Answers
Answer:
The answer should be -1 degree
Step-by-step explanation:
Combine all temperatures then divide by amount added together in this case five
Related Questions
Let f(x) = 3x2 + 1 and g(x) = - 2x +6. Find the following. (f-9)(-2) (f-9)(-2) = Let f(x) = x2 - 20 and g(x) = 10 - x. Perform the composition or operation indicated. (f9)(-7) (19)(-7)=0 Let f(x) = 2x - 1 and g(x) = je Find (f+g)(x), (-9)(x), (fg)(x), and 19. (x). Give the domain of each. (f +9)(x) = (Simplify your answer.) (f-g)(x) = (Simplify your answer.) (fg)(x) = (Simplify your answer.) (h) = (simplify your answer) The domain off+g is (Type your answer in interval notation.) The domain off-g is (Type your answer in interval notation) The domain of fg is (Type your answer in interval notation) The domain of is (Type your answer in interval notation.) f(x + h) – f(x) For the function f(x) = x2 -9, find (a) f(x + h), (b) f(x + h) – f(x), and (c) h (a) f(x +h) = (Simplify your answer.) (b) f(x + h) – f(x) = (Simplify, your answer.) f(x+h)-f(x) (c) h (Simplify your answer.) Let f(x) = 4x - 1, h(x) = - X+4. Find (f o h)(-4). (fo h)( - 4) = 0
Answers
The expressions involving those variables remain.Let's go through each part of the question one by one:
For f(x) =\(3x^2 + 1\) and
g(x) = -2x + 6,
we are asked to find (f-9)(-2):
(f-9)(-2) = \((3x^2 + 1 - 9)(-2)\)
=\((3x^2 - 8)(-2)\)
= \(-6x^2 + 16\)
For f(x) =\(x^2 - 20\) and
g(x) = 10 - x,
we are asked to perform the composition or operation indicated:
(f9)(-7)
(f9)(-7) = f(9)
=\(9^2 - 20\)
= 81 - 20
= 61
For f(x) = 2x - 1
and g(x) = je,
we are asked to find (f+g)(x), (-9)(x), (fg)(x), and 19(x), and give the domain of each:
(f+g)(x) = (2x - 1) + (je)
= 2x - 1 + je
(-9)(x) = -9x
(fg)(x) = (2x - 1)(je)
= 2xje - je
= 2jex - je
19(x) = 19x
The domain of each function is not specified, so we assume it to be all real numbers.
For (f+9)(x) and (f-g)(x), we are asked to simplify our answer:
(f+9)(x) = (2x - 1) + 9
= 2x + 8
(f-g)(x) = (2x - 1) - (-2x + 6)
= 2x - 1 + 2x - 6
= 4x - 7
For (fg)(x), we are asked to simplify our answer:
(fg)(x) = (2x - 1)(je)
= 2xje - j*e
= 2jex - je
The domain of f+g, f-g, fg, and 19 are not specified, so we assume it to be all real numbers.
For f(x) =\(x^2 - 9\),
we are asked to find (a) f(x + h), (b) f(x + h) - f(x), and (c) h:
(a) \(f(x + h) = (x + h)^2 - 9\)
= \(x^2 + 2hx + h^2 - 9\)
(b) f(x + h) - f(x)
= \((x^2 + 2hx + h^2 - 9) - (x^2 - 9)\)
= 2hx + h^2
(c) h is a variable and is not simplified further.
For f(x) = 4x - 1 and
h(x) = -x + 4,
we are asked to find (f o h)(-4):
(f o h)(-4) = f(h(-4))
= f(-(-4) + 4)
= f(8) = 4*8 - 1
= 31
Please note that in some cases, the expressions contain variables (such as j and e) which were not given specific values.
Therefore, the expressions involving those variables remain
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4. Marcy deposits $320 in an account that earns 3.5% simple interest per year. What is the balance in
the account after 4 years?
A. $448.00
B. $331.00
C. $364.80
D. $768.00
Answers
answer: c. $364.80
explanation: find the interest, then add the interest to the principal
to find interest:
interest = principal x rate x time
>> interest = 320 x 0.035 x 4
after multiplying, you get 44.80, which is the simple interest
to find account balance:
account balance = principal + interest
>> 320 + 44.80 = 364.80
If the probability of flooding is 2% per year, what is the chance of
flooding 2 times in 50 years?
