Answer:
Graph 2
Step-by-step explanation:
As you can see the first equation is present with a negative slope, and none of the graphs have a line plotted with a negative slope, besides the second graph. That is your solution.
Which polynomial represents the sum below?
Answer:
The sum is represented by the polynomial:
[tex]5\,x^9+2 \,x^7+13\,x+4[/tex]
Step-by-step explanation:
Recall that polynomials are added by combining like terms. The only like terms in this addition are: 5 x and 8 x which added render: 13 x. therefore, the addition of these polynomials renders;
[tex]5\,x^9+2 \,x^7+13\,x+4[/tex]
What is the value of 1/3x-3/4 when x =1/4
Answer:
The value of 1/3x-3/4 when x=1/4 is 0.08333 repeated.
Step-by-step explanation:
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%
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
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
If the item regularly cost d dollars and is discounted 12percent which of the following represents discount price dollar
Answer:
-12
Step-by-step explanation:
Suppose a triangle has two sides of length 33 amd 37, and that the angle between these two sides is 120°. What is the length of the third side of the triangle
Answer:
c = 60.65 cm
Step-by-step explanation:
Given that,
The two sides of a triangle are 33 cm and 37 cm.
The angle between these two sides is 120°.
We need to find the length of the third side of the triangle. Let c is the third side. Using cosine rule,
[tex]c^2=a^2+b^2-2ab\cos C[/tex]
a = 33 cm, b = 37 cm and C is 120°
So,
[tex]c^2=(33)^2+(37)^2-2\times 33\times 37\cos (120)\\\\c=60.65\ cm[/tex]
So, the length of the third side of the triangle is 60.65 cm.
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]
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
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.
What is the best way you learn math?
Answer:
to provide interest in the subject
As per my experience,I used to hate math and always scored less marks,the moment I was going to high school I realized the importance of math towards the future, see you'll find maths in nearly all subjects like the 3 sciences, economics, geography, business e.t.c
Why did you write this question at first?, just take some free time and think about it,the only best way to learn maths is to take maths positively as the best and most valuable subject,if you want to ace math you have to race it, challenge math like you'd challenge anyone to a game, practice math if it's your weakest point, practice is very much needed to skill maths and never be shy to ask your teachers whether you are studying online/offline. You'll need to get the shy behaviour out of you whether you like /don't like your teacher or your an average student.
Concentrate while learning math, whether there's noise in you background or not, Nothing can stop you in excelling math if you have full concentration, positiveness and the "will" to do so.
if you're next to your exams then just one thing, Start now!!
hope this helps!
What is the difference between a consistent and inconsistent system of equations?
Answer:
A consistent of equations has at least one solution,and an inconsistent system has no solution, watch an example of analyzing a system to see if its consistent or inconsistent.
Answer: see below
Step-by-step explanation:
Consider the standard form of a linear equation in Slope-Intercept form:
y = mx + b where
m is the slopeb is the y-interceptA CONSISTENT system of equations is where the equations have different slopes OR the same slope and y-intercept.
This results in the lines crossing so they have at least one solution.
An INCONSISTENT system of equations is where the equations have the same slope but different y-intercepts.
This results in parallel lines so they have no solutions.
4. Identify the means and the extremes in each of the following proportions.
a. 4 : 24 = 2 : 12
b. 24/6 = 164
c. 4:8 = 8:16
d. 650 = 3/25
Answer:
a) Means: 24 and 2; Extremes: 4 and 12
b) Means: 6 and 16; Extremes: 24 and 4
c) Means: 8 and 8; Extremes: 4 and 16
d) Means: 50 and 3; Extremes: 6 and 25
Step-by-step explanation:
The Means and Extremes in a proportion are defined based on the writing the proportion in one lie using colons the indicate the fraction, like in:
a : b = c : d The extremes values here are those that you see at the extreme left and extreme right of that expression. That is: a, and d.
The Means are the values that appear in the middle of the one line expression, that is: b and c.
Recall as well that the proportion can also be written with fractions:
a : b = c : d is the same as: a / b = c / d
so convert the expression to a one line with colons when the question comes in fraction form, and that way you can answer.
