Answer:
The lower limit is 75.04
The upper limit is 78.96
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 25[/tex]
The sample mean is [tex]\= x = 77[/tex]
The standard deviation is [tex]\sigma = 5[/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 for [tex]\frac{\alpha }{2}[/tex] obtained 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} } * \frac{\sigma }{\sqrt{n} }[/tex]
=> [tex]E = 1.96* \frac{5 }{\sqrt{25} }[/tex]
=> [tex]E = 1.96[/tex]
The 95% confidence interval is mathematically represented as
[tex]\= x -E < \mu < \= x +E[/tex]
=> [tex]77 - 1.96 < \mu < 77 + 1.96[/tex]
=> [tex]75.04 < \mu < 78.96[/tex]
if i bought a product for $74.83 and get a 10% refund how much do i get back?
What the answer S4• s8 •s3
Answer:
s^15
Step-by-step explanation:
When multiplying exponents with the same base, add the exponents
please fine me the solution
Answer:
16/3a^22b^2
I used a calculator to solve this
Four different linear functions are represented below.
a) which function has the graph with the greatest slope?
b) which functions have graphs with y intercepts greater than 3?
c)which function has the graph with a y intercept closest to 0
Answer:
A) Function 4
B) Function 2
C) Function 3
Step-by-step explanation:
(20x^3-7x^2+3x-7)/-13x^2-5
Answer:
x = ((30 sqrt(1462809) + 36253)^(2/3) - 131)/(60 (30 sqrt(1462809) + 36253)^(1/3)) + 7/60 or x = 7/60 - 1/60 ((-1)/(30 sqrt(1462809) + 36253))^(1/3) (131 (-1)^(1/3) + (30 sqrt(1462809) + 36253)^(2/3)) or x = 1/60 (131 (-1/(36253 + 30 sqrt(1462809)))^(1/3) + (-1)^(2/3) (36253 + 30 sqrt(1462809))^(1/3)) + 7/60
see atachement it's more legible.
Step-by-step explanation:
Solve for x:
(20 x^3 - 7 x^2 + 3 x - 7)/(-13 x^2 - 5) = 0
Hint: | Multiply both sides by a polynomial to clear fractions.
Multiply both sides by -13 x^2 - 5:
20 x^3 - 7 x^2 + 3 x - 7 = 0
Hint: | Look for a simple substitution that eliminates the quadratic term of 20 x^3 - 7 x^2 + 3 x - 7.
Eliminate the quadratic term by substituting y = x - 7/60:
-7 + 3 (y + 7/60) - 7 (y + 7/60)^2 + 20 (y + 7/60)^3 = 0
Hint: | Write the cubic polynomial on the left hand side in standard form.
Expand out terms of the left hand side:
20 y^3 + (131 y)/60 - 36253/5400 = 0
Hint: | Write the cubic equation in standard form.
Divide both sides by 20:
y^3 + (131 y)/1200 - 36253/108000 = 0
Hint: | Perform the substitution y = z + λ/z.
Change coordinates by substituting y = z + λ/z, where λ is a constant value that will be determined later:
-36253/108000 + (131 (z + λ/z))/1200 + (z + λ/z)^3 = 0
Hint: | Transform the rational equation into a polynomial equation.
Multiply both sides by z^3 and collect in terms of z:
z^6 + z^4 (3 λ + 131/1200) - (36253 z^3)/108000 + z^2 (3 λ^2 + (131 λ)/1200) + λ^3 = 0
Hint: | Find an appropriate value for λ in order to make the coefficients of z^2 and z^4 both zero.
Substitute λ = -131/3600 and then u = z^3, yielding a quadratic equation in the variable u:
u^2 - (36253 u)/108000 - 2248091/46656000000 = 0
Hint: | Solve for u.
Find the positive solution to the quadratic equation:
u = (36253 + 30 sqrt(1462809))/216000
Hint: | Perform back substitution on u = (36253 + 30 sqrt(1462809))/216000.
Substitute back for u = z^3:
z^3 = (36253 + 30 sqrt(1462809))/216000
Hint: | Take the cube root of both sides.
