Answer:
[tex] P(X<12000)[/tex]
And for this case we can use the cumulative distribution function given by:
[tex] P(X\leq x) =\frac{x-a}{b-a}, a \leq x \leq b[/tex]
And using this formula we have this:
[tex] P(X<12000)= \frac{12000-10100}{14700-10100}= 0.41[/tex]
Then we can conclude that the probability that your bid will be accepted would be 0.41
Step-by-step explanation:
Let X the random variable of interest "the bid offered" and we know that the distribution for this random variable is given by:
[tex] X \sim Unif( a= 10100, b =14700)[/tex]
If your offer is accepted is because your bid is higher than the others. And we want to find the following probability:
[tex] P(X<12000)[/tex]
And for this case we can use the cumulative distribution function given by:
[tex] P(X\leq x) =\frac{x-a}{b-a}, a \leq x \leq b[/tex]
And using this formula we have this:
[tex] P(X<12000)= \frac{12000-10100}{14700-10100}= 0.41[/tex]
Then we can conclude that the probability that your bid will be accepted would be 0.41
A homogeneous second-order linear differential equation, two functions y 1y1 and y 2y2, and a pair of initial conditions are given. First verify that y 1y1 and y 2y2 are solutions of the differential equation. Then find a particular solution of the form y = c1y1 + c2y2 that satisfies the given initial conditions. Primes denote derivatives with respect to x.
y'' + 49y = 0; y1 = cos(7x) y2 = sin(7x); y(0) = 10 y(0)=-4
1.Why is the function y, = e * a solution to the differential equation?
A. The function y1 =e 4X is a solution because when the function and its indefinite integral, , are substituted into the equation, the result is a true statement.
B. The function y1 = e 4X is a solution because when the function and its second derivative, y1" = 16 e 4x, are substituted into the equation, the result is a true statement.
2. Why is the function y2 solution the differential equation?
A. The function y2 = e 4x is a solution because when the function and its indefinite integral, are substituted into the equation, the result a true statement. The function y2 = e 4X is a solution because when the function and its second derivative, y2" = 16 e -4x are substituted into the equation, the result is a true statement. The particular solution of the form y = c, y, +c,y2 that satisfies the initial conditions y(0) 2 and y'(0) = 9 is y =.
Answer:
[tex]y = 10cos (7x) - \frac{4}{7}sin ( 7x )[/tex]
B.
B.
[tex]y = \frac{17}{8}e^4^x - \frac{1}{8}e^-^4^x[/tex]
Step-by-step explanation:
Question 1:
- We are given a homogeneous second order linear ODE as follows:
[tex]y'' + 49y = 0[/tex]
- A pair of independent functions are given as ( y1 ) and ( y2 ):
[tex]y_1 = cos ( 7x )\\\\y_2 = sin ( 7x )[/tex]
- The given ODE is subjected to following initial conditions as follows:
[tex]y ( 0 ) = 10\\\\y ' ( 0 ) = -4[/tex]
- We are to verify that the given independent functions ( y1 ) and ( y2 ) are indeed the solution to the given ODE. If the functions are solutions then find the complete solution of the homogeneous ODE of the form:
[tex]y = c_1y_1 + c_2y_2[/tex]
Solution:-
- To verify the functions are indeed the solution to the given ODE. We will plug the respective derivatives of each function [ y1 and y2 ] into the ODE and prove whether the equality holds true or not.
- Formulate the second derivatives of both functions y1 and y2 as follows:
[tex]y'_1 = -7sin(7x) , y''_1 = -49cos(7x)\\\\y'_2 = -7cos(7x) , y''_2 = -49sin(7x)\[/tex]
- Now plug the second derivatives of each function and the functions itself into the given ODE and verify whether the equality holds true or not.
[tex]y''_1 + 49y_1 = 0\\\\-49cos(7x) + 49cos ( 7x ) = 0\\0 = 0\\\\y''_2 + 49y_2 = 0\\\\-49sin(7x) + 49sin ( 7x ) = 0\\0 = 0\\\\[/tex]
- We see that both functions [ y1 and y2 ] holds true as the solution to the given homogeneous second order linear ODE. Hence, are the solution to given ODE.
- The complete solution to a homogeneous ODE is given in the form as follows:
[tex]y = c_1y_1 + c_2y_2\\\\y = c_1*cos(7x) + c_2*sin(7x)\\[/tex]
- To complete the above solution we need to determine the constants [ c1 and c2 ] using the initial conditions given. Therefore,
[tex]y (0) = c_1cos ( 0 ) + c_2sin ( 0 ) = 10\\\\y'(0) = -7c_1*sin(0) + 7c_2*cos(0) = -4\\\\c_1 ( 1 ) + c_2 ( 0 ) = 10, c_1 = 10\\\\-7c_1(0) + 7c_2( 1 ) = -4 , c_2 = -\frac{4}{7}[/tex]
- Now we can write the complete solution to the given homogeneous second order linear ODE as follows:
[tex]y = 10cos (7x) - \frac{4}{7}sin ( 7x )[/tex] .... Answer
Question 2
- We are given a homogeneous second order linear ODE as follows:
[tex]y'' -16y =0[/tex]
- A pair of independent functions are given as ( y1 ) and ( y2 ):
[tex]y_1 = e^4^x\\\\y_2 = e^-^4^x[/tex]
- The given ODE is subjected to following initial conditions as follows:
[tex]y( 0 ) = 2\\y'( 0 ) = 9[/tex]
- We are to verify that the given independent functions ( y1 ) and ( y2 ) are indeed the solution to the given ODE. If the functions are solutions then find the complete solution of the homogeneous ODE of the form:
[tex]y = c_1y_1 + c_2y_2[/tex]
Solution:-
- To verify the functions are indeed the solution to the given ODE. We will plug the respective derivatives of each function [ y1 and y2 ] into the ODE and prove whether the equality holds true or not.
- Formulate the second derivatives of both functions y1 and y2 as follows:
[tex]y'_1 = 4e^4^x , y''_1 = 16e^4^x\\\\y'_2 = -4e^-^4^x , y''_2 = 16e^-^4^x[/tex]
- Now substitute the second derivatives of each function and the functions itself into the given ODE and verify whether the equality holds true or not.
[tex]y''_1 - 16y_1 = 0\\\\16e^4^x - 16e^4^x = 0\\\\0 = 0\\\\y''_2 - 16y_2 = 0\\\\16e^-^4^x - 16e^-^4^x = 0\\\\0 = 0[/tex]
- We see that both functions [ y1 and y2 ] holds true as the solution to the given homogeneous second order linear ODE. Hence, are the solution to given ODE.
- The complete solution to a homogeneous ODE is given in the form as follows:
[tex]y = c_1y_1 + c_2y_2\\\\y = c_1*e^4^x + c_2*e^-^4^x[/tex]
- To complete the above solution we need to determine the constants [ c1 and c2 ] using the initial conditions given. Therefore,
[tex]y ( 0 ) = c_1 * e^0 + c_2 * e^0 = 2\\\\y' ( 0 ) = 4 c_1 * e^0 - 4c_2 * e^0 = 9\\\\c_1 + c_2 = 2 , 4c_1 - 4c_2 = 9\\\\c_1 = \frac{17}{8} , c_2 = -\frac{1}{8}[/tex]
- Now we can write the complete solution to the given homogeneous second order linear ODE as follows:
[tex]y = \frac{17}{8} e^4^x - \frac{1}{8}e^-^4^x[/tex] .... Answer
$5.60 is what perecentage of $17.50?
Answer:
To find it's percentage divide $5.60 by
$17.50 and multiply it by 100%
That is
5.60/ 17.50 × 100%
= 32%
Hope this helps you
what solid 3D object is produced by rotating the triangle about line m with a height of 8 and radius 4
Answer:
The diagram of the question is missing, I found a matching diagram, and it is attached to this answer
The 3D object produced is a cone with height 8 and diameter 8 (radius 4)
Step-by-step explanation:
A 3 dimensional solid figure can be formed when a 2 dimensional object is rotated about a line without displacing the object.
when the object in the diagram is rotated about line m, the rotation forms an object with a circular base of diameter 8 units (radius 4) from the base of the triangle and height 8 units, and the 3D object formed is called a cone.
The average lifetime of a set of tires is 3.4 years. The manufacturer will replace any set of tires failing within three years of the date of purchase. The lifetime of these tires is known to follow an exponential distribution. What is the probability that the tires will fail within three years of the date of purchase?
Answer: the probability that the tires will fail within three years of the date of purchase is 0.12
Step-by-step explanation:
The average lifetime of a set of tires is 3.4 years. It means that μ = 3.4
Decay parameter, m = 1/3.4 = 0.294
The probability density function is
f(x) = me^-mx
Where x is a continuous random variable representing the time interval of interest(the reliability period that we are testing)
Since x = 3 years,
Therefore, the probability that the tires will fail within three years of the date of purchase is
f(3) = 0.294e^-(0.294 × 3)
f(3) = 0.294e^- 0.882
f(3) = 0.12
Please answer this correctly
Answer:
13 students
Step-by-step explanation:
At least 30 and fewer than 67 makes it 30-66
So,
30-66 => 13 students
Answer:
16
Step-by-step explanation:
There are two columns in the diagram.
The column headed stem represents tens while the column headed leaf represents units. e.g. 2 3 = 23
So we just have to count how many of the numbers are less than 8 in the 6th Stem column and all the numbers below it, which are:
20, 23, 28, 31, 31, 34, 38, 40, 44, 50, 51, 53, 54, 65, 65, 66
What is the slope of a line that is perpendicular to the line 2y – 3x = 8?
Answer:
[tex] = \frac{3}{2} [/tex]
Step-by-step explanation:
[tex]y = mx + c[/tex]
Here,
m => slopec => interceptIn this equation ,
[tex]2y - 3x = 8[/tex]
to find the value of m or the value of slope we have to solve for y
Let's solve,
[tex]2y - 3x = 8 \\ 2y = 8 + 3x \\ \frac{2y}{2} = \frac{8 + 3x}{2} \\ y = 4 + \frac{3x}{2} \\ y = \frac{3x}{2} + 4[/tex]
So, the slope is,
[tex] = \frac{3}{2}[/tex]
Need help ASAP!! thank you sorry if u can’t see it good :(
Answer/Step-by-step explanation:
==>Given:
=>Rectangular Pyramid:
L = 5mm
W = 3mm
H = 4mm
=>Rectangular prism:
L = 5mm
W = 3mm
H = 4mm
==>Required:
a. Volume of pyramid:
Formula for calculating volume of a rectangular pyramid us given as L*W*H
V = 5*3*4
V = 60 mm³
b. Volume of prism = ⅓*L*W*H
thus,
Volume of rectangular prism given = ⅓*5*3*4
= ⅓*60
= 20mm³
c. Volume of the prism = ⅓ x volume of the pyramid
Thus, 20 = ⅓ × 60
As we can observe from our calculation of the solid shapes given, the equation written above is true for all rectangular prism and rectangular pyramid of the same length, width and height.
Which of the following is a polynomial with roots: − square root of 3 , square root of 3, and −2? (6 points) Question 7 options: 1) x3 − 2x2 − 3x + 6 2) x3 − 3x2 − 5x + 15 3) x3 + 2x2 − 3x − 6 4) x3 + 3x2 − 5x − 15
Answer:
The polynomial is [tex]x^{3} - 1.46x^{2} - 3.93x + 6[/tex]
Step-by-step explanation:
A nth order polynomial f(x) has roots [tex]x_{1}, x_{2}, ..., x_{n}[/tex] such that [tex]f(x) = (x - x_{1})*(x - x_{2})*...*(x - x_{n}}[/tex],
Which of the following is a polynomial with roots: − square root of 3 , square root of 3, and −2?
So
[tex]x_{1} = x_{2} = \sqrt{3}[/tex]
[tex]x_{3} = -2[/tex]
Then
[tex](x - \sqrt{3})^{2}*(x - (-2)) = (x - \sqrt{3})^{2}*(x + 2) = (x^{2} -2x\sqrt{3} + 3)*(x + 2) = x^{3} + 2x^{2} - 2x^{2}\sqrt{3} - 4x\sqrt{3} + 3x + 6[/tex]
Since [tex]\sqrt{3} = 1.73[/tex]
[tex]x^{3} + 2x^{2} - 3.46x^{2} - 6.93x + 3x + 6 = x^{3} - 1.46x^{2} - 3.93x + 6[/tex]
The polynomial is [tex]x^{3} - 1.46x^{2} - 3.93x + 6[/tex]
The sum of a number and its reciprocal is 41/20. Find the numbers. smaller value larger value
Answer:
The numbers are 5/4 and 4/5The smaller value is 4/5The larger value is 5/4Step-by-step explanation:
Let the number be x.
The reciprocal of the number will be 1/x
If the sum of the number and its reciprocal is 41/20, this can be represented as;
[tex]x+\frac{1}{x} = 41/20\\\frac{x^{2}+1}{x} = \frac{41}{20} \\20x^{2} +20 = 41x\\20x^{2} -41x+20 = 0\\[/tex]
Uisng the general formula to get x
x = -b±√b²+4ac/2a
x = 41±√41²-4(20)(20)/2(20)
x = 41±√1681-1600/40
x = 41±√81/40
x = 41±9/40
x = 50/40 or 32/40
x = 5/4 or 4/5
if the value is 5/4, the other value will be 4/5
The numbers are 5/4 and 4/5
The smaller value is 4/5
The larger value is 5/4
Answer:
a=5/4 or 4/5
Therefore, the smaller value = 4/5
The larger value = 5/4
Step-by-step explanation:
Let the number be represented by a
And it's reciprocal be represented by 1/a
So we have
a + 1/a = 41/20
Cross Multiply
20( a +1/a) = 41
20a +20/a =41
Find the LCM which is a
20a² + 20 = 41a
20a² + 20 - 41a =0
20a² - 41a +20 = 0
20a²-25a - 16a + 20 =0
5a(4a - 5) -4( 4a - 5) = 0
(5a - 4)(4a - 5) = 0
5a - 4 = 0
5a = 4
a = 4/5
or
4a - 5 = 0
4a =5
a = 5/4
Therefore, the number which is represented by a is
1) a = 4/5 while it's reciprocal which is 1/a is 5/4
or
2) a = 5/4 which it's reciprocal which is 1/a = 4/5
Therefore, the smaller value = 4/5
The larger value = 5/4
Find the volume of the cone.
Diameter: 20 m, Slant Height: 26 m
Round to the nearest whole number.
Volume
=
[?] m3
Answer:
2513the step-by-step explanation for height first :
[tex]h=\sqrt{h^{2} } +r^{2} =26[/tex]
[tex]h=\sqrt{h^{2} } +10^{2} =676[/tex]
[tex]h=\sqrt{h^{2} } + 100 = 676[/tex]
[tex]100-100 = 0[/tex]
[tex]676-100=576[/tex]
[tex]\sqrt{576}[/tex]
[tex]height =[/tex] 24 m
________________
step-by-step explanation for the problem :
FORMULA : [tex]v = \frac{1}{3}[/tex] · [tex]\pi[/tex] · [tex]r^{2}[/tex] · [tex]h[/tex]
v = [tex]\frac{1}{3}[/tex] · [tex]\pi[/tex] · [tex]10^{2}[/tex] · [tex]24[/tex] = [tex]800\pi[/tex] = [tex]2513.27412[/tex] = 2513
Find the scale ratio for the map described below. 1 mm(map) equals 500 m (actual) The scale ratio is 1 to ? .
Answer:
1 : 500,000
Step-by-step explanation:
The scale of a map scale refers to the relationship (or ratio) between the distance on a map and the corresponding distance on the ground.
In the given map:
1 mm(map) = 500 m (actual)
1 meter = 1000 millimeter
Therefore:
500 meters = 1000 X 500 =500,000 millimeter
Therefore, the scale ratio of the map is:
1:500,000
In a certainâ state, the recent average critical reading standardized test score was 514. Assume that the standard deviation is 50 and that standardized test scores are Normally distributed. Complete partsâ (a) andâ (b) below. Include a Normal curve for each part.
Required:
a. What percentage of standardized test takers scored 550 or less?
b. What percentage of standardized test takers scored 524?
Answer:
a) Percentage of standardized test takers that scored 550 or less = 76.4%
b) Percentage of standardized test takers that scored 524 = 0.782%
Step-by-step explanation:
This is a normal distribution problem with
Mean = μ = 514
Standard deviation = σ = 50
a) Percentage of standardized test takers scored 550 or less = P(x ≤ 550)
We first normalize or standardize 550
The standardized score for any is the value minus the mean then divided by the standard deviation.
z = (x - μ)/σ = (550 - 514)/50 = 0.72
To determine the required probability
P(x ≤ 550) = P(z ≤ 0.72)
We'll use data from the normal distribution table for these probabilities
P(x ≤ 550) = P(z ≤ 0.72) = 0.76424 = 76.424%
The normal curve for this question and the b part are sketched in the first attached image to this solution.
b) Percentage of standardized test takers that scored 524 = P(x = 524)
On standardizing,
z = (x - μ)/σ = (524 - 514)/50 = 0.20
For this part, since it's an exact probability, we will use the normal distribution formula
P(z = Z) = [1/(σ√2π)] × e^(-z²/2)
Since z = (x - μ)/σ
It can be written properly as presented in the second attached image to this question.
Putting x = 524 or z = 0.20 in this expression, we get
P(x = 524) = P(z = 0.20) = 0.0078208539 = 0.782%
Hope this Helps!!!
2x^2+8x = x^2-16
Solve for x
Answer:
x=-4
Step-by-step explanation:
[tex]2x^2+8x=x^2-16[/tex]
Move everything to one side:
[tex]x^2+8x+16=0[/tex]
Factor:
[tex](x+4)^2=0[/tex]
By the zero product rule, x=-4. Hope this helps!
Answer:
x=-4
Step-by-step explanation:
Move everything to one side and combine like-terms
x²+8x+16
Factor
(x+4)²
x=-4
Which lists the ratios in order from least to greatest 2:9,1:6,7:36
Answer:
1:6, 7:36, 2:9
Step-by-step explanation:
2 : 9 → 8 : 36
1 : 6 → 6 : 36
7 : 36
Least → Greatest
1:6, 7:36, 2:9
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down,drag into the correct position in the answer box.Release your mouse button when the item is place. If you change your mind,drag the item to the trash can,click the trash and to clear all your answers. Divide the following polynomials,then place the answer in the proper location on the grid. Write the answer in descending powers of x. 9x^2-18x-7 divided by (3x+1)
Answer:
[tex]\boxed{\sf \ \ 9x^2-18x-7 \ \ divided \ by \ (3x+1) \ is \ (3x-7) \ }[/tex]
Step-by-step explanation:
Hello,
let's find a and b reals so that
[tex]9x^2-18x-7=(3x+1)(ax+b)[/tex]
[tex](3x+1)(ax+b)=3ax^2+(3b+a)x+b[/tex]
we identify the terms in [tex]x^2[/tex]
9 = 3a
we identify the terms in x
-18 = 3b + a
we identify the constant terms
-7 = b
so ti goes with a = 9/3 = 3, b = -7
so we can write
[tex]9x^2-18x-7=(3x+1)(3x-7)[/tex]
so [tex]9x^2-18x-7 \ divided \ by \ (3x+1) \ is \ (3x-7)[/tex]
hope this helps
Kaya figured out that she will need $47,592 to attend college. What is the amount rounded to the nearest ten thousand? Help meeee
Answer:
50,000
Step-by-step explanation:
ten thousand thousand hundreds tens ones
4 7 5 9 2
When rounding to the ten thousands, we look at the thousands place
If it is 5 or higher we round the ten thousands place up
7 is five or higher so we round the 4 up one place 4 becomes 5 and the rest becomes 0
5 0 0 0 0
Answer:
$50,000
Step-by-step explanation:
=> $47,592
While rounding off to the nearest thousand, we check the thousands place. If the digit in the thousands place is greater than 5, 1 will be added to the T. Th. place while if its less than 5, there will be no change and The digits except the ten thousands place will all become zero.
So,
=> $50,000
someone pls help me! ❤️❤️❤️
Answer:
(x-1) ( x -i) (x+i)
Step-by-step explanation:
x^3 -2x^2 +x-2
Factor by grouping
x^3 -2x^2 +x-2
x^2(x-2) +1(x-2)
Factor out (x-2)
(x-2) (x^2+1)
Rewriting
(x-1) ( x^2 - (-1)^2)
(x-1) ( x -i) (x+i)
Answer:
Should be b
Step-by-step explanation:
Since it's a multiple choice question you know that -2 or 2 has to be a root for the cubic.
You can test both -2 and 2 and see that replacing x for 2 has the expression evaluate to 0.
Then, since you know the imaginary roots have to be conjugates, you get B.
Can someone please help
Use the In key on your calculator to estimate
the logarithm.
In 44
Round your answer to the nearest thousandth.
Answer:
3.784
Step-by-step explanation:
Please answer this correctly
Answer:
1/2
Step-by-step explanation:
There is a 50/50 chance for the coin to land either heads or tails. Convert that to probability and it is 1/2.
The only time a coin would not be 50/50 chance is if the coin is weighted.
Answer:
1/2 is probability
becoz one side is head or one is tail
Decide whether the method of undetermined coefficients together with superposition can be applied to find a particular solution of the given equation. Do not solve the equation Can the method of undetermined coefficients together with superposition be applied to find a particular solution of the given equation?
A. No, because the right side of the given equation is not the correct type of function
B, Yes °
C. No, because the differential equation is not linear.
D. No, because the differential equation does not have constant coefficients.
Answer:
D. No, because the differential equation does not have constant coefficients.
Step-by-step explanation:
The undetermined coefficient method cannot be applied to non homogeneous variables. The differential equation does not have constant variables therefore the method of undetermined superposition can not be applied. To complete a solution of non homogeneous equation the particular solution must be added to the homogeneous equation.
A robotic machine fills containers with an acid solution at the rate of 50 + 5 t milliliters (mL) per second, where t is in seconds and 0 ≤ t ≤ 60 . How many mL are put into a container in 60 seconds? Evaluate your answer to a whole number.
Answer:
12,000
Step-by-step explanation:
The machine fills the containers at a rate of 50+5t milliliters (mL) per second.
Therefore, the rate of change of the number of containers, N is:
[tex]\dfrac{dN}{dt}=50+5t, 0\leq t\leq 60[/tex]
[tex]dN=(50+5t)dt\\$Taking integrals of both sides\\\int dN=\int (50+5t)dt\\N(t)=50t+\frac{5t^2}{2}+C $(C a constant of integration)\\\\When t=0, , No containers are filled, therefore:$ N(t)=0\\0=50(0)+\frac{5(0)^2}{2}+C\\C=0\\$Therefore, N(t)=50t+2.5t^2[/tex]
When t=60 seconds
[tex]N(60)=50(60)+2.5(60)^2\\N(60)=12000$ mL[/tex]
Therefore, 12,000 milliliters of acid solution are put into a container in 60 seconds.
Insurance companies track life expectancy information to assist in determining the cost of life insurance policies. AIB Insurance randomly sampled 100 recently paid policies and determined the average age of clients in this sample to be 77.7 years with a standard deviation of 3.6. The 90% confidence interval for the true mean age of its life insurance policy holders is
A. (76.87, 80.33)
B. (72.5, 82.9)
C. (77.1, 78.3)
D. (74.1, 81.3)
E. (74.5, 80)
Answer:
[tex]77.7-1.66\frac{3.6}{\sqrt{100}} =77.102[/tex]
[tex]77.7+1.66\frac{3.6}{\sqrt{100}} =78.30[/tex]
And the best option would be:
C. (77.1, 78.3)
Step-by-step explanation:
Information given
[tex]\bar X=77.7[/tex] represent the sample mean
[tex]\mu[/tex] population mean (variable of interest)
s=3.6 represent the sample standard deviation
n=100 represent the sample size
Confidence interval
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
The degrees of freedom are given by:
[tex]df=n-1=100-1=99[/tex]
Since the Confidence is 0.90 or 90%, the significance would be [tex]\alpha=0.1[/tex] and [tex]\alpha/2 =0.05[/tex], and the critical value for this case would be [tex]t_{\alpha/2}=1.66[/tex]
And replacing we got:
[tex]77.7-1.66\frac{3.6}{\sqrt{100}} =77.10[/tex]
[tex]77.7+1.66\frac{3.6}{\sqrt{100}} =78.30[/tex]
And the best option would be:
C. (77.1, 78.3)
Marty’s parents paid $1,800 in electric bills last year. What was their average electric rate per month?
Answer: 150
Step-by-step explanation:
How many months are in a year? 12.
The average rate per month is therefore 1800/12 = 150.
Hope that helped,
-sirswagger21
Let x1 = 12, y1 = 15, and y2 = 3. Let y vary inversely with x. Find x2.
Answer:
x2 = 60
Step-by-step explanation:
If the variables x and y are inversely proportional, the product x * y is a constant.
So using x1 and y1 we can find the value of this constant:
[tex]x1 * y1 = k[/tex]
[tex]12 * 15 = k[/tex]
[tex]k = 180[/tex]
Now, we can use the same constant to find x2:
[tex]x2 * y2 = k[/tex]
[tex]x2 * 3 = 180[/tex]
[tex]x2 = 180 / 3 = 60[/tex]
So the value of x2 is 60.
A study of women’s weights found that a randomly selected sample of 234 women had a mean weight of 157.3 lb. Assuming that the population standard deviation is 15.6 lb., construct a 95% confidence interval estimate of the mean weight of all women.
A. (145.3, 160.5)
B. (155.3, 159,3)
C. (165.5, 173.5)
D. (185.7, 199.3)
Answer:
[tex]157.3-1.96\frac{15.6}{\sqrt{234}}=155.301[/tex]
[tex]157.3+1.96\frac{15.6}{\sqrt{234}}=159.299[/tex]
So on this case the 95% confidence interval would be given by (155.301;159.299)
And the best option would be:
B. (155.3, 159,3)
Step-by-step explanation:
Information given
[tex]\bar X=157.3[/tex] represent the sample mean
[tex]\mu[/tex] population mean (variable of interest)
[tex]\sigma =15.6[/tex] represent the population standard deviation
n=234 represent the sample size
Confidence interval
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (1)
The Confidence level is is 0.95 or 95%, the significance is [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], the critical value for this case would be [tex]z_{\alpha/2}=1.96[/tex]
And replacing we got:
[tex]157.3-1.96\frac{15.6}{\sqrt{234}}=155.301[/tex]
[tex]157.3+1.96\frac{15.6}{\sqrt{234}}=159.299[/tex]
So on this case the 95% confidence interval would be given by (155.301;159.299)
And the best option would be:
B. (155.3, 159,3)
1/5divided by (-5/7)
Answer:
-0.28
Step-by-step explanation:
(1/5) : (-5/7)=(1*5)/(5*(-5))=-(7/25)=-0.28
Answer:
[tex]-7/25[/tex]
Step-by-step explanation:
[tex]1/5 \div -5/7[/tex]
Do the reciprocal of the second fraction.
[tex]1/5 \times 7/-5[/tex]
Multiply the first fraction by the reciprocal of the second fraction.
[tex]7/-25=-0.28[/tex]
The answer in decimal form is -0.28.
i need help on this. anyone ?
Answer:
Read below
Step-by-step explanation:
To copy a segment, you have to open your compass to the length of the given segment. The instructions say to have an endpoint at R, so, with the compass open to the length of the given line segment, place one end of the compass at R and draw an arc that intersects the line that R lies on. This new segment is congruent to the given segment.
I hope this helps!
State whether the data described below are discrete or continuous, and explain why.
The exact lengths (in kilometers) of the ocean coastlines of different countries.
a. The data are continuous because the data can only take on specific values.
b. The data are discrete because the data can only take on specific values.
c. The data are continuous because the data can take on any value in an interval.
d. The data are discrete because the data can take on any value in an interval.
Answer:
c. The data are continuous because the data can take on any value in an interval.
Step-by-step explanation:
A variable is said to be continuous if it can take on any value in an interval. Examples are lengths, temperature, etc
A discrete variable, on the other hand, can only take on specific values. Examples of discrete variables are the number of students and age.
The exact lengths (in kilometers) of the ocean coastlines of different countries is a continuous variable because it can take on any value in an interval.
A stated earlier, Lengths are in general, continuous variables.
Find the solutions to x^2 = 8
Answer:
x=2√2 is the answer
Step-by-step explanation:
x²=8
TAKING SQUARE ROOT ON BOTH SIDES
√x²=√8
x=√2×2×2
x=√2²×√2
x=2√2
i hope this will help you
Answer:
The value of x is -2.828 or 2.828
Step-by-step explanation:
In order to eliminate of square of x, you have to square root both sides :
[tex] {x}^{2} = 8[/tex]
[tex] \sqrt{ {x}^{2} } = ± \sqrt{8} [/tex]
[tex]x = \sqrt{8} \\ x = 2 \sqrt{2} \: or \: 2.828[/tex]
[tex]x = - \sqrt{8} \\ x = - 2 \sqrt{2} \: or \: - 2.828[/tex]
Find the LCM of the set of algebraic expressions.
28x2,49xy, 28y
Answer
Answer:
196x^2y
Step-by-step explanation: The least common multiple (LCM) of two or more non-zero whole numbers is the smallest whole number that is divisible by each of those numbers. In other words, the LCM is the smallest number that all of the numbers divide into evenly.