Rural speed limits: Rural speed limits for some states are indicated below.choose one state at random. Find the probabilities of the following. Enter your answers as simplified fractions or decimals rounded to three decimal places.a) 65 or 70 mphP (65 mph or 70 mph) =_____?b) Greater than 70 mph.P(Greater than 70 miles)=_____?c) 60 mph or less.P( 65 mph or less)=_____?
Answers
Probability of the speed limits are:
(a) P(65mph or 75mph) = 0.62
(b) P(x > 70mph) = \(\frac{18}{50}\) = 0.36
(c) P(x < 65mph) = \(\frac{1}{50}\) = 0.02
Speed Limits --- States
60 mph ---------- 1
65 mph ----------- 18
70 mph ----------- 18
75 mph ---------- 13
Total -------------- 50
(a): Probability of 65mph or 75mph
This is represented as:
P(65mph or 75mph)
We only consider states with speed limits of 65 and 75mph.
So, we have:
P(65mph or 75mph) = P(65mph) + P(75mph)
P(65mph or 75mph) = \(\frac{18}{50}+\frac{13}{50}\)
Now, Taking the L.C.M
P(65mph or 75mph) = \(\frac{18+13}{50}\)
P(65mph or 75mph) = \(\frac{31}{50}\)
P(65mph or 75mph) = 0.62
(b) Greater than 70mph
This is represented as:
P(x > 70mph)
We only consider states with speed limits of 75mph.
So, we have:
P(x > 70mph) = \(\frac{18}{50}\)
(c): 65mph or less
This is represented as:
We only consider states with speed limits of 60mph
So, we have:
P(x < 65mph) = \(\frac{1}{50}\)
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Related Questions
geologists unearth a sample of zircon that appears to be a closed system. they find 0.686 microgram of 206pb for 1.000 microgram of 238u present. approximately how old is the sample? yrs
Answers
geologists unearth a sample of zircon that appears to be a closed system. they find 0.686 micro gram of 206 Pb for 1.000 micro gram of 238U present. approximately 3.7973 × 10⁹ years old is the sample.
What is decay constant?The reciprocal of the time period during which the number of atoms in the radioactive element drops to almost A. 50% of its initial number is the decay constant.
According to the radioactive decay law, a nucleus's likelihood of decaying is a constant that is independent of time.
t1/2 of U₂₃₈ is 4.5 × 10⁹ years
moles of U₂₃₈ : (1 × 10⁻⁶ / 238) moles
moles of Pb₂₀₆ : (0.686 × 10⁻⁶ / 206) moles
Now, U₂₃₈ → Pb₂₀₆
As Pb₂₀₆ comes from U₂₃₈ hence,
moles of U₂₃₈ decayed = moles of Pb₂₀₆
= (0.686 × 10⁻⁶ / 206) moles
Therefore, initial moles of U₂₃₈:
N₀ = [(1 × 10⁻⁶ / 238) + (0.686 × 10⁻⁶ / 206)] moles
and N = (1 × 10⁻⁶ / 238) moles
Now, λ (decay constant) = 0.693 / (t1/2)
= 0.693 / ( 4.5 × 10⁹ years)
So,
t = 2.303 / λ × log (N₀ / N)
t = 2.303 / [0.693 / ( 4.5 × 10⁹ years)] × log [1 + (0.686/206)/(1/238)]
t = 14.95 × 10⁹ × 0.254
t = 3.7973 × 10⁹ years.
Thus, the sample is: 3.7973 × 10⁹ years old.
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If (a−8)/3=(a−3)/2 , then a = ?
Answers
Answer:
\( \frac{(a - 8)}{3} = \frac{(a - 3)}{2} \\ 2(a - 8) = 3(a - 3) \\ 2a - 16 = 3a - 9 \\ 3a - 2a = - 7 \\ a = - 7\)
Answer:
The value of a is -7. You can see the solution in the picture.
a) by using Venn-diagram. 75 students in a class like picnic or hiking or both. Out of them 10 like both the activities. The ratio of the number of students who like picnic to those who like hiking is 2 : 3. (i) Represent the above information in a Venn-diagram. (ii) Find the number of students who like picnic. (iii) Find the number of students who like hiking only. (iv) Find the percentage of students who like picnic only.
Answers
(i) A Venn-diagram of this information is shown below.
(ii) The number of students who like picnic = 34
(iii) The number of students who like hiking only = 51
(iv) The percentage of students who like picnic only. = 45.33%
Let us assume that A represents the set of students who like picnic.