Answers
The chance of flooding exactly 2 times in 50 years, with a 2% annual probability, is approximately 0.2704 or 27.04%.
To calculate the probability of an event occurring multiple times over a given period, we can use the binomial probability formula.
The binomial probability formula is given by: P(x) = C(n, x) * p^x * (1 - p)^(n - x)
Where:
P(x) is the probability of x successes
n is the total number of trials
p is the probability of success in a single trial
C(n, x) is the binomial coefficient, which represents the number of ways to choose x successes from n trials
In this case, the probability of flooding in a single year is 2% or 0.02. We want to find the probability of flooding exactly 2 times in 50 years. So, n = 50 and x = 2.
Plugging the values into the formula:
P(2) = C(50, 2) * (0.02)^2 * (1 - 0.02)^(50 - 2)
Calculating C(50, 2):
C(50, 2) = 50! / (2! * (50 - 2)!)
Substituting the values:
P(2) = (50! / (2! * 48!)) * (0.02)^2 * (0.98)^48
Calculating the expression:
P(2) ≈ 0.2704
Therefore, the chance of flooding exactly 2 times in 50 years, with a 2% annual probability, is approximately 0.2704 or 27.04%.
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Help aspp please thank you
Answers
The equation of the line would be y = (-3/4)x + 5.
What is the slope-point form of the line?
For the line having slope "m" and the point (x1, y1) the equation of the line passing through the point (x1, y1) having slope 'm' would be
y - y1 = m(x - x1)
The given equation is \(y=-\frac{3}{4}x-17\)
The required line is parallel to the given line.
and we know that the slopes of the parallel lines are equal so the slope of the required line would be m = -3/4
And the required line passes through (8, -1)
so by using slope - point form of the line,
y - (-1) = (-3/4)(x - 8)
y + 1 = (-3/4)x - (-3/4)8
y + 1 = (-3/4)x + 24/4
y = (-3/4)x + (12/2 - 1)
y = (-3/4)x + 5
Hence, the equation of the line would be y = (-3/4)x + 5.
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What is the following sale price
for a phone charger with an
original price of $12.99 after
applying a discount of 45%?
Answers
Answer:
$5.85
Step-by-step explanation:
To find the percentage of things you can use the percentage formula
p%*x=y
45%*12.99=y
.45*12.99=y
y=5.8455
I rounded up but the question may call for something different. Hope this Helps!
PLEASE HURRY 100 POINTS
Which expression represents the total surface area, in square meters, of the rectangular pyramid below?
A rectangular pyramid. The rectangular base has a length of 27.6 meters and height of 18.4 meters. 2 triangular sides have a base of 27.6 meters and height of 17.6 meters. 2 triangular sides have a base of 18.4 meters and height of 20.4 meters.
(18.4) (27.6) + 2 ((18.4) (20.4)) + 2 ((27.6) (17.6))
(18.4) (27.6) + 2 ((18.4) (22.4)) + 2 ((27.6) (22.4))
(18.4) (27.6) + 2 (one-half (18.4) (20.4)) + 2 (one-half (27.6) (17.6))
(18.4) (27.6) + 2 (one-half (18.4) (22.4)) + 2 (one-half (27.6) (22.4))
Answers
hope you have a good day or night
3. Mr. Sanchez’s class sold fruit pies for $1.45 each and Mr. Kelly’s class sold bottles of fruit juice for $1.25 each. Together, the classes sold 53 items and earned $70.85 for their school.
(a) Write and solve a system of equations that model the problem. Show all your work.
(b) Which class earned more money?
(c) How much more money did that class earn?
Answers
Let x be the number of fruit pies sold by Mr. Sanchez's class, and y be the number of bottles of fruit juice sold by Mr. Kelly's class.
(a) We can set up a system of equations to model the problem:
x + y = 53 (total number of items sold)
1.45x + 1.25y = 70.85 (total amount earned)
To solve this system using substitution, we can rearrange the first equation to solve for one variable in terms of the other:
x + y = 53
x = 53 - y
Then substitute x = 53 - y into the second equation:
1.45x + 1.25y = 70.85
1.45(53 - y) + 1.25y = 70.85
76.85 - 1.45y + 1.25y = 70.85
0.2y = 6
y = 30
Substituting y = 30 into the equation x + y = 53 gives:
x + y = 53
x + 30 = 53
x = 23
So Mr. Sanchez's class sold 23 fruit pies and Mr. Kelly's class sold 30 bottles of fruit juice.