Taking cube roots gives 1/60 (36253 + 30 sqrt(1462809))^(1/3) times the third roots of unity:
z = 1/60 (36253 + 30 sqrt(1462809))^(1/3) or z = -1/60 (-36253 - 30 sqrt(1462809))^(1/3) or z = 1/60 (-1)^(2/3) (36253 + 30 sqrt(1462809))^(1/3)
Hint: | Perform back substitution with y = z - 131/(3600 z).
Substitute each value of z into y = z - 131/(3600 z):
y = 1/60 (30 sqrt(1462809) + 36253)^(1/3) - 131/(60 (30 sqrt(1462809) + 36253)^(1/3)) or y = -1/60 (-30 sqrt(1462809) - 36253)^(1/3) - (131 (-1)^(2/3))/(60 (30 sqrt(1462809) + 36253)^(1/3)) or y = 131/60 ((-1)/(30 sqrt(1462809) + 36253))^(1/3) + 1/60 (-1)^(2/3) (30 sqrt(1462809) + 36253)^(1/3)
Hint: | Simplify each solution.
Bring each solution to a common denominator and simplify:
y = ((30 sqrt(1462809) + 36253)^(2/3) - 131)/(60 (36253 + 30 sqrt(1462809))^(1/3)) or y = -1/60 (-1/(36253 + 30 sqrt(1462809)))^(1/3) ((30 sqrt(1462809) + 36253)^(2/3) + 131 (-1)^(1/3)) or y = 1/60 (131 ((-1)/(30 sqrt(1462809) + 36253))^(1/3) + (-1)^(2/3) (30 sqrt(1462809) + 36253)^(1/3))
Hint: | Perform back substitution on the three roots.
Substitute back for x = y + 7/60:
Answer: x = ((30 sqrt(1462809) + 36253)^(2/3) - 131)/(60 (30 sqrt(1462809) + 36253)^(1/3)) + 7/60 or x = 7/60 - 1/60 ((-1)/(30 sqrt(1462809) + 36253))^(1/3) (131 (-1)^(1/3) + (30 sqrt(1462809) + 36253)^(2/3)) or x = 1/60 (131 (-1/(36253 + 30 sqrt(1462809)))^(1/3) + (-1)^(2/3) (36253 + 30 sqrt(1462809))^(1/3)) + 7/60
Althea paid five dollars each for two bracelets and later sold each for $15. She paid eight dollars each for three bracelets and sold each of them for nine dollars. Write an expression that represents the profit Althea made.
Answer:
2(15 - 5) + 3(9 - 8)
Step-by-step explanation:
Profit for each $5 bracelet: 15 - 5
Profit for 2 $5 bracelets: 2(15 - 5)
Profit for each $8 bracelet: 9 - 8
Profit for 3 $8 bracelets: 3(9 - 8)
Total profit: 2(15 - 5) + 3(9 - 8)
Answer:
2(-5)+3(-8)+2(15)+3(9)=23
Step-by-step explanation:
For this expression, every time she payed for something we will use a negative number, and whenever she sold it we will use a positive number.
Lets start off with what she payed for, she bought two 5 dollar bracelets, and three 8 dollar bracelets.
2(-5)+3(-8)
Now we will see what she sold. She sold two bracelets for 15 dollars, and then sold three bracelets for 9 dollars.
2(15)+3(9)
Now we combine these to find out her profit.
2(-5)+3(-8)+2(15)+3(9)=23
You need a total of 60 pounds of two commodities costing $1.35 and $2.85 per pound.
A) Verify that the total cost is y = 1.35x + 2.85(60 - x), where x is the number of pounds of the less expensive commodity.
Let x be the number of pounds of the commodity costing $1.35 per pound. Because there are_____pounds total, the amount of the second commodity is______. The total cost, in dollars, is y = 1.35x + 2.85(60 - x).
B) Find the inverse function of the cost function.
What does each variable represent in the inverse function?
1) X represents the commodity costing $1.35 per pound and Y represents the commodity costing $2.85 per pound.
2) X represents pounds and Y represents cost.
3) X represents the commodity costing $2.85 per pound and Y represents the commodity costing $1.35 per pound.