15. What is the next number in this series?
6, 11, 9, 14, 12,
a. 17
b. 10
C. 18
d. 16
Answer:
a. 17
Step-by-step explanation:
The pattern is add 5 then subtract 2
If you randomly select a card from a well-shuffled standard deck of 52 cards, what is the probability that the card you select is a heart or Ace
Answer:
[tex]P(A\ or\ H) = \frac{4}{13}[/tex]
Step-by-step explanation:
Given
Number of Cards = 52
Required
Determine the probability of picking a heart or ace
Represent Ace with Ace and Heart = H
In a standard pack of cards; there are
[tex]n(A) = 4[/tex]
[tex]n(H) = 13[/tex]
[tex]n(A\ and\ H) = 1[/tex]
[tex]Total = 52[/tex]
Because the events are non mutually exclusive
[tex]P(A\ or\ H) = P(A) + P(H) - P(A\ and\ H)[/tex]
Where
[tex]P(A) = \frac{n(A)}{Total} = \frac{4}{52}[/tex]
[tex]P(H) = \frac{n(H)}{Total} = \frac{13}{52}[/tex]
[tex]P(A\ and\ H) = \frac{n(A\ and\ H)}{Total} = \frac{1}{52}[/tex]
Substitute these values in the above formula
[tex]P(A\ or\ H) = P(A) + P(H) - P(A\ and\ H)[/tex]
[tex]P(A\ or\ H) = \frac{4}{52} + \frac{13}{52} - \frac{1}{52}[/tex]
Take LCM
[tex]P(A\ or\ H) = \frac{4 + 13 - 1}{52}[/tex]
[tex]P(A\ or\ H) = \frac{16}{52}[/tex]
Reduce fraction to lowest term
[tex]P(A\ or\ H) = \frac{4}{13}[/tex]
Hence, probability of a heart or ace is 4/13
A certain animal's body temperature has a mean of F and a standard deviation of F. Convert the given temperatures to z scores.
A certain animal's body temperature has a mean of 94.72° F and a standard deviation of 0.57°F. Convert the given temperatures to z scores.
a. 93.52 °F b. 95.22 °F c. 94.72 °F
Answer:
a. z = - 2.1053
b. z = 0.87719
c. z = 0
Step-by-step explanation:
Given that :
The population mean μ = 94.72
The standard deviation σ = 0.57
the formula for calculating the standard normal z score, which can be represented as:
[tex]z= \dfrac{\overline x - \mu}{\sigma}[/tex]
For a.
The sample mean [tex]\bar x[/tex] = 93.52
The z score can be computed as follows:
[tex]z= \dfrac{\overline x - \mu}{\sigma}[/tex]
[tex]z= \dfrac{93.52 - 94.72}{0.57}[/tex]
[tex]z= \dfrac{-1.2}{0.57}[/tex]
z = - 2.1053
For b.
The sample mean [tex]\bar x[/tex] = 95.22
[tex]z= \dfrac{\overline x - \mu}{\sigma}[/tex]
[tex]z= \dfrac{95.22 - 94.72}{0.57}[/tex]
[tex]z= \dfrac{0.5}{0.57}[/tex]
z = 0.87719
For c.
The sample mean [tex]\bar x[/tex] = 94.72
[tex]z= \dfrac{\overline x - \mu}{\sigma}[/tex]
[tex]z= \dfrac{94.72 - 94.72}{0.57}[/tex]
[tex]z= \dfrac{0}{0.57}[/tex]
z = 0
In a genetics experiment on peas, one sample of offspring contained green peas and yellow peas. Based on those results, estimate the probability of getting an offspring pea that is green. Is the result reasonably close to the value of that was expected? 350 127 3 4 The probability of getting a green pea is approximately . (Type an integer or decimal rounded to three decimal places as needed.) Is this probability reasonably close to ? Choose the correct answer below. 3 4 A. No, it is not reasonably close. B. Yes, it is reasonably close.