(b) To find out which class earned more money, we can calculate the total amount earned by each class:
Mr. Sanchez's class: 1.45 x 23 = $33.35
Mr. Kelly's class: 1.25 x 30 = $37.50
Mr. Kelly's class earned more money.
(c) The amount by which Mr. Kelly's class earned more than Mr. Sanchez's class is:
$37.50 - $33.35 = $4.15
Use the power series method to find the solution of the given IVP dy dy – x) + y = 0 dx (x + 1) dx2 Y(0) = 2 ((0) = -1 =
Answers
The required solution of the series is: y = 2 - x - (2/3)x² + (2/9)x³ - (8/45)x⁴ + (2/1575)x⁵ + ...
The given differential equation is y″ - (x / (x + 1)) y′ + y / (x + 1) = 0 and initial conditions y(0) = 2 and y′(0) = -1.
Using the power series method, we assume that the solution of the differential equation can be written in the form of power series as:
y = ∑(n = 0)^(∞) aₙxⁿ
Differentiating y once and twice, we get
y′ = ∑(n = 1)^(∞) naₙx^(n - 1) and
y″ = ∑(n = 2)^(∞) n(n - 1)aₙx^(n - 2)
Substitute y, y′, and y″ in the differential equation and simplify the equation:
∑(n = 2)^(∞) n(n - 1)aₙx^(n - 2) - ∑(n = 1)^(∞) [(n / (x + 1))aₙ + aₙ₋₁]x^(n - 1) + ∑(n = 0)^(∞) aₙx^(n - 1) / (x + 1) = 0
Rearranging the terms, we get
aₙ(n + 1)(n + 2) - aₙ(x / (x + 1)) - aₙ₋₁
= 0aₙ(x / (x + 1))
= aₙ(n + 1)(n + 2) - aₙ₋₁a₀ = 2 and
a₁ = -1
Let's find some of the coefficients:
a₂ = - 2a₀ / 3,
a₃ = 2a₀ / 9 - 5a₁ / 18,
a₄ = - 8a₀ / 45 + 2a₁ / 15 + 49a₂ / 360,
a₅ = 2a₀ / 1575 - a₁ / 175 - 59a₂ / 525 + 469a₃ / 4725 + 4307a₄ / 141750...
The solution of the differential equation that satisfies the initial conditions is:
y = 2 - x - (2/3)x² + (2/9)x³ - (8/45)x⁴ + (2/1575)x⁵ + ...
Therefore, the required solution is: y = 2 - x - (2/3)x² + (2/9)x³ - (8/45)x⁴ + (2/1575)x⁵ + ...
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Solve each equation for x(2/5)(x+1) = g
Answers
To solve the equation $\frac{2}{5}(x+1) = g$ for $x$, we can follow these steps:
Step 1: Distribute the $\frac{2}{5}$ to the terms inside the parentheses:
$\frac{2}{5}x + \frac{2}{5} = g$
Step 2: Subtract $\frac{2}{5}$ from both sides to isolate the term with $x$:
$\frac{2}{5}x = g - \frac{2}{5}$
Step 3: Multiply both sides by $\frac{5}{2}$ to eliminate the fraction:
$x = \frac{5}{2}(g - \frac{2}{5})$
Step 4: Simplify the expression on the right-hand side:
$x = \frac{5}{2}g - \frac{5}{2} \cdot \frac{2}{5}$
Step 5: Further simplify the expression:
$x = \frac{5}{2}g - 1$
Therefore, the solution to the equation $\frac{2}{5}(x+1) = g$ is $x = \frac{5}{2}g - 1$.
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DUE FRIDAY PLEASE HELP WELL WRITTEN ANSWERS ONLY!!!! 20 POINTS
Students in a high school mathematics class decided that their term project would be a study of the strictness of the parents or guardians of students in the school. Their goal was to estimate the proportion of students in the school who thought of their parents or guardians as “strict”. They do not have time to interview all 1000 students in the school, so they plan to obtain data from a sample of students.
1. Describe the parameter of interest and a statistic the students could use to estimate the parameter.
2. Is the best design for this study a sample survey, an experiment, or an observational study? Explain your reasoning.
3. The students quickly realized that, as there is no definition of “strict”, they could not simply ask a student, “Are your parents or guardians strict?” Write three questions that could provide objective data related to strictness.
4. Describe an appropriate method for obtaining a sample of 100 students, based on your answer in question 1.
Answers
The percentage of students at the school who describe their parents or guardians as "strict" is the key statistic. 2. A sample survey is the ideal research design for this project.
What is Proportion?Since it would be impractical to poll all 1000 kids at the school, the students intend to collect data from a sample of students in order to concentrate on the strict guardians, which is a population parameter.
The sample proportion could be used by the students as a statistic to determine this population proportion. They can ask a sample of pupils drawn at random from the school whether they think their parents or guardians are "strict". The percentage of sample kids who respond "yes" can be used to approximate the percentage of school-wide students who view their parents or guardians as "strict". A statistic that offers an estimate of the population parameter of interest is the sample proportion.
Random sampling would be a suitable technique for generating a sample of 100 pupils. Each kid in the school might be given a number, and the pupils could then use a random number generator to choose 100 numbers from the list. The chosen students might then be contacted and asked to take part in the study. This technique lessens the possibility of bias in the sample selection process and aids in ensuring that the sample is representative of the population.
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help me i don't understand
Answers
The volume of the fully inflated balloon is \(\frac{19652}{3}\)π inch³ and volume of half inflated balloon is \(\frac{19652\pi }{6}\).
What is Volume?Volume of a three dimensional shape is the space occupied by the shape.
Given that,
Diameter of a fully inflated balloon = 34 inch
Radius is half the diameter.
Radius of fully inflated balloon = 34 / 2 = 17 inches
Volume of a sphere = \(\frac{4}{3}\) π r³, where r is the radius.
(a) Volume of fully inflated balloon = \(\frac{4}{3}\) π (17)³
= \(\frac{19652}{3}\)π inch³
(b) Volume of the half inflated balloon = Half of the fully inflated volume
= (\(\frac{19652}{3}\)π / 2) inch³
= \(\frac{19652\pi }{6}\) inch³
(c) Volume of half inflated balloon = \(\frac{19652\pi }{6}\)
\(\frac{4}{3}\) π r³ = \(\frac{19652\pi }{6}\)
\(\frac{4}{3}\) r³ = \(\frac{19652}{6}\)
r³ = \(\frac{19652}{8}\)
r = 13.49 inch
Hence the volume and radius are found.
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On Dec. 10, Merchandise is sold for $2,0002/10, n/30 to ABC who sends a remittance on Dec. 26 . What is the amount of remittance? a. 1,800 b. 1,400 c. 1,960 d. 2,000
Answers
The amount of the remittance from ABC is $1,960.
The given information states that merchandise is sold for $2,000 with terms of 2/10, n/30 to ABC. The terms 2/10, n/30 imply a 2% discount if payment is made within 10 days, with the full amount due within 30 days.
Since ABC sends a remittance on Dec. 26, it means the payment is made after the discount period but within the credit period. Therefore, ABC is not eligible for the discount of 2%.
To calculate the amount of the remittance, we simply subtract the discount from the total amount. In this case, the discount is $2,000 * 2% = $40. Thus, the remittance amount is $2,000 - $40 = $1,960.
In conclusion, the amount of the remittance from ABC is $1,960, as they did not qualify for the early payment discount.
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Write an expression for 88 added to v
Answers
Answer:
\(\mathrm{88 + v}\)
Find the measure of
Answers
Answer:
Z = 108º
Step-by-step explanation:
The interior angles of a quadrilateral (4-sided figure) sum to 360º (think about a rectangle). Therefore,
(x + 2x + 4x + 3x)º = 360º
↓ combining like terms
10xº = 360º
↓ dividing by 10º
x = 36
We can use this x-value to find the measure of angle Z.
Z = 3xº
Z = 3(36)º
Z = 108º
Solve
7x - 3x - 8 = 24
Answers
Answer:
x = 8
Step-by-step explanation:
Factor:
7x - 3x = 4x
24 + 8 = 32
32 ÷ 4 = 8
---------------------------------------------------------------------------------------------------------------
Double check:
56 - 24 - 8 = 24
---------------------------------------------------------------------------------------------------------------
Have a great summer :)
Answer:
x = 33 / 4
Given :-
7x - 3x -9 = 24
We have to find
The value of x .
Step-by-step explanation:
Let's begin:-
7x - 3x -9 = 24
Step 1 :- Combine like terms.
4x - 9 = 24.
Step 2 :- Move constant to the right-hand and change their sign.
4x = 24 + 9.
Step 3 :- Add 24 and 9.
4x = 33
Step 4 :- Divide both side by 4.
4x / 4 = 33 / 4
Hence, x = 33 / 4
1.
(06.01 LC)
3^4 + 2 ⋅ 5 =
. (Input whole numbers only.)
Answers
Answer:
91
Step-by-step explanation:
Because the equation is equal to 91
Answer:
91 is the answer. :0
Step-by-step explanation:
Suppose you are given the function t(x) = x^2 + 8x - 20 Explain how you would graph this function, making sure to include the following information: Coordinate(s) of the solutions/rootscoordinate of the y-intercept location of the line of symmetrycoordinate of the vertex whether the graph opens up or down and how you know
Answers
t(x) = x² + 8x - 20
Coordinate(s) of the solutions/roots
x² + 8x - 20 = 0 ==> (x -2)(x + 10) = 0
roots: x= 2 and x = -10
coordinate of the y-intercept
y-intercept is when x = 0 ==> t(x) = x² + 8x - 20 when x = 0: t(0) = -20
y-intercept: y = -20
location of the line of symmetry
x = -4
y = (x + 4)² - 36, therefore coordinates of the vertex (-4, 36) and line of symetry x = -4
coordinate of the vertex
(-4, -36)
y = (x + 4)² - 36, therefore coordinates of the vertex (-4, 36)
whether the graph opens up or down and how you know
Opens up
Because the coefficient of x² is positive
A school's K-Pop club is learning a new dance to a Korean pop song. They pay the dance
teacher from their bank account, which showed three changes this week.
First, a $60 withdrawal was represented using the number - 60.
• The second change was the opposite of the first.
• The third change was the opposite of the second.
What number represents the third change made to the account?
●
Type the number in the box.
Answers
The number which represents the third change made to the account according to.tge task content is; -60.
What number represents the third change made to the account?According to the task content, the second change was the opposite of the first, -60.
Hence, the second change is; +60 which is the additive inverse.
Ultimately, since the third change was the opposite of the second, it follows that the third change is; -60.
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A student goes to the library. Let events B = the student checks out a book and D = the student checks out a DVD. Suppose that P(B) = 0.45, P(D) = 0.50 and P(DJB) = 0.30. a. Find P(BND). (2) b. Find P(B U D). (2) c. What is the probability that a student does not select a book nor a DVD?
Answers
P(BND) = 0.65, P(B U D) = 0.65 and the probability that a student does not select a book nor a DVD is 0.35.
a.P(BND) = 0.3015
b.P(B U D) = 0.65
To find the probability of both events B and D occurring, we use the formula P(BND) = P(B) * P(D|B). Given that P(B) = 0.45 and P(D|B) = 0.67 (which is the probability of D given that B has occurred), we can calculate P(BND) as follows:
P(BND) = 0.45 * 0.67 = 0.3015.
b.P(B U D) = 0.65
To find the probability of either event B or event D or both occurring, we use the formula P(B U D) = P(B) + P(D) - P(BND). Given that P(B) = 0.45, P(D) = 0.50, and we already calculated P(BND) as 0.3015, we can calculate P(B U D) as follows:
P(B U D) = 0.45 + 0.50 - 0.3015 = 0.6485 ≈ 0.65.
P(not selecting a book nor a DVD) = 0.05
The probability of not selecting a book nor a DVD is the complement of selecting either a book or a DVD or both. Since P(B U D) represents the probability of selecting either a book or a DVD or both, the complement of P(B U D) will give us the probability of not selecting a book nor a DVD:
P(not selecting a book nor a DVD) = 1 - P(B U D) = 1 - 0.65 = 0.35 = 0.05.
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It costs Widgeco $2,000 to purchase a machine that produces widgets and $2.75 to produce each widget. If widgets are sold for $4.99 each, which of these represents the profit, P(w), received when Widgeco sells w widgets?
A
P(w) = 2.24w + 2,000
B.
P(w) = 7.74w + 2,000
C.
P(w) = 2.24w – 2,000
D.
P(w) = 7.74w – 2,000
Answers
Answer:
B
Step-by-step explanation:
You would add the 2.75 and 4.99 to get 7.74 and you would add the variable for how much widgets are made and since its the profit you would have to add the 2,000 so the equation would be P(w) = 7.74w + 2,000
Hope this helps
(oﾟvﾟ)ノ
can someone do this
Answers
Answer:
2
Step-by-step explanation:
m= (y-y1)/(x-x1)
Points are (3, -2) and (6, 4)
m= (-2-4)/(3-6)= -6/-3= 2
m=2 to replace ? mark
The product of Bart's age and 26 is 338. Write and solve a multiplication equation to find Bart's age. Yeah
Answers
Answer:
13 years old
Step-by-step explanation:
A product is 2 numbers that are multiplied together.
So, to find the unknown number, simply divide 338 by 26
338/26=13
Bart is 13 years old.
what is the area of the front of the prism? area = cm2 2 by 6 by 3
Answers
The area of the front face of the prism with dimensions 2 cm by 6 cm by 3 cm is 12 square centimeters.
To find the area of the front face of the prism, we need to calculate the product of its length and width. In this case, the front face has dimensions of 2 cm by 6 cm.
To determine the area, we multiply the length and width of the front face:
Area = Length × Width
Area = 2 cm × 6 cm
Multiplying these values, we obtain:
Area = 12 cm²
Therefore, the area of the front face of the prism is 12 square centimeters. It is important to note that the given dimensions of 2 cm by 6 cm by 3 cm refer to the overall dimensions of the prism but to find the area of a specific face, we need to consider only the relevant length and width. In this case, the front face dimensions are 2 cm by 6 cm, resulting in an area of 12 square centimeters.
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For continuous data to be statistically significant, a good rule
of thumb is that there should be at least how many samples?
A. 5
B. 25
C. 50
D. 100
Answers
While a common rule of thumb is to have a minimum sample size of 100 for continuous data to be statistically significant, the actual appropriate sample size may vary depending on the specific study design and research question. Option(D)
In statistics, the term "statistical significance" refers to whether an observed effect or relationship in the data is likely to be real and not just due to random chance. To determine statistical significance, we often perform hypothesis testing.
The sample size is a crucial factor in hypothesis testing. A larger sample size generally provides more reliable and precise estimates of population parameters and increases the statistical power of the test. With a larger sample size, even smaller effects or differences between groups can become statistically significant.
While there is no hard and fast rule for the minimum sample size to achieve statistical significance, a common guideline is to aim for at least 30 samples. This guideline is often used in the context of the Central Limit Theorem, which states that the sampling distribution of the sample mean becomes approximately normally distributed with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.
In practice, the appropriate sample size depends on various factors, including the nature of the data, the effect size being studied, the desired level of confidence, and the statistical test used. Researchers often conduct sample size calculations based on these factors before conducting their studies to ensure they have an adequate sample size to achieve meaningful results and detect significant effects if they exist.
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Nisrin and Sawin are making a string of beads for the School day. The
string already has 70 beads. If there are only 30 more days until school day and
they want to string 1000 beads by then, at least how many beads do they have to
string each day?
Answers
According to the word problem states that they must string at least 31 beads per day.
What is a mathematical word problem ?Math word problems require students to apply their arithmetic abilities in a "real-life" setting and are mathematical questions that are described in one or more sentences. Kids must therefore be familiar with the vocabulary associated with the mathematical symbols they are used to in order to comprehend the word problem.
According to the given information:given the string's existing 70 beads They intend to string 1000 beads by both the start of class in just 30 more days.
The minimal number of beads that must be strung each day is calculated by dividing the remaining beads by the number of days:
The quantity of beads needed to reach 1000 = 1000 - 70 = 930
Now, putting the values,
= (1000 - 70)/30
= 930/30
= 31
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If Half the number is 40 less than 56. Find the number
Answers
Answer:
32
Step-by-step explanation:
half the number is 56 - 40 which is 16 and it says half the nuber is 16 so 16 x 2 is 32
Answer:
The number is 8
Step-by-step explanation:
Lets say the number is x.
x/2=56-40
combine 56 and -40
x/2=4
multiply 2 by both sides
x= 8
Construct a 98% confidence interval for the population mean. Assume the population has a normal distribution. A random sample of 20 college students has an annual earning of $3140 with a standard deviation of $686.
Answers
There is 98% confidence that the true population mean falls within the range of $2782.11 and $3497.89 based on the provided sample data.
To construct a 98% confidence interval for the population mean, use the following formula:
Confidence Interval = mean ± Z * (σ/√n)
where:
- Z is the critical value corresponding to the desired confidence level
- σ is the population standard deviation
- n is the sample size
Given the information provided:
(sample mean) = $3140
- σ (population standard deviation) = $686
- n (sample size) = 20
First, find the critical value Z for a 98% confidence level. The confidence level of 98% corresponds to a significance level (α) of 0.02.
Half of the significance level is distributed in each tail of the standard normal distribution.
Looking up the critical value for a significance level of 0.02/2 = 0.01 in a standard normal distribution table or using statistical software, Z ≈ 2.33.
Substituting the values into the formula, calculate the confidence interval:
Confidence Interval = $3140 ± 2.33 * ($686/√20)
Calculating the expression inside the square root:
($686/√20) ≈ $153.45
Therefore, the confidence interval for the population mean is approximately:
Confidence Interval = $3140 ± 2.33 * $153.45
Confidence Interval ≈ $3140 ± $357.89
This can be expressed as:
Confidence Interval ≈ ($2782.11, $3497.89)
Thus, it is 98% confident that the true population mean falls within the range of $2782.11 and $3497.89 based on the provided sample data.
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HELP PLEASE 1O POINTS
Answers
Answer: 35
Step-by-step explanation:
I am rowing on a river between two cities that are 12 miles apart. When going downstream, I make the journey in 2/3 hour(s). When I return upstream, it takes me 3/2 hour(s). What is the current of the river? miles per hour What is the speed I would row at in still water? miles per hour
Answers
The current of the river is 3 miles per hour and the speed you would row at in still water is 15 miles per hour.
To find the current of the river and the speed you would row at in still water, we can use the formula:
Speed downstream = Speed in still water + Current of the river
Speed upstream = Speed in still water - Current of the river
Let's start by solving for the current of the river.
Given:
Distance between the two cities = 12 miles
Time downstream = 2/3 hour
Time upstream = 3/2 hour
To find the current of the river, we need to compare the time it takes to row downstream to the time it takes to row upstream.
1. Finding the speed downstream:
Distance = Speed downstream × Time downstream
12 miles = Speed in still water + Current of the river × 2/3 hour
2. Finding the speed upstream:
Distance = Speed upstream × Time upstream
12 miles = Speed in still water - Current of the river × 3/2 hour
Now we have a system of two equations:
Equation 1: 12 miles = (Speed in still water + Current of the river) × 2/3 hour
Equation 2: 12 miles = (Speed in still water - Current of the river) × 3/2 hour
We can solve this system of equations to find the values of the current of the river and the speed in still water.
Multiplying Equation 1 by 3 and Equation 2 by 2, we get:
Equation 3: 36 miles = (Speed in still water + Current of the river) × 2 hour
Equation 4: 24 miles = (Speed in still water - Current of the river) × 3 hour
Adding Equation 3 and Equation 4, we eliminate the Current of the river:
36 miles + 24 miles = (Speed in still water + Current of the river) × 2 hour + (Speed in still water - Current of the river) × 3 hour
60 miles = (2 × Speed in still water × 2 hour)
Dividing both sides by 4 hours:
15 miles/hour = Speed in still water
Now, to find the current of the river, substitute the value of Speed in still water into either Equation 3 or Equation 4.
Let's use Equation 3:
36 miles = (15 miles/hour + Current of the river) × 2 hour
Dividing both sides by 2:
18 miles = 15 miles/hour + Current of the river
Subtracting 15 miles/hour from both sides:
3 miles/hour = Current of the river
So, the current of the river is 3 miles per hour and the speed you would row at in still water is 15 miles per hour.
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The directed line segment from L to N has endpoints L(–6, 2) and N(5, –3). What are the x- and y-coordinates of point M, which partitions the directed line segment into the ratio 2:5?
Answers
Answer:
the answer is -6, 2
Step-by-step explanation:
Answer:
the answer is -6, 2
Step-by-step explanation:
Answer:
ANSWER
x = { - 20}{7}
y={ 4}{7}
Step-by-step explanation: