Number of books in the box.
Then as per given,
Cost of x books = $300
Cost of one book = [tex]\$(\dfrac{300}x)[/tex]
Books left after giving 15 of them = x-15
Selling price of (x-15) books= $330
Selling price of one book = [tex]\$(\dfrac{330}{x-15})[/tex]
Profit on each book= $1.50
Profit = selling price - cost price
[tex]\Rightarrow 1.50=\dfrac{330}{x-15}-\dfrac{300}{x}\\\\\Rightarrow\ 1.50=\dfrac{330(x)-300(x-15)}{x(x-15)}\\\\\Rightarrow\ 1.50=\dfrac{330x-300x+4500}{x^2-15x}\\\\\Rightarrow\ 1.50(x^2-15x)=30x+4500\\\\\Rightarrow\ 1.50x^2-22.5x=30x+4500\\\\\Rightarrow\ 1.50x^2-52.5x-4500=0\\\\\Rightarrow\ 1.50x^2-52.5x-4500=0\\\\\Rightarrow\ x^2-25x-3000=0\ \ [\text{divide by 1.5}][/tex]
[tex]\Rightarrow (x+40)(x-75)=0\\\\\Rightarrow\ x=-40,75[/tex]
Number of books cannot be negative.
So, there are 75 books.
Price of each book = [tex]\dfrac{300}{75}=\$4[/tex]
So price of each book = $4.
musah stands at the center of a rectangular field . He first takes 50 steps north, then 25 step west and finally 50 steps on a bearing of 315°. How far west and how far north is Musah final point from the center?
Answer:
85.36 far north from the center
10.36 far east from the center
Step-by-step explanation:
The extra direction taken in the north side is x
X/sin(360-315)=50/sin 90
Sin 90= 1
X/sin 45= 50
X= sin45 *50
X= 0.7071*50
X= 35.355 steps
X= 35.36
Then the west direction traveled
West =√(50² - 35.355²)
West = √(2500-1249.6225)
West= √1250.3775
West= 35.36 steps
But this was taken in an opposite west direction
From the center
He is 35.36 +50
= 85.36 far north from the center
And
25-35.36=-10.36
10.36 far east from the center
simplify the expression 10 divided by 5 times 3
Answer:
= 2/3
Step-by-step explanation:
10 / (5*3)
= 10/15
= 2/3
In the multiplication below, each of A, B and
C represents a different digit. What is ABC?
A B C
X
3
В В В
Answer:
ABC = 148, 3*148 = 444
Step-by-step explanation:
We know that 111 = 3* 37, so all numbers of the form BBB has the factor 37.
So we need a multiple of 37 such thant when multiplied, we get three digits the same as the middle digit.
Try 4*37 = 148, 148*3 = 444, bingo, we got the right combination.
So ABC is 148.
write 32 1/2 in radical form
Answer:
Nothing further, the simplest answer is 32 1/2
Step-by-step explanation:
Write the polar form of a complex number in standard form for [tex]8[cos(\frac{\pi}{2}) + isin(\frac{\pi}{2})][/tex]
Answer:
Solution : 8i
Step-by-step explanation:
We can use the trivial identities cos(π / 2) = 0, and sin(π / 2) = 1 to solve this problem. Let's substitute,
[tex]8\left[cos\left(\frac{\pi }{2}\right)+isin\left(\frac{\pi \:}{2}\right)\right][/tex] = [tex]8\left(0+1i\right)[/tex]
And of course 1i = i, so we have the expression 8(0 + i ). Distributing the " 8, " 8( 0 ) = 0, and 8(i) = 8i, making the fourth answer the correct solution.
How much would you need to deposit in an account now in order to have $6,000 in the account in 8 years? Assume the account earns 6% interest compounded monthly. (could anyone do this whole problem out?
Answer:
$3,717
Step-by-step explanation:
Hello, in 1 year there are 12 months.
Let's note I the Initial amount.
So, after 1 month we will get the following, because we compute the interest amount for one month only.
I * ( 1 + 6% * (1/12) )
And the next month, we will have interest of the amount available from previous month so it gives
[tex]I * ( 1+6\% * \dfrac{1}{12} ) * ( 1+6\% * \dfrac{1}{12} ) \\\\=I*(1+\dfrac{6}{12*100})^2\\\\=I*(1+\dfrac{1}{200})^2\\\\=I*(1.005)^2[/tex]
... and after n months ...
