The sphere's radius is 5, and its center is at (0, 3, -4).
What is a sphere?A sphere is a geometrical object that resembles a two-dimensional circle in three dimensions.
In three-dimensional space, a sphere is a collection of points that are all located at the same distance from a single point.
The radius of the sphere is denoted by the letter r, and the given point is its center.
List a few typical sphere examples from everyday life.
In everyday objects, sphere shapes can be found in the form of marbles, balls, oranges, yarn, and bubbles.
So, the center and radius of the sphere will be:
We have the sphere's equation, which is given by and has a radius of r.
(x - h)² + (y - k)² + (z - l)² = r² ...(1)
We must convert the following equation in order to determine the center and radius of the provided sphere.
x² + y² + z² - 6y + 8z = 0
By combining the x, y, and z terms and filling in the square, we obtain
x² + (y² - 6y + 9) +(z² + 8z + 16) = 9 + 16
(x - 0)² + (y - 3)² + (z + 4)² = 52
So, the sphere's center is at (0, 3, -4) and its radius is 5.
Therefore, the sphere's radius is 5, and its center is at (0, 3, -4).
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Complete question:
Find the center and radius of the sphere x2 + y2 + z2 - 6y + 8z = 0.
You need to buy some chicken for dinner tonight. You found an ad showing that the store across town has it on sale for $2.99 a pound, which is cheaper than your usual neighborhood store, which sells it for $3.29 a pound. Is it worth the extra drive?
First, determine what information you need to answer this question, then click here to display that info (along with other info).
How much chicken will you be buying? 5 pounds
How much far are the two stores? My neighborhood store is 2.3 miles away, and takes about 7 minutes. The store across town is 8.8 miles away, and takes about 21 minutes.
How kind of mileage does your car get? It averages about 19 miles per gallon in the city.
How many gallons does your car hold? About 14 gallons
How much is gas? About $3.66/gallon right now.
Based on the total costs of buying at the two stores, it is not worth the extra drive going to the store across town.
How are the total costs determined?The total costs for buying 5 pounds of chicken at each store are added to the total gas costs to and from each location to determine the total costs of each option.
Based on the cost difference of $1 ($18.34 - $17.34), it is not advisable to travel across town just for 5 pounds of chicken, especially when you factor in the wear and tear of the car along the distance and the time difference.
The cost of a pound of chicken at a neighborhood store = $2.99
The cost of a pound of chicken at the store across town = $3.29
The number of pounds of chicken required = 5 pounds
The distance to and from the neighborhood store = 4.6 miles (2.3 miles x 2)
The distance to and from the store across town = 17.6 miles (8.8 miles x 2)
The total time to and from the neighborhood store = 14 minutes (7 x 2)
The total time to and from the store across town = 42 minutes (21 x 2)
The time difference = 28 minutes.
Car's mileage per gallon = 19 mpg
The cost of gas per gallon = $3.66
The total cost of buying at the neighborhood store = $17.34 ($3.29 x 5 + $3.66 x 4.6/19)
The total cost of buying at the store across town = $18.34 ($2.99 x 5 + $3.66 x 17.6/19)
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y.y^3.y^2 pleas help me and spread the gospel of God
Answer:
[tex]y^6[/tex]
Step-by-step explanation:
1) Use Product Rule: [tex]x^ax^b=x^{a+b}[/tex].
[tex]y^{1+3+2[/tex]
2) Simplify 1 + 3 to 4.
[tex]y^{4+2}[/tex]
3) Simplify 4 + 2 to 6.
[tex]y^6[/tex]
Thank you,
Eddie
The table shows Tonya's homework assignment. Tonya's teacher instructed the class to simplify each expression by dividing the numerator and denominator by the GCF.
Complete the table by simplifying each expression and then finding the value.
Divide the numerator and denominator by the GCF to reduce a fraction. (This is also referred to as "writing a fraction in the simplest terms.") The common factors are sometimes shown to be "cancelled." It is worth noting that the result is an equivalent fraction in its simplest form.
How do you divide the numerator to the denominator by GCF?To put it simply, we must divide the numerator (x) by the denominator (y) to simplify it. For example, after simplifying 3 6, represent it as a fraction and identify the numerator and denominator. 3 6 can be written as 3/6. Further simplification yields 1/2.
Let's pretend the fraction is a proper fraction. The denominator is the numerator. We want to reduce the fraction to its simplest form.
a) Use Numerator =Remainder* as the denominator.
Now Numerator >Remainder* b)Numerator Remainder*=Remainder** c) ••• (keep going until Remainder =0)
d) When the Remainder equals zero, the Divisor is the GCD (or GCF, as you say). GCF is a misnomer because it only deals with numbers. Only the term GCF applies to variables (with numerical values, as in algebraic expression).
Let us look at an example.
407/3367 is the fraction.
As evident, the numbers407 ,3367 does not appear to have share Divisors 2 or 3 or 5 or 7 or 11 from prima facie considerations. So we may take recourse of successive division method.
3367 ÷407 =Remainder 111 (quotient 8)
407 ÷ 111 =Remainder 74 (quotient 3)
111 ÷74=Remainder 37 (quotient 1)
74 ÷37 =Remainder 0 (ZERO )
Here 37 divides leaving Remainder zero. Therefore the GCD is 37
Fraction 407 /3367 =(407 ÷37)/(3367÷37)=11/91
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Please help will mark Brainly
Answer:
neither narrower or broader
Step-by-step explanation:
if you look at your problem it says identical so that means exactly the same so it would be the second choice neither narrower or broader
Is ABCD a rhombus explain?
The ABCD parallelogram turns into a rhombus if all of its sides are equal.
What are the geometric properties of a parallelogram and a rhombus?Geometry of a parallelogramEqual are the sides that oppose.Equal angles are opposite angles.Each other in a diagonal.Nevertheless, the length of diagonals varies.Geometric characteristics of rhombusAll Sides are equal.
Diagonals bisect at 90°.
In our question,
AB = DC is given for a quadrilateral ABCD (parallelogram).
When a parallelogram's sides are uneven, symmetry is disrupted and its diagonals do not bisect at 90 degrees. However, when all of the sides are equal, the diagonal does bisect at 90 degrees and the parallelogram becomes a rhombus.
Therefore, when all of a parallelogram's sides are equal, it becomes a rhombus.
The complete question is:
You are trying to prove that quadrilateral ABCD is a rhombus. You know that both pairs of opposite sides are parallel (a parallelogram). Which additional fact would prove that ABCD is a rhombus?
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please help!!!
A group of friends wants to go to the amusement park. They have no more than $125 to spend on parking and admission. Parking is $9, and tickets cost $20 per person, including tax. Write and solve an inequality which can be used to determine pp, the number of people who can go to the amusement park.
Answer:
9 + 20p ≤ 125
Step-by-step explanation:
This does not include the tax.
In which quadrant is the number 5i located on the complex plane?
The number 5i located on the complex plane in I Quadrant.
What is Complex Plane?
The real axis and the imaginary axis are the graph's horizontal and vertical axes, which are orthogonal (or perpendicular). The labels Re and Im are typically present. The complex plane is the plane defined by these coordinates.
We are aware that in a two-dimensional plane, an ordered pair's x- and y-coordinates are treated as the real and imaginary parts of the complex number, respectively.
i.e., a+bi=(a,b) -- Quadrant I,
-a+bi=(-a,b) -- Quadrant II,
a-bi=(a,-b) -- Quadrant III
and
-a-bi=(-a,-b) -- Quadrant IV
The complex number that is being presented is 5i, aland it is located in quadrant I.
As a result, the complex number in question belongs in Quadrant I.
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Describe the function‘s end behavior. f(x)=−10+2x^5−9x^3
as x→∞,f(x)→
as x→−∞,f(x)→
The function‘s end behavior is falls to the left and rises to the right.
The given function is [tex]f(x)=-10+2x^5-9x^3[/tex].
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
Use the degree and the leading coefficient to determine the behavior.
Falls to the left and rises to the right.
Find where the first derivative is equal to 0 to find the local maxima and minima.
x =−3√30/10 is a local maximum
x = 3√30/10 is a local minimum
Therefore, the function‘s end behavior is falls to the left and rises to the right.
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On Tuesday, the Soto Salad restaurant served 6 ½ cups of Italian salad dressing. If the restaurant serves ¼ cup of dressing with each salad, how many salads were ordered with Italian dressing?
Group of answer choices
26
22
24
28
Answer:
26
Answer choice 1.