B represents the set of students who like the hiking.
The total number of students in a class are: n(A U B) = 75
Out of 75 students, 10 like both the activities.
n(A ∩ B) = 10
The ratio of the number of students who like picnic to those who like hiking is 2 : 3
Let number of students like tea n(A) = 2x
and the number of students like coffee n(B) = 3x
n(A U B) = n(A) + n(B) - n(A ∩ B)
75 = 2x + 3x - 10
75 + 10 = 5x
85/5= x
x = 17
The number of students like picnic = 2x
= 2 × 17
= 34
The number of students like hiking = 3x
= 3 × 17
= 51
This informtaion in Venn diagram is shown below.
The percentage of students who like picnic only would be,
(34/75) × 100 = 45.33%
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I've tried geometric, alternating, and lagrange error bound i need help thank you
Answers
The Lagrange error bound is a method for estimating the error in approximating a function using a polynomial
Let's say you have a function f(x) and you want to approximate it using a polynomial of degree n, denoted by Pn(x). The Lagrange error bound states that the absolute error between f(x) and Pn(x) is bounded by:
|f(x) - Pn(x)| ≤ M/[(n+1)!] |x - c|^(n+1)
where M is a bound on the (n+1)th derivative of f(x) on an interval containing x and c is some constant value in that interval (typically the midpoint of the interval). Note that the bound depends on the choice of x and c.
In practice, the Lagrange error bound can be used to estimate the error in polynomial approximations. You can choose a value of x and a degree n for the polynomial, then use the bound to find an upper bound on the absolute error. If the error is too large, you may need to increase the degree of the polynomial or choose a different value of x.
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The given question is complete, the complete question is:
What is Lagrange error bound ?
16. ) during the soccer season, carla scored goals on 7% of the shots she took. if she scored 14 goals, how many shots did she take?
Answers
Total 200 number of shots Carla took to goal 14 goals.
What is percentage means?
A number or ratio that can be expressed as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The percentage therefore refers to a part per hundred. Per cent refers to one hundred percent.
Carla scored goals on 7% of the shots she took.
If she scored 14 goals. How many shots did she take.
Let's suppose she took x number of shots.
7% of the total number of shots = 14
7% of x = 14
7*x/100 = 14
7*x = 14*100
x = 200.
So Total 200 number of shots Carla took to goal 14 goals.
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The ratio of boys to girls in Ms. Ballou’s class is 3 to 4. If there are 28 total students in the class, how many more girls are in the class than boys?
Answers
Answer:
12 girls than boys
Step-by-step explanation:
3+4=7
3/7 x 28 = 12
So add 3+4 and then put 3 the first number and then answer into a fraction 3/7 and multiply with how many students their and that's it
a. 5x10 to the third power
Answers
Answer:
5000
Step-by-step explanation:
the answer is 5000 because the third power to ten is 1000 and since 5x10= 50 you just have to make it a thousand so, 5000
Answer:5000
Step-by-step explanation: take notes
assume the triangle has the given measurements. Solve for the remaining sides and angles.
Answers
The missing angles are sides are;
a = 9.8 B = 60 degreesC = 90 degreesHow do you solve a triangle?We can see that we would have to first apply the cosine rule here;
\(a^2 = b^2 + c^2 - 2abCos A\\a^2 = (17)^2 + (19.6)^2 - 2(17 * 19.6)Cos 30\\a^2 = 673.16 - 666.4Cos 30\)
a = 9.8
We can now apply the sine rule to obtain the angle B
\(a/Sin A = b/Sin B\\SinB = bSin A/a\\B = Sin-1 ( bSin A/a)\\B = Sin-1(17 * Sin 30/9.8)\)
B = 60
Then;
C = 180 - (30 + 60)
C = 90 degrees
Thus the triangle in the problem have been solved.
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Write the equations in slope intercept form.
Answers
Answer:
10. y = -1/2x + 2
11. y = 2x + 3
12. y = 1/3x - 2
13. y = -2x - 2
What are the points for y=-3x+4 and how do I graph it
Answers
Answer:
(-3,13) (-2,10) (-1,7) (0,4) (1,1) (2,-2) (3,5) (4,8) are your graph points.
Step-by-step explanation:
Okay so to find the points, you have to create a table graph with a set of x values.
in this case, your equation y=-3x+4 the x can be replace with a set of numbers and these will be your plots.
