Answer:
Option 4 - 0.8508
Step-by-step explanation:
Given : A multiple choice test consists of 60 questions. Each question has 4 possible answers of which one is correct. If all answers are random guesses.
To find : Estimate the probability of getting at least 20% correct ?
Solution :
20% correct out of 60,
i.e. [tex]20\%\times 60=\frac{20}{100}\times 60=12[/tex]
Minimum of 12 correct out of 60 i.e. x=12
Each question has 4 possible answers of which one is correct.
i.e. probability of answering question correctly is [tex]p=\frac{1}{4}=0.25[/tex]
Total question n=60.
Using a binomial distribution,
[tex]P(X\geq 12)=1-P(X\leq 11)[/tex]
[tex]P(X\geq 12)=1-[P(X=0)+P(X=1)+P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)+P(X=5)+P(X=6)+P(X=7)+P(X=8)+P(X=9)+P(X=10)+P(X=11)][/tex]
[tex]P(X\geq 12)=1- [^{60}C_0(0.25)^0(1-0.25)+^{60-0}+^{60}C_1(0.25)^1(1-0.25)^{60-1}+^{60-1}+^{60}C_2(0.25)^2(1-0.25)^{60-2}+^{60}C_3(0.25)^3(1-0.25)^{60-3}+^{60}C_4(0.25)^4(1-0.25)^{60-4}+^{60}C_5(0.25)^5(1-0.25)^{60-5}+^{60}C_6(0.25)^6(1-0.25)^{60-6}+^{60}C_7(0.25)^7(1-0.25)^{60-7}+^{60}C_8(0.25)^8(1-0.25)^{60-8}+^{60}C_9(0.25)^9(1-0.25)^{60-9}+^{60}C_{10}(0.25)^{10}(1-0.25)^{60-10}+^{60}C_{11}(0.25)^{11}(1-0.25)^{60-11}][/tex]
[tex]P(X\geq 12)\approx 0.8508 [/tex]
Therefore, option 4 is correct.
Let point M be outside of △ABC. Point N is the reflected image of M about the midpoint of segment AB . Point K is the reflected image of N about the midpoint of segment BC , and point K is the reflected image of L about the midpoint of segment AC . Prove that point A is the midpoint of segment ML .
Explanation:
Define points D, E, F as the midpoints of AB, BC, and AC, respectively. Point D is the midpoint of both AB and MN, so AMBN is a parallelogram, and side AM is parallel to and congruent with side NB.
Point E is the midpoint of both BC and NK, so BNCK is a parallelogram with side NB parallel and congruent to side CK, and by the transitive property of congruence, also to segment AM.
Point F is the midpoint of both AC and KL, so AKCL is a parallelogram with side CK parallel and congruent to side LA. By the transitive properties of congruence and of parallelism, sides AM, NB, CK, and LA are all congruent and parallel. Since AM and LA are congruent to one another and parallel, and share point A, point A must be their midpoint.
Jacob distributed a survey to his fellow students asking them how many hours they'd spent playing sports in the past day. He also asked them to rate their mood on a scale from 000 to 101010, with 101010 being the happiest. A line was fit to the data to model the relationship.
Jacob's survey is a study in statistics, specifically looking at the correlation between the amount of time spent on sports and student's mood ratings. A line is fit to the data to determine the relationship, with the direction of the line offering insights into how these two variables correlate, but this does not imply causation.
Explanation:From your question, Jacob performed a survey asking about the number of hours students spent playing sports in the past day and asked them to rate their mood. It's a study of basic statistics, specifically focusing on correlation between two variables, here those are the number of hours spent on sports and mood ratings. To determine a relationship between these variables, a line is often fit to the data, using methods like linear regression.
For example, if the line on the graph is rising, it indicates a positive correlation between the amount of sports played and a student's mood, meaning that as sports playtime goes up, so does mood ratings. A falling line means there's a negative correlation. If there's no clear direction, it's likely that there's no significant correlation between the two variables. But remember that correlation doesn't mean causation: just because two things correlate doesn't mean that one causes the other.
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I REALLY NEED HELP!! FAST!! PLZ DONT GUESS! THANKS!
A neighborhood is trying to set up school carpools, but they need to determine the number of students who need to travel to the elementary school (ages 5–10), the middle school (ages 11–13), and the high school (ages 14–18). A histogram summarizes their findings:
Histogram titled Carpool, with Number of Children on the y axis and Age Groups on the x axis. Bar 1 is 5 to 10 years old and has a value of 3. Bar 2 is 11 to 13 years old and has a value of 7. Bar 3 is 14 to 18 years old and has a value of 4.
Which of the following data sets is represented in the histogram?
A. {3, 3, 3, 7, 7, 7, 7, 7, 7, 7, 4, 4, 4, 4}
B. {5, 10, 4, 11, 12, 13, 12, 13, 12, 11, 14, 14, 19, 18}
C. {5, 6, 5, 11, 12, 13, 12, 13, 14, 15, 11, 18, 17, 13}
D. {3, 5, 10, 11, 13, 7, 18, 14, 4}
Answer:
c
Step-by-step explanation:
An automobile travels past the farmhouse at a speed of v = 45 km/h. How fast is the distance between the automobile and the farmhouse increasing when the automobile is 3.7 km past the intersection of the highway and the road?
Answer:
[tex]\frac{ds}{dt} = 39.586 km/h[/tex]
Step-by-step explanation:
let distance between farmhouse and road is 2 km
From diagram given
p is the distance between road and past the intersection of highway
By using Pythagoras theorem
[tex]s^2 = 2^2 +p^2[/tex]
differentiate wrt t
we get
[tex]\frac{d}{dt} s^2 = \frac{d}{dt} (4 + p^2)[/tex]
[tex]2s \frac{ds}{dt} =2p \frac{dp}{dt} [/tex]
[tex]\frac{ds}{dt} = \frac{p}{s}\frac{dp}{dt}[/tex]
[tex]\frac{ds}{dt} = \frac{p}{\sqrt{p^2 +4}} \frac{dp}{dt}[/tex]
putting p = 3.7 km
[tex]\frac{ds}{dt} = \frac{3.7}{\sqrt{3.7^2 +4}} 45[/tex]
[tex]\frac{ds}{dt} = 39.586 km/h[/tex]
The distance between the automobile and the farmhouse is increasing at the automobile's constant speed of 45 km/h, which is the same as the car's rate of change of distance as it moves away from the farmhouse.
Explanation:The question asks us to determine how fast the distance is increasing between an automobile and a farmhouse when the car is 3.7 km past a certain intersection, given the car's speed is 45 km/h. This is a problem that can be solved using the concepts of rates of change and kinematics.
Given that the car is moving in a straight line away from the farmhouse and there are no other factors altering the speed, the rate at which the distance between the car and farmhouse is increasing is constant and is equal to the speed of the car.
Since the car's speed is constant at 45 km/h, and it moves directly away from the farmhouse without any acceleration or deceleration, the rate at which the distance increases is exactly the car's speed. Therefore, when the car is 3.7 km past the intersection, the distance between the car and the farmhouse is still increasing at 45 km/h.
This straightforward problem shows that when an object moves away from a point at constant speed, the rate at which the distance between the object and the point increases is simply the speed of the object. This concept is very useful in solving more than 100 questions involving rates of change in kinematics, which is a part of classical mechanics.
A recipe for a pan of brownies requires 1 ½ cups of milk, 2/3 cups of sugar, and 1 1/5 cups of oil. How many cups of ingredients will there be in the mixing Bowl
Answer:
Step-by-step explanation:
A recipe for a pan of brownies requires 1 ½ cups of milk. Converting the 1 1/2 to improper fraction, it becomes 3/2 cups of milk
The recipe also requires 2/3 cups of sugar
It also requires 1 1/5 cups of oil. Converting to improper fraction, it becomes 6/5 cups of sugar
Total number of cups of ingredients in the mixing Bowl will be sum of the amount if milk, sugar and oil. It becomes
3/2 + 2/3 + 6/5 = (45 + 20 + 36)/30
= 101/30 cups of ingredients
− 2 3 + 20 24 −1.75=minus, start fraction, 3, divided by, 2, end fraction, plus, start fraction, 24, divided by, 20, end fraction, minus, 1, point, 75, equals
The simplified expression is -19/12.
First, the least common multiple (LCM) of the denominators, which in this case is 24.
Now, convert the fractions to have a denominator of 24:
-2/3 = -16/24
20/24 remains the same
-1.75 can be written as -42/24
Now we can add and subtract the fractions:
-16/24 + 20/24 - 42/24 = -38/24
Finally, we can simplify the fraction:
-38/24 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 2.
-38/24 ÷ 2/2 = -19/12
Therefore, the simplified expression is -19/12.
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A wise old troll wants to make a small hut. Roofing material costs five dollars per square foot and wall materials cost three dollars per square foot. According to ancient troll customs the floor must be square, but the height is not restricted.
(a) Express the cost of the hut in terms of its height h and the length x of the side of the square floor. ($)
(b) If the troll has only 960 dollars to spend, what is the biggest volume hut he can build? (ft^3)
Answer:
a) Cost (h,x) = 12*x*h + 5*x²
b)
V = V(max) = 355.5 ft³
Dimensions of the hut:
x = 9.48 ft (side of the base square)
h = 3.95 ft ( height of the hut)
Step-by-step explanation:
Let x be the side of the square of the base
h the height of the hut
Then the cost of the hut as a function of "x" and "h" is
Cost of the hut = cost of 4 sides + cost of roof
cost of side = 3* x*h then for four sides cost is 12*x*h
cost of the roof = 5 * x²
Cost(h,x) = 12*x*h + 5*x²
If the troll has only 900 $
900 = 12xh + 5x² ⇒ 900 - 5x² = 12xh ⇒(900-5x²)/12x = h
And the volume of the hut is V = x²*h then
V (h) = x² * [(900-5*x²)]/12x
V(h) = x (900-5x²) /12 ⇒ V(h) = (900*x - 5*x³) /12
Taking derivatives (both sides of the equation):
V´(h) = (900 - 10* x²)/12 V´(h) = 0
900 - 10*x² = 0 ⇒ x² = 90 x =√90
x = 9.48 ft
And h
h = (900-5x²)/12x ⇒ h = [900 - 90(5)]/12*x ⇒ h = 450/113,76
h = 3.95 ft
And finally the volume of the hut is:
V(max) = x²*h ⇒ V(max) = 90*3.95
V(max) = 355.5 ft³
A hut will consist of four walls and one roof. The figures needed evaluates to:
The cost of the hut expressed in terms of its height h and the length x of the side of the square floor is [tex]12hx + 5x^2 \text{\:(in dollars) }[/tex]The biggest volume hut that can be build with 960 dollars at max is 426.67 sq. ft approxHow to find the volume of cuboid?Let the three dimensions(height, length, width) be x, y,z units respectively.
Then the volume of the cuboid is given as
[tex]V = x \times y \times z \: \rm unit^3[/tex]
How to obtain the maximum value of a function?To find the maximum of a continuous and twice differentiable function f(x), we can firstly differentiate it with respect to x and equating it to 0 will give us critical points.
Putting those values of x in the second rate of function, if results in negative output, then at that point, there is maxima. If the output is positive then its minima and if its 0, then we will have to find the third derivative (if it exists) and so on.
For this case, we're specified that:
Cost of roofing material = $5 / sq. footCost of wall material = $3 / sq. footThe side length of floor = side length of roof = [tex]x \: \rm ft[/tex]The height of the room = [tex]h \: \rm ft[/tex]Four walls are attached to sides of floor. Thus, their one edge's length = length of side of floor = [tex]x \: \rm ft[/tex]
Thus, we get:
Area of four walls = [tex]4 \times (h \times x)[/tex] sq. ftThus, cost of four walls' material = [tex]3 \times 4 \times h \times x = \$ 12hx[/tex]
Area of roof = [tex]side^2 = x^2 \: \rm ft^2[/tex]Thus, cost of roofing material for this roof = [tex]5 \times x^2 = \$5x^2[/tex]
Thus, cost of hut = cost for walls + cost for roof = [tex]12hx + 5x^2 = x(12h+5x) \: \rm (in \: dollars)[/tex]
The volume of the hut is: [tex]x\times x\times h =x^2.h \: \rm ft^3[/tex]
If troll has got only $960, then,
[tex]12hx + 5x^2 \leq 960\\\\\text{Multiplying x on both the sides}\\\\12x^2h + 5x^3 \leq 960x\\\\x^2h \leq \dfrac{960x-5x^3}{12}[/tex]
Let we take [tex]f(x) =\dfrac{960x-5x^3}{12}[/tex]
Then, taking its first and second derivative, we get:
[tex]f(x) =\dfrac{960x-5x^3}{12}\\\\f'(x) = 80 -1.25x^2\\\\f''(x) = -2.5x[/tex]
Putting first derivative = 0, we get critical points as:
[tex]80-1.25x^2 = 0\\\\x = 8 \text{\:(positive root as x denotes side length, thus a non-negative quantity)}[/tex]
At x = 8, the second derivative evaluates to:
[tex]f''(8) = -2.5(8) < 0[/tex]
Thus, we obtain maxima at x = 8.
Thus, we get the maximum value of function when x = 8.
Since we have:
[tex]V = x^2h \leq f(x)[/tex] (V is volume of the hut)
and [tex]max(f(x)) = f(8) = \dfrac{960(8) - 5(8)^3}{12} = 640-213.3\overline{3} \approx 426.67[/tex]
Thus, max(V) = 426.67 sq. ft approximately.
Thus, the figures needed evaluates to:
The cost of the hut expressed in terms of its height h and the length x of the side of the square floor is [tex]12hx + 5x^2 \text{\:(in dollars) }[/tex]The biggest volume hut that can be build with 960 dollars at max is 426.67 sq. ft approxLearn more about maxima and minima here:
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From a sample of 9,750 Ajax trucks, 273 developed transmission problems within the first two years of operation. What is the probability that an Ajax truck will develop transmission problems within the first two years?
Answer:
0.028
Step-by-step explanation:
Let sample space, S, be the trucks.
Hence, n(S)= number of trucks=9750
Let E be the event of the truck failing within the first two years of operation.
Hence, n(E)=273
Therefore by classical definition of probability, the probability of occurrence of the event E, denoted by P(E), is
P(E)=[tex]\frac{n(E)}{n(S)}[/tex]=[tex]\frac{number of trucks failed within two years of operation}{Total number of trucks}[/tex]
⇒P(E)=[tex]\frac{273}{9750}[/tex]=0.028
The probability that an Ajax truck will develop transmission problems within the first two years is 2.8%, calculated by dividing the number of trucks with transmission problems (273) by the total number of trucks (9,750).
To calculate the probability that an Ajax truck will develop transmission problems within the first two years, we can use the formula for simple probability:
P(event) = Number of favorable outcomes / Total number of possible outcomes
Given that 273 out of 9,750 Ajax trucks developed transmission problems, the probability P is calculated as:
P(transmission problems) = 273 / 9,750
P(transmission problems) = 0.028 or 2.8%
The probability is 0.028, which means there is a 2.8% chance that an Ajax truck will develop transmission problems within the first two years of operation.
In a recent Super Bowl, a TV network predicted that 50 % of the audience would express an interest in seeing one of its forthcoming television shows. The network ran commercials for these shows during the Super Bowl. The day after the Super Bowl, and Advertising Group sampled 106 people who saw the commercials and found that 48 of them said they would watch one of the television shows.Suppose you are have the following null and alternative hypotheses for a test you are running:H0:p=0.5Ha:p≠0.5Calculate the test statistic, rounded to 3 decimal placesz=
Answer:
z= -0.968
We can conclude that we fail to reject the null hypothesis, and we can said that at 5% of significance the proportion of people who says that they would watch one of the television shows not differs from 0.5 or 50% .
Step-by-step explanation:
1) Data given and notation n
n=106 represent the random sample taken
X=48 represent the people who says that they would watch one of the television shows.
[tex]\hat p=\frac{48}{106}=0.453[/tex] estimated proportion of people who says that they would watch one of the television shows.
[tex]p_o=0.5[/tex] is the value that we want to test
[tex]\alpha[/tex] represent the significance level
z would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value (variable of interest)
2) Concepts and formulas to use
We need to conduct a hypothesis in order to test the claim that 50% of people who says that they would watch one of the television shows.:
Null hypothesis:[tex]p=0.5[/tex]
Alternative hypothesis:[tex]p \neq 0.5[/tex]
When we conduct a proportion test we need to use the z statisitc, and the is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
The One-Sample Proportion Test is used to assess whether a population proportion [tex]\hat p[/tex] is significantly different from a hypothesized value [tex]p_o[/tex].
3) Calculate the statistic
Since we have all the info requires we can replace in formula (1) like this:
[tex]z=\frac{0.453 -0.5}{\sqrt{\frac{0.5(1-0.5)}{106}}}=-0.968[/tex]
4) Statistical decision
P value method or p value approach . "This method consists on determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.
The significance level is not provided, but we can assume [tex]\alpha=0.05[/tex]. The next step would be calculate the p value for this test.
Since is a bilateral test the p value would be:
[tex]p_v =2*P(z<-0.968)=0.333[/tex]
So based on the p value obtained and using the significance level assumed [tex]\alpha=0.05[/tex] we have [tex]p_v>\alpha[/tex] so we can conclude that we fail to reject the null hypothesis, and we can said that at 5% of significance the proportion of people who says that they would watch one of the television shows not differs from 0.5 or 50% .
If all men had identical body types, their weight would vary directly as the cube of their height. The tallest person reached a record height of 8 feet 11 inches (107 inches) before his death at age 22. If a man who is 5 feet 10 inches tall (70 inches) with the same body type as the tallest person weighs 170 pounds, what was the tallest person's weight shortly before his death?
Answer: The weight of tallest person would be 607.16 pounds.
Step-by-step explanation:
Since we have given that
height of the tallest person = 8 feet 11 inches = 107 inches
If all men had identical body types, their weight would vary directly as the cube of their height.
If a man who is 5 feet 10 inches tall (70 inches) with the same body type as the tallest person weighs 170 pounds,
So, it becomes,
[tex]W=xh^3[/tex]
[tex]170=x(70)^3\\\\\dfrac{170}{70^3}=x\\\\x=\dfrac{170}{343000}[/tex]
So, weight of tallest person would be
[tex]W=\dfrac{170}{343000}\times 107^3\\\\W=607.16\ pounds[/tex]
Hence, the weight of tallest person would be 607.16 pounds.
First, let's consider the information we're given and set up an equation. We know that, given identical body types, a person's weight would vary directly as the cube of their height. What this means is that the ratio between the weight of two people and the cube of their respective heights will be the same regardless of their individual heights or weights. We can represent this as:
W_tall / W_normal = (Height_tall ^ 3) / (Height_normal ^ 3)
Where:
W_tall is the weight of the tallest person.
W_normal is the weight of the normal person (which we know is 170 pounds).
Height_tall is the height of the tallest person (which we know is 107 inches).
Height_normal is the height of the standard person (which we know is 70 inches).
We are looking to find the weight of the tallest person, so, to isolate W_tall in the equation above, we will multiply both sides of the equation by W_normal:
W_tall = W_normal * (Height_tall ^ 3) / (Height_normal ^ 3)
Substituting the known values into the equation, we get:
W_tall = 170 * (107 ^ 3) / (70 ^ 3)
Computing the values on the right-hand side of the equation, we find that the tallest person weighed approximately 607.16 pounds just before his death.
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In a box of 15 tablets, 4 of the tablets are defective. Three tablets are selected at random. what is the probability that a store buys three tablets and receives: a) no defective tablets, b) one defective tablet, and c) at least one non-defective tablet.
Answer:
a) 0.394
b) 0.430
c) 0.981
Step-by-step explanation:
Use binomial probability:
P = nCr pʳ (1−p)ⁿ⁻ʳ
where n is the number of trials,
r is the number of successes,
and p is the probability of success.
Here, n = 3 and p = 4/15.
r is the number of defective tablets.
a) If r = 0:
P = ₃C₀ (4/15)⁰ (1−4/15)³⁻⁰
P = 1 (1) (11/15)³
P = 0.394
b) If r = 1:
P = ₃C₁ (4/15)¹ (1−4/15)³⁻¹
P = 3 (4/15) (11/15)²
P = 0.430
c) If r ≠ 3:
P = 1 − ₃C₃ (4/15)³ (1−4/15)³⁻³
P = 1 − 1 (4/15)³ (1)
P = 0.981
To find the probability of selecting no defective tablets, multiply the probabilities of selecting non-defective tablets.
Explanation:a) To find the probability of selecting no defective tablets, we need to find the probability of selecting 3 non-defective tablets. There are 11 non-defective tablets out of the total of 15 tablets. So, the probability is:
Multiplying these probabilities together:
(11/15) * (10/14) * (9/13) = 990/2730 ≈ 0.362 = 36.2%
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Mia recently bought a car worth $20,000 on loan with an interest rate of 6.6%. She made a down payment of $1,000 and has to repay the loan within two years (24 months). Calculate her total cost.
Answer:
$22,508
Step-by-step explanation:
Edmentum
The total cost that she pays for car will be $22,508.
What is simple interest?Simple interest is the concept that is used in many companies such as banking, finance, automobile, and so on.
A = P + (PRT)/100
Where P is the principal, R is the rate of interest, and T is the time.
Mia as of late purchased a vehicle worth $20,000 borrowed with a financing cost of 6.6%. She made an initial investment of $1,000 and needs to reimburse the credit in the span of two years (two years).
Then the total cost that she pays will be calculated as,
A = $20,000 + ($19,000 x 6.6 x 2) / 100
A = $20,000 + $2,508
A = $22,508
The total cost that she pays will be $22,508.
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University officials say that at least 70% of the voting student population supports a fee increase. If the 95% confidence interval estimating the proportion of students supporting the fee increase is [0.75, 0.85], what conclusion can be drawn?
A. 70% is not in the interval, so another sample is needed.
B.70% is not in the interval, so assume it will not be supported.
C.The interval estimate is above 70%, so infer that it will be supported.
D.Since this was not based on population, we cannot make a conclusion.
the correct answer is C. The interval estimate is above 70%, so infer that it will be supported.The 95% confidence interval (0.75, 0.85) indicates that we can expect around 75% to 85% of students to support the fee increase, which is more than the presumed 70%. So, we can infer that the fee increase will be supported.
Explanation:In the scenario given, the 95% confidence interval for the proportion of students supporting the fee increase is [0.75, 0.85].
This means that we are 95% confident that the true proportion of students who support the fee increase falls within this interval. Since the entire range is above 70%, we can be pretty confident that more than 70% of the student population supports the fee increase.
The confidence interval is a statistical method that gives us a range in which the true parameter likely falls based on our sample data. This shows us that statistical inference can give us insights about a population based on a sample.
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What is the value of x?
Answer:
Step-by-step explanation:
Set this up according to the Triangle Proportionality Theorem:
[tex]\frac{3x}{4x}=\frac{3x+7}{5x-8}[/tex]
Cross multiply to get
[tex]3x(5x-8)=4x(3x+7)[/tex]
and simplify to get
[tex]15x^2-24x=12x^2+28x[/tex]
Get everything on one side of the equals sign and solve for x:
[tex]3x^2-52x=0[/tex] and
[tex]x(3x-52)=0[/tex]
By the Zero Product Property,
x = 0 or 3x - 52 = 0 so x = 17 1/3
What is the volume of the cylinder?
Answer:
B. 2010.62 ft³
Step-by-step explanation:
The formula for the volume of a cylinder is ...
V = πr²h . . . . . where r is the radius and h is the height
Filling in the numbers and doing the arithmetic, we get ...
V = π(8 ft)²(10 ft) = 640π ft³ ≈ 2010.6193 ft³ ≈ 2010.62 ft³
The volume of the cylinder is about 2010.62 ft³.
In the game of Dubblefud, red chips, blue chips and green chips are each worth 2, 4 and 5 points respectively. In a certain selection of chips, the product of the point values of the chips is 16,000. If the number of blue chips in this selection equals the number of green chips, how many red chips are in the selection?A. 1
B. 2
C. 3
D. 4
E. 5
Final answer:
The problem is solved by finding the prime factorization of 16,000 and assigning the factors to the chips based on their point values, resulting in there being 3 red chips.
Explanation:
The student's question is a typical problem in combinatorics, a field of mathematics concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. This problem also involves prime factorization as a method to solve for the number of chips.
To solve the problem, let us denote by R, B, and G the number of red, blue, and green chips respectively. Since the blue chips and green chips have the same quantity, the problem can be solved by first finding the prime factorization of the point value product of 16,000, which is 2⁷ × 5³, and then distributing these prime factors to match the point values of the chips.
Since the point values of blue and green chips are 4 (2²) and 5 respectively and their quantities are equal, we match the prime factors of 5 first. There are 3 factors of 5, so we assign one to each blue and green chip, resulting in 1 remaining.
Then, we match 2² or 4 to each blue and green chip, using 4 out of 7 factors of 2, leaving us with 3 factors of 2, which can be matched with 3 red chips since they have a value of 2 each.
Therefore, we have 3 red chips which is answer option C.
A protected wilderness area in the shape of a rectangle is 3 kilometers long and 3.2 kilometers wide. The forest is to be surrounded by a hiking trail that will cost $11 comma 000 per mile to construct. What will it cost to install the trail? Note that 1 mile (mi)almost equals1.6 kilometers (km).
Answer: $66
Step-by-step explanation:
Area of a rectangular =length*breadth
= 3.2 km * 3.0 km = 9.6km(squared)
Note, 1.6km = 1 mile
Cost of a hiking trail = $11 per mile
Converting kilometer to kill = 9.6km/1.6km = 6 miles
Hence, cost of a hiking trail to surround the rectangular shaped wilderness = $11 * 6 = $66
In case the cost is $11,000 per mile; total cost of hiking trails to surround the wilderness equals $66,000
You can find the cost of the trail by first calculating the perimeter of the rectangular wilderness area in kilometers, converting this into miles, and then multiplying by the given cost per mile. The total cost to install the trail would be approximately $85,250.
Explanation:To calculate the cost of installing the hiking trail, we first need to find the perimeter of the rectangular forest, which will represent the length of the trail. In a rectangle, the perimeter is calculated as 2*(length + width).
Thus, the perimeter of the forest is 2*(3 km + 3.2 km) = 2*6.2 km = 12.4 km.
Next, we need to convert this into miles, as the cost is given in dollars per mile. We know that 1 mile is approximately equivalent to 1.6 km, so to convert km to miles, we can divide the distance in kilometers by 1.6.
The length in miles is therefore 12.4 km / 1.6 = 7.75 miles.
Finally, to find the total cost, we multiply the length of the trail in miles by the cost per mile: $11,000*7.75 miles = $85,250.
So, the cost to install the trail surrounding the wilderness area would be approximately $85,250.
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Barry and his wife, Mary, have accumulated over $3.5 million during their 50 years of marriage. They have three children and five grandchildren. How much money can they gift to their children in 2017 without any gift tax liability?
Answer:
$208,000
Step-by-step explanation:
For 50 years of marriage, Barry and Mary accumulated over $3.5million.
They have 3 children and 5 grandchildren which gives a total of 8.
You are allowed to give up $13,000 each year to a person without incurring tax liability.
This means Barry and Mary can give $13,000 to anyone each
For the 3 children and 5 grandchildren, Barry and Mary can gift $(13000 * 8) each
= $104,000 each
Therefore, Barry and Mary can gift $208,000 (104,000*2) to their children in 2017 without gift tax liability
An employment agency requires applicants average at least 70% on a battery of four job skills tests. If an applicant scored 70%, 77%, and 81% on the first three exams, what must he score on the fourth test to maintain a 70% or better average.
Answer:
atleast 52
Step-by-step explanation:
Given that an employment agency requires applicants average at least 70% on a battery of four job skills tests.
An applicant scored 70%, 77%, and 81% on the first three exams,
Since weightages are not given we can assume all exams have equal weights
Let x be the score on the 4th test
Then total of all 4 exams = [tex]70+77+81+x\\= 228+x[/tex]
Average should exceed 70%
i.e.[tex]\bar X \geq 70\\Total\geq 70(4) =280[/tex]
Comparing the two totals we have
[tex]228+x\geq 280\\x\geq 280-228 = 52[/tex]
Hemust score on the fourth test a score atleast 52 to maintain a 70% or better average.
Each person in a simple random sample of 1,800 received a survey, and 267 people returned their survey. How could nonresponse cause the results of the survey to be biased?
-Those who did not respond reduced the sample size, and small samples have more bias than large samples.
- Those who did not respond caused a violation of the assumption of independence.
-Those who did not respond are indistinguishable from those who did not receive the survey.
-Those who did not respond may differ in some important way from those who did respond.
-Those who did not respond represent a stratum, changing the random sample into a stratified random sample.
Nonresponse can cause bias in survey results due to differences in characteristics, the representation of strata, and the smaller sample size.
Explanation:Nonresponse can cause the results of a survey to be biased in several ways:
Those who did not respond may differ in some important way from those who did respond. This means that the characteristics of the nonresponders may be different from the characteristics of the responders, leading to biased results.Those who did not respond may represent a stratum, changing the random sample into a stratified random sample. This can introduce bias if the nonresponders differ from the rest of the population in a systematic way.Those who did not respond may reduce the sample size, and small samples have more bias than large samples. When the sample size is small, the results may not accurately reflect the population.Overall, nonresponse can introduce bias into a survey by excluding certain individuals or groups from the sample, leading to potentially inaccurate and biased results.
As students move to thinking about formulas it supports their conceptual knowledge of how the perimeter of rectangles can be put into general form. What formula below displays a common student error for finding the perimeter?
A) P = l + w + l + w
B) P = l + w
C) P = 2l + 2w
D) P = 2(l + w)
Answer:
B. [tex]P=l+w[/tex]
Step-by-step explanation:
Let l represent length of rectangle and w represent width of rectangle.
We have been given four formulas for the perimeter of rectangle. We are asked to choose the formula that displays a common student error for finding the perimeter.
We know that perimeter of a polygon is sum of all sides of the polygon. We also know that rectangle is polygon having two sets of equal sides.
The perimeter, P, of rectangle will be sum of its all sides that is:
[tex]P=l+w+l+w[/tex]
Combine like terms:
[tex]P=2l+2w[/tex]
Factor out 2:
[tex]P=2(l+w)[/tex]
Upon looking at our given choices, we can see that formula represented by option B displays a common student error for finding the perimeter.
Mrs Wright spent 2/9 of her paycheck on food and 1/3 on rent. She spent 1/4 of the remainder on transportation. She had $210 left. How much was Mrs. Wright's paycheck ?
Answer:
Mrs. Wright's paycheck is $630
Step-by-step explanation:
Let x = Mrs. Wright's paycheck.
Mrs. Wright spent 2/9 of her paycheck on food. This means that the amount of money spent on food is 2/9 × x = 2x/9
She spent 1/3 on rent. This means that the amount spent on rent is
1/3 ×x x = x/3
Amount she spent on food and rent is x/3 + 2x/9 =3x + 2x /9
= 5x/9
The remainder is her pay check - the amount that she spent on food and rent. It becomes
x - 5x/9 = (9x- 5x)/9 = 4x/9
She spent 1/4 of the remainder on transportation. It means that she spent 1/4 × 4x/9 = x /9 on transportation.
Amount left = 4x /9 - x/9= 3x/9
She had $210 left. Therefore,
210 = 3x/9
3x = 9×210 = 1890
x = 1890/3
x = $630
What is the remainder when 6x+12 is divided by 2x-8.
Answer:
4(3x-2)
Step-by-step explanation
6x+12/2x-8
6x+6x-8
12x-8
4(3x-2)
Answer:
Step-by-step explanation:
2x-8 ) 6x+12 ( 3
6x-24
- +
-----------
36
quotient=3
remainder=36
A recent survey showed that in a sample of 100 elementary school teachers, 15 were single. In a sample of 180 high school teachers, 36 were single. Is the proportion of high school teachers who were single greater than the proportion of elementary teachers who were single? Use α = 0.01.
Answer:
By using hypothesis test at α = 0.01, we cannot conclude that the proportion of high school teachers who were single greater than the proportion of elementary teachers who were single
Step-by-step explanation:
let p1 be the proportion of elementary teachers who were single
let p2 be the proportion of high school teachers who were single
Then, the null and alternative hypotheses are:
[tex]H_{0}[/tex]: p2=p1
[tex]H_{a}[/tex]: p2>p1
We need to calculate the test statistic of the sample proportion for elementary teachers who were single.
It can be calculated as follows:
[tex]\frac{p(s)-p}{\sqrt{\frac{p*(1-p)}{N} } }[/tex] where
p(s) is the sample proportion of high school teachers who were single ([tex]\frac{36}{180} =0.2[/tex])p is the proportion of elementary teachers who were single ([tex]\frac{15}{100} =0.15[/tex])N is the sample size (180)Using the numbers, we get
[tex]\frac{0.2-0.15}{\sqrt{\frac{0.15*0.85}{180} } }[/tex] ≈ 1.88
Using z-table, corresponding P-Value is ≈0.03
Since 0.03>0.01 we fail to reject the null hypothesis. (The result is not significant at α = 0.01)
The proportion of single high school teachers (0.20) is greater than the proportion of single elementary school teachers (0.15). However, further statistical testing would be required to determine if this difference is significant.
Explanation:To answer the student's question regarding proportions, we first need to calculate the proportion of single teachers in both samples. For elementary school teachers, the proportion is 15 out of 100, or 0.15. For high school teachers, the proportion is 36 out of 180 or 0.20.
Now, to determine if the proportion of high school teachers who were single is statistically greater than the proportion of elementary school teachers, we would typically perform a hypothesis test for the difference in proportions. However, in this simplified comparison, we can see that the proportion of single high school teachers (0.20) is indeed greater than the proportion of single elementary school teachers (0.15).
It's important to note that this does not mean there is a significant difference, we would need to conduct a significance test (like a Z-test for two proportions at the α = 0.01 level ) to determine this.
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The regression equation for predicting number of speeding tickets (Y) from information about driver age (X) is Y = -.065(X) + 5.57. How many tickets would you predict for a twenty-year-old? a. 4 b. 5.57 c. 4.27 d. 6 e. 1
Answer:
c. 4.27
Step-by-step explanation:
We have been given the regression equation of for predicting number of speeding tickets (Y) from information about driver age (X) as [tex]Y=-0.065(X)+5.57[/tex].
To find the predicted number of tickets for a twenty-year-old, we will substitute [tex]X=20[/tex] in our given equation.
[tex]Y=-0.065(20)+5.57[/tex]
[tex]Y=-1.3+5.57[/tex]
[tex]Y=4.27[/tex]
Therefore, the predicted number of tickets for a twenty-year-old would be 4.27 tickets.
Dividing in scientific notation
Answer: it’s easy your teacher should’ve taught this in 9th
Step-by-step explanation:
Answer:
The answer to your question is 2 x 10¹⁴
Step-by-step explanation:
Process
1.- Divide the whole numbers
[tex]\frac{4}{2} = 2[/tex]
2.- Apply rule of exponents
8 - (-6) = 8 + 6 = 14
3.- Write the answer
2 x 10¹⁴
Solve for x (log equation) (don’t mind the work)
Answer:
Step-by-step explanation:
A sample of 16 ATM transactions shows a mean transaction time of 67 seconds with a sample standard deviation of 12 seconds. State the hypotheses to prove that the mean transaction time exceeds 60 seconds. Assume that times are normally distributed.a. Determine your hypotheses.b. Compute the test statistic. What’s the rejection rule?d. At the α =.05 level of significance, your Critical Value ise. What conclusion can be drawn from this test at a 0.05 significance level?
Answer:
We conclude that the mean transaction time exceeds 60 seconds.
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = 60 seconds
Sample mean, [tex]\bar{x}[/tex] = 67 seconds
Sample size, n = 16
Alpha, α = 0.05
Sample standard deviation, s = 12 seconds
First, we design the null and the alternate hypothesis
[tex]H_{0}: \mu = 60\text{ seconds}\\H_A: \mu > 60\text{ seconds}[/tex]
We use One-tailed(right) t test to perform this hypothesis.
Formula:
[tex]t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }[/tex] Putting all the values, we have
[tex]t_{stat} = \displaystyle\frac{67 - 60}{\frac{12}{\sqrt{16}} } = 2.34[/tex]
Now, [tex]t_{critical} \text{ at 0.05 level of significance, 15 degree of freedom } = 1.753[/tex]
Since,
[tex]t_{stat} > t_{critical}[/tex]
We fail to accept the null hypothesis and reject it. Thus, we conclude that the mean transaction time exceeds 60 seconds.
Final answer:
The hypothesis test for the mean ATM transaction time given a sample mean of 67 seconds and a standard deviation of 12 seconds involves a one-tailed Z-test, where the null hypothesis H0: μ = 60 is rejected in favor of the alternative hypothesis Ha: μ > 60 since the test statistic of 2.33 exceeds the critical value of 1.645 at an α = .05 significance level.
Explanation:
Conducting a Hypothesis Test for Mean Transaction Time
For the sample of 16 ATM transactions with a mean of 67 seconds and a standard deviation of 12 seconds, the goal is to test the hypothesis that the mean transaction time exceeds 60 seconds.
a. Determine your hypotheses
The null hypothesis (H0) is that the mean transaction time is 60 seconds (H0: μ = 60). The alternative hypothesis (Ha) is that the mean transaction time is greater than 60 seconds (Ha: μ > 60).
b. Compute the test statistic
To compute the test statistic, we use the following formula for a sample mean with a known standard deviation: Z = (Xbar - μ0) / (s / sqrt(n)) where Xbar is the sample mean, μ0 is the hypothesized population mean, s is the sample standard deviation, and n is the sample size. Plugging in the values we get: Z = (67 - 60) / (12 / sqrt(16)) = 7 / (12 / 4) = 2.33.
c. Rejection rule
The rejection rule is if the computed test statistic is greater than the critical value at α = .05 significance level, we reject H0.
d. Critical Value at α = .05
The critical value for a one-tailed Z-test at α = .05 is approximately 1.645.
e. Conclusion
Because our test statistic of 2.33 exceeds the critical value of 1.645, we reject the null hypothesis, concluding that there is sufficient evidence at the 0.05 significance level to suggest that the mean transaction time exceeds 60 seconds.
A 17-year-old high school senior suddenly developed a high fever and chills, headache, stiff neck, and vomiting. His parents called the doctor, who told them to bring their son to the Emergency Department immediately. What disease does this boy probably have?
Answer:
Meningitis
Step-by-step explanation:
Meningitis is a inflammation of the membrane surrounding your brain and spinal cord.
In most cases it is caused by viral infection.
Some cases it improve without treatment in few days
Symptoms include:
sudden high feverHeadacheSevere HeadacheSeizuresSkin rashConstant CryingStiffness in a baby's bodyAs 17 year old had some symptoms such as headache,stiff neck, chills and vomiting o might be he have been suffered from Meningitis.
A large explosion causes wood and metal debris to rise vertically into the air with an initial velocity of 160 feet per second. The function h(t) = 160 t − 16 t 2 160t-16t2 gives the height of the falling debris above the ground, in feet, t t seconds after the explosion.
a. Use the given polynomial to find the height of the debris 2 second(s) after the explosion.
b. Factor the given polynomial completely.
Answer:
a) The debris was 256 feet into the air after 2 seconds of the explosion.
b)
[tex]h(t) = -16t(t-10)[/tex]
Step-by-step explanation:
We are given the following in the question:
Initial Velocity = 160 feet per second
[tex]h(t) = 160t-16t^2[/tex]
The above function gives the height in feet and t is seconds after the explosion.
a) Height of the debris 2 second(s) after the explosion.
We put t = 2 in the above function
[tex]h(2) = 160(2)-16(2)^2 = 256[/tex]
Thus, the debris was 256 feet into the air after 2 seconds of the explosion.
b) Factor the polynomial
[tex]h(t) = 160t-16t^2\\= 16t(10-t)\\=-16t(t-10)[/tex]
Final answer:
The height of the debris 2 seconds after the explosion is 256 feet. The given polynomial can be factored completely as -16t(t - 10)
Explanation:
To find the height of the debris 2 seconds after the explosion, we can substitute t = 2 into the equation h(t) = 160t - 16t^2.
So, h(2) = 160(2) - 16(2)^2 = 320 - 16(4) = 320 - 64 = 256 feet.
Therefore, the height of the debris 2 seconds after the explosion is 256 feet.
To factor the given polynomial completely, we can rewrite it as:
h(t) = -16t^2 + 160t.
Now, we can factor out a common factor of -16t:
h(t) = -16t(t - 10).
This gives us the completely factored form of the polynomial.