Complete Question
In a genetic experiment on peas, one sample of offspring contained 436 green peas and 171 yellow peas. Based on those results, estimate the probability of getting an offspring pea that is green. Is the result reasonably close to the value of 3/4 that was expected? The probability of getting a green pea is approximately: Is the probability reasonably close to 3/4?
Answer:
The probability is [tex]P(g) =0.72[/tex]
Yes the result is reasonably close
Step-by-step explanation:
From the question we are told that
The number of of green peas is [tex]g = 436[/tex]
The number of yellow peas is [tex]y = 171[/tex]
The sample size is [tex]n = 171 + 436 = 607[/tex]
The probability of getting an offspring pea that is green is mathematically represented as
[tex]P(g) = \frac{g}{n}[/tex]
[tex]P(g) = \frac{436}{607}[/tex]
[tex]P(g) =0.72[/tex]
Comparing [tex]P(g) =0.72[/tex] to [tex]\frac{3}{4} = 0.75[/tex] we see that the result is reasonably close
If 2 = 5, what is 2 3 − 4?
Answer:
27.5
Step-by-step explanation:
3 = 7.5
4 = 10
5*7.5=37.5-10=27.5
Seriously. 2=5 contradicts.
An architectural drawing lists the scale as 1/4" = 1'. If a bedroom measures 6 3/4" by 4 1/2" on the drawing, how large is the bedroom? Please Help! (No other information was given.)
1 inch = four 1/4’s
1 inch = 4 feet
6 X 4 = 24 feet
3/4 inches = 3 feet.
6 3/4 inches = 27 feet
4 x 4 = 16
1/2 inch = 2 feet
4 1/2 inches = 18 feet
Room is 27 feet x 18 feet
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.
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
find the total area of the prism
Answer:
63.5
Step-by-step explanation:
We want to model the daily movement of a particular stock (say Amazon, ticker = AMZN) using a homogeneous markov-chain. Suppose at the close of the market each day, the stock can end up higher or lower than the previous day’s close. Assume that if the stock closes higher on a day, the probability that it closes higher the next day is .65. If the stock closes lower on a day, the probability that it closes higher the next day is .45.
(a) What is the 1-step transition matrix? (Let 1 = higher, 2 = lower)
(b) On Monday, the stock closed higher. What is the probability that it will close higher on Thursday (three days later)
Answer:
See the explanation and attached images for the answers.
Step-by-step explanation:
a) 1-step transition matrix:
See the attached image for transition matrix.
Let the matrix be M
if the stock closes higher on a day, the probability that it closes higher the next day is 0.65.
If the stock closes lower on a day, the probability that it closes higher the next day is 0.45
if the stock closes higher on a day, the probability that it closes lower the next day is 1 - 0.65 = 0.35
if the stock closes lower on a day, the probability that it closes lower the next day is 1 - 0.45 =0.55
b)
To compute probability for 3 days later multiply matrix M (from part a) thrice i.e. M*M *M
[tex]M^{3} = \left[\begin{array}{ccc}0.65&0.35\\0.45&0.55\end{array}\right]*\left[\begin{array}{ccc}0.65&0.35\\0.45&0.55\end{array}\right]*\left[\begin{array}{ccc}0.65&0.35\\0.45&0.55\end{array}\right][/tex]
[tex]M^{3} = \left[\begin{array}{ccc}0.65 * 0.65 + 0.35 * 0.45 &0.65 * 0.35 + 0.35 * 0.55 \\0.45 * 0.65 + 0.55 * 0.45 &0.45 * 0.35 + 0.55 * 0.55 \end{array}\right] * \left[\begin{array}{ccc}0.65&0.35\\0.45&0.55\end{array}\right][/tex]
[tex]M^{3} = \left[\begin{array}{ccc}0.58&0.42\\0.54&0.46\end{array}\right]*\left[\begin{array}{ccc}0.65&0.35\\0.45&0.55\end{array}\right][/tex]
[tex]M^{3} = \left[\begin{array}{ccc} 0.58 * 0.65 + 0.42 x 0.45&0.58 * 0.35 + 0.42 * 0.55 \\0.54 * 0.65 + 0.46 * 0.45 &0.54 * 0.35 + 0.46 * 0.55 \end{array}\right][/tex]
[tex]M^{3} = \left[\begin{array}{ccc}0.566&0.434\\0.558&0.442\end{array}\right][/tex]
The probability that it will close higher on Thursday is 0.566. See the transmission matrix of M³ for higher-higher. This can be interpreted as:
if the stock closed higher on Monday, the probability that it closes higher the on Thursday (three days later) is 0.566
paul worked 50 hours last week. if he earns $10 per hour plus time-and-a-half for any hours worked beyond 40 in a week, how much did he earn last week?
Answer: 4150
Step-by-step explanation:
You take the 50, becuse the amount earned increases once you surpass 40 you do 40 x 10 and that = 4000 then you take the remaining 10 and times that by 15 (becuse after 40 it is 1.5 of what you where earning before you hit 40 hours and half of ten is 5 so you do 10 plus 5 and times that by 10) then add both numbers together and you have 4150! Hope that helped!
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 :)
The length and width of a rectangle are measured as 58 cm and 45 cm, respectively, with an error in measurement of at most 0.1 cm in each. Use differentials to estimate the maximum error in the calculated area of the rectangle.
Answer:
Error in calculated area = [tex]\pm 10.3 cm^2[/tex]
Step-by-step explanation:
x = 58 cm
y = 45 cm
A = x*y
delta A
= delta (x*y)
= y delta x + x delta y (neglecting small qty delta x * delta y = 0.01)
= 45(0.1) + 58(0.1)
= 103(0.1)
= 10.3 cm^2
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
Evaluate the polynomial when x = 3 and y = - 8
x2 + y2 + xy
Work Shown:
Replace x with 3, replace y with -8. Use order of operations PEMDAS to simplify.
x^2 + y^2 + x*y
3^2 + (-8)^2 + 3*(-8)
9 + 64 - 24
73 - 24
49
Answer:
49
Step-by-step explanation:
We are given the polynomial:
[tex]x^2+y^2+xy[/tex]
We want to evaluate when x=3 and y= -8. Therefore, we must substitute 3 for each x and -8 for each y.
[tex](3)^2+(-8)^2+(3*-8)[/tex]
Solve according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction
Solve the parentheses first. Multiply 3 and -9.
3*-8=-24
[tex](3)^2+(-8)^2 + -24[/tex]
[tex](3)^2+(-8)^2-24[/tex]
Now, solve the exponents.
3^2= 3*3 =9
[tex]9+ (-8)^2 -24[/tex]
-8^2= -8*-8= 64
[tex]9+64-24[/tex]
Add 9 and 64
[tex]73-24[/tex]
Subtract 24 from 73
[tex]49[/tex]
The polynomial evaluated for x=3 and y= -8 is 49.
A basketball player scored 33 points during a game by shooting 1-point free throws, 2-point field goals, and 3-point field goals. The player scored 17 times. She scored 3 more 2-point field goals than 1-point free throws. The system of equations below represents the situation, where x is the number of 1-point free throws, y is the number of 2-point field goals, and z is the number of 3-point field goals. x + y + z = 17 x + 2y + 3z = 33 y – x = 3
Answer:
No. of 1 pt free throws = 5, No. of 2 pt goals = 8, No. of 3 pt goals = 4
Step-by-step explanation:
Equations : x + y + z = 17 [ Total times taken to score ]
1x + 2y + 3z = 33 [ Total Score ]
Also, y = x + 3
Putting the value of 'y' in both equations :
x + (x + 3)+ z = 17 → 2x + 3 + z = 17 → 2x + z = 14 (i)
1x + 2 (x + 3) + 3z = 33 → x + 2x + 6 + 3z = 33 → 3x + 3z = 27 (ii)
Solving these equations :
From (i), z = 14 - 2x
Putting this value in (ii), 3x + 3(14 - 2x) = 27 → 3x + 42 - 6x = 27
42 - 3x = 27 → 3x = 15 → x = 5
y = x + 3 = 5 + 3 → y = 8
z = 17 - x - y → z = 17 - 5 - 8 = 17 - 13 → z = 4
Answer:
4
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.