Answer:
A. = 27 B. = 16
Step-by-step explanation:
A. 36/4 = 9 3X9 = 27
B. 36/9 = 4 4X4 =16
Find the indicated margin of error. In a clinical test with 2161 subjects, 1214 showed improvement from the treatment. Find the margin of error for the 95% confidence interval used to estimate the population proportion.
Answer:
The margin of error is [tex]E = 0.021[/tex]
Step-by-step explanation:
From the question we are told that
The population size is [tex]n = 2161[/tex]
The number that showed improvement is [tex]k = 1214[/tex]
Generally the sample proportion is mathematically represented as
[tex]\r p = \frac{ 1214}{2161}[/tex]
=> [tex]\r p = 0.56[/tex]
Given that the confidence level is 95% then the level of significance is mathematically represented as
[tex]\alpha =(100-95) \%[/tex]
=> [tex]\alpha =0.05[/tex]
The critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\r p (1 - \r p )}{n} }[/tex]
=> [tex]E = 1.96 * \sqrt{\frac{ 0.56(1 - 0.56 )}{2161} }[/tex]
=> [tex]E = 0.021[/tex]
Use the Method of Lagrange Multipliers to find the Minimum and Maximum of f(x,y) = xy subject to x^2+y^2-xy = 9 g
Answer: The Max fun is 9, and the Min fun is -3
Step-by-step explanation:
Please follow the steps carefully;
Let us consider the function f(x,y) = xy -------------- (1)
We will apply the Lagrange multipliers to maximize the function f(x,y) subject to the constraint g(x,y) = x^2+y^2-xy = 9
By differentiating (1) w.r.t x, we get fx(x,y) = y
By differentiating (1) w.r.t y, we get fy(x,y) = x
By differentiating g(x,y) w.r.t x, we get gx(x,y) = 2x - y
Also By differentiating g(x,y) w.r.t y, we get gy(x,y) = 2y - x
let us take
fx = λgx
where y = λ(2x - y)
y/2x - y = λ ----------- (2)
fy = λgy
where x = λ(2y - x)
λ = x/2y -x ----------- (2)
Let us equate (2) and (3)
y/2x - y = x/2y -x
2y² - xy = 2x² - xy
2y² = 2x² after cancelling like terms
y² = x²
So y = ±x
Now let us substitute y = x into the given constraint
x² + y² - xy = 9
x² + x² - x(x) = 9
x² = 9
therefore x = ± 3
We can conclude that when x = ±3, ⇒ y = ±3
The corresponding points are (3,3), (-3,-3)
Substitue y = -x in the given constraint gives
x² + y² - xy = 9
x² + (-x)² -x(-x) = 9
3x² = 9
x² = 3
x = ±√3
The corresponding points are (√3,-√3), (-√3,√3)
The function value is
f(x,y) = xy
f (√3,-√3) = (√3)(-√3) = -3
f (-√3,√3) = (-√3)(√3) = -3
we get;
f(3,3) = (3)(3) = 9
and
f (-3,-3) = (-3)(-3) = 9
We can conclusively say that ;
The Maximum value of the function is 9
The Minimum value of the function is -3
cheers i hope this helped
What is the slope of the line that contains these points? x,12,13,14,,15. y,-4, 2,8,14.
Answer:
[tex]\huge \boxed{{m=6}}[/tex]
Step-by-step explanation:
Let's take two points,
(12, -4) and (13, 2).
slope = (difference of y) / (difference of x)
m = (2 - - 4) / (13 - 12)
m = (2 + 4) / 1
m = 6 / 1 = 6
The slope of the line is 6.
Answer:
6
Step-by-step explanation:
The slope is the change in y over the change in x
m = ( y2-y1)/(x2-x1)
= (14-8)/(15-14)
= 6/1
Name the image of C after a rotation of 180° about the origin.
