a) The 90% confidence interval of the percentage of all mangoes on the truck that fail to meet the standards is: (7.55%, 12.45%).
b) The margin of error is: 2.45%.
c) The 90% confidence is the level of confidence that the true population percentage is in the interval.
d) The needed sample size is: 271.
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The margin of error is given by:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The variables are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The confidence level is of 90%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.90}{2} = 0.95[/tex], so the critical value is z = 1.645.
The sample size and the estimate are given as follows:
[tex]n = 150, \pi = \frac{15}{150} = 0.1[/tex]
The margin of error is of:
[tex]M = z\sqrt{\frac{0.1(0.9)}{150}} = 0.0245 = 2.45\%[/tex]
The interval is given by the estimate plus/minus the margin of error, hence:
The lower bound is: 10 - 2.45 = 7.55%.The upper bound is: 10 + 2.45 = 12.45%.For a margin of error of 3% = 0.03, the needed sample size is obtained as follows:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 1.645\sqrt{\frac{0.1(0.9)}{n}}[/tex]
[tex]0.03\sqrt{n} = 1.645\sqrt{0.1(0.9)}[/tex]
[tex]\sqrt{n} = \frac{1.645\sqrt{0.1(0.9)}}{0.03}[/tex]
[tex](\sqrt{n}})^2 = \left(\frac{1.645\sqrt{0.1(0.9)}}{0.03}\right)^2[/tex]
n = 271 (rounded up).
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On average, Jaya drinks of a 6-ounce glass of water in 13 hours. How many glasses of water does she drink in one hour?
On average, Jaya drinks 0.46 ounces glasses of water does she drink in one hour.
Average:
Average refers the mean value which is equal to the ratio of the sum of the number of a given set of values to the total number of values present in the set.
Given,
On average, Jaya drinks of a 6-ounce glass of water in 13 hours.
Here we need to find the number of glasses of water does she drink in one hour.
Let x be the number of glasses of water does she drink in one hour.
We know that, Jaya drinks of a 6-ounce glass of water in 13 hours.
So, in order to find the average we have to divide the number of glasses by the time taken.
So, it can be written as,
=> 6/13
=> 0.46
Therefore, for one hour Jaya drinks 0.46 ounces of water.
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Type the area of the rectangle into the box.
Answer:
30
Step-by-step explanation:
Answer:
30
Step-by-step explanation:
A = 15 x 2 = 30
Ellie bought cookies and cupcakes for $102.44. If she spent $36.44 on cookies
and the cupcakes are $11 per box, how many boxes did she buy?
Answer:
Step-by-step explanation: First since the cookies are 36.44 dollars and the total spent is 102.44, use 102.44-36.44= 66 dollars
66/11=6 cupcake boxes
6 cupcake boxes + 1 cookie box = 7 boxes in total
Which graph represents a system of equations that has no solution?
Answer:
It is A
Step-by-step explanation:
I have brainly tutor and had that exact question
d) Three bus services A, B and C arrive at a station. Service A arrives at the station every 15 minutes, service B arrives every 20 minutes and service C arrives every 30 minutes. All three buses arrive at the station together at 9 a.m. At what time will the three buses next arrive at the station. (Decide which will you use to find the answer: GCF or LCM)
The time that the three buses will next arrive at the station, given the time between their individual arrivals is 10 am.
How to find the time of arrival?Service A arrives every 15 minutes. Service B arrives every 20 minutes. Service C arrives every 30 minutes.
The goal is to find the time when all services arrive at the same time. This can be found by finding the LCM of all three times. This will show the shortest time till all services arrive.
The LCM of 15 minutes, 20 minutes, and 30 minutes is 60 minutes.
The three bus services will arrive at the same time in 60 minutes which is:
= 9 am + 60 minutes
= 10 am
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Enrique has a pay-per-use plan on his cell phone. It costs $0.10 per minute talk, $0.20 per text message, and $0.25 per picture message. His total bill last month was $30.95. The total number of text and picture messages sent was 87. The cost for the use of minutes was $1.60 less than the cost of the text messages. Find the number of talk minutes, text messages, and picture messages he used.
The number of minute talk's, text message's and picture message's are 128, 72 and 15 respectively.