[tex]I*(1.005)^n[/tex]
8 years is 8*12 = 96 months. so we are looking for I such that
[tex]I*(1.005)^{96}=6000\\\\<=> I =\dfrac{6000}{1.005^{96}}\\\\=\boxed{3717.14345....}[/tex]
Thank you.
what are the next terms in the number pattern -11, -8, -5, -2, 1
Answer:
4, 7, 10, 13
Step-by-step explanation:
Hey there!
Well in the given pattern,
-11, -8, -5, -2, 1
we can conclude that the pattern is +3 every time.
-11 + 3 = -8
-8 + 3 = -5
-5 + 3 = -2
-2 + 3 = 1
And so on
4, 7, 10, 13Hope this helps :)
Yiadom is y
years now.
What would be
his age in the next ten
years.
Answer:
(y+10 ) years
Step-by-step explanation:
If Yiadom is y years now.
Then after 10 years, his anew age will be = (y+10) yrs
WHY CAN'T ANYONE HELP ME PLEASE?A 40% solution of fertilizer is to be mixed with a 80% solution of fertilizer in order to get 80 gallons of a 70% solution. How many gallons of the 40% solution and 80% solution should be mixed? 40% solution =? gallons, 80% solution =? gallons
Answer:
40% solution = 20 gallons
80% solution = 60 gallons
Step-by-step explanation:
x = gallons of 40% solution
y = gallons of 80% solution
Total volume is:
x + y = 80
Total amount of fertilizer is:
0.40 x + 0.80 y = 0.70 (80)
Solve by substitution.
0.40 x + 0.80 (80 − x) = 0.70 (80)
0.40 x + 64 − 0.80 x = 56
0.40 x = 8
x = 20
y = 60
use the product of powers property to simplify the numeric expression.
4 1/3 • 4 1/5 = _____
Answer:
The value of [tex]4^{\dfrac{1}{3}} {\cdot} 4^{\dfrac{1}{5}[/tex] is [tex]4^{\dfrac{8}{15}}[/tex] .
Step-by-step explanation:
We need to simplify the numeric expression using property. The expression is as follows :
[tex]4^{\dfrac{1}{3}} {\cdot} 4^{\dfrac{1}{5}[/tex]
The property to be used is : [tex]x^a{\cdot} x^b=x^{a+b}[/tex]
This property is valid if the base is same. Here, base is x.
In this given problem, x = 4, a = 1/3 and b = 1/5
So,
[tex]4^{\dfrac{1}{3}} {\cdot} 4^{\dfrac{1}{5}}=4^{\dfrac{1}{3}+\dfrac{1}{5}}\\\\=4^{\dfrac{5+3}{15}}\\\\=4^{\dfrac{8}{15}}[/tex]
So, the value of [tex]4^{\dfrac{1}{3}} {\cdot} 4^{\dfrac{1}{5}[/tex] is [tex]4^{\dfrac{8}{15}}[/tex] .
For this year's fundraiser, students at a certain school who sell at least 75 magazine subscriptions win a prize. If the fourth grade students at this school sell an average (arithmetic mean) of 47 subscriptions per student, the sales are normally distributed, and have a standard deviation of 14, then approximately what percent of the fourth grade students receive a prize
Answer:
The percentage is k = 2.3%
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 47[/tex]
The standard deviation is [tex]\sigma = 14[/tex]
Given that the sales are normally distributed and that students at a certain school who sell at least 75 magazine subscriptions win a prize then the percent of the fourth grade students receive a prize is mathematically represented as
[tex]P(X > 75) = P(\frac{X - \mu }{\sigma } > \frac{75 - \mu }{\sigma })[/tex]
Generally
[tex]\frac{X - \mu }{\sigma } = Z (The \ standardized \ value \ of \ X )[/tex]
So
[tex]P(X > 75) = P(Z > \frac{75 - 47 }{14 })[/tex]
[tex]P(X > 75) = P(Z > 2)[/tex]
From the standardized normal distribution table
[tex]P(Z > 2) =0.023[/tex]
=> [tex]P(X > 75) = 0.023[/tex]
The percentage of the fourth grade students receive a prize is
k = 0.023 * 100
k = 2.3%
A spinner has 10 equally sized sections, 5 of which are gray and 5 of which are blue. The spinner is spun twice. What is the probability that the first spin lands on gray and the second spin lands on blue? Write your answer as a fraction in the simplest form.
Answer:
[tex]P(Gray\ and\ Blue) = \frac{1}{4}[/tex]
Step-by-step explanation:
Given
[tex]Sections = 10[/tex]
[tex]n(Gray) = 5[/tex]
[tex]n(Blue) = 5[/tex]
Required
Determine P(Gray and Blue)
Using probability formula;
[tex]P(Gray\ and\ Blue) = P(Gray) * P(Blue)[/tex]
Calculating P(Gray)
[tex]P(Gray) = \frac{n(Gray)}{Sections}[/tex]
[tex]P(Gray) = \frac{5}{10}[/tex]
[tex]P(Gray) = \frac{1}{2}[/tex]
Calculating P(Gray)
[tex]P(Blue) = \frac{n(Blue)}{Sections}[/tex]
[tex]P(Blue) = \frac{5}{10}[/tex]
[tex]P(Blue) = \frac{1}{2}[/tex]
Substitute these values on the given formula
[tex]P(Gray\ and\ Blue) = P(Gray) * P(Blue)[/tex]
[tex]P(Gray\ and\ Blue) = \frac{1}{2} * \frac{1}{2}[/tex]
[tex]P(Gray\ and\ Blue) = \frac{1}{4}[/tex]
A buoy floating in the sea is bobbing in simple harmonic motion with amplitude 13 in and period 0.25 seconds. Its displacement d from sea level at time t=0 seconds is 0in, and initially it moves downward. (Note that downward is the negative direction.)Required:Give the equation modeling the displacement d as a function of time t.
Answer:
The equation is [tex]x(t) = -13 cos (8 \pi t )[/tex]
Step-by-step explanation:
From the question we are told that
The amplitude is [tex]A = 13 \ in[/tex]
The period is [tex]T = 0.25[/tex]
Generally the displacement function for a simple harmonic motion is mathematically represented as
[tex]x(t) = A cos (wt )[/tex]
Here [tex]w[/tex] is the angular frequency which is mathematically represented as
[tex]w = \frac{2 \pi }{T}[/tex]
substituting values
[tex]w = \frac{2 \pi }{ 0.25}[/tex]
[tex]w = 8\pi[/tex]
Given that at t = 0 the displacement is equal to 0 it means that there is no phase shift and also we are told that it is initially moving downward which implies that its Amplitude is [tex]A = -13\ in[/tex]
So the equation modeling the displacement d as a function of time t is mathematically represented as
[tex]x(t) = -13 cos (8 \pi t )[/tex]
slope of -4/3x with point (7,20) find equation
Answer:
y= -4/3x+10 2/3
Step-by-step explanation:
To do this, just put the equation in point slope form and then rearrange it to y=mx+b, or slope intercept form. Slope point form is arranged like this, y-y1=m(x-x1). Now, just insert in the variables (x1=x coordinate of point, y1= y coordinate of point, m=slope). So your equation is now y-20=-4/3(x-7), which simplifies to y-20=-4/3x-9 1/3. Now rearrange it so that y in by itself, and all like terms are combined, making it look like this: y=-4/3x+10 2/3. Now its in slope intercept form and you've got your answer.
I hope my explanation wasn't confusing and that my answer helped.
Stepwise regression is a variable screening method, not a model building method.
A. True
B. False
Answer:
A. True
Step-by-step explanation:
Stepwise regression is a variable-selection method for independent variables.
Stepwise regression helps us to recognize and choose the most handy descriptive variables from a list of several reasonable independent variables.
It entails a series of steps that is drafted to locate the most handy X-variable to incorporate in a regression model. During each step of the course of action or method, each X - variable is estimated by applying a set criterion to determine if it is meant to exist in the model.
The basis for selection can be choosing a variable which satisfies the stipulated criterion or removing a variable that least satisfies the criterion. A typical illustration of such criterion is the t value.
The cost of performance tickets and beverages for a family of four can be modeled using the equation 4x+12=48,where x represents the cost of a. Ticket.how much is one ticket
Answer:
x=9; one ticket is $9
Step-by-step explanation:
4x+12=48
4x=48-12
4x=36
x=36/4
x=9
Which, if any, pair of sides are parallel? AB II DC and AD II BC Cannot be determined AB II DC only AD II BC only
Answer:
120%
Step-by-step explanation:
Emily thinks the perfect tomato sauce has 8 cloves of garlic in every 500 mL, of sauce. Raphael's tomato sauce has 121 cloves of garlic in every 900 mL of sauce. What will Emily think of Raphael's tomato sauce? Choose 1 answer: Choose 1 answer: (Choice A) A It is too garlicky. (Choice B) B It is not garlicky enough. (Choice C) C It is perfect.
Answer:
A
Step-by-step explanation:
Let's find the ml per garlic for each sauce. Emily's has 1 clove of garlic for 62.5 ml. Raphael's has 1 clove of garlic for 7.438... ml. So, A, it will be too garlicky.
Y * 3 = 81 please i need it for today
Answer:
Y = 27
Step-by-step explanation:
Y * 3 = 81
Divide each side by 3
Y * 3/3 = 81/3
Y = 27
find the total area of the prism
Answer:
63.5
Step-by-step explanation:
6(x + 2) = 30Solve the following linear equation
Answer:
[tex]\huge \boxed{x=3}[/tex]
Step-by-step explanation:
[tex]6(x+2)=30[/tex]
[tex]\sf Divide \ both \ sides \ by \ 6.[/tex]
[tex]x+2=5[/tex]
[tex]\sf Subtract \ 2 \ from \ both \ sides.[/tex]
[tex]x=3[/tex]
Answer:
3
Step-by-step explanation:
30 = 6(x+2)
30/6 = 5
5 = x+2
5-2 = 3
3=x
This is a pretty simple question and I tried to make it as simple as possible when explaining it.
Solve the following system of equations.
2x + y = 3
x = 2y-1
ANSWER: ______
plz help me
(1,1) is your answer.
Work is shown below.
Any questions? Feel free to ask.
Answer: (1,1)
Step-by-step explanation:
Determine the value(s) for which the rational expression 2x^2/6x is undefined. If there's more than one value, list them separated by a comma, e.g. x=2,3.
Answer:
0
Step-by-step explanation:
Hello, dividing by 0 is not defined. so
[tex]\dfrac{2x^2}{6x}[/tex]
is defined for x different from 0
This being said, we can simplify by 2x
[tex]\dfrac{2x^2}{6x}=\dfrac{2x*x}{3*2x}=\dfrac{1}{3}x[/tex]
and this last expression is defined for any real number x.
Thank you
If the average fixed cost (AFC) of producing 5 bags of rice is $20.00, the average fixed cost of producing 10 bags will be
Answer:$40.00
Step-by-step explanation:first divide 20 by 5 and the answer will be 4. now multiply 10 into 4 and you'll get the answer $40.00
Help please I need help as soon as possible!all answers are appreciated! Keisha tried to evaluate an expression step by step. 3+(−4)−7
Answer:
D no mistakes
Step-by-step explanation:
3+(-4)-7 is equal to 3-4-7=-8
Answer:0
Step-by-step explanation:
3+(-4)-7 when there are parenthesis around a negative number you flip it to positive and then 4+3-7=0
12. Consider the function ƒ(x) = x^4 – x^3 + 2x^2 – 2x. How many real roots does it have?
options:
A) 2
B) 1
C) 3
D) 4
Answer:
Step-by-step explanation:
Hello, let's factorise as much as we can.
[tex]x^4-x^3 + 2x^2-2x\\\\=x(x^3-x^2+2x-2)\\\\=x(x-1)(x^2+2)[/tex]
So, the solutions are
[tex]0, \ 1, \ \sqrt{2}\cdot i, \ -\sqrt{2}\cdot i[/tex]
There are only 2 real roots.
Thank you.
Answer:
So, the solutions are
There are only 2 real roots.
Step-by-step explanation:
4x + 1 -5x =2x +4(x-5)
Answer:
x = 3
Step-by-step explanation:
To answer for x first distribute the 4 in the parenthesis
4x + 1 - 5x = 2x +4x - 20
Next add or subtract the x's
-x + 1 = 6x - 20
Now subtract 6x and 1 on both sides to get x on the left and the rest on the right
-7x = -21
Lastly, divide -7 on both sides
x = 3
I need help please help me!
Answer:
36ft³
Step-by-step explanation:
Bottom rectangular prism: 2x2x6=24
Top rectangular prism: 2x2x3=12
24+12=36ft³
Answer:
[tex]\boxed{36ft^3}[/tex]
Step-by-step explanation:
Hey there!
Well to solve for V we need to find the volume of the 2 rectangular prism's given.
Rec#1: 2•3•2 = 12
Rec#2: 6•2•2 = 24
Rec#1 + Rec#2 = V
12 + 24 = 36ft³
Hope this helps :)
