Answer:
z-score=7.5-6 1.5
___________=______=0.5
3 3
Step-by-step explanation:
Look up -0.1 on a z-table. The result is 0.4602. The means there is a 0.4602 probability the random variable will be below 5.7.
The find the probability the random variable will be between 7.5 and 5.7, simply subtract the two probabilities we found (above) from one another:
0.6915+-+0.4602+=+0.2313
So, there is a 0.2313 probability the random variable will fall between 7.5+and 5.7.
A baseball player had a batting average of 0.334 for the season. Write this numbwr in expanded form
Answer:
0.300 + 0.030 + 0.004
or
0.100 x 3 + 0.01 x 3 + 0.001 x 4
Please help
Solve the inequality.
|14 – 5x] > 8
[?]
x <
or x >
A
Answer:
x< -4/1 or x > 6/5
If our answers are different, just say so :)
(1/5) to the power of 2
Answer:
0.04
Step-by-step explanation:
first we change 1/5 into a decimal which is 0.2
the we just multiply it by itself which is
0.04
Which of the following statements is true for the following data set?
7, 5, 6, 4, 7, 8, 12
a. Only the mean and median are equal.
b. Only the mean and mode are equal.
c. Only the median and mode are equal.
d. The mean, median, and mode are all equal.
Answer:
D.
Step-by-step explanation:
Mean : 7 + 5 + 6 + 4 + 7 + 8 + 12 = 12 + 10 + 7 + 20 = 30 + 19 = 49. 49/7= 7
Mode : 7.
Median 4 , 4, 6, 7, 7, 8, 12. 7 is the middle number
The points represented by the (x,y) coordinate pairs in the table below all lie on line k. What is the slope of line k?
Answer:
the slope is -2/1
You can find it by using the equation [tex]\frac{y_{1}- y_{2} }{x_{1}- x_{2} }[/tex]
so 3-1/1-2= 2/-1, which is also written as -2/1
If z=(x+y)e^y and x=5t and y=1−t^2, find the following derivative using the chain rule. Enter your answer as a function of t.
dz/dt= ?
By the chain rule, if [tex]z=f(x,y)=f(x(t),y(t))[/tex], then
[tex]\dfrac{\mathrm dz}{\mathrm dt} = \dfrac{\partial f}{\partial x}\dfrac{\mathrm dx}{\mathrm dt} + \dfrac{\partial f}{\partial y}\dfrac{\mathrm dy}{\mathrm dt}[/tex]
We have [tex]f(x,y)=(x+y)e^y[/tex], for which
• [tex]\dfrac{\partial f}{\partial x} = e^y[/tex]
• [tex]\dfrac{\partial f}{\partial y} = e^y + (x+y)e^y = (x+y+1)e^y[/tex]
and [tex]x(t)=5t[/tex] and [tex]y(t)=1-t^2[/tex], so that
• [tex]\dfrac{\mathrm dx}{\mathrm dt} = 5[/tex]
• [tex]\dfrac{\mathrm dy}{\mathrm dt} = -2t[/tex]
Putting everything together, we get
[tex]\dfrac{\mathrm dz}{\mathrm dt} = 5e^y - 2t(x+y+1)e^y \\\\ \dfrac{\mathrm dz}{\mathrm dt} = 5e^{1-t^2} - 2t(5t-t^2+2)e^{1-t^2} = \boxed{\left(2t^3-10t^2-4t+5\right)e^{1-t^2}}[/tex]
The solution of the derivative using the chain rule is [tex]\dfrac{dz}{dt}=(2t^3-10t^2-4t+5)e^{1-t^2}[/tex].
What is the Chain rule?The chain rule explains how to calculate a composite function's derivative.
What is a composite function?If you may write [tex]f(g(x))[/tex] , a function is composite. It's a function within a function, or a function of a function, in other words.
By the chain rule, we can write if [tex]z=f(x,y)=f(x(t),y(t))[/tex], then,
[tex]\dfrac{dz}{dt}=\dfrac{\partial f}{\partial x} \dfrac{dx}{dt}+\dfrac{\partial f}{\partial y} \dfrac{dy}{dt}[/tex]
As it is given to us, [tex]f(x,y)=(x+y)e^y[/tex], therefore, we can write,
[tex]\dfrac{\partial f}{\partial x}=e^y[/tex][tex]\dfrac{\partial f}{\partial y}=e^y+(x+y)e^y=(x+y+1)e^y[/tex]And x(t)=5t, while y(t)=1-t², So,
[tex]\dfrac{dx}{dt}=5[/tex][tex]\dfrac{dy}{dt}=-2t[/tex]Now, Substitute all the values together, in the equation,
[tex]\dfrac{dz}{dt}=\dfrac{\partial f}{\partial x} \dfrac{dx}{dt}+\dfrac{\partial f}{\partial y} \dfrac{dy}{dt}[/tex]
Substituting the values we will get,
[tex]\dfrac{dz}{dt} &=(5 \times e^y)+[-2t(x+y+1)e^y]\\\\[/tex]
[tex]=5e^{1-t^2}-2t(5t-t^2+2)e^{1-t^2}\\\\=(2t^3-10t^2-4t+5)e^{1-t^2}[/tex]
Hence, the solution of the derivative using the chain rule is [tex]\dfrac{dz}{dt}=(2t^3-10t^2-4t+5)e^{1-t^2}[/tex].
Learn more about Chain Rule:
https://brainly.com/question/2285262
solve -5x+y=1 and 9x-2y=4 using multiplication and then elimination.
Answer:
x = - 6, y = - 29
Step-by-step explanation:
Elimination:
2*(-5x + y = 1) = -10x + 2y = 2
9x - 2y = 4 = + (9x - 2y = 4) =
-x = 6
x = -6
9(-6)-2y=4
-54-2y=4
-2y=58
y=-29
State the domain of each function.
1. [tex]g(a)=\sqrt{1+a^{2}}[/tex]
2. [tex]f(x)=\frac{2}{x} + \frac{4}{x+1}[/tex]
Please show your work, as the steps are the only reason I'm asking.
Answer:
[tex] \rm \displaystyle g(a) = \sqrt{1 + {a}^{2} } \xrightarrow{ \rm Domain}a \in \mathbb{R}[/tex]
[tex] \rm\displaystyle f(x)=\frac{2}{x} + \frac{4}{x+1} \xrightarrow{ \rm Domain}x \in \mathbb{R} / \{0, - 1 \}[/tex]
Step-by-step explanation:
Question-1:we want to figure out the domain of the following function:
[tex] \displaystyle g(a) = \sqrt{1 + {a}^{2} } [/tex]
remember that, the domain of an even root function are all values of x for which the redicand is positive or 0 that is being said the domain of the function g(a) belong to [tex]\mathbb{R}[/tex] . another way to think about it, the domain of square root function f(x) belong to x≥0. In this case we have square variable in the redical so when we input a negative number, it yields a positive number with that said the domain of the function g(a) belong to all the real numbers.Thus,
[tex] \rm \displaystyle g(a) = \sqrt{1 + {a}^{2} } \xrightarrow{ \rm Domain}a \in \mathbb{R}[/tex]
Question-2:we'd like to find the domain of the following function:
[tex] \displaystyle f(x)=\frac{2}{x} + \frac{4}{x+1}[/tex]
in order to do so we need to simplify it further,so simplify addition in order to do so the first step is to figure out the LCM of the denominator i.e x(x+1) ⇒ x²+x, secondly divide the denominator of every fraction by the LCM and multiply the result by the numerator of very fraction ,then finally add them therefore,
[tex] \displaystyle f(x)=\frac{2x + 2+4x}{ {x}^{2} + x } \\ \displaystyle \boxed{\frac{6x + 2}{ {x}^{2} + x }} [/tex]
we know that the domain of a rational function are all the values of x for which the denominator is different than 0.
the denominator of the function would be 0 when x=0 and -1 thus,
[tex] \rm\displaystyle f(x)=\frac{2}{x} + \frac{4}{x+1} \xrightarrow{ \rm Domain}x \in \mathbb{R} / \{0, - 1 \}[/tex]
and we're done!
6 large boxes an 2 small boxes weighs 92 kilograms 3 large boxes and 5 small boxes weigh 71 kilograms how much does each type of box weigh
Answer:
Large Box weighs
13.25 kg and Small box weighs 6.25 kg
Step-by-step explanation:
Let the large box be L and small box be S
According to question,
6L + 2S = 92 kg .... (i)
and 3L + 5S = 71 kg ....(ii)
Subtracting we get,
3L - 3S = 21 kg
or L - S = 7 kg
or L = 7 + S kg ... (iii)
Now, putting the value of L in eqn (i) we get
6 (7+S) + 2S = 92 kg
or 42 + 6S + 2S = 92
or 8S = 50
or S = 50/8
or S = 6.25 Kg
Then, 6L + (2×6.25) = 92 kg
or, 6L = 92 - 12.5
or, L = 79.5/6
or, L = 13.25 kg
Three foreign languages are offered at Cliff High School. 1/6 of the students take French, 1/5 take Spanish, and 1/3 German. Which
fraction represents the number of students taking a foreign language at Cliff HS?
Answer:
1/3
Step-by-step explanation:
The perimeter of the triangle below is 4x + 3y. Find the measure of the missing side.
Answer:
let side be t
t + x + y +x + y = 4x + 3y
t + 2x + 2y = 4x + 3y
t = 2x +y
so missing side length is 2x + y
(PLEASE ANSWER) Drag the inequalities and end points to make the domain below correct
Answer:
Step-by-step explanation:
-3≤x≤3
Find the exact sum or difference. (1 point)
$5.03-$3.30=
A. $1.67
B. $1.63
C. $1.73
D. $1.83
Answer:
C. $1.73
Step-by-step explanation:
$5.03
$3.30
---------
$1.73
4. Tabatha is dining out at Mandee's and decides to get an order of curly fries,
chicken fingers, and a coca-cola. The total cost of the food with sales tax came to
$18.61. If Tabatha decides to give the cashier a 20% gratuity (tip), what does her
total bill come to?
Help I need an equation and an answer
37. Mia won $77 in a raffle at her team's fundraiser. Later she split it amongst her friends and gave $14 to each, keeping $21 for herself. How many friends did she share it with?
she share it to thirty seven people
What are two ways you could represent the expression 3-4n
There are not just "the two ways" to represent this expression. There are two ways, surely, but they are not the only ways as implied.
You could expose 4 and get something like [tex]4(\frac{3}{4}-n)[/tex] or expose 3 and get something like [tex]3(1-\frac{4}{3}n)[/tex].
But you could also say something like [tex]3-(1+3)n=3-n-3n=-3(n-1)-n[/tex]... in fact there are a lot of ways to write any expression.
Hope this helps :)
Finds real root off(x)=x3 +x2 +x+7=0
9514 1404 393
Answer:
x ≈ −2.10487278573
Step-by-step explanation:
I find a graphing calculator to be a very useful tool for the purpose. It shows the only real root is irrational and gives an approximation as x=-2.105.
The calculator also provides the means to perform Newton's method iteration easily to refine the value of the root to full calculator precision.
__
The Newton's method iterator for finding the next iteration of the root (x') is ...
x' = x - f(x)/f'(x)
Starting with the approximation shown on the graph, it only takes two iterations to get the root to the full precision of the calculator.
a rectangle is 9 inches wide and 2 inches long. What is the area of this rectangle
Answer:
18 inches²
Step-by-step explanation:
The formula for the area of a rectangle is: [tex]A=lw[/tex]
l = lengthw = widthSubstitute the given values for the variables.
[tex]A=(9)(2)=18[/tex]
Therefore, the area of the rectangle is 18 inches².
Answer: Area = 18 inches²
Concept:
Here, we need to know how to find the area of a rectangle.
Area (rectangle) = l × w
l = length
w = width
If you are still confused, please refer to the attachment below for a graphical explanation.
Solve:
Given information
l = 2 inches
w = 9 inches
Given equation
Area = l × w
Substitute values into the equation
Area = 2 × 9
Area = 18 inches²
Hope this helps!! :)
Please let me know if you have any questions
A parallelogram has a base of 10 centimeters and a height of 4 centimeters. What is the area of the parallelogram?
Answer:
Formula = base x height
10 x 4 = 40
Area = 40cm
Step-by-step explanation:
Barry is checking his bank account for a few transactions that he completed. He had $230
in his account to start and then contributed a check for $360. He paid his water, electric and
cable bill, which were $100, $46 and $107. How much money is in his bank account?
A. $253
B. $383
C. $590
D. $337
Answer:
D.
Step-by-step explanation:
$230 + $360 = $590
$590 - $253* = $337
$337
*( total sum of all the bills )
State the gradient of the line 2y = 3 - 2x.
Answer:
Step-by-step explanation:
2y = 3 -2x
Rearrange the equation to slope-intercept form
y = -x + 3/2
Slope of line is 3/2.
Among 2000 respondents, 113 said that they've experienced depression in the past 12 months. What percentage of respondents said they've experienced depression in the past 12 months?
Type your answer as a percent without the percent sign. Do not round.
Answer:
5.65%
Step-by-step explanation:
Find the percent of respondents that said they had experienced depression by dividing 113 by 2000:
113/2000
= 0.0565
Multiply this by 100:
0.0565(100)
= 5.65
So, 5.65% of the respondents said they had experienced depression in the past 12 months.
New Orleans is 2 meters below sea level.
Baton Rouge is 17 meters above sea level.
How much higher is Baton Rouge than New Orleans?
Answer:
Baton Rouge is 19 meters higher that New Orleans.
Does anyone know how to finish this equation?
A troop leader recorded whether the members of two troops prefer hiking or swimming. The troop leader plans to create a two-way table to display the results.
Which variables can the troop leader use as the row and column headings of the table?
troop number and number who prefer hiking
troop number and activity preference
activity preference and number of troop 1 members
activity preference and number of troop 2 members
Answer:
troop number and activity preference or b
Step-by-step explanation:
Do the following graphs represent a mathematical function? If not, explain why.
Answer:
Yes for bothStep-by-step explanation:
In such cases use the vertical line test. If the graph is intersected at more than one point, it is not a function.
Both the given graphs represent a function as both pass the vertical line test.
Answer:
Yes
Step-by-step explanation:
Whenever you are given a problem that's asking to see if a graph is a function or not, always use the vetical line test to determine that. In short, you draw a line accross each y axis point and if the line only goes accross one point throughout the graph then it's a function. Following the test we will see that both graphs are indeed functions.
Best of Luck!
Find the value of x.
95
38°
X
Answer:
47
Step-by-step explanation:
x is one of the three angles of a triangle. The other two are given as 95 and 38.
Together all three have to make 180 degrees.
x + 95 + 38 = 180
x + 133 = 180
x = 180 - 133
x = 47
Answer:
47
Step-by-step explanation:
as we know that sum of a triangle is always=180°
so x+38°+95°=180
so x+133=180
and x=180-133
so x= 47
Find the output, k, when the input, t, is -7.
k= 10t - 19
k=
Answer:
Here is the answer . hope this helps.
PLS PLS PLS IM BEGGING YOU, HELP ME, i’ve been trying so hard to solve this for hours and i still dont get it :( pls help me
Answer:
m=79
t=54
Step-by-step explanation:
yes these are the answers
Answer:
angle t = 54 degrees
angle m=79(alternate angles)
Step-by-step explanation:
angle p=126 degrees
angle z=79 degrees
angle p + angle t=180(allied angles)
126 + t =180
t =180-126
t = 54 degrees
u=79(vertically opposite angles)
therefore;
angle m=79(alternate angles)
HELP ME HELP ME !!
A line is drawn so that it passes through the points (3, 4) and (4, 1).
What is the slope of the line?
A) 1/3
B) 3
C) -1/3
D)-3
Answer:
-3
Step-by-step explanation: