Hence, the total gallons of water made use of in the park after the new ride is installed is 9.51*10⁵ gallons
The form of the container the water is contained in affects how much water is contained inside. You must know the length, breadth, and depth of a square or rectangular vessel in order to calculate its volume using the volume equation V=L*W*D, where L stands for length, W for width, and D for depth. The volume equation in this case reads: V= (r²)Dπ, where r stands for the radius, D for depth, and, or pi, is a constant value that is typically rounded to 3.14. To perform the same volume calculation for a circular vessel, you must know the vessel's depth and diameter or radius.
Given, the water park has water which is 8.6*10⁵ gallons.
We know that 10⁵ = 100000
Thus, 8.6*10⁵ = 860000
The new ride would use an additional 9.1*10⁴ gallons.
Again, 10⁴ = 10000
Thus, 9.1*10⁴ = 91000
Total water that would be required now is equal to the sum of the original water volume and the volume required by the new ride
= (860000+91000) gallons
= 951000 gallons
= 9.51*10⁵ gallons
Hence, the total gallons of water made use of in the park after the new ride is installed is 9.51*10⁵ gallons
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17.match graph to what motion is occurring
1. The object is accelerating at an increasing rate
2. The object is moving at a constant velocity
3. The object is not moving
4 The object moved at a constant speed, then stopped. It returned to the beginning. Then it
moved back in the original direction at a very fast constant speed.
Type here tot
paads
Distance
Distance
Time
Time
Time
The solution is : the velocity of the person on the walk way with respect to the observers on the ground is D 1.7 m/s.
Here, we have,
In order to find the velocity of the person on the walk way with respect to the person on the ground we have to apply relative velocity concept.
Consider the observer on the ground as B and the person walking on the pathway as A.
The relative velocity is the velocity that the body A would appear to an observer on the body B and vice versa.
Mathematically speaking the relative velocity is the vector difference between the velocities of two bodies.
Relative velocity = Velocity of Body A- Velocity of Body B.
Velocity of the person walking on the walkway (A)= 1.5 m/s.(given)
Velocity of the observer on the ground (B)= -0.2 m/s(given).
Relative velocity of object A with respect to B = 1.5 - (-0.2)= 1.7 m/s.
Thus the velocity of the person on the walk way with respect to the observers on the ground is 1.7 m/s.
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complete question:
A person is strolling along a moving walkway at a constant velocity of +1.00 m/s with respect tot he walkway, which moves at a constant velocity of +0.50 m/s with respect to the ground. An observer on the ground is walking at a constant velocity of -0.2 m/s. what is the velocity of the person on the walk way with respect to the observers on the ground?
A - 0.7 m/s
B + 1.3 m/s
C - 0.3 m/s
D + 1.7 ms
two standard 6 sided dice are rolled. one is blue and one is red. what is the probability that sum of the two dice on a roll is 5 given that the blue die for that roll landed on 6?
The probability that sum of the two dice on a roll is 5 given that the blue die for that roll landed on 6 is 0.25 or 25%.
If we know that the blue die landed on 6, then we only need to consider the possible outcomes of the roll of the red die that would result in a sum of 5.
If red die shows 1, 2, 3 or 4, then the sum of the dice will be 6. There are a total of 6 possible outcomes for the roll of the red die (since it is a standard 6-sided die), but we can eliminate the outcomes 5 and 6 since they would result in a sum greater than 5.
So, out of the 4 possible outcomes for the roll of the red die that would result in a sum of 5, only one of them will occur if the blue die landed on 6. Therefore, the probability of getting a sum of 5 given that the blue die landed on 6 is:
1/4 = 0.25 or 25%
Hence the probability of the sum being 5 is 0.25 or 25%.
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A spinner with repeated colors numbered from 1 to 8 is shown. Sections 1 and 8 are purple. Sections 2 and 3 are yellow. Sections 4, 5, and 6 are blue. Section 7 is red.
Spinner divided evenly into eight sections with three colored blue, one red, two purple, and two yellow.
Determine the theoretical probability of the spinner not landing on red, P(not red).
0.125
0.250
0.675
0.875
The probability of not getting red is 87.5%.
Hence, The correct option is C.
We know that;
Probability = Number of favorable outcomes / Number of samples
Given that;
A spinner with repeated colors numbered from 1 to 8 is shown.
Sections 1 and 8 are purple. Sections 2 and 3 are yellow. Sections 4, 5, and 6 are blue. Section 7 is red .
You only have one of eight (1/8) evenly divided orange sections.
The rest is not red,
P = (1 - 1/8
P = 7/8
P = 0.875
P = 87.5%
Therefore, spinning once will yield 7/8 odds of not landing on red are,
⇒ 0.875 or 87.5%.
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PLEASE ANSWER THIS QUESTION LIKE ASAP
John has 8 boxes of apples. Each box holds 10 apples. If 5 of the boxes are full, and 3 of the boxes are half full, how many apples does John have?
Answer:
65 apples
Step-by-step explanation:
We Know
John has 8 boxes of apples.
Each box holds 10 apples.
If 5 of the boxes are full, and 3 of the boxes are half full, how many apples does John have?
Let's solve
5 boxes are full: 5 x 10 = 50 apples
3 boxes are half full = 3(1/2 · 10) = 15 apples
50 + 15 = 65 apples
So, John has 65 apples.
Find the value of x.
Answer:
80°
Step-by-step explanation:
the sum of the internal angles of a regular or irregular pentagon is 540°, we remove the known angles and we will have the answer
540 - 110 - 110 - 120 - 120 =
80°
two similar solids have surface areas of 45 in.^2 and 80 in.^2. the volume of the larger solid is 320 in.^3. what is the volume of the smaller solid?
The volume of the smaller solid is 292 in³ under the condition that two similar solids have surface areas of 45 in² and 80 in². The volume of the larger solid is 320 in³.
Given the two solids are similar, so their corresponding sides are proportional. Let us consider them calling the ratio of the corresponding sides k. The ratio regarding their surface areas is k² and the ratio of their volumes is k³.
Let us consider the volume of the smaller solid V. It is given the surface area of the smaller solid is 45 in² and that of the larger solid is 80 in²
k² = 80/45 = 8/9
k = √(8/9)
= 0.94 (approx.)
It is given the volume of the larger solid is 320 in³.
k³ = 320/V
0.94³ = 320/V
V = 320/(0.94³)
= 292 in³ (approx.)
The volume of the smaller solid is 292 in³.
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5/8 - ( 3 - 1/4) + 2/3
a target is 16 inches by 20 inches and the center target is 4 inches by 3 inches. what is the probability the ball will hit the center target to the nearest tenth of a percent?
The probability of hitting the center target is 3.8%.
To find the probability of hitting the center target, we need to know the total area of the larger target and the area of the center target.
The area of the larger target is:
16 inches x 20 inches = 320 square inches
The area of the center target is:
4 inches x 3 inches = 12 square inches
So, the probability of hitting the center target is:
12 square inches / 320 square inches = 0.0375 or 3.75%
Rounded to the nearest tenth of a percent, the probability of hitting the center target is 3.8%.
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a coin is biased so that the probability a head comes up when it is flipped is 0.6. what is the expected number of heads that come up when it is flipped 10 times
A coin is biased so that the probability a head comes up when it is flipped is 0.6. Therefore, we can expect to get 6 heads when a biased coin with a probability of 0.6 for heads is flipped 10 times.
To find the expected number of heads when a biased coin is flipped 10 times, we can use the formula:
Expected number of heads = Probability of getting a head × Number of times the coin is flipped
In this case, the probability of getting a head is 0.6 and the coin is flipped 10 times. So the expected number of heads is:
Expected number of heads = probability of getting a head x number of times flipped
Expected number of heads = 0.6 x 10
Expected number of heads = 6
Therefore, the expected number of heads when the coin is flipped 10 times is 6.
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A 95% confidence interval for the mean of a population is computed to be 6 to 14. Which one of the following claims would the interval tend to support?
A. The population mean is less than 15.
B. The population mean is between 8 and 10.
C. The population mean is exactly 9.
D. The population mean is more than 17.
E. The population mean is more than 7.
Thus, option B, "The population mean is between 8 and 10," is the claim that is most supported by the interval.
Based on the given confidence interval of 6 to 14, we can say with 95% confidence that the true population mean falls between those values. Therefore, option B, "The population mean is between 8 and 10," is the claim that is most supported by the interval.
Option A, "The population mean is less than 15," and option E, "The population mean is more than 7," are also supported by the interval but are less specific than option B.
Option C, "The population mean is exactly 9," is not necessarily supported by the interval, as the true mean could be any value within the interval.
Option D, "The population mean is more than 17," is not supported by the interval, as the upper limit of the interval is only 14.
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Select the correct answer. Which equation represents circle W? A. (x − 6)2 + (y + 4)2 = 4 B. (x − 6)2 + (y + 4)2 = 16 C. (x + 6)2 + (y − 4)2 = 4 D. (x + 6)2 + (y − 4)2 = 16
(the twos on the side are exponents, they're being squared)
Answer:
I believe the answer is C. (x + 6)2 + (y − 4)2 = 4
Step-by-step explanation:
Hope this helps :)
Please let me know if its incorrect
expand each logarithm
Hence, log(sqrt(3.5.11),9) in its enlarged version is roughly similar to 0.2148. We may answer this question by using the definition of logrithmic.
Describe logrithmic.Mathematical operations that relate to a number's logarithm are known as logarithmic functions. The power that a given basis must be increased in order to obtain a particular number is known as the logarithm of the number.
Although 10 (also known as the common logarithm) is the base that is most frequently used, logarithms can be calculated in relation to any positive base higher than 1. If the base is 10, the logarithm of such an integer x with regard to a base b is written by log(base b)(x), or just log(x).
We can compress the given logarithm via the logarithmic identity log(base a)(bc) = c * log(base a)(b):
Sqrt(3.5.11) = Log((3.5.11)(1/2), 9) = Log((3.5.11)*(1/2), 9) = (1/2) * Log (3.5.11, 9)
We must now calculate that logarithm of 9 in base 3.5.11. This can be changed to a log with a more recognisable column, such as base 10 or base e, using the change-of-base formula. Using the base 10 scale
3.5.11, 9) = 9)/log (3.5.11)
We can calculate this using a calculator:
log(9) = 0.9542 (reduced to 4 decimal places)
log(3.5.11) = log(3) + log(5) + log(11) = 0.4771, 0.6978, and 1.0414, respectively, yielding 2.2174. (rounded to 4 decimal places)
Therefore:
sqrt(3.5.11),9 = (1/2) log(3.5.11,9) = (1/2) log(9)/log(3.5.11)) = (1/2) log(0.9542/2.2174) = 0.2148 log(3.5.11,9) = (1/2) log(3.5.11, 9) = (1/2)
Hence, log(sqrt(3.5.11),9) in its enlarged version is roughly similar to 0.2148.
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The expanded form of the logarithm is:
log base 9 √(3.5.11) = log base 9 (3) + log base 9 (5) + log base 9 (11)
What is logarithm?
A logarithm is a mathematical function that tells us what exponent is needed to produce a given number, when that number is expressed as a power of a fixed base. In other words, logarithms tell us how many times we need to multiply the base by itself to get the desired number.
We can use the property of logarithms that says:
log base b (a * c) = log base b (a) + log base b (c)
to expand the logarithm.
Therefore, we have:
log base 9 √(3.5.11) = log base 9 √(3 * 5 * 11)
= log base 9 (3) + log base 9 (5) + log base 9 (11)
So, the expanded form of the logarithm is:
log base 9 √(3.5.11) = log base 9 (3) + log base 9 (5) + log base 9 (11)
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HELP !!!! HELP ASAPPPP
Determine if the relation is a function and explain your reasoning.
Day of the week Whether I went for a walk
Monday
No walk
Tuesday
Walked
Wednesday
No walk
Thursday
Walked
Friday
No walk
Saturday
Walked
Sunday
Walked
O The relation is a function because all of the input values have different output values.
O The relation is not a function because the output value Walking has different input values, and the same with No walk.
O The relation is not a function because some of the input values have different output values.
O The relation is not a function because there are 7 different input values.
Is the relation a function and explain your reasoning: B. The relation is not a function because the output value Walking has different input values, and the same with No walk.
How to determine whether or not the relation represent a function?In Mathematics, a function is generally used for uniquely mapping an independent value (domain or input variable) to a dependent value (range or output variable).
This ultimately implies that, an input value (domain) represents the value on the x-coordinate of a cartesian coordinate while a dependent value (range) represents the output value on the y-coordinate of a cartesian coordinate.
Based on the table, we can logically deduce that the relation does not represent a function because each of its input value (domain) has more than one dependent value (range) i.e Walked and No Walk.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
If events E and F are disjoint (mutually exclusive) and the events F and G are disjoint, must the events E and G necessarily be disjoint? Give an example to illustrate your opinion. Choose the correct answer below.A.Yes, events E and G must be disjoint. For example, E = {0,1,2}, F = {3,4,5}, and G= {6,7,8} show that E and F are disjoint events, F and G are disjoint events, and E and G are also disjoint events.B.No, events E and G are not necessarily disjoint. For example, E = {0,1,2}, F = {3,4,5}, and G = {2,6,7} show that E and F are disjoint events, F and G are disjoint events, and E and G are events that are not disjoint.C.Yes, events E and G must be disjoint. For example, E = {0,1,2}, F = {3,4,5}, and G = {2,6,7} show that E and F are disjoint events, F and G are disjoint events, and E and G are also disjoint events.D.No, events E and G are not necessarily disjoint. For example, E = {0,1,2}, F = {3,4,5}, and G = {6,7,8} show that E and F are disjoint events, F and G are disjoint events, and E and G are events that are not disjoint.
The correct answer is D. No, events E and G are not necessarily disjoint. The mutual exclusivity of events F and G does not guarantee the mutual exclusivity of events E and G.
The example provided in option D shows that events E and F are disjoint, events F and G are disjoint, but events E and G are not disjoint. This is because they share the element 2.
For example, E = {0,1,2}, F = {3,4,5}, and G = {2,6,7} .
Therefore, the mutual exclusivity of events F and G does not guarantee the mutual exclusivity of events E and G.
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For which value of x is the inequality −2x≥6
true?
A. -3
B. -2
C. -1
D. 0
E. 4
Answer:
-2x > 6, so x < -3
So A is correct.
HELP! Image attached
The data distribution is skewed and the mean of the emails is less than the median number of emails.
The median is 22 and the mean is 20.2.
How to find the mean and median ?The mean can be found by adding up the number of emails and dividing it by the number of days :
= ( 15 + 16 + 18 + 19 + 22 + 22 + 22 + 22 + 23 + 23 ) / 10
= 20. 2
The median is the number in the middle. As there are 10 numbers, the median would be:
= (Position 5 + Position 6) / 2
= ( 22 + 22 ) / 2
= 22
The mean is less than the median.
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It is the end of the semester and Kyle has one test left. His 5 test grades were 90, 83, 75, 84, 96. What does he need to make on the sixth test to have a mean test grade of 90
Answer:
Kyle needs 112 marks on his sixth test for the mean test grade to be 90.
Step-by-step explanation:
Let the marks Kyle needs for the sixth test be x.
The mean of all tests is given as 90. The formula for mean would be: (sum of marks obtained in each test)/(total number of tests)
which implies,
(90+83+75+84+96+x)/6 = 90,
(428+x)/6 = 90,
428+x = 540,
x = 112
Therefore, Kyle needs 112 marks on his sixth test for the mean test grade to be 90.
The sum of all values divided by the total number of values determines a dataset's mean (also known as the arithmetic mean, which differs from the geometric mean). It is the most widely applied central tendency measure and is frequently called the "average."
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Golf Tournament In a golf tournament, the top 6 men's scores are 65, 68, 70, 72, 73, 75. The top women's scores are 69, 71, 73, 74, 77, 80. Compare the spread of the data for the two sets of scores using (a) the range and (b) the mean absolute deviation.
Answer:
Range: Men: 10, Women: 11
MAD: Men: 2.833333 (17/6), Women: 3
Step-by-step explanation:
The range of the men's scores is 75-65 (highest-lowest), which is 10.
The range of the woman's scores is 80-69, which is 11.
The MAD is the mean of the absolute difference between the terms and the mean, which is very painful to do, but in the sake of the problem, I will be doing.
Men's MAD:
The mean is [tex]\frac{65+68+70+72+73+75}{6}[/tex], which is 70.5.
Sigh.
Now, we find the difference of each term to the mean.
[tex]70.5-65= 5.5[/tex]
[tex]70.5-68=2.5[/tex]
[tex]70.5 - 70 = 0.5[/tex]
[tex]72-70.5=1.5[/tex]
[tex]73-70.5=2.5[/tex]
[tex]75-70.5=4.5[/tex]
wow. Now, we find the mean of these numbers.
[tex]\frac{5.5 + 2.5 + 0.5 + 1.5 + 2.5 + 4.5}{6}[/tex]= 17/6=2.8333333333 This is the MAD.
For the Women's, I'll speed over it.
The mean is 74.
The MAD is 3.
Alyssa is tracking the growth of a plant. The plant grows c inches in the first week and n inches in the second week. Enter an equation to show that the plant grows 2 inches more in the second week than in the first week
The equation is given as n = c + 2
How to derive the equationThe plant grows c inches in the first week.
The plant grows n inches in the second week.
mаthеmаticаlly, the equаtion requires that wea rea to to show thе relаtionship between thе growth in thе first wееk (c) and thе growth in thе seсond wееk (n).
thе growth in thе seсond wееk (n) is said to be 2 inсhes more than thе growth in thе first wееk (c) from the given question.
The equation would be
n = c + 2
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The expression 1500 (1.085)^3 represents an account balance in dollars after three years with an initial deposit of $1,500. The account pays 8.5% interest, compounded annually for three years.
A. Explain how the expression would change if the bank had compounded the interest quarterly for the three years.
B. Write a new expression to represent the account balance, in dollars, if interest is compounded quarterly.
A. If the bank had compounded the interest quarterly for the three years, the interest rate would be divided by 4 (since there are 4 quarters in a year) and the number of compounding periods would be multiplied by 4. This is because the interest would be calculated and added to the account balance every quarter, rather than just once a year.
B. To represent the account balance if interest is compounded quarterly, we need to use the formula for compound interest with quarterly compounding:
A = P(1 + r/n)^(nt)
where A is the account balance, P is the principal (initial deposit), r is the annual interest rate (8.5%), n is the number of times the interest is compounded per year (4 for quarterly compounding), and t is the number of years (3).
Substituting the given values into the formula, we get:
A = 1500(1 + 0.085/4)^(4×3)
A = 1500(1.02125)^12
A ≈ $1,969.36
Therefore, the new expression for the account balance, in dollars, if interest is compounded quarterly is:
$1,969.36 = 1500(1 + 0.085/4)^(4×3)
2y-2.3=4.1 answer that
To solve the equation 2y − 2.3 = 4.1 for y, we can use algebraic manipulation.
Step 1:In order to remove the constant term on the left-hand side of the equation, we first add 2.3 to both sides of the equation:
2y - 2.3 = 4.1
+2.3 +2.3
2y = 6.4
Step 2:Now, we divide both sides by 2 to isolate y:
2y = 6.4
÷2 ÷2
y = 3.2
So, the solution to this equation is y = 3.2
----------------------------------------------------------------------------------------------------------
SummaryWe need to isolate the variable on one side of the equation in order to solve an equation like this. By carrying out the same method on both sides of the equation, we can do this. In this example, we divided both sides by 2 to isolate y after adding 2.3 to both sides to remove the constant term on the left-hand side.
----------------------------------------------------------------------------------------------------------
FAQWhat is a constant term?- A term in an algebraic equation that has no variables and is steady is known as a constant term in mathematics. A constant is a fixed, unchanging value. A constant in algebra can be a number on its own or sometimes a letter like a, b, or c to show a fixed integer.
What isolating y mean, in this case?- To separate y from all other terms in an equation, the equation must be rewritten so that y is on one side and all other terms are on the other side. It allows us to calculate the value of y and solve for it.
What is algebraic manipulation?- Mathematical operations including addition, subtraction, multiplication, and division are used to rearrange algebraic expressions or equations to try to simplify or solve them. This process is known as algebraic manipulation. By doing the opposite operations (undoing) to any equation, algebraic manipulation tries to isolate a variable or simplify an expression in order to solve for a certain variable.
Solve for x to make A||B.
A = x + 12
B = x + 48
X = [?]
(Make sure to look at the pic for better understanding in the question)
Answer:
x=80
Step-by-step explanation:
x+12 and x+48 must equal 180 so 60 is the answer
60+12=72
60+48=108
72+108=180
Answer: 60
Step-by-step explanation:
When you have 2 parrallel lines the angles will either be = or =180 in this case =180
so
A+B=180
x + 12 + x + 48 = 180
2x + 60 =180
2x = 120
x=60
Fill in the missing words
Lex has opened a savings account with $1,200. His account has an annual interest rate of 6.8%
compounded annually. How much money will Lex have after 6 years?
Answer:
$1780.77------------------------------
Use the formula for compound interest :
[tex]A = P(1 + r/n)^{nt}[/tex]Where:
A = the future value' P = the principal investment amount,r = the annual interest rate,n = the number of compounds,t = the number of years.In this problem, we have:
P = $1,200, r = 6.8% = 0.068, n = 1, t = 6Now, let's plug these values into the formula:
[tex]A = 1200(1 + 0.068/1)^{1*6} = 1200(1 + 0.068)^6 = 1200(1.068)^6 = 1780.77[/tex]After 6 years, Lex will have approximately $1780.77 in his savings account.
help please will give brainliest
The minimum value of the function on the interval [2, 11] is -100,000,000,000.
What is the minimum value of the function?The function f(x) = -10ˣ is a decreasing exponential function, which means that its value decreases as x increases.
f(x) = -10ˣ on the interval [2, 11]
The minimum value of the function will be at the endpoint of the interval, which is at x=11.
f(11) = -10¹¹
f(11)= -100,000,000,000
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The graph of f(x) and table for g(x) = f(kx) are given.
The graph shows an upward opening parabola labeled f of x that passes through a point negative 2 comma 8, a point negative 1 comma 2, a vertex 0 comma 0, a point 1 comma 2, and a point 2 comma 8.
x g(x)
−8 8
−4 2
0 0
4 2
8 8
What is the value of k?
k is equal to one fifth
k = 5
k is equal to one fourth
k = 4
Answer: C. k is equal to one fourth
Step-by-step explanation:
formula for parabola in vertex form
y= a(x-h)²+k (h, k) is vertex here it is (0,0)
f(x)=ax² another point we can plug in is (1,2)
2=a1
a= 2
so f(x)= 2x²
g(x)= f(kx) plug in kx into f(x)
g(x) = 2(kx)²
g(x) = 2(k²)(x²) plug in a point and find k (4,2)
2 = 2 k²4²
k²=1/16
k=1/4
C
A cell phone that was bought for 2500 was sold at 15% calculate the selling price
Answer:
The answer to your question is $375
The selling price of the cell phone is $375.
Step-by-step explanation:
15% x 2500
100 = 375
I hope this helps and have a wonderful day!
Test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, and then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. Among 2094 passenger cars in a particular region, 227 had only rear license plates. Among 330 commercial trucks, 46 had only rear license plates. A reasonable hypothesis is that commercial trucks owners violate laws requiring front license plates at a higher rate than owners of passenger cars. Use a 0.10 significance level to test that hypothesis.a. Test the claim using a hypothesis test.b. Test the claim by constructing an appropriate confidence interval.
Since the p-value is less than the significance level of 0.10, we reject the null hypothesis. Since the confidence interval does not contain 0, it supports the alternative hypothesis that commercial trucks have a higher proportion of violations than passenger cars.
a. Hypothesis Test:
Null Hypothesis: The proportion of passenger cars with only rear license plates is equal to or greater than the proportion of commercial trucks with only rear license plates.
Alternative Hypothesis: The proportion of commercial trucks with only rear license plates is greater than the proportion of passenger cars with only rear license plates.
Let p1 be the proportion of passenger cars with only rear license plates, and p2 be the proportion of commercial trucks with only rear license plates.
The test statistic for comparing two proportions is the z-test.
z = ((p1 - p2) - 0) / √(p_hat * (1 - p_hat) * (1/n1 + 1/n2))
where p_hat = (x1 + x2) / (n1 + n2) is the pooled sample proportion, and x1 and x2 are the number of successes (only rear license plates) in the two samples, and n1 and n2 are the sample sizes.
Plugging in the values, we get:
p1 = 227/2094 = 0.1084
p2 = 46/330 = 0.1394
p_hat = (227 + 46) / (2094 + 330) = 0.1116
n1 = 2094
n2 = 330
z = ((0.1084 - 0.1394) - 0) / √(0.1116 * (1 - 0.1116) * (1/2094 + 1/330))
= -1.68
The p-value for this one-tailed test is P(Z < -1.68) = 0.0475.
Conclusion: The data provides sufficient evidence to support the claim that commercial truck owners violate laws requiring front license plates at a higher rate than owners of passenger cars.
b. Confidence Interval:
We can also construct a confidence interval to estimate the difference in proportions with a specified level of confidence.
A 90% confidence interval for the difference in proportions can be calculated as:
(p1 - p2) ± z√(p1(1-p1)/n1 + p2*(1-p2)/n2)
Plugging in the values, we get:
(p1 - p2) ± 1.645√(0.1084(1-0.1084)/2094 + 0.1394*(1-0.1394)/330)
= (-0.0499, 0.0094)
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A certain quadratic function has a graph which contains the points (1, 7), (2, 16), and (3, 29). Using a quadratic regression (or a system of linear equations), find the equation for this function in standard form. As your answer, give the coefficient on x2 (that is, a).
Group of answer choices
–2
2
–1
1
The required coefficient on x² is 2, so the answer is 2. Option B is correct.
We can start by assuming that the quadratic function has the form:
y = ax² + bx + c
where a, b, and c are unknown coefficients to be determined. We can use the three given points on the graph to set up a system of three equations in three unknowns:
7 = a(1)² + b(1) + c
16 = a(2)² + b(2) + c
29 = a(3)² + b(3) + c
Simplifying each equation, we get:
a + b + c = 7
4a + 2b + c = 16
9a + 3b + c = 29
We can solve this system of equations using any method of our choice, such as elimination or substitution. One possible approach is to subtract equation 1 from equation 2 and equation 2 from equation 3, which gives:
a + b + c = 7
3a + b = 9
5a + b = 13
a = 2; b = 3; c = 2
Therefore, the equation for the quadratic function in standard form is:
y = 2x² + 3x + 2
The coefficient on x² is 2, so the answer is 2.
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47. For a certain type of computers, the length of time between charges of the battery is normally
distributed with a mean of 50 hours and a standard deviation of 15 hours. John owns one of
these computers and wants to know the probability that the length of time will be between
40 and 70 hours.
A. .344
B. .656
C. .748
D. .908
The probability that the length of time between charges will be between 40 and 70 hours is 0.656.
To solve this problem, we need to standardize the values of 40 and 70 using the given mean and standard deviation, and then use the standard normal distribution table to find the probability.
Standardizing 40: z = (x - mu) / sigma z = (40- 50)/15 z = -2/3
Standardizing 70: z = (x-mu) / sigma z = (70- 50)/15 z 4/3
Now we look up the probabilities associated
with the standardized values -2/3 and 4/3 in the
standard normal distribution table.
Using the table, we find that the probability of z being less than -2/3 is 0.2525 and the probability of z being less than 4/3 is 0.9082.
So the probability of the length of time being between 40 and 70 hours can be found by subtracting the probability of z being less than -2/3 from the probability of z being less than 4/3:
P(40 < x <70) = P(-2/3 <z < 4/3) = P(z < 4/3) - P(z< -2/3)
P(40 < x < 70) = 0.9082-0.2525 P(40 < x <70) = 0.6557
Therefore, the probability that the length of time between charges will be between 40 and 70 hours is approximately 0.656, which is closest to option B.
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