4) X represents cost and Y represents pounds.
5) X represents the commodity costing $1.35 per pound and Y represents cost.
C) What is the domain of the inverse function?
Validate or explain your answer using the context of the problem.
1. The domain of the inverse function is equal to the range of the original function.
2. The domain of the inverse function is equal to the domain of the original function.
3. The domain of an inverse function is always R.
D) Determine the number of pounds of the less expensive commodity purchased when the total cost is $78.
Answer: provided in the explanation section
Step-by-step explanation:
We will take this problem step by step to ensure we have easy understanding of the problem at hand.
(a). taking x as the number of pounds of the commodity costing $1.35 per pound.
Also since we have 60 pounds as total
The amount of second commodity is 60 - x
then the total cost (in dollars) is
y = 1.35x + 2.85(60 - x)
(b). since we have that;
y = 1.35x + 2.85(60 - x)
solving for y gives
y = 1.35x + 171 - 2.85x
y = 171 - 1.5x
doing exchange of variables y and x we have;
x = 171 - 1.5y
where;
1.5y = 171 - x
y = 171 - x / 1.5
f(x) = y and y = f⁻¹(x)f⁻¹(x) = 2/3 [171 - x] ------------- (1)
Here x represents the cost and y represents the pounds
(c). Given that less commodity is purchased, the Cost will be at its lowest and will be 60 (1.35) = $81.
Also, if only the more expensive commodity is purchased, the Cost will be at its maximum and will be 60(2.85) = $171
Therefore the domain of inverse becomes [81,171]That is to say that the domain of inverse function is equal to the range of original function.
(d). plug in x = $78 in the inverse function
where y = 2/3 [171-78]
y = 2/3[93] = 2[31]
y = 62
The number of pounds of the less expensive commodity purchased when the total cost is $78 is given as
y = 62
cheeers i hope this solution was helpful
when the polynomial f(x)=2x^3+ax^2+b is divisible by (x+1) and that there is a remainder of 16 when it is divided by (x-3) find the values of a and b
Answer:
hjgyjgyjyjhhh
Step-by-step explanation:
ygjyjygyjjg
the ratio of Encik Arif's mass to his sons mass is 3:2 . If his son's mass is 42 kg, find Encik Arif's mass.
Answer:
Encik Arif's mass is 63kgStep-by-step explanation:
Let Encik Arif's mass be x
the ratio of Encik Arif's mass to his son's mass is 3:2
That's
[tex] \frac{3}{2} [/tex]The son's mass is 42, so the ratio of Encik Arif's mass to his son's is
x : 42
That's
[tex] \frac{x}{42} [/tex]Now equate the two fractions
That's
[tex] \frac{3}{2} = \frac{x}{42} [/tex]Cross multiply
3(42) = 2x
126 = 2x
Divide both sides by 2
We have the final answer as
x = 63Hope this helps you
How many times larger than the number (1 − 8 /15 ) is the number (1.2 + 2/ 3 )?
Answer:
1- 8/15= 7/15 = 0.4(6)
1.2 + 2/3 = 28/15 = 1.8 (6)
Write the equation of a line with a slope of -2 and a y-intercept of 5
Answer:
y = - 2x + 5Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
From the question
Slope / m = - 2
y intercept / c = 5
Substitute the values into the general equation above
We have the final answer as
y = - 2x + 5Hope this helps you
50 points Its really geometry Distance Formula
Step-by-step explanation:
1) 51
2)32
3) 18
4)9
5)12
Answer:
slime tee
Step-by-step explanation:
charli damelio
refr
rt
gr
grt
g
rgt
123ssroblEvaluate the expression when x= -3 X^2+8x-7
Two cities, Ashville and Boulder, are 2.5 inches
apart on a map. A third city, Wellspring, is
located exactly halfway between Ashville
and Boulder. If the map uses a scale of 0.5
inch = 15 miles, find the actual distance from
Wellspring to Boulder.
Answer:
The distance between W and B is 18.75 mi.
