To make F the subject of the formula in the Celsius to Fahrenheit conversion, multiply by 9, divide by 5, and then add 32, resulting in F = (9/5)C + 32.
Explanation:To make F the subject of the formula when given the Celsius to Fahrenheit conversion formula c = 5(f - 32)/9, we start by isolating Fahrenheit on one side of the equation. Here's a step-by-step process:
Multiply both sides of the equation by 9: 9c = 5(f - 32).Divide both sides by 5: (9/5)c = f - 32.Add 32 to both sides to isolate f: f = (9/5)c + 32.Now the formula for F in terms of C is in the form aC + b with a = 9/5, b = 32, and there's no c as in the denominator since the conversion is direct.
[tex]\( F = \frac{9c + 160}{5} \).[/tex] In form [tex]\( aC + \frac{b}{c} \), \( a = 9 \), \( b = 160 \),[/tex] and [tex]\( c = 5 \).[/tex]
Let's break down the process of rearranging the formula step by step.
Given formula: [tex]\( c = \frac{5(F - 32)}{9} \)[/tex]
We want to isolate [tex]\( F \)[/tex] on one side of the equation.
1. Multiply both sides by [tex]\( \frac{9}{5} \):[/tex]
[tex]\[ \frac{9}{5} \cdot c = \frac{9}{5} \cdot \frac{5(F - 32)}{9} \][/tex]
This cancels out the fraction on the right side.
[tex]\[ \frac{9}{5} \cdot c = F - 32 \][/tex]
2. Add 32 to both sides to isolate [tex]\( F \):[/tex]
[tex]\[ \frac{9}{5} \cdot c + 32 = F \][/tex]
Now, [tex]\( F \)[/tex] is isolated on the right side of the equation.
3. Rewrite [tex]\( F \)[/tex] in the required form [tex]\( aC + \frac{b}{c} \):[/tex]
[tex]\[ F = \frac{9}{5}c + 32 \][/tex]
To express [tex]\( F \)[/tex] in the required form, we can rewrite [tex]\( \frac{9}{5}c \) as \( \frac{9c}{5} \),[/tex]so the form becomes [tex]\( aC + \frac{b}{c} \).[/tex]
So, [tex]\( a = 9 \), \( b = 32 \), and \( c = 5 \).[/tex]
4. Final Form:
[tex]\[ F = \frac{9c + 160}{5} \][/tex]
So, in the form [tex]\( aC + \frac{b}{c} \),[/tex] we have [tex]\( a = 9 \), \( b = 160 \), and \( c = 5 \).[/tex]
find the volume of the cylinder someone help please
Answer:
The answer to your question is in terms of π, Volume = 54π units³
as an exact number Volume = 169.56 units³
Step-by-step explanation:
Data
radius = 3
height = 6
π = 3.14
Process
1.- Look for the formula to calculate the volume of a cylinder
Volume = πr²h
2.- Substitution
Volume = π(3)²(6)
3.- Simplification
Volume = π(9)(6)
4.- Volume in terms of π
Volume = 54π units³
5.- As an exact number
Volume = 54(3.14)
-Result
Volume = 169.56 units³
I found the expected value for the number of boys for a family with five children to be 2.5. I must have made an error because a family with 2.5 boys cannot occur
Answer:
We are meant to round down fractions of persons to the nearest whole number possible
Step-by-step explanation:
Here we have the question with regards the result of a fraction of a person to a solution of a statistic question.
Where the result is a fraction, the format is, since most solutions to questions in statistics with regards to people pertain to the maximum amount of persons that fit a class, and since it is not technically feasible to account for the next half of the person after getting your result, we have to put down only the number of whole people possible which means as a rule we always round down the decimal or fractions to the nearest whole number of person
Therefore, you are correct, only that we can put 2 instead of 2.5 as your answer.
The statement does not make sense because the expected value of 2.5 represents the average number
of boys for all the families with five children. In a five-child family, half the children are expected to be boys, so the expected value of 2.5 is consistent.