What is Equation Modelling?Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
We have Enrique who has a pay-per-use plan on his cell phone. It costs $0.10 per minute talk, $0.20 per text message, and $0.25 per picture message. His total bill last month was $30.95. The total number of text and picture messages sent was 87. The cost for the use of minutes was $1.60 less than the cost of the text messages
Assume that [x], [y] and [z] represents the number of minute talk's, text message's and picture message's respectively. Then -
0.1x + 0.2y + 0.25z = 30.95 ..[1]
y + z = 87 ..[2]
0.1x = 0.2y - 1.6 ...[3]
We can write Eq[1] as -
0.2y - 1.6 + 0.2y + 0.25z = 30.95
z = 87 - y
0.2y - 1.6 + 0.2y + 0.25(87 - y) = 30.95
Solving, we get y = 72.
So z = 87 - 72 = 15
and
0.1x = 0.2 x 72 - 1.6
0.1x = 14.4 - 1.6
x = 128
Therefore, the number of minute talk's, text message's and picture message's are 128, 72 and 15 respectively.
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In a study of helicopter usage and patient survival, among the 49,401 patients transported by helicopter, 244 of them left the treatment center against medical advice, and the other
49,157 did not leave against medical advice. If 40 of the subjects transported by helicopter are randomly selected without replacement, what is the probability that none of them left
the treatment center against medical advice?
The probability is
(Round to three decimal places as needed)
Answer:
40%
Step-by-step explanation:
Which graph represents an odd function?
There are 6 points on a coordinate plane. The points are (negative 5, 3), (negative 3, 1), (negative 1, 1), (1, 3), (3, negative 5), (5, negative 1).
There are 8 points on a coordinate plane. The points are (negative 4, 2), (negative 3, negative 1), (negative 1, negative 3), (0, 1), (1, 0), (2, negative 4), (4, 5), (5, 4).
There are 8 points on a coordinate plane. The points are (negative 4, 0), (negative 3, 1), (negative 2, negative 3), (negative 1, negative 2), (1, 2), (2, 3), (3, negative 1), (4, 0)
There are 11 points on a coordinate plane. The points are (negative 4, 3), (negative 4, 4), (negative 3, 5), (negative 2, 1), (negative 1, negative 1), (0, negative 3), (1, negative 1), (2, 1), (3, 5), (4, 3), (4, 4).
Answer: first graph
Step-by-step explanation:
What is the equation of the line that passes through the point (4, 6) and has a slope
of o?
Rewrite −12(4x + 5y) using distribution.
−48x + 60y
−48x + 5y
−48x − 60y
−4x − 17y
To distribute this, multiply each term in the parentheses by -12
-12(4x) + -12(5y)
-48x - 60y
Hope this helps :)
Comment if you need any more explanation
Answer:
-48x - 60y
Step-by-step explanation:
Distributive Property of multiplication over addition:
[tex]\boxed{a(b + c) = ab + ac}[/tex]
Apply the distributive property to the given expression:
[tex]\begin{aligned}-12(4x + 5y) & = -12 \cdot 4x + (-12) \cdot 5y\\& = -48x +(- 60y)\\&=-48x-60y\end{aligned}[/tex]
Therefore, the given expression rewritten using distribution is:
-48x - 60y
A company's identification card consists of 4 letters followed by 2 digits. How many cards can be
made if repetition of digits are allowed, but letters must only be consonants and have NO
repetition. Note: y is not a vowel.
The possible cards can be made 6719448100.
What is permutation & combination?
Subsets of a set can be created in two separate ways combination and permutation. The subset's components can be listed in any order when combined. The components of the subset are listed in a permutation in a certain order.
We have,
Letters must only be consonants = 26 - 5.
So, the total number of consonants are 21.
There are 21 choices for the first letter, 21 choices for the second letter, 21 choices for the thirds letter, 21 choices for the fourth letter. For each of these letters, therefore 21 × 21 × 21 × 21 = 194481 possible pairs of letters.
There are 10 possibilities for the first digit & 10 possibilities for the second. therefore there are 10 x 10 = 100 different numbers.
Combining these results, it follows that there are 67194481 x 100 = 6719448100 different cards.
Hence, The possible cards can be made 6719448100.
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A candidate for mayor is calling 882 registered voters to remind them about the upcoming election if the candidate has 49 volunteers and each person calls the same numbers of voters how many voters will volunteer call
The number of voters that each volunteer call is 18.
What is voting?It is important to note that voting is done to choose a particular person during elections.
In this case, the candidate for mayor is calling 882 registered voters to remind them about the upcoming election and the candidate has 49 volunteers.
Since they gave same number of voters, this will be:
= Number of voters / Number of volunteers
= 882 / 49
= 18
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The monthly cost of operation at a company, C, given in dollars as a function of the number of units produced per month, u, is given below.
C = $3,173 + $31u
If the company wants to keep the cost of operation under $14,000 per month, what is the maximum number of units they can produce?
A. 3,490
B. 350
C. 3,491
D. 349
If the company wants to keep the cost of operation under $14,000 per month, The maximum number of units they can produce is: D. 349.
How to find the number of units?Given function:
C = $3,173 + $31u
Hence,
Let u represent number of units
Let c represent the operation cost
Where c = $14,000 per month
$14,000 = $3,173 + $31u
Combine like terms
$14,000 - $3,173 = $31u
$10,827 = $31u
Divide both side by $31u
u = $10,827 / 31
u = 349 units
Therefore the correct option is D.
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A solution contains 7% salt. How much water should be added to 30 ounces of this solution to make a 5% solution?
12 ounces of water.
Step-by-step explanation:1. Set the initial values.Total mass of the solution: 30 ounces.
Total mass of salt (solute): (30*0.07)= 2.1 ounces.
Total mass of water (solvent): (30*0.93) 27.9 ounces.
2. Find an equation that relates amount of water and percentage of salt.
Since we know that the amount of salt is 2.1 ounces, and it has to remain constant, we have to create a function such that the variable is the amount of water and it gives us the percentage of solution we are looking for. The function should look like this:
[tex]\frac{2.1}{x} =0.05[/tex]; where x is the mass of the water in the solution.
Side note: The number "0.05" is 5% converted into a decimal.
3. Solve the equation for x.[tex]\frac{2.1}{x} =0.05\\ \\\frac{x}{2.1} =\frac{1}{0.05} \\ \\x=\frac{2.1}{0.05} \\ \\x=42[/tex]
42 would be the total amount of ounces the solution should have in order to be a 5% solution. Therefore, 12 ounces (42-30) have to be added.
4. Conclude.12 ounces of water have to be added to this solution in order to make it a 5% solution, where 2.1 ounces is salt and 39.9 is water.
A tank contains 60 kg of salt and 2000 L of water. Water containing 0.8kgL of salt enters the tank at the rate 8 L/min. The solution is mixed and drains from the tank at the rate 2 L/min. A(t) is the amount of salt in the tank at time t measured in kilograms.
A(t)= ?kg
Transcribed image text: (1 point) A tank contains 60 kg of salt and 2000 L of water. Water containing 0.8 min of salt enters the tank at the rate 6 min. The solution is mixed and drains from the tank at the rate 3 IA(t) is the amount of salt in the tank at time t measured in kilograms. min (a) A(0) = (kg) = 0.
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Answer: yes
Step-by-step explanation:
The second and fifth terms of a geometric sequence are 750 and -6 respectively. Find the
common ratio and first term of the sequence.
Step-by-step explanation:
T2= -6
T5=750
ar=-6
ar4=750
both a's cancel each other
we have;
r=-6
r4=750
r4-1(The law of indices) =750
r3=750
r=3√750
r=9.1
PART B
How can the stage manager use the constant of proportionality to find the
dimensions of any new props the director requires?
a) the constant of proportionality multiplies every actual linear dimension
b) height of a can of fruit juice is 3.85 inches high
What is Proportionality?
The term proportionality describes any relationship that is always in the same ratio.
Explanation for answer:
Since the desire is to have students look twice as tall, we expect the constant of proportionality to be [tex]\frac{1}{2}[/tex].
Instead, we're told that the stage manager is using a height of 44 inches to represent an 80-inch door.
This means their constant of proportionality is [tex]\frac{40}{80} = 0.55[/tex]
a) Any new props can be scaled by this factor (0.55) to find their height on set.
b) A 7-inch can would be scaled to [tex]7\times 0.55 = 3.85\ inches[/tex]
Question: The school's theater club is building sets that will make ordinary students look like giants. The actors need a door, a table, and a stool that will make them look almost twice as tall!
DOOR: actual height is 80 inches and Height on Set is 44 inches
TABLE: actual height is 28 inches
STOOL: actual height is 18 inches
How can the stage manager use the constant of proportionality to find the dimensions of any new props the director requires?
What should the height of a can of fruit juice used as a prop be if its actual height is 7 inches? Show your work.
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The three angles of a triangle measure x,y and 39. What is the equation to solve ?
The equation to solve when the three angles of a triangle measure x,y and 39 is x + y + 39 = 180°.
What is an equation?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.
It is important to note that the total angles in a triangle is 180°.
Therefore, in this case, the angles will be illustrated thus:
x + y + 39 = 180. This illustrates the equation.
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In the fraction three-fifths, which statement best describes the denominator?
A. It tells the number of equal parts out of the total number of parts.
B. It tells how many are shaded.
C. It represents the number of equal parts into which the whole is divided.
D. The denominator means three out of five are shaded.
Answer:
D. The denominator means three out of five are shaded
If LM = 2x - 9 and KN = x + 15 in rhombus KLMN, find the value of x.
The value of x in the rhombus is 24 units.
According to the question,
We have the following information:
LM = 2x - 9 and KN = x + 15 in rhombus KLMN.
Now, we know that in a rhombus opposite sides are equal. In this case, LM and KN are opposite sides.
So, we have the following expression:
2x-9 = x+15
Adding 9 to both sides of the equation:
2x = x+15+9
2x = x+24
Subtracting x from both sides of the equation:
2x-x = 24
x = 24
Hence, the value of x for the given rhombus is 24 units.
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6x^2+12x+63=0 solve by factor
Answer:
x=2 and =-4
Step-by-step explanation:
Consider the function graphed at right.
The function has a maximum
of 3
The function is increasing on the interval(s):
The function is decreasing on the interval(s):
at x =
-4
4
-32
-5--
3 4 5
1 2 3 4 5
Answer:
heyyyyyyyyyyyyyyyyyyyyyyyy
The scatter plot shows the relationship between the number of coffee drinks sold and the total expenses of a coffee shop.
The slope of the line is....
The intercept of the line is.....
The regression equation is
For the linear function built from the scatter plot, it is found that:
The slope of the line is of: 5.The intercept of the line is of: b = 500.The equation is of: y = 5x + 500.What is a linear function?The slope-intercept representation of a linear function is the rule presented as follows:
y = mx + b
The coefficients of the function and their meaning are listed as follows:
m is the slope of the function, representing the change in the numeric value of the output variable y when the input variable x increases by one.b is the y-intercept of the function, which is the numeric value of the output variable y when the input variable x has a value of 0.From the graph, we have that when x = 0, y = 500, hence the intercept of the line is:
b = 500.
When the input increases by 200, the output increases by 1000, hence the slope is:
m = 1000/2 = 5.
Thus the equation is:
y = 5x + 500.
Missing InformationThe graph is given by the image at the end of the answer.
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If x = -4 and y = 3, what is the value of 1/2x + 3xy^2
If x = -4 and y = 3, then the value of 1/2x + 3xy² is -110.
What is a value function?
The value function represents the optimal payoff of the system over the interval [t, t1] when started at the time- t state variable x(t)=x.
What is a variable?
A quantity that could take on any of a number of different values. : a sign that denotes a variable. : anything has a range. : a variable that might alter in a scientific experiment.
Here, we have
x = -4 and y = 3
then by putting the value of a function in a given equation, we get
1/2*(-4) + 3*(-4)*(3)²
= -110
Hence, If x = -4 and y = 3, then the value of 1/2x + 3xy² is -110.
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Kaleigh paid $37.45 for a calculator, after-tax, and the tax rate is 7%. What was the original cost of the calculator?
Step-by-step explanation:
that means that
$37.45 = 107%
as the price was 100% base price + 7% tax.
1% = 107%/107
100% = 1% × 100 = 107% × 100 / 107
so, the basic price (the "original cost") is
37.45 × 100/107 = $35.00
The equation for line u can be written as y = -x + 1. Line v, which is perpendicular to line
u, includes the point (-3, 2). What is the equation of line v?
Write the equation in slope-intercept form. Write the numbers in the equation as simplified
proper fractions, improper fractions, or integers.
미미
Submit
Answer:
Line v: y = x + 5
Step-by-step explanation:
Given two lines are perpendicular and the equation of one line, we use the following formula to find the slope of the other line where m1 is the slope of the line we're given and m2 is the slope of the line we want to find:
[tex]m_{2}=-\frac{1}{m_{1} }\\m_{2}=1[/tex]
The general equation of a line is y = mx + b, where m is the slope and b is the y-intercept.
Therefore we plug in our slope and the point (-3, 2) to find the y-intercept of line v:
[tex]2=1(-3)+b\\2=-3+b\\5=b[/tex]
A certain vehicle can accelerate from a standing start to a speed of v(t) = −0.24t2 + 12t feet per second after t seconds (for 0 ≤ t < 30).
a.
Find a formula for the distance that it will travel from its starting point in the first t seconds. [Hint: Integrate velocity to find distance, and then use the fact that distance is 0 at time
t = 0.]
b.
Use the formula that you found in part (a) to find the distance (in ft) that the car will travel in the first 10 seconds. (Round your answer to the nearest whole number.)
The distance (in ft) that the car will travel in the first 10 seconds is 16.8 feet.
What is the relation between speed and distance?Speed describes how accelerated something or somebody is moving. If you know the distance traveled and the time it took, you can calculate the average speed of an object.
The speed formula is speed = distance/time.
We have been given certain vehicles that can accelerate from a standing start to a speed of v(t) = −0.24t² + 12t feet per second after t seconds (for 0 ≤ t < 30).
Then the distance that it will travel from its starting point in the first t seconds is;
[tex]\int\limits^{30}_b {v(t) } \, dx \\\\\\\int\limits^{30}_b {-0.24t^2 + 12t } \, dt \\\\\\\int\limits^{30}_b {-0.48t + 12} \, dt \\\\-0.48(30) + 12\\\\14.4 + 12 = 26.4[/tex]
At zero it will be 12 feet.
b. the distance (in ft) that the car will travel in the first 10 seconds.
-0.48(10) + 12 = 16.8 feet.
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100 POINTS!!!
2. Millicent's password for a website is a 5-digit number. The digits are the prime factors of 2,205 listed from least to greatest. What is Millicent's password?
33577
D 35577
B 33557
A 33357
Answer:
Step-by-step explanation:
I
Select the correct answer. Four figures. Figure 1 shows a right triangle A C B with a line D E parallel to base B C. Figures 2, 3, and 4 shows a triangle A B C with a line D E parallel to base B C. In which figure is ? A. figure 1 B. figure 2 C. figure 3 D. figure 4
Answer: going to take a wild guess and say figure 2 or figure 4 is correct but I'm going with figure 2
Step-by-step explanation:
Answer: Figure 4
Step-by-step explanation:
I got it right on Edmentum
The stem-and-leaf plot displays the distances that a heavy ball was thrown in feet.
2 0, 1, 4
3 1, 2, 6
4 1, 3, 7
5 1, 1
6 5
Key: 3|2 means 3.2
What is the mean, and what does it tell you in terms of the problem?
Using the stem-and-leaf plot, the mean of the data is 3.85.
It means the average feet that the heavy ball was thrown is 3.85 feet, which is the typical number.
How to calculate the Mean of a Data Set represented by Stem-and-Leaf Plot?To find the mean of a data set that is represented by a stem-and-leaf plot, first, list out all the data values that are represented on the stem-and-leaf plot, add all the values and divide by the number of values that was represented on the stem-and-leaf plot.
Given the stem-and-leaf plot above, using the key, the data points represented are:
2.0, 2.1, 2.4, 3.1, 3.2, 3.6, 4.1, 4.3, 4.7, 5.1, 5.1, 6.5
Mean = [2.0 + 2.1 + 2.4 + 3.1 + 3.2 + 3.6 + 4.1 + 4.3 + 4.7 + 5.1 + 5.1 + 6.5]/12
Mean = 46.2/12
Mean = 3.85 feet
The mean of 3.85 feet means that the average distance that the heavy ball was thrown in feet is 3.85.
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The Answer is:
3.85 ft.
* *
-