Step-by-step explanation:
2.5 inches converts to
2.5 in 15 mi
------------ * ---------- = 37.5 mi
1 1 in
Half of this distances places us at the midpoint between W and B:
37.5 mi
--------------- = 18.75 mi
2
Given the preimage: A(3, 2), B(3, 6), C(11, 6), D(11, 2). Translate down 4 units. What is B'?
Answer:
B' is (3,2)
Step-by-step explanation:
In the original B coordinate pair, 6 is the y-coordinate. When we talk about shifting images or points up or down, we will normally see a change in the y-coordinate. In this case, the image is being translated 4 units down, so subtract 4 from 6 to get 2 as your y-ccoordinate for B'. Since no horizontal shift is being made, the x-coordinate from the original B point stays the same and B' becomes (3,2).
Answer:
b is (3,2)
Step-by-step explanation:
ggchvvbggggghhh
Explain how to perform a two-sample z-test for the difference between two population means using independent samples with
σ1 and σ2 known.
Answer:
Z= (X1`-X2`)- (u1-u2)/[tex]\sqrt{ \frac{ s_1^2}{n_1^2} +\frac{ s_2^2}{n_2}[/tex] (here s1=σ1 and s2= σ2)
Step-by-step explanation:
Let X1` be the mean of the first random sample of size n1 from a normal population with a mean u1 and known standard deviation σ1.Let X2` be the mean of the second random sample of size n2 from another normal population with a mean u2 and known standard deviation σ2. Then the sampling distribution of the difference X1`-X2` is normally distributed with a mean of u1-u2 and a standard deviation of
[tex]\sqrt{ \frac{ s_1^2}{n_1^2} +\frac{ s_2^2}{n_2}[/tex] . (here s1=σ1 and s2= σ2) In other words the variable
Z= (X1`-X2`)- (u1-u2)/[tex]\sqrt{ \frac{ s_1^2}{n_1^2} +\frac{ s_2^2}{n_2}[/tex] (here s1=σ1 and s2= σ2)
is exactly standard normal no matter how small sample sizes are . Hence it is used as a test statistic for testing hypotheses about the difference between two population means.
The procedure is stated below.
1) Formulate the null and alternative hypotheses.
2) Decide on significance level ∝
3) Use the test statistic Z= (X1`-X2`)- (u1-u2)/[tex]\sqrt{ \frac{ s_1^2}{n_1^2} +\frac{ s_2^2}{n_2}[/tex] (here s1=σ1 and s2= σ2)
4) Find the rejection region
5)Compute the value of Z from the sample data
6) Rehect H0 if Z falls in the critical region, accept H0 , otherwise.
last one anyone know it?
Answer:
6/(-2) = -3
Step-by-step explanation:
rule - when you divide positive number by a negative number then it is negatie so with the same rule applied it is
6/-2
-3
6 + (-2) means we start at 0 and go up 6 units to arrive at 6 on the number line. In terms of a building, you can think of starting on the ground floor and then going up 6 floors. Then adding on the -2 means we go down 2 floors to arrive at 6 + (-2) = 6-2 = 4
Answer: Choice B) go up 6, then down 2Simplify using a calculaor. Not sure how to plug it in
Hi there! Hopefully this helps!
----------------------------------------------------------------------------------------------------
Answer: 1000~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Calculate 10000 to the power of [tex]\frac{3}{4}[/tex].
[tex]\frac{3}{4} = 0.75[/tex]
[tex]10000^{0.75}= 1000[/tex].
logx+log(3x-5)=log2
Answer:
x=2
Step-by-step explanation:
Match the parent function name with the equation. Linear Quadratic Radical Absolute Value Rational Exponential Log Cubic Cube Root
Step-by-step explanation: The correct graph is #6. Cubic Function
Given the diagram below, Hannah writes m 1+ m 4 = 180°, m 2 + m 5 = 180°, and m 3+ m 26 = 180°. Which of the following reasons allows her to write these sums?
Answer:
A. Definition of linear pair
Step-by-step explanation:
A linear pair of angles is formed when two lines intersect. Since angle on a straight line = 180°, angles of a linear pair sum up to 180°.
angles 1 and 4, angles 2 and 5, angles 3 and 6 are all linear pairs. Each pair = 180°.
Answer:
a
Step-by-step explanation:
a pex
What is the vertex for y=|x-3|-2
Answer:
The vertex is [3,0]
Step-by-step explanation:
y=a(x−h)2+k , where ( h,k ) is the vertex of the parabola. By comparing the two equations, we see that h=3 and k=0 . The vertex is at ( 3,0 ).
Answer:
The vertex is [3,0]
Step-by-step explanation:
y=a(x−h)2+k , where ( h,k ) is the vertex of the parabola. By comparing the two equations, we see that h=3 and k=0 . The vertex is at ( 3,0 ).
0,01,9,12,18,3,27,4,36,5,45 Types of variable input variable (input variable) .
Answer:
please mark my answer brainliest
Step-by-step explanation:
these types of input variables are called integer...
i need help on this, i don’t understand it.
Answer:
D
Step-by-step explanation:
From law of indices,( X^3)^2= x^3×2=x^6
Then the other one, also from law of indices, square
root of 5 is the same as 5 raised to power 1/2, then we multiply the powers, that will give us 5 and we have our complete expression which is x^6-5
Draw a square with side-length x. Write an expression that represents the perimeter.
Answer:
4x
Step-by-step explanation:
Length of square = x cm
Perimeter; p = 4 × length of square
p = 4x
If the two solids shown have the same height and the same cross-sectional area at every level, then what is the radius of the oblique cylinder?
Answer:
8
Step-by-step explanation:
If the two solids have the same height and same cross-sectional area at every level, this means that the radius of the oblique cylinder is the same as the radius of the right cylinder.
Since the radius of the right cylinder is 16/2=8, this means that the radius of the oblique cylinder must also be 8.
Algebraically, the area of the cross-section is given by:
[tex]A=\pi r^2[/tex]
If the areas of them are the same:
[tex]A_{right}=A_{oblique}[/tex]
Then:
[tex]\pi r_{right}^2=\pi r_{oblique}^2\\r_{right}=r_{oblique}[/tex]
A triangle has vertices at (−4,−6),(3,3),(7,2). Rounded to two decimal places, which of the following is the closest approximation of the perimeter of the triangle?
19.34
29.12
12.36
15.52
The answer is
29.12
hope this helps
If a=mg-kv2/m,find,correct to the nearest whole number the value of v when a=2.8,m=12,g=9.8 and k=8/3
Answer:
The value of [tex]v[/tex] is ± 22.729.
Step-by-step explanation:
Let be [tex]a=m\cdot g -\frac{k\cdot v^{2}}{m}[/tex], the variable [tex]v[/tex] is now cleared:
[tex]\frac{k\cdot v^{2}}{m}=m\cdot g -a[/tex]
[tex]k\cdot v^{2} = m^{2}\cdot g- m\cdot a[/tex]
[tex]v^{2} = \frac{m^{2}\cdot g - m\cdot a}{k}[/tex]
[tex]v =\pm \sqrt{\frac{m^{2}\cdot g-m\cdot a}{k} }[/tex]
If [tex]a = 2.8[/tex], [tex]m=12[/tex], [tex]g = 9.8[/tex] and [tex]k = \frac{8}{3}[/tex], the value of [tex]v[/tex] is:
[tex]v=\pm \sqrt{\frac{(12)^{2}\cdot (9.8)-(12)\cdot (2.8)}{\frac{8}{3} } }[/tex]
[tex]v \approx \pm 22.729[/tex]
The value of [tex]v[/tex] is ± 22.729.
Please help slove for AB.
Answer:
Based on triangles of angles: 45-45-90:
chord/2=(radius√2)/2
chord/2=(10√2)/2
chord/2=5√2
chord=10√2
Step-by-step explanation:
Hope it helps ;)
Consider the following. x = e4t, y = t + 7
Eliminate the parameter to find a Cartesian equation of the curve.
Answer:
y = 7 +ln(x)/4
Step-by-step explanation:
Maybe your parameterized equation is ...
(x, y) = (e^(4t), t +7)
Using t = y-7, we can substitute for t in the expression for x:
x = e^(4(y -7))
ln(x) = 4(y -7)
ln(x) +28 = 4y
y = 7 +ln(x)/4