16. You deposit $468 into a mutual fund account. It decreases in value by 1% per week for six
months. How much do you have after 14 weeks?
Answer:
V(m)=320 (1.005).
Step-by-step explanation:
I have no clue how to do this
Answer:
14
Step-by-step explanation:
5x + 12 = 7x - 16
28 = 2x
14 = x
Angle 3's alternate interior angle is Angle 2. Angle two is equal to angle 4 (thi is just a rule in geometry). So that means Angle 3 is also equal to angle $. So just make the equations equal to eachother and solve for x as shown above.
which is true about rational numbers
Answer:
a rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q.
Step-by-step explanation:
Answer:
Any number that can be written in fraction form is a rational number.
Step-by-step explanation:
Billy and tommy are playing a dice game with a six sided dice. Billy needs to roll a 5 or higher to win the game. What is the probability that billy will rool a 5 or higher
The correct option is b) 1/3. Billy's probability of rolling a 5 or higher on a six-sided die is 0.333 or 33.33%.
Probability of Rolling a 5 or Higher
Billy needs to roll a 5 or higher on a six-sided die (with faces numbered 1 through 6) to win the game. Let's calculate the probability.
→ The possible outcomes that satisfy Billy's condition are 5 and 6. Therefore, there are 2 favorable outcomes.
The total number of possible outcomes when rolling a six-sided die is 6.
Calculation
→ Number of favorable outcomes: 2 (rolling a 5 or a 6)
Total possible outcomes: 6
→ Probability (P) = (Number of favorable outcomes) / (Total possible outcomes)
→ P(E) = 2 / 6
= 1 / 3
≈ 0.333
Therefore, the probability that Billy will roll a 5 or higher to win the game is approximately 0.333 or 1/3.
The complete question is:
Billy and Tommy are playing a dice game with a six-sided die. Billy needs to roll a 5 or higher to win the game. What is the probability that Billy will roll a 5 or higher?
a) 1/2
b) 1/3
c) 2/3
d) 1/6
Use the zero product property to find the solutions to the equation 6x2 – 5x = 56.
O x=-8 or x= 7/6
O х=-8/3 or x = 7/2
O x= -1/2 or x= 56/3
O x = -3/7 or x= 2/3
Please hurry I need the answer ASAP
Answer:
O х= -8/3 or x = 7/2
Step-by-step explanation:
6x² - 5x - 56 = 0
6x² - 21x + 16x - 56 = 0
3x(2x - 7) + 8(2x - 7) = 0
(2x - 7)(3x + 8) = 0
x = 7/2, -8/3
The solutions of the equation 6x² - 5x + 56 using the zero product property is x = -8/3 or x = 7/2.
What are Quadratic Expressions?Quadratic expressions are polynomial expressions of second degree.
The general form of a quadratic expression is ax² + b x + c.
The given is a quadratic expression,
6x² - 5x = 56
We have to find the solutions using zero product property.
Zero product property states that, if a.b = 0, the either a = 0 or b = 0.
Let 6x² - 5x = 56
6x² - 5x - 56 = 0
Dividing throughout by 6,
x² - 5/6 x - 56/6 = 0
We can factorize it as (x + p)(x + q) such that pq = -56/6 and p + q = -5/6.
We know that,
8/3 × -7/2 = -56/6
8/3 - 7/2 = 16/6 - 21/6 = -5/6
So,
x² - 5/6 x - 56/6 = 0
(x + 8/3) (x - 7/2) = 0
Using zero product property,
(x + 8/3) = 0 or (x - 7/2) = 0
x = -8/3 or x = 7/2
Hence the solutions are x = -8/3 or x = 7/2.
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8x + 7 = 2x + 37 ????
Answer: 5
Step-by-step explanation:Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-2x' to each side of the equation.
7 + 8x + -2x = 37 + 2x + -2x
Combine like terms: 8x + -2x = 6x
7 + 6x = 37 + 2x + -2x
Combine like terms: 2x + -2x = 0
7 + 6x = 37 + 0
7 + 6x = 37
Add '-7' to each side of the equation.
7 + -7 + 6x = 37 + -7
Combine like terms: 7 + -7 = 0
0 + 6x = 37 + -7
6x = 37 + -7
Combine like terms: 37 + -7 = 30
6x = 30
Divide each side by '6'.
x = 5
Simplifying
x = 5
Mr. McBride asks students to find the volume of the triangular pyramid below. Which student wrote the correct expression for the value of B, the area of the base?
Given:
Given that Mr. McBride asks students to find the volume of the triangular pyramid.
The two students wrote the expression for the value of B, the area of the base of the pyramid which is attached in the picture below.
We need to determine the student who correctly wrote the value of B.
Expression for value of B:
The area of the base of the triangular prism can be determined using the formula,
[tex]B=\frac{1}{2}bh[/tex]
where b is the base of the triangle and h is the height of the triangle.
From the figure, the base of the triangle is 9 inches and the height of the triangle is 12 inches.
Substituting in the above formula, we get;
[tex]B=\frac{1}{2}(9 \cdot 12)[/tex]
Thus, the correct expression for the area of the base is [tex]B=\frac{1}{2}(9 \cdot 12)[/tex]
Hence, the expression wrote by MAE is correct.
Chelsea and Pedro manipulated the rational expression \dfrac{14k^3 + 7k^2}{7k^3 + 14k^2} 7k 3 +14k 2 14k 3 +7k 2 start fraction, 14, k, cubed, plus, 7, k, squared, divided by, 7, k, cubed, plus, 14, k, squared, end fraction. Their responses are shown below.
Answer:
Step-by-step explanation:
[tex]\frac{14k^3+7k^2}{7k^3+14k^2} =\frac{7k^2(2k+1)}{7k^2(k+2)} =\frac{2k+1}{k+2}}[/tex]
Answer:
Both Chelsea and Pedro wrote an expression that is equivalent to the original expression
Step-by-step explanation:
first simplify the expression 14k^3 + 7k^2 / 7k^3 + 14k^2 can you get Chelsea's expression. If you simplify Pedro's equation you get the same expression as Chelsea's
Each baseball team in a baseball league has 14 players. A total of 56 players signed up to play. If t represents the number of teams in the league which statement is true?
Answer:
56 player divided by 14 on each team
Step-by-step explanation:
There will be 4 teams
An investment services company experienced dramatic growth in the last two decades. The following models for the company's revenue R and expenses or costs C (both in millions of dollars) are functions of the years past 1990. R(t) = 21.4e0.131t and C(t) = 18.6e0.131t (a) Use the models to predict the company's profit in 2020. (Round your answer to one decimal place.)(b) How long before the profit found in part (a) is predicted to double? (Round your answer to the nearest whole number.) years after 1990
Answer: a) 138.32 and b) 35 years approx.
Step-by-step explanation:
Since we have given that
[tex]R(t)=21.4e^{0.13t}\\\\C(t)=18.6e^{0.13t}[/tex]
So, Profit is given by
[tex]Profit=R(t)-C(t)\\\\Profit=21.4e^{0.13t}-18.6e^{0.13t}\\\\Profit=e^{0.13t}(21.4-18.6)\\\\Profit=2.8e^{0.13t}[/tex]
Difference in years of 1990 and 2020=30
So, Profit becomes :
[tex]P(30)=2.8e^{0.13\times 30}\\\\P(30)=2.8\times 49.40\\\\P(30)=138.32[/tex]
(b) How long before the profit found in part (a) is predicted to double? (Round your answer to the nearest whole number.) years after 1990.
So, profit doubles , we get :
[tex]138.32\times 2=2.8e^{0.13t}\\\\276.65=2.8e^{0.13t}\\\\\dfrac{276.65}{2.8}=e^{0.13t}\\\\98.80=e^[0.13t}\\\\\ln 98.80=0.13t\\\\4.593=0.13t\\\\\dfrac{4..593}{0.13}=t\\\\35.33=t[/tex]
Hence, a) 138.32 and b) 35 years approx.
Final answer:
(a) To predict the company's profit in 2020, substitute the given revenue and cost functions into the profit equation. Calculate the value of the profit at t = 30. (b) To find the time it takes for the profit to double, set the profit equation equal to twice the profit in part (a) and solve for t.
Explanation:
(a) To predict the company's profit in 2020, we need to calculate the difference between the revenue and expenses. The profit (P) is given by the equation P(t) = R(t) - C(t), where R(t) is the revenue function and C(t) is the cost function. Substituting the given functions into the equation, we have P(t) = 21.4e0.131t - 18.6e0.131t. To find the profit in 2020 (t = 30), we plug in t = 30 into the equation and calculate the value of P(30).
(b) To find the time it takes for the profit to double, we need to determine when P(t) is equal to twice the profit in part (a). We set P(t) = 2P(30) and solve for t.
Identify the surface whose equation is given. rho2(sin2(φ) sin2(θ) + cos2(φ)) = 49
Answer:
The surface is a cylindrical surface with radius 7 units
Step-by-step explanation:
The equation is properly written as:
[tex]\rho^{2} (sin^{2} \phi sin^{2} \theta + cos^{2} \phi) = 49[/tex]
The above equation takes the form [tex]y^{2} + z^{2} = r^{2}[/tex]
Where [tex]y^{2} = \rho^{2} sin^{2} \phi sin^{2} \theta[/tex]
[tex]y = \rho sin \phi sin \theta[/tex]
and [tex]z^{2} = \rho^{2}cos^{2} \phi[/tex]
[tex]z = \rho cos \phi[/tex]
[tex]r^{2} = 49[/tex]
r = 7 units
The surface is a cylindrical surface with radius 7 units
10 customers entered a store over the course of 5 minutes. At what rate were the
customers entering the store in customers per minute?
Answer:
like 2 per minute?
Step-by-step explanation:
The rate at which customers are entering the store is calculated by dividing the number of customers by the time it took them to enter. In this case, 10 customers entered the store over 5 minutes, so the rate is 2 customers per minute.
Explanation:The rate at which customers are entering the store is calculated by dividing the total number of customers by the total time it took for them to enter. Here, the total number of customers is 10, and the total time is 5 minutes. So, the calculation would be: 10 customers / 5 minutes. This equals 2 customers per minute. Therefore, the rate of customers entering the store is 2 customers per minute.
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Choose 3 ratios in simplest form. 3:9
Answer:
Step-by-step explanation:
1:3
6:18
9:27
are all equivlent ratios
Final answer:
To choose 3 ratios in the simplest form, you must simplify the given ratios by dividing all the numbers by their greatest common divisor or the smallest among them. In genetics and chemistry, these simplified ratios are used to predict genetic outcomes and determine molecular compositions.
Explanation:
Choosing 3 ratios in the simplest form involves simplifying the given ratio. A ratio compares two quantities and can be written in various forms such as fractions, with a colon, or with the word 'to.' For example, 3:9, when simplified, becomes 1:3 as both numbers can be divided by 3. To express ratios as whole numbers or in the simplest form, divide all the numbers by the smallest number among them. For example, the ratio of 55:10:12 simplifies to 5.5:1:1.2, and when expressed as whole numbers, it becomes 5:1:1. In the subject of genetics, ratios such as 9:3:3:1 are used to predict outcomes based on genetic theory, and we can use data to test these ratios.
In chemistry, the mole ratio can be determined by dividing the molar amounts by the smallest molar amount. This is used to determine the ratio between different elements in a compound. For instance, if the molar amounts of elements in a compound were 0.03567 mol of Oxygen, 0.1070 mol of Carbon, and 0.2140 mol of Hydrogen, dividing each by the smallest molar amount of 0.03567 would give us a ratio that should then be expressed as whole numbers.
In order for you to answer the question correctly, please use the following image below:
Find the value of c.
What is the value of C?
Please show all the work on how you got your answer.
Answer:
28°
Step-by-step explanation:
Angle on the circumference is half the angle at the centre
c = ½(56)
c = 28°
What is the asnwer for 1-1
Answer:
Using a deduction theorem of 1.01%, we can use a punnet square to help. Being that both sides of an dissociates triage is always equal to the third we can punch in the calculations and conclude that the answer is... 1 - 1 = 0
Step-by-step explanation:
In a survey of 90 students 20 choose rock.40 chose hip hop 30 chose country. In a school of 360 students how many would be expected to chose hip hop or rock
Answer:
The students would be expected to choose rock be 80 or students choose hip hop be 160 or choose to country be 120.
Step-by-step explanation:
Given:
In a survey of 90 students 20 choose rock, 40 choose hip hop and 30 choose country.
Now, to find the students expected to choose hip hop or rock or country in a school of 360 students.
Let the number of students expected to choose rock be [tex]x.[/tex]
Let the number of students expected to choose hip hop be [tex]y.[/tex]
Let the number of students expected to choose country be [tex]z.[/tex]
Total number of students = 360.
Now, to get the number of students choosing hip hop or rock or country by using cross multiplication method:
In a survey of 90 students 20 choose rock.
So, 90 is equivalent to 20.
Thus, 360 is equivalent to [tex]x[/tex].
[tex]\frac{90}{20} =\frac{360}{x} \\\\By\ cross\ multiplying\ we\ get:\\\\90x=7200\\\\Dividing\ both\ sides\ by\ 90\ we\ get:\\\\x=80.[/tex]
Thus, the number of students expected to choose rock is 80.
Now,
In a survey of 90 students 40 choose hip hop.
So, 90 is equivalent to 40.
Thus, 360 is equivalent to [tex]y.[/tex]
[tex]\frac{90}{40} =\frac{360}{y} \\\\By\ cross\ multiplying\ we\ get:\\\\90y=14400\\\\Dividing\ both\ sides\ by\ 90\ we\ get:\\\\y=160.[/tex]
Therefore, 160 students expected to choose hip hop.
And,
In a survey of 90 students 30 choose country.
So, 90 is equivalent to 30.
Thus, 360 is equivalent to [tex]y.[/tex]
[tex]\frac{90}{30} =\frac{360}{z} \\\\By\ cross\ multiplying\ we\ get:\\\\90x=10800\\\\Dividing\ both\ sides\ by\ 90\ we\ get:\\\\x=120.[/tex]
Hence, 120 students expected to choose country.
Therefore, the students would be expected to choose rock be 80 or students choose hip hop be 160 or choose to country be 120.
A magnet is an example what type of force A:applied force B: non-contact force
Answer:
B)non contact force
Step-by-step explanation:
Answer:
Non contract force
Step-by-step explanation:
Im sure its correct Good luck!
Use the Divergence Theorem to evaluate the following integral S F · N dS and find the outward flux of F through the surface of the solid bounded by the graphs of the equations. Use a computer algebra system to verify your results. F(x, y, z) = 2(x???? + y???? + z????) S: z = 0, z = 4 − x2 − y2
Answer:
Result;
[tex]\int\limits\int\limits_S { \textbf{F}} \, \cdot \textbf{N} d {S} = 32\pi[/tex]
Step-by-step explanation:
Where:
F(x, y, z) = 2(x·i +y·j +z·k) and
S: z = 0, z = 4 -x² - y²
For the solid region between the paraboloid
z = 4 - x² - y²
div F
For S: z = 0, z = 4 -x² - y²
We have the equation of a parabola
To verify the result for F(x, y, z) = 2(x·i +y·j +z·k)
We have for the surface S₁ the outward normal is N₁ = -k and the outward normal for surface S₂ is N₂ given by
[tex]N_2 = \frac{2x \textbf{i} +2y \textbf{j} + \textbf{k}}{\sqrt{4x^2+4y^2+1} }[/tex]
Solving we have;
[tex]\int\limits\int\limits_S { \textbf{F}} \, \cdot \textbf{N} d {S} = \int\limits\int\limits_{S1} { \textbf{F}} \, \cdot \textbf{N}_1 d {S} + \int\limits\int\limits_{S2} { \textbf{F}} \, \cdot \textbf{N}_2 d {S}[/tex]
Plugging the values for N₁ and N₂, we have
[tex]= \int\limits\int\limits_{S1} { \textbf{F}} \, \cdot \textbf{(-k)}d {S} + \int\limits\int\limits_{S2} { \textbf{F}} \, \cdot \frac{2x \textbf{i} +2y \textbf{j} + \textbf{k}}{\sqrt{4x^2+4y^2+1} } d {S}[/tex]
Where:
F(x, y, z) = 2(xi +yj +zk) we have
[tex]= -\int\limits\int\limits_{S1} 2z \ dA + \int\limits\int\limits_{S2} 4x^2+4y^2+2z \ dA[/tex]
[tex]= -\int\limits^2_{-2} \int\limits^{\sqrt{4-y^2}} _{-\sqrt{4-y^2}} 2z \ dA + \int\limits^2_{-2} \int\limits^{\sqrt{4-y^2}} _{-\sqrt{4-y^2}} 4x^2+4y^2+2z \ dA[/tex]
[tex]= \int\limits^2_{-2} \int\limits^{\sqrt{4-y^2}} _{-\sqrt{4-y^2}} 4x^2+4y^2 \ dxdy[/tex]
[tex]= \int\limits^2_{-2} \frac{(16y^2 +32)\sqrt{-(y^2-4)} }{3} dy[/tex]
= 32π.
What does automation mean in this sentence The automation telephone answering surveyed frustrated many people
Answer:
Automation means something that does not require human input, automatic.
Answer:
answer is the use of machines that function on their own.
Step-by-step explanation:
The table below shows the amount that must be repaid, y, when x dollars are borrowed. Amount Borrowed Amount Repaid $100 $135 $200 $260 $500 $635 $800 $1,010 Which equation represents the relationship? y = StartFraction 5 Over 4 EndFraction x y = StartFraction 4 Over 5 EndFraction x y = StartFraction 5 Over 4 EndFraction x + 10 y = StartFraction 4 Over 5 EndFraction x + 55
Answer:
a
Step-by-step explanation:
Answer:
A.y=5/4x
Step-by-step explanation:
The following graph is not linear, exponential, or quadratic. Explain why.
Answer:
It is not linear because it isn't a straight line.It isn't exponential because it doesn't have a constant rate of change. It isn't a quadratic equation because it can't be made into a simple form.
Hope this helps:)
How many times can you expect to roll a 4 if you rolls a fair number cube 120 times? (A fair number cube has 6 sides numbered 1 through 6. If a 4 appears 1 time out of 6 then how many times would it appear out of a 120?)
Answer:
20times
Step-by-step explanation:
A fair of die has 6sides.
If 4 appears 'once' out of a 6.
Then, 4 will appear 2times out of 12 i.e
6faces = 1time
12faces = 2times.
But remember that we want to know how many times 4 will appear out of a 120
120faces = x times
Since 6faces = 1time (i.e 4 occur one time in six faces)
cross multiplying:
6 × x = 120
x = 120/6
x = 20times
This means 4 will appear 20times out of a 120
Juan has already run 6 miles this month. He plans to run an additional 2.5 miles per day. At this rate, how long will take Juan to run 41 miles?
Answer:
x=14
Step-by-step explanation:
Hope that helped
Answer: 14 days
Step-by-step explanation:
2.5x + 6 = 41
-6. -6
2.5x = 41
——————
2.5
x = 14
Schadek Silkscreen Printing Inc. purchases plastic cups on which to print logos for sporting events, proms, birthdays, and other special occasions. Zack Schadek, the owner, received a large shipment this morning. To ensure the quality of the shipment, he selected a random sample of 300 cups. He found 15 to be defective.
a. What is the estimated proportion defective in the population?
b. Develop a 95 percent confidenceinterval for the proportion defective.c. Zack has an agreement withhis supplier that he is to return lots that are 10 percent or moredefective. Should he return this lot? Explain your decision.
Given Information:
Number of defective cups = 15
Total number of cups = 300
Required Information:
a) defective proportion = p = ?
b) 95% confidence interval of defective proportion = ?
Answer:
a) defective proportion = p = 0.05 = 5%
b) 95% confidence interval of defective proportion = (2.5%, 7.5%)
Step-by-step explanation:
The estimated defective proportion is given by
p = Number of defective cups/Total number of cups
p = 15/300
p = 0.05
p = 5%
The confidence interval of defective proportion is given by
[tex]CI = p \pm z\sqrt{\frac{p(1-p)}{n} }[/tex]
Where p is the defective proportion, z is the z-score corresponding to 95% confidence level and n is the total number of cups.
The z-score corresponding to 95% confidence level is 1.96
[tex]CI = 0.05 \pm 1.96\sqrt{\frac{0.05(1-0.05)}{300} }[/tex]
[tex]CI = 0.05 \pm 1.96(0.01258)[/tex]
[tex]CI = 0.05 \pm 0.025[/tex]
[tex]Upper = 0.05 + 0.025 = 0.075[/tex]
[tex]Lower = 0.05 - 0.025 = 0.025[/tex]
[tex]CI = (0.025, 0.075)[/tex]
CI = (2.5%, 7.5%)
So that means we are 95% confident that the defective proportion is between 2.5% to 7.5%.
Zack should not return this lot since the defective percentage is below 10%
Final answer:
Zack Schadek calculated the proportion of defective cups to be 5%, and then he developed a 95% confidence interval which did not surpass the 10% defectivity threshold set by his agreement with the supplier. Therefore, he should not return the lot based on this sample's data.
Explanation:
To answer the question of whether Zack Schadek should return the shipment of cups, we first need to calculate the estimated proportion defective in the population. We do this by dividing the number of defective cups by the total number of cups in the sample. In this case, it is 15 defective cups out of 300, which equals 0.05 or 5%.
Next, we will develop a 95 percent confidence interval for the proportion defective. To construct this confidence interval, the binomial distribution can be approximated by a normal distribution since np and n(1-p) are both greater than 5. Plugging in the values, we obtain the confidence interval.
Finally, considering Zack's agreement with his supplier to return lots that are 10% or more defective, the calculated proportion defective is well below 10%. Additionally, since the confidence interval does not include 10% or higher values, Zack should not return the lot based on the data from his sample.
Toby invested £4500 for 2 years in a saving accounts . he was paid 4% per annum compound interest .
How much did Toby have in his saving account after 2 years ?
Final answer:
Toby will have £4867.20 in his savings account.
Explanation:
To determine how much Toby will have in his savings account after 2 years with a 4% per annum compound interest rate, we can use the formula for compound interest:
A = P(1 + r)ⁿ
Where:
A is the amount of money accumulated after n years, including interest.P is the principal amount (the initial amount of money).r is the annual interest rate (decimal).n is the number of years the money is invested.Given:
Toby's initial investment (P) is £4500.The annual interest rate (r) is 4%, or 0.04 when expressed as a decimal.The money is invested for n = 2 years.Using these values in the formula:
A = £4500(1 + 0.04)²
A = £4500(1.04)²
A = £4500(1.0816)
A = £4867.20
Therefore, Toby will have £4867.20 in his savings account after 2 years.
What is the side length of a cube with a volume of 64 mm??
Cube V= 53
Answer:
side length= 4 mm
Step-by-step explanation:
The explanation is pretty easy;
You know that to get the volume of a cube the formula is length times width times height. You also know that all sides of a cube are equal. so what multiplied by itself 3 times = 64?
That would be 4; 4 times 4 = 16 then 16 times 4 = 64
Sorry if the explanation wasn't great:(
Suppose Alani could modify option A and still pay off the bike in 5 weeks. Describe the relationship between the down payment and the weekly payments.
Answer:
y = 5x + 180
Step-by-step explanation:
The question is incomplete. The complete question is stated below:
Alani wants to buy a $360 bicycle. She is considering two payment
options. The image shows Option A, which consists of making an initial down payment then smaller, equal-sized weekly payments. Option B consists of making 6 equal payments over 6 weeks.
A) What factors should Alani take into consideration before deciding
between Option A and Option B?
B) Suppose Alani could modify Option A and still pay off the bike in 5 weeks. Describe the relationship between the down payment and the weekly payments.
The image would be sent as an attachment.
SOLUTION:
We would only be providing answer to question B as it corresponds to the question being asked in brainly.com.
To solve this question, we would apply slope intercept form to get a linear equation:
y = mx + c
m = slope, c= constant
Option A initially involves making an initial down payment together with smaller, equal-sized weekly payments.
Modification of Option A: weekly payment would be done in 5weeks while down payment amount would be assumed to be half of total payment. Also it is assumed there is 0% interest rate.
As it is constant, Let the initial down payment = c
c = 1/2 * total payment
c = 1/2 * $360 = $180
m = 5weeks
y = total amount to be paid for the bike
y = $360
x = amount to be paid weekly after the down payment.
Relationship between down payment and weekly payment:
y = mx + c
mx = y-c
x = (y - c)/ m
y = 5x + c
y = 5x + 180
The relationship between a down payment and weekly payments during any sort of payment plan, including for a bike purchase, is an inverse one. If a down payment is introduced, it can either lower the amount of each weekly payment (with same total payment duration), or reduce the duration of the payments (with same weekly payment rate).
Explanation:The question posed pertains to the relationship between a down payment and weekly payments when purchasing an item, in this instance, a bike. This is a concept of financial mathematics. Though the information provided in the references talking about burger and bus ticket purchases, it doesn't directly pertain to the student's question. So, let's illustrate with a different example.
Let's consider that the total price of the bike is $500. If Alani's weekly payments total up to $100, considering no down payment, she can indeed pay off the bike in 5 weeks. However, if a down payment is introduced, the total amount remains the same ($500) but it's divided differently. If Alani puts down $200 initially as a down payment, she still has $300 to pay off. Therefore, if she continues with her original plan of $100 weekly payment, she would be able to pay off the remaining amount in 3 weeks, not 5. However, if she still wishes to extend her payments to 5 weeks, she would need to pay less weekly. With the remaining $300 divided over 5 weeks, her weekly payments would reduce to $60.
The key take-away is that the introduction of a down payment reduces the amount payoff balance, and thus can reduce weekly payments if the payoff time remains constant. Alternatively, it can reduce the payoff period with unchanged weekly payments. This illustrates the inverse relationship between a down payment and the subsequent weekly payments.
Learn more about Financial Mathematics here:https://brainly.com/question/31955701
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Alma and Blanca are playing a game where they roll a pair of fair six-sided dice and try to predict the outcomes. Blanca thinks that the probability of rolling a one and a five is greater than the probability of rolling a one or a five. Alma disagrees. She thinks that the probability of rolling a one or a five is greater.Who is correct, Alma or Blanca?
Answer:
Alma is correct because the probability of getting a five or a one is 1/9 compared to Blanca's which is 1/36
Step-by-step explanation:
Please refer to the attached image for explanations
Answer:
-Blanca is correct.
Step-by-step explanation:
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