What is the equation of a line that passes through the point (2, 7) and is perpendicular to the line whose equation is y=x4+5 ?
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Related Questions
Simplify 3 + c (8n + 4) + 9n
A. 49n + 20
B. 3+33n
C. 25n + 11
D. 19n + 7
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the sum of 2 3/5 + (-1/5) write in simplest form
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if today is wednsday what day will it be in 100 days and why
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We know that every week (every seven days) it will be Wednesday if today is Wednesday. So, how may weeks are in 100 days? 14. Why? Because 14(7) = 98. So, in order to get to 100 we must add 2. So what is Wednesday plus two more days? Friday. So if today is Wednesday it will be Friday in 100 days. Why? Well, that's how our calendar is set up.
what square root lies between 17 and 18
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if x is the number
sqrt x is between 17 and 18
17<√x<18
squaer the whole thing
289x could be 300
it could be sqrt of 300
√300=10√3
one is 10√3
What is the solution set of the equation
X^2+3x-4=6
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Two solutions were found : x = 5; x = -2. Reformatting the input : Changes made to your input should not affect the solution: (1): "x2" was replaced by "x^2". Rearrange: Rearrange the equation bAnswer:
Step-by-step explanation:Two solutions were found : x = 5; x = -2. Reformatting the input : Changes made to your input should not affect the solution: (1): "x2" was replaced by "x^2". Rearrange: Rearrange the equation b
Suppose △DEF≅△MNO.
Which congruency statement is true?
A) DF≅NO
B) DE≅MN
C) EF≅MN
D) EF≅MO
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When triangles are congruent, their corresponding sides and angles are the same. Hence in congruent triangles △DEF and △MNO, side DF is congruent to side MN, thus option B) DE≅MN is the correct answer.
Explanation:In the case of congruent triangles, the corresponding sides and angles are essentially the same. Therefore, we must match up the corresponding sides. A correct statement would be that side DF, from the first triangle, is congruent to side MN, from the second triangle. Hence the correct option is B) DE≅MN.
Additionally, DE would be congruent to MN, and EF would be congruent to NO, completing the congruence between triangles △DEF and △MNO.
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The fourth grade collected 40,583 cans and plastic bottles. Write the number in word form?
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Answer is 'Forty thousand, five hundred eighty-three'.
When we write numbers in word form, we express each digit's value in words. In the number 40,583, we have:
"Forty" represents the digit 4 in the ten thousands place.
"Five hundred" represents the digit 5 in the hundreds place.
"Eighty" represents the digit 8 in the tens place.
"Three" represents the digit 3 in the ones place.
For a laboratory assignment, if the equipment is working, the density function of the observed outcome x is f(x) = 2(1 − x), 0
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The Variance is [tex]\int\limits^1_0 {(x- \mu)^2(2(1-x))} \, dx[/tex].
What is Variance?Variability is measured by the variance. The average of the squared deviations from the mean is used to calculate it. The degree of spread in your data set is indicated by variance. The variance is greater in respect to the mean the more dispersed the data.
Given:
E(x) = [tex]\int\limits^1_0 {x(2(1-x))} \, dx[/tex]
= [tex]\int\limits^1_0 {(2x - 2x^2)} \, dx[/tex]
For the variance, if μ is the mean, then
Var(x) = E( x- μ)²
= [tex]\int\limits^1_0 {(x- \mu)^2(2(1-x))} \, dx[/tex]
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If each weighs 2/3 pound, how many potatoes are there in a 50-pound case?
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The number of potatoes that are there in a 50-pound case are 75 potatoes.
In Mathematics and Euclidean Geometry, an expression simply refers to a mathematical equation which is typically used for illustrating the relationship that exist between two (2) or more variables and numerical quantities (number).
Since each potato weighs 2/3 pound, the number of potatoes that are there in a 50-pound case can be modeled by the following expression;
Number of potatoes = 50 ÷ 2/3
Number of potatoes = 50 × 3/2
Number of potatoes = 150/2
Number of potatoes = 75 potatoes.
A problem states
there are 5 more girls than boys and girls there are 27 students in the class in all How many boys are in the class
What are the unknowns in this problem
A Number of students in the class
B The number of boys in the class
C The number of girls in class
D The number of boys and the number of girls in class
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the problem only stats there are 27 students and that there are 5 more girls than boys
it does not say how many boys or how many girls there are so D should be the answer
I don't get why price(max)=$80
Can someone help me
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as a matter of elasticity, if you sell 100 popsicles for $1, you get a revenue of $100.
However, if your price goes to $5 per popsicle, then folks will begin to find it too expensive and won't be buying 100, but just 15, so, even though $5 is a higher price, 5 * 15 is a much smaller revenue than 1 * 100.
Point P is reflected across two lines. Point A is its reflection image. Which two lines is point P reflected across?
x = 3 and y = 2
x = -2 and y = 2
x = 3 and y = -3
x = -2 and y = -3
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Answer: The two lines are x = -2 and y = 2.
Step-by-step explanation: Given that the point P on the co-ordinate plane is reflected across two lines and A is its image after the reflection.
We are to find the two lines across which the point P is reflected.
The co-ordinates of point P are (0, 0) and the co-ordinates of its image A after reflection from two lines are (-4, 4).
From the given figure, we can note that
the first line of reflection is y = 2. Point C(0, 4) is the image after reflection from first line.
The second line of reflection is x = -2. Point A(-4,4) is the final image after second reflection.
Thus, the two lines are x = -2 and y = 2.
Y=2x^2-x-10 write in intercept form
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x-intercept: Let y = 0 and solve for x.
Then 0 = 2x^2 - x - 10. a=2, b= -1 and c = -10.
-(-1) plus or minus sqrt[ (-1)^2 - 4(2)(-10)
Then x = ------------------------------------------------------------
2(2)
1 plus or minus sqrt(81) 1 plus or minus 9
x = ----------------------------------- = ---------------------------
4 4
Calculate the 2 x-values. Let's call them "a" and "b." Then the x-intercepts (there are 2) are
(a, 0) and (b, 0)
Mia's cat weighs 13 pounds, 7 ounces
About how many kilograms is this
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Sampling is ordinarily used when the number of items comprising the population is relatively small.
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Jennifer's grandmother buys carrots at the farm stand. She and her 3 grandchildren equally share the carrots. The total weight of the carrots she bought is 28 kilograms. How many kilograms of carrots will Jennifer get ?
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28/4=7
The table shows the steps for solving the given inequality for x.
−3(4−6x)
Select the reason for each step from the drop-down menus.
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- 3 (4 - 6x) < x + 5
- 12 + 18x < x + 5 distributive property (to solve the left side)
-12 + 17x < 5 subtraction property of equality (to transpose x
from right to left side)
subtraction of like terms (18x - x = 17x)
17x < 17 addition property of equality (to tranpose - 12
from left to right side)
addition of like terms (12 + 5 =17)
x < 1 division property of equality
Answer:step justification
- 3 (4 - 6x) < x + 5
- 12 + 18x < x + 5 distributive property (to solve the left side)
-12 + 17x < 5 subtraction property of equality (to transpose x
from right to left side)
subtraction of like terms (18x - x = 17x)
17x < 17 addition property of equality (to tranpose - 12
from left to right side)
addition of like terms (12 + 5 =17)
x < 1 division property of equality
Step-by-step explanation:
Given four int values x1, x2, y1, y2 write the code to compute the distance between the two point
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Please tell me the language java, c++, cetc?
The ordered pair (2, 1) is a solution of a direct variation equation. Write the equation and identify the constant of variation.
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A new iPhone user receives an average of 4.2 phone calls per hour. The calls occur randomly in time so if X = the number of calls received in an hour, then we can assume that X has a Poisson distribution with parameter λ = 4.2. Let Y = the number of phone calls received in a day. Assume all necessary independence in the following.
a. Y also has a Poisson distribution. What is the λ for Y?
b. What is the standard deviation of X?
c. What is the standard deviation of Y?
d. What is the probability that no calls are received in an hour?
e. What is the probability that more than 120 calls are received in a day?
f. What is the probability that Y is between 90 and 110 inclusive? (i.e. 90 ≤ Y≤110)
g. What is the variance of square root of 2Y?
h. Assume this distribution holds for all hours and days and that one call is independent from another. What is the probability that 120 or fewer calls are received for every day of this week? (Assume appropriate independence
Add any comments below.
Answers
Given that Y is the number of phone calls received in a day and that a new iPhone user receives an average of 4.2 phone calls per hour.
Thus, the average number of phone calls received in a day is 4.2 * 24 = 100.8
Therefore, the λ for Y is 100.8
Part B:
The standard deviation of a Poisson distribution is given by
[tex]\sigma=\sqrt{\lambda}[/tex]
Thus, the standard deviation of X is given by
[tex]\sigma=\sqrt{4.2}=2.05[/tex]
Therefore, the standard deviation of X is 2.05.
Part C:
The standard deviation of Y is given by
[tex]\sigma=\sqrt{100.8}=10.04[/tex]
Therefore, the standard deviation of X is 10.04.
Part D:
The probability of a Poisson distribution is given by
[tex]P(X=x)=e^{-\lambda} \frac{\lambda^x}{x!} [/tex]
where, x is the number of occurence of the event in the given period.
Thus, the probability that no calls are received in an hour is given by
[tex]P(X=0)=e^{-4.2} \frac{(4.2)^0}{0!} =0.015[/tex]
Therefore, the probability that no calls are received in an hour is 0.015
Part E:
We approximate the Poisson distribution using Normal distribution by noting that for a Poisson distribution
[tex]\mu=\lambda \\ \\ \sigma^2=\lambda \\ \\ \sigma=\sqrt{\lambda}[/tex]
The probability of a normal distribution is given by
[tex]P(X\ \textless \ x)=P\left(z\ \textless \ \frac{x-\mu}{\sigma} \right)[/tex]
Thus, the probability that more than 120 calls are received in a day is given by
[tex]P(X\ \textgreater \ 120)=1-P(X\leq120) \\ \\ =1-P\left(z\leq \frac{120-100.8}{10.04} \right)=1-P(z\leq1.912) \\ \\ =1-0.97208=0.0279[/tex]
Therefore, the probability that more than 120 calls are received in a day is 0.0279
Part F:
We also approximate this using Normal distribution
The probability of a normal distribution between two value (a, b) is given by
[tex]P(a\ \textless \ X\ \textless \ b)=P\left(z\ \textless \ \frac{b-\mu}{\sigma} \right)-P\left(z\ \textless \ \frac{a-\mu}{\sigma} \right)[/tex]
Thus, the probability that Y is between 90 and 110 inclusive is given by
[tex]P(90\leq X\leq 110)=P\left(z\leq \ \frac{110-100.8}{10.04} \right)-P\left(z\leq \frac{90-100.8}{10.04} \right) \\ \\ =P(z\leq0.916)-P(-1.076)=0.82025-0.14103=0.67922[/tex]
Therefore, the probability that Y is between 90 and 110 is 0.67922
Part G:
The variance of aY is given by
[tex]Var(aY)=a^2Var(Y)[/tex]
Thus, the variance of [tex] \sqrt{2} Y[/tex] is given by
[tex]Var( \sqrt{2} Y)=( \sqrt{2} )^2Var(Y)=2(100.8)=201.6[/tex]
Therefore, the variance of [tex] \sqrt{2} Y[/tex] is 201.6
Part H:
We approximate this using Normal distribution
The probability of a normal distribution is given by
[tex]P(X\ \textless \ x)=P\left(z\ \textless \ \frac{x-\mu}{\sigma} \right)[/tex]
Thus, the probability that 120 or fewer calls are received in a day is given by
[tex]P(X\leq120)=P\left(z\leq \frac{120-100.8}{10.04} \right) \\ \\ =P(z\leq1.912)=0.97208[/tex]
Since, this distribution holds for all hours and days and one call is independent from another. Assuming that there are seven days in a week.
The probability that 120 or fewer calls are received for every day of this week is given by
[tex](0.97208)^7=0.8202[/tex]
Therefore, the probability that 120 or fewer calls are received for every day of this week is 0.8202
Write the equation for the following relation. Include all of your work in your final answer. Submit your solution. P = {(x, y): (1, 0), (2, 4), (3, 8), (4, 12), . . .}
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The general equation for linear equations is : y = mx + c where m is the slope and c is the y-intercept
To get the slope, we will need to use two points. Let's take the first and the last points: (1,0) and (4,12)
The slope is calculated as: (y2-y1) / (x2-x1)
Use the chosen points to substitute in the equation and get the slope as follows:
m = (12-0) / (4-1) = 12/3 = 4
Now, the equation of the line became: y = 4x + c
The given points all satisfy the equation of the line, we can use any of them to substitute in the equation and get the value of c.
For instance, I will use the first point: (1,0)
y = 4x + c
0 = 4(1) + c
c = -4
The equation of the line is:
y = 4x - 4
What is the number 0.093 expressed in Scientific notation?
A. 9.3 * 10^2
B. 0.93 * 10^1
C. 9.3 * 10^-3
D. 9.3 * 10^-2
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=
9.3 x 10^-2
answer
D. 9.3 * 10^-2
Option D is correct. 0.093 can be expressed in scientific notation as [tex]9.3 \times 10^{-2}[/tex].
To express the number 0.093 in scientific notation, we need to determine the coefficient and exponent.
0.093 can be written as 9.3 multiplied by a power of 10.
Since 0.093 is less than 1, the exponent should be negative.
To shift the decimal point to the right to form the original number, we move it three places to the right:
[tex]0.093 \rightarrow 9.3 \times 10^{-2}[/tex]
Therefore, 0.093 can be expressed in scientific notation as [tex]9.3 \times 10^{-2}[/tex], option D is correct.
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Verify the identity Cotx/tanx+cotx = 1-sin^2x
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[tex]\bf \cfrac{\frac{cos(x)}{sin(x)}}{\frac{1}{cos(x)sin(x)}}\implies \cfrac{cos(x)}{\underline{sin(x)}}\cdot \cfrac{cos(x)\underline{sin(x)}}{1}\implies cos^2(x)\implies 1-sin^2(x)[/tex]
The price of one share of a stock fell $12.50 each day for 8 days. Which expression represents this situation?
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Find the maximum and minimum values of the function.
y=7cosx
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So maximum of 7 cos x = 7 and minimum is -7.
Can someone please solve this?
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[tex]\bf \begin{cases} x=3\implies &x-3=0\\ x=2\implies &\begin{cases} x-2=0\\ x-2=0\\ x-2=0 \end{cases} \end{cases} \\\\\\ (x-3)(x-2)~~(x-2)(x-2)=\textit{original polynomial} \\\\\\ (x^2-5x+6)~~(x^2-4x+4)=y \\\\\\ x^4-4x^3+4x^2-5x^3+20x^2-20x+6x^2-24x+24=y \\\\\\ 1x^4-9x^3+30x^2-44x+24=y[/tex]
Stuck on this question. Any help would be appreciated.
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10-2h
r = --------------
5
(10-2h)^2
Then r^2 = ----------------
25
Substitute this r and this r^2 into the first equation and simplify. This will result in a formula for V as a function of h (V in terms of h).
tep 1: –10 + 8x < 6x – 4 Step 2: –10 < –2x – 4 Step 3: –6 < –2x Step 4: ________
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I hope this helps love! :)
2x^5+12x^4+16x^3-12x^2-18x=0
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On the blueprint of a house, 48 millimeters represents 7 meters. the length of the living room is 60 millimeters on the blueprint, what is the actual length of the living room?