Step-by-step explanation:
6 1/2 ÷ 1/4 is our equation.
6 1/2 as an improper fraction is 13/2
Our new equation is 13/2÷1/4
flip the divisor into a reciprocal and multiply:
13/2×4/1
simplify:
13/1×2/1
26/1
=26
PLEASE MARK BRAINLIESTAnswer: The answer is A or 26
Step-by-step explanation: I have my ways ;>
please I need help on question 5
The value of x is 19 and the measure of angles in triangle ABC are 75°, 75° and 30° respectively.
What is a triangle?triangle is a three-sided polygon that consists of three edges and three vertices. The most important property of a triangle is that the sum of the internal angles of a triangle is equal to 180 degrees. This property is called angle sum property of triangle.
If ABC is a triangle, then it is denoted as ∆ABC, where A, B and C are the vertices of the triangle. A triangle is a two-dimensional shape, in Euclidean geometry, which is seen as three non-collinear points in a unique plane.
The sum of ∠A + ∠B + ∠C = 180°( sum of angles in a triangle )
3x + 18 + 7x - 58 + 2x - 8 = 180°
12x -48° = 180°
12x = 228
x = 228/12
x = 19
but ∠A = 3x + 18, but x = 19
∠A = 3(19) + 18 which is 75°
Also ∠B = 7x -58
∠B = 7(19) - 58 which is 75°
∠C = 2x -8
∠C = 2(19) - 8 which is 30°
In conclusion, the value of x = 19, ∠A = 75°, ∠B = 75° ∠C = 30°
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7. What is Mrs. Dudley's waming to the guests regarding her leaving the property at night?
a. If they do not clear the dinner table, she will not "wait on people" the following moming
(b.) If they get into trouble, she wouldn't be able to hear them "in the night"
c. If they decide they want to leave, no one will be there to "open the gate" for them
d. If they experience anything, not to "confront" it
8. Which statement best embodies Eleanor's feelings about Hill House?
a. "There is a comforting calmness that accompanies the silence that fills these halls"
b. "My confidence grew that my journcy will end with lovers mecting" "It's awful and I don't want to stay...get away from here, get away"
a. "I am finally starting to feel wanted because of these three people I can call friends"
9. The second guest claims that Eleanor is like his/her...
a. Best friend
b. Sister
(c) Cousin
d. mother
10. Which of the following statements does NOT describe Hill House or how it made its inhabitants feel?
a. "Hill House gave its guests a false sense of comfort and security"
b. "Hill House seemed awake"
c. "Hill House would stay as it was until it was destroyed"
d. "I am like a small creature swallowed whole by a monster [Hill House]"
In the end, Hill House stands for the enigmas of the human mind, whether it is "sane" or not, as well as the horror that the mind's intrinsic weirdness can arouse. Hill House is intricate, convoluted, and appears to be unknowable, just like the mind.
How does Dr Montague describe Hill House?The history of Hill House is first described by Doctor Montague.
He asserts that "the concept of certain houses as filthy or banned" is an old one, much like the idea that some places on earth are fundamentally good and good, while others are sacred or holy.
Possibly "evil from the start," the Hill House has been uninhabitable for more than twenty years.
Instead of being malicious, Doctor Montague sees the home as sick or "deranged."
Doctor Montague learned about the rental from a previous tenant a year ago.
After researching it, he found that no renter had kept it for more than a few days.
Even finding a short-term lease, according to Montague, was challenging.
10) "Hill House provided its visitors with a false sense of security and comfort"
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what is the fourth term of d 4b3
The fourth term of the polynomial (d - 4b)³ is D. -64d³.
What is a polynomial?A polynomial is an expression involving the operations of addition, subtraction, multiplication of variables.
Given the expression (d - 4b)³, we need to open the bracket, hence:
(d - 4b)³ = d³ + 3(d²)(-4b) + 3(d)(-4b)²
= d³ - 12bd² + 48b²d - 64d³
Therefore, the fourth term of (d - 4b)³ is D. -64d³
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The half-life of nitrogen-16 is approximately 7.13 seconds.
Step 3 of 3 : How much of a 3 gram sample of nitrogen-16 would remain after 4 seconds? Round to three decimal places.
Using half-life and disintegration constant, the sample that will remain 4 seconds 2.03g
RadioactivityThis is the spontaneous decay of an active radioactive sample. The decay curve is exponential and it slope is constantly changing.
The half-life of this sample given can be used to find the disintegration constant of the sample.
The formula of half - life is given as
T₁/₂ = ln2 / λ
T₁/₂ = Half-Life λ = disintegration constantSubstitute the values into the equation;
7.13 = 0.693 / λ
λ = 0.693 / 7.13
λ = 0.0972
The amount of sample left after 4 seconds will be
A = Ne⁻(λt)
A = 3e⁻(0.0972 * 4)
A = 2.03g
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An exponential function will have:
Answer:
Exponential functions have the form f(x) = bx, where b > 0 and b ≠ 1.
Step-by-step explanation:
Determine which set of ordered pairs represent a
Function and justify your selection.
{(-1,4), (2, 4), (8,4), (10,4)}
{(0, -2), (3, 7), (0, 2), (18,2))
{(-1,3), (-1,-1), (-1,-12), (-1,0)}
{(1, 2), (2, 3), (3, 4), (3,5)}
Justification: (What is your reasoning?)
Answer:
{(-1,4), (2, 4), (8,4), (10,4)}
all of the x-values are different
Step-by-step explanation:
The other three options have duplicate x-values with different y-values.
help please the function f(x) = 3x -8 , solve f(x) = 7
Answer:
f(x) = 13
Step-by-step explanation:
f(x) = 7 means that x = 7
Plug this in:
3(7) - 8
21 - 8
13
f(x) = 13
Need help pls on maths question
Answer please anyone help same doubht
Step-by-step explanation:
Answer:
Refer to the photos taken.
Step-by-step explanation:
How do you define a function?
A function, according to a technical definition, is a relationship between a set of inputs and a set of potential outputs, where each input is connected to precisely one output.
This means that a function f will map an object x to exactly one object f(x) in the set of potential outputs if the object x is in the set of inputs (referred to as the domain) (called the codomain).
The metaphor of a function machine, which accepts an object as its input and produces another object as its output based on that input, makes the concept of a function simple to understand.
Given a collection of possible outputs Y (codomain) and a set of inputs X (domain), a function is more precisely defined as f: X→Y which shows that f is a function from X to Y using this notation.
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How do you find equivalent in math?
To find equivalent expression in math is the fractions with distinct numerators and denominators but the same value are said to be equivalent fractions.
In mathematics, equivalent fractions are those with the same denominator and differing numerators.
The multiplicity of a member of a multiset in mathematics is the number of times the member appears in the multiset. The multiplicity of a root, for instance, is how many times a given polynomial has a root at a particular point.
It's crucial to understand the concept of multiplicity in order to correctly count without mentioning exceptions (for example, double roots counted twice). Thus, "counted with multiplicity" is used.
This can be highlighted by counting the number of different elements, as in "the number of separate roots," if multiplicity is disregarded. However, multiplicity is always taken into account when a set (as opposed to a multiset) is established, therefore the word "different" is not necessary.
For instance, if we simplify 5/15, we get a fraction that is equal to 1/3, which is equal to 5/15.
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You recently joined a gym. You had to pay a joining fee of $40, and you will pay $20 per month to maintain the membership. Part A (6 points) Write an equation in slope-intercept form that represents the cost of the membership in relation to time.
The cost of the membership is the initial joining fee plus the cost per month multiplied by the number of months.
If the cost after [tex]m[/tex] months is [tex]c[/tex] dollars, then [tex]c=20m+40[/tex].
Cindy is attempting to calculate how much her car payment would be for a car that costs $27,000 to be repaid with monthly payments in 4 years at 4% APR.
Cindy's monthly payment of $609.63 will cost her $29,262.24 in 4 years at a 4% APR.
How is the total cost determined?The total cost that Cindy will spend on the car which costs $27,000 is computed by multiplying the monthly payment by 48 months (the payment period).
The monthly payment can be determined using an online finance calculator that compounds the interest rate monthly for four years.
Cost of car = $27,000
Annual Percentage Rate (APR) = 4%
Payment period = 4 years (monthly)
N (# of periods) = 48 months (4 years x 12)
I/Y (Interest per year) = 4%
PV (Present Value) = $27,000
FV (Future Value) = $0
Results:
PMT = $609.63
Sum of all periodic payments = $29,262.24
Total Interest = $2,262.45
Thus, Cindy will spend $29,262.24 for a car that costs $27,000, if she repays monthly for 4 years.
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Find the amount Erica owes at the end of 6 years if $ 5300 is loaned to her at a rate of 8 % compounded monthly. use A=P(1+r÷n)ⁿt
The amount owed is $
(Do not round until the final answer. Then round to the nearest cent as needed.)
The final amount compounded monthly at a rate of 8% over 6 years on a principal of $5300 is $8551.56
Compound InterestCompound interest is the interest calculated on the principal and the interest accumulated over the previous period. It is different from simple interest, where interest is not added to the principal while calculating the interest during the next period.
The formula of compound interest as given in the questions is
A = Final amount P = principalr = ratet = timen = number of times compoundedA = P[(1 + r/n)^nt
Substituting the values into the formula
A = 5300(1 + 0.08/6)^12 * 6
A = 8,551.56
Erica will owe $8551.56
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Question 1: Multiply: 12.10²
A 120
B 12000
c 1200
D 1.2
Am pula mare!
Da aaaaaaaaaaa????
A small toy rocket is launched from a 18-foot pad. The height (h, in feet) of the rocket t seconds after
taking off is given by the formula h = - 3t^2 + 3t+18. How long will it take the rocket to hit the
ground?
The time it would take the rocket to hit the ground upon launch is; 3 seconds.
At what time does the rocket hit the ground?It follows from the task content that the time taken for the rocket in discuss to hit the ground upon launch is to be determined.
Since the given formula for the height in terms of time, t is;
h = - 3t² + 3t + 18
It follows that ; when the rocket hits the ground; the height; h = 0.
Therefore;
0 = - 3t² + 3t + 18
0 = -3t² + 9t - 6t + 18
0 = -3t ( t - 3 ) - 6 ( t - 3)
-3t - 6 = 0 OR. t - 3 = 0.
t = -2. OR. t = 3.
Therefore, since the time after launch can only be positive; the time taken for the rocket to hit the ground is; 3 seconds.
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What are the steps in solving rational expressions?
The steps in solving two rational numbers is using the cross multiplication method and then do the arithmetic operation on the numerator
The rational expression is defined as the expression with both numerator and denominator has polynomials.
Consider two rational expressions
Add two expression using cross multiplication
a/b + c/d
Cross multiply the expression
a/b + c/d = (ad + cb) / bd
Subtract two expression using cross multiplication
a/b - c/d
Cross multiply the expression
a/b + c/d = (ad - cb) / bd
Therefore, the two rational expression can be solved by using the cross multiplication method and do the arithmetic operation
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Given f(x)=4(3-x), what is the value of f(-11)? How do I solve these types of equations?
Answer:
-32
Step-by-step explanation:
Simple
you will just substitute where there is x
for example if f(x)=3x+1 what is f(-2) so we will just substitute( place 2 for x)
it will now be f(-2)=3(-2)+1
=-6+1
=-5
so back to your question My friend
f(x)=4(3-x)
f(-11)=4(3-11)
=4(-8)
=-32
Thanks
A rectangular yard measuring 35 ft by 55 ft is bordered (and surrounded) by a fence. Inside, a walk that is 3 ft wide goes all the way along the fence. Find the area of this walk. Be sure to include the correct unit in your answer.
The area of walk is 504 square feet
Area of rectangleThe area of rectangle is define as a product of length L and width w
calculate the area of rectangle yard
Area = L x W,
where A equal the Area, L equals the length and W equal width.
A = 35 x 55
A= 1925 square feet
Area of the rectangular yard is 1925 square feet
From the question, we have 3ft wide goes all the way along the fence inside.
Therefore, we subtract six feet from each of the value of length ( 35) and width (55) because each side has 3feet .
Area = L x W
A = 29 x 49
A = 1421 square feet
Area of new rectangle formed by allowing for three foot walk is 1421 square feet
Area of Walk
To get the area walk; we subtract area of new rectangular formed from area of rectangular yard
Area of Walk = Area of Rectangular yard - Area of new rectangle
Area of Walk = 1925 - 1421
Area of Walk = 504 square feet.
Therefore, the area of walk is 504 square feet.
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Help Please!
3. An exercise equipment company is producing 45 lb. weights. To ensure the quality of their weights, they randomly select 60 weights and find that the mean weight of their sample is 45.07 lbs. with a standard deviation of 0.09 lbs. Create a 95% confidence interval and interpret the answer in context.
A. (45.0509, 45.0891); The exercise equipment company can be 95% confident the population mean of their 45 lb. weights lies between 45.0509 and 45.0891 lbs.
B. (44.8423, 45.2977); The exercise equipment company can be 95% confident the population mean of their 45 lb. weights lies between 44.8423 and 45.2977 lbs.
C. (44.9772, 45.0228); The exercise equipment company can be 95% confident the population mean of their 45 lb. weights lies between 44.9772 and 45.0228 lbs.
D. (45.0472, 45.0928); The exercise equipment company can be 95% confident the population mean of their 45 lb. weights lies between 45.0472 and 45.0928 lbs.
4. Raul is analyzing a set of data he collected and creating a confidence interval. If he chose to reduce the size of the sample and increase the level of confidence, how would that affect the confidence interval? Explain.
A. The size of the confidence interval would decrease because Raul would be dividing by a larger z-score and multiplying by a smaller sample size.
B. The size of the confidence interval would increase because Raul would be dividing by a smaller z-score and multiplying a larger sample size.
C. The size of the confidence interval would increase because Raul would be multiplying by a larger z-score and dividing by a smaller sample size.
D. The size of the confidence interval would decrease because Raul would be multiplying by a smaller z-score and dividing by a smaller sample size
The responses for the confidence intervals of the 45 lbs weight and the set of data are;
3. D. (45.0472, 45.0928); The exercise equipment company can be 95% confident the population mean of their 45 lb weights lies between 45.0472 and 45.0928
4. C. The size of the confidence interval would increase because Raul would be multiplying by a larger z-score and dividing by a smaller sample size.
What is a confidence interval?The confidence interval is the likelihood of a parameter of a population can be found within a range of values during a specified percentage or proportion of the time.
3. The confidence interval can be found using the formula;
[tex]CI = \overline x \pm z\cdot \dfrac{s}{\sqrt{n} }[/tex]
Where;
[tex]\overline x[/tex] = The mean of the sample = 45.07 lbs
s = The standard deviation of the sample = 0.09 lbs
n = The sample size
z = The confidence level = 1.96 at 95% confidence level
Therefore;
[tex]CI = 45.07 \pm 1.96\times \dfrac{0.09}{\sqrt{60} }[/tex]
45.0472 < μ < 45.0928
The correct option is therefore, option D
Therefore;
The company can be 95% sure that the mean of the population of the 45 lb weights are between 45.0472 and 45.0928 lbs4. Decreasing the sample size, n, will decrease the value by which the term on the right of the ± is being divided, increasing the confidence interval.
Increasing the level of confidence will increase z, thereby also increasing the confidence interval.
The correct option is therefore, option C.
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HELP ME OUT PLEASE ITS DUE IN 5 MINS
The equation that can be used to find the number of wolves in the state on January 1 is w - 23 = 84
How to represent a situation with an equation?A zoologist is recording the loss of wolves in her state. She notes the number of wolves, w, in the state on January 1. One year later, there were 84 wolves in the state, which is 23 fewer wolves than were in the state a year earlier.
The equation that can be used to find the number of wolves in the state on January 1 can be calculated as follows:
where
w = number of wolves in the state January 1.Therefore, the equation to represent the situation is as follows:
w - 23 = 84
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The total monthly charges, $C, for a mobile plan consist of a fixed amount of $ 120 and a variable amount which depends on the usage. For every minute used, $0.20 is charged. If the duration of usage is 120 minutes, calculate the total monthly charges for the mobile plan
The total monthly charges for the mobile plan if the usage is 120 minutes is $480.
Given that,
A mobile plan's total monthly costs, $C, are made up of a fixed fee of $ 20 and a variable fee that is based on usage. The cost is $0.20 per minute used.
We have to calculate the total monthly charges for the mobile plan if the usage is 120 minutes.
We know that,
A mobile plan fee is $20
For 1 min $0.20 for mobile plan
For 120 minutes
=120×0.2
=24
=24×20
=480
Therefore, the total monthly charges for the mobile plan if the usage is 120 minutes is $480.
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