Answer:
C'(-5, 2)
Step-by-step explanation:
Rule to be followed for a point rotated 180° about the origin,
(x, y) → (-x, -y)
From the figure attached,
When ABCD is rotated 180° about the origin, the new points of the image will be
A(2, 0) → A'(-2, 0)
B(4, 0) → B'(-4, 0)
C(5, -2) → C'(-5, 2)
D(1, -2) → D'(-1, 2)
Therefore, image of C will be C'(-5, 2).
Please please someone help me
Here is a graph of the function h
Use the graph to find the following
If there is more than one answer , separate them with commas
Answer:
minimum is -3,0
Step-by-step explanation:
Simplify the following expression as much as possible.
4^10/4^10 x 7^O=?
Answer:
1
Step-by-step explanation:
4^10/4^10 x 7^O =
= 4^(10 - 10) * 1
= 4^0 * 1
= 1 * 1
= 1
Answer:
1
Step-by-step explanation:
4^10/4^10 = 1
7^0 = 1
1 x 1 = 1
calculate 65 L to quarts. Final answer round two places
Step-by-step explanation:
The approximate equation to convert from liters to quarts is : x • 1.056688.
We enter 65 for x and multiply.
65 • 1.056688 = 68.68472
We round that to the nearest 100th to get our final answer.
Our final answer: 68.68 liters
A company issues 10% Irredeemable preference shares. The face value per share is RO 10, but the issue price is RO 9.5. what is the cost of preference share?
Answer:
The answer of the question is 10.53%.
Which of the following are solutions to the equation below?
Check all that apply.
X^2+18=-9x
Answer:
The solution set is {-3, -6}.
Step-by-step explanation:
x^2 + 18 = -9x
x^2 + 9x + 18 = 0
(x + 3)(x + 6) = 0
x = -3, -6.
A local diner has started selling cupcakes and is using the bar chart given below to keep track of how many are sold each day. How many cupcakes will be sold on day n?
Answer:
a + (n-1)*4
Step-by-step explanation:
Day n could be any particular day located on the x-axis of the bar chart. Each bar represents the amount of cupcakes sold on each of the four days numbered from 1 to 4. The height of each bar marks the number of cupcakes sold. According to the chart attached, the number of cupcakes sold on each day is listed below:
Day 1 : 1 cupcake sold
Day 2 : 5 cupckaes sold
Day 3: 9 cupcakes sold
Day 4: 13 cupckaes sold
Studying the graph carefully fully, it will be observed that the number of cupcakes sold increases by a margin of 4 after day one.
As such the number of cupcakes sold in n days can be modeled by:
Using the Arithmetic progression formula:
Tn = a + (n-1)d
d = common difference, = 4
a = first term = 1
n = number of days
Hence, number sold in day n:
a + (n-1)*4
Arithmetic progressio
Answer:
3n−1 cupcakes
Step-by-step explanation:
If a new movie is selling for $20, and the local city charges 8% sales tax, how much tax will be charged? $_____
Answer: $1.6
Step-by-step explanation:
price × percentage of tax=amount of tax
$20 × 8%=20 × 0.08= $1.6
Hope this helps!! :)
After a shipwreck, 120 rats manage to swim from the wreckage to a deserted island. The rat population on the island grows exponentially, and after 15 months, there are 280 rats on the island.
A. Find a function that models the population t months after the arrival of the rats.
B. What will the population be 3 years after the shipwreck?
C. When will the population reach 2000 rats?
Answer:
a. [tex]X(T) = 120 (1.058)^T[/tex]
b. Population after 3 years is 142
c. 50 years
Step-by-step explanation:
Given
Type of growth: Exponential
Initial number of rats = 120
Number of rats (15months) = 280
Solving (a)
Since the growth type is exponential, we make use of the following exponential progression
[tex]X_T = X_0 (1 + R)^T[/tex]
Where Xo is the initial population;
Xo = 125
[tex]X_T[/tex] is the current population at T month
So;
[tex]X_T = 280[/tex]; when [tex]T = 15[/tex]
Substitute these values in the above formula
[tex]280 =120 * (1 + R)^{15}[/tex]
Divide both sides by 120
[tex]\frac{280}{120} =(1 + R)^{15}[/tex]
[tex]2.3333 =(1 + R)^{15}[/tex]
Take 15th root of both sides
[tex]\sqrt[15]{2.3333} =1 + R[/tex]
[tex]1.05811235561 = 1 + R[/tex]
Subtract 1 from both sides
[tex]R = 1.05811235561 - 1[/tex]
[tex]R = 0.05811235561[/tex]
[tex]R = 0.058[/tex] (Approximated)
Plug in values of R and Xo in [tex]X_T = X_0 (1 + R)^T[/tex]
[tex]X_T = 120 (1 + 0.058)^T[/tex]
[tex]X_T = 120 (1.058)^T[/tex]
Write as a function
[tex]X(T) = 120 (1.058)^T[/tex]
Hence, the function is [tex]X(T) = 120 (1.058)^T[/tex]
Solving (b):
Population after 3 years
In this case, T = 3
So:
[tex]X(T) = 120 (1.058)^T[/tex]
[tex]X(3) = 120 (1.058)^3[/tex]
[tex]X(3) = 120 * 1.18466445254[/tex]
[tex]X(3) = 142.159734305[/tex]
[tex]X(3) = 142[/tex] (Approximated)
Solving (c): When population will reach 2000
Here: X(T) = 2000
So:
So:
[tex]2000 = 120 (1.058)^T[/tex]
Divide both sides by 120
[tex]\frac{2000}{120} = 1.058^T[/tex]
[tex]16.667 = 1.058^T[/tex]
Take Log of both sides
[tex]Log(16.667) = Log(1.058^T)[/tex]
Apply law of logarithm
[tex]Log(16.667) = TLog(1.058)[/tex]
Divide both sides by Log(1.058)
[tex]T = \frac{Log(16.667)}{Log(1.058)}[/tex]
[tex]T = 49.9009236926[/tex]
Approximate
[tex]T = 50\ years[/tex]
Help me please thank y’all
Answer:
125°
Step-by-step explanation:
Sum of angles of triangle equals 180°:
x + 25° + 30° = 180°x + 55° = 180°x = 180° -55°x = 125°Answer:
x=125
Step-by-step explanation:
because sum of interior angles of a triangle is 180
What does 5x evaluate to if x is equal to 2?
Answer: Hi!
Since 5 is being multiplied by x, and x is equal to 2, be would multiply 5 and 2. 5 * 2 is equal to 10.
Hope this helps!
Answer:
Step-by-step explanation:
PLEASE HELP ME!! 10 POINTS!
number 1: you make 35 bracelets in 5 hours. Find the unit rate.
Number 2:
Identify the terms, coefficients, and constants in the expression 14x + 19.
Answer: Number 1- you make 7 bracelets in 1 hour.
Step-by-step explanation:
Number 1- You divide 35 by 5 and get 7. The hour (5) goes at the denominator and the number of bracelets(35)goes on the numerator and you divide
Damien worked at a grocery store earning $9.00 an hour. He worked 30 hours a week and was paid every two weeks. He paid $62 in taxes and had a $50 savings account deduction. What was Damien's gross income?
Answer:
$540
Step-by-step explanation:
We know Damien earned $9 per hour, worked 30 hours a week and was paid every 2 weeks.
We can write an expression to something like this:
(9 x 30) x 2
Which would give us 540
The question asks for the Gross income (the total income, before any taxes or deductions)
Which means that his gross income was $540
Help please I would appreciate it !
Answer/Step-by-step explanation:
Given:
Line equation => [tex] 2.1x + 9.9y - 9.2 = 0 [/tex]
Required:
x-intercept and y-intercept of the line.
SOLUTION:
The x-intercept is the point where the line intercepts the x-axis. To find the x-intercept of the line for which the equation is given above, set y = 0 and solve for x.
[tex] 2.1x + 9.9(0) - 9.2 = 0 [/tex]
[tex] 2.1x + 0 - 9.2 = 0 [/tex]
[tex] 2.1x - 9.2 = 0 [/tex]
[tex] 2.1x - 9.2 + 9.2 = 0 + 9.2 [/tex]
[tex] 2.1x = 9.2 [/tex]
[tex] \frac{2.1x}{2.1} = \frac{9.2}{2.1} [/tex]
[tex] x = 4.4 [/tex] (approximated)
The y-intercept is the point where the line intercepts the y-axis. At this point, x = 0. Set x = 0 and solve for y to find the y intercept.
[tex] 2.1(0) + 9.9y - 9.2 = 0 [/tex]
[tex] 9.9y - 9.2 = 0 [/tex]
[tex] 9.9y - 9.2 + 9.2 = 0 + 9.2 [/tex]
[tex] 9.9y = 9.2 [/tex]
[tex] y = \frac{9.2}{9.9} [/tex]
[tex] y = 0.9 [/tex] (approximated)
If you throw a single die twice, what's the probability of first getting a 3 and then getting another odd number?
Answer:
the answer is one twelve 1/12
02
Question 3 (2 points)
Find the estimate
At a certain university. It costs a student $689 per credit hour to attend. Estimate
the cost for a student to attend one semester if he registers for 9 credit hours.
Answer:
About $6000
Step-by-step explanation:
Multiply 689 × 9.
When you are estimating, you should round the numbers off to values that you can easily work in your head.
I would round 9 up to 10 and 689 down to 600 to compensate. Then,
10 credit hours × $600/credit hour ≈ $6000.
It should cost about $6000 to register for 9 credit hours.
A computers is on on sale for $1085. if the original price was reduced by 30%, what was the original price of the Computer ?
Answer:
1.131,5
Step-by-step explanation:
Simplify the following polynomial, then evaluate for x = -2 . 2x^2-4x+3x^2+x-7
Answer:
19
Step-by-step explanation:
first you would combine like terms to get 5x^2-3x-7. plug in -2 into the x's and you will get 19!
Convert 0.00001 to a power of 10
Answer:
1 * 10 ^ -7
Step-by-step explanation:
including a 8% sales tax an inn charges $140.40 per night find the inns nightly cost before tax is added
Answer:
129.168
Step-by-step explanation:
multiply- 140.40*0.08=11.232
subtract- 140.40-11.232= 129.168
Which shows a true math fact? A 18.7×3.47=58.157 B 86.128−29.473=56.655 C 37.561+28.94=40.455 D 36.26÷0.50=725.2
Answer:
The correct answer is B.
Explanation:
Putting it into your calculator as you see it gives you the correct answer.
Have a good day! :)
Let p0, p1, and p2 be the orthogonal polynomials described below, where the inner product on P4 is given by evaluation at -2, -1, 0, 1, 2. Find the othogonal projection of 3t^(3) onto Span{p0,p1,p2}.
p0(t) = 4
p1(t) = 3t
p2(t) = t^(2) -2
Answer:
[tex]$\frac{51}{5}t$[/tex]
Step-by-step explanation:
Let W = [tex]$(p_0, p_1, p_2)$[/tex] be orthogonal polynomials which is equal to [tex]$(4, 3t, t^2 -2)$[/tex], which defines the inner products as
[tex]$(f,g)=f(-2)g(-2)+f(-1)g(-1)+f(0)g(0)+f(1)g(1)+f(2)g(2)$[/tex]
Now, we find the orthogonal projection of [tex]$p=3t^3$[/tex] on W.
So the projection is
[tex]$Proj_W p = \frac{(p_0,p)}{(p_0,p_0)}p_0+\frac{(p_1,p)}{(p_1,p_1)}p_1+\frac{(p_2,p)}{(p_2,p_2)}p_2$[/tex]
[tex]$(p_0,p)=p_0(-2)p(-2)+p_0(-1)p(-1)+p_0(0)p(0)+p_0(1)p(1)+p_0(2)p(2)$[/tex]
[tex]$=4(-24)+4(-3)+4(0)+4(3)+4(24)=0$[/tex]
[tex]$(p_0,p_0)=p_0(-2)p_0(-2)+p_0(-1)p_0(-1)+p_0(0)p_0(0)+p_0(1)p_0(1)+p_0(2)p_0(2)$[/tex]
[tex]$=4(4)+4(4)+4(4)+4(4)+4(4)=80$[/tex]
[tex]$(p_1,p)=p_1(-2)p(-2)+p_1(-1)p(-1)+p_1(0)p(0)+p_1(1)p(1)+p_1(2)p(2)$[/tex]
[tex]$=(-6)(-24)+(-3)(-3)+0(0)+3(3)+6(24)=306$[/tex]
[tex]$(p_1,p_1)=p_1(-2)p_1(-2)+p_1(-1)p_1(-1)+p_1(0)p_1(0)+p_1(1)p_1(1)+p_1(2)p_1(2)$[/tex]
[tex]$=(-6)(-6)+(-3)(-3)+0(0)+3(3)+6(6)=90$[/tex]
[tex]$(p_2,p)=p_2(-2)p(-2)+p_2(-1)p(-1)+p_2(0)p(0)+p_2(1)p(1)+p_2(2)p(2)$[/tex]
[tex]$=2(-24)+(-1)(-3)+(-2)(0)+(-1)(3)+2(24)=0$[/tex]
[tex]$(p_2,p_2)=p_2(-2)p_2(-2)+p_2(-1)p_2(-1)+p_2(0)p_2(0)+p_2(1)p_2(1)+p_2(2)p_2(2)$[/tex]
[tex]$=(2)(2)+(-1)(-1)+(-2)(-2)+(-1)(-1)+2(2)=14$[/tex]
Therefore,
[tex]$Proj_W p = \frac{(p_0,p)}{(p_0,p_0)}p_0+\frac{(p_1,p)}{(p_1,p_1)}p_1+\frac{(p_2,p)}{(p_2,p_2)}p_2$[/tex]
[tex]$=\frac{0}{80}(4)+\frac{306}{90}(3t)+\frac{0}{14}(t^2-2)$[/tex]
[tex]$=\frac{51}{5}t$[/tex]
How do I graph this? Also how do identify which values of c for which
lim f(x) exist?
x -> c
Answer:
Step-by-step explanation:
Hello, I attached the graph.
This is a parabola, then a line and finally an horizontal line.
The vertex of the parabola is (0,0) and (2,4) is on the graph.
For the second part, draw a line which is passing by (2,4) and (0,4)
Finally, draw the line y = 4
You can see that f is continuous everywhere except in x = 4.
So, for any c real different from 4 the limit of f(x) exists.
Thank you
Eddie Lange earns $11.50 per hour. He worked 40 hours, plus time and a half
for 7 hours.
Answer:580
Step-by-step explanation:
Solve the inequalities (i) 5 ≤ 2x − 4 ≤ 8 (ii) −10 < 4 −3y/− 5 ≤ 4
Step-by-step explanation:
(i) 5 ≤ 2x − 4 ≤ 8 add 4 to all three expressions
9 ≤ 2x ≤ 12 divide by 2
9/2 ≤ x ≤ 6
(ii) −10 < (4 −3y)/− 5 ≤ 4 multiply all sides by -5
-20 ≤ 4 - 3y < 50 subtract 4
-24 ≤ -3y < 46 divide with -3
-46/3 < y ≤ 8
Distribute a negative -(5.5q+7)
Hi there! :)
Answer:
[tex]\huge\boxed{-5.5q - 7}[/tex]
-(5.5q + 7)
Distribute:
-(5.5q) -(7)
-5.5q - 7
Answer:
Z≥0 = {0, 1, 2, .
Step-by-step explanation:
Just took test
1 lb = 16 oz. How many lbs (pounds) are in 14 oz (ounces)?
Answer:
0.875
Step-by-step explanation:
14÷16= 0.875
divide the mass value by 16