-3(-3)+4= 13
-3(-2)+4= 10
-3(-1)+4= 7
-3(0)+4= 4
-3(1)+4= 1
-3(2)+4= -2
-3(3)+4= -5
-3(4)+4= -8
Naturally with these points a shape will form ideally a straight line. Hopefully this helps and good luck!
Blake is eliminating contributing factors to ensure accuracy in his results. Which step of the scientific method is he performing?.
Answers
Test the hypothesis step of the scientific method is he performing.
Making conjectures (hypothetical explanations) is a step in the scientific method. Predictions are then derived from the hypotheses as logical conclusions, and experiments or actual observations are conducted based on those predictions.
Since at least the 17th century, the scientific method—an empirical approach to learning—has guided the advancement of science. Since one's interpretation of the observation may be distorted by cognitive presumptions, it requires careful observation and the application of severe skepticism regarding what is observed.
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find the slope of the line through each pair of points (-19,20) (20,7)
Answers
Answer:
m (slope) = 13/-39 (13 over -39)
Step-by-step explanation:
To find the slope by using two points, we do rise over run (y over x)
y2-y1 (the numbers 1 and two don't matter, it's just to be sure that each point's numbers line up, for example, that -19 and 20 line up, and that 20 and 7 line up)
x2-x1
20-7 = 13
-19-20 = -39
Then, simplify
13/-39 cannot be simplified, so that is your answer.
Find the area of the region enclosed by the curves y=36x2−1 and y=∣x∣√1−36x^2.
The area of the region enclosed by the curves is (Type an exact answer.)
Answers
The curves y = 36x^2 - 1 and y = |x|√(1 - 36x^2) intersect at x = -1/6 and x = 1/6. The area is 2/9 + 1/54√35.
To find the area between these curves, we integrate the difference between the upper curve (y = 36x^2 - 1) and the lower curve (y = |x|√(1 - 36x^2)) over the interval [-1/6, 1/6]:
Area = ∫[-1/6, 1/6] (36x^2 - 1 - |x|√(1 - 36x^2)) dx
Evaluating this integral, we get:
Area = [12x^3 - x - 1/54√(36x^2 - 1)] evaluated from x = -1/6 to x = 1/6
Simplifying further, we obtain:
Area = [12/6^3 - 1/6 - 1/54√(36/6^2 - 1)] - [12/(-6^3) - (-1/6) - 1/54√(36/(-6^2) - 1)]
Calculating the values and simplifying, the final answer for the area of the region enclosed by the curves is:
Area = 2/9 + 1/54√35
Therefore, the area is 2/9 + 1/54√35.
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If Rolle's Theorem can be applied, find all values of c in the open interval (a, b). such that f '(c) = 0. (Enter your answers as a comma-separated list. If Rolle's Theorem cannot be applied, enter NA.)
f(x) = (x-2)(x-3)(x-6), [2,6]
After multiplying out f(x) I got: x^3 -11x^2 +36x -36
Answers
In function f(x) is continuous in [ 2,6] and differentiable in ( 2, 6) by Rolle's theorem .
What is the simple definition of Rolle's theorem?
In accordance with Rolle's Theorem, if a function f is continuous on the closed interval [a, b] and differentiable on the open interval (a, b) such that f(a) = f(b), then f′(x) = 0 for some x where a x b.
f(x) = ( x - 2) ( x - 4 ) ( x - 6 ) [ 2,6 ]
= ( x² - 4x -2x + 8 ) ( x - 6 )
= x³ - 6x² - 4x² + 24x - 2x² + 12x + 8x - 48
= x³ - 12x² + 44x - 48
Polynomial functions are continuous and differentiable everywhere ( - ∞ , ∞)
given function is also continuous in [ 2,6] and differentiable in ( 2, 6)
f( a) = f(2) = ( 2- 2 )( 2 - 4 )( 2 - 6 ) = (0 )( - 2)( -4) = 0
f(b ) = f(6) = ( 6 -2 ) ( 6 - 4 )( 6 - 6 ) = (4)(2)(0) = 0
f(a) = f(b)
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The height of a cone is two times its base diameter. What is the volume of the cone in terms of its base radius r?
options are on the picture:)
Answers
Answer:-
The option B is the right answer.
Solution:-
\( \sf h = 2d = 2 \: • \: 2r = 4r\)
\( \sf = \frac{1}{3} \pi {r}^{2} h\)
\( \sf = \frac{1}{3} \pi {r}^{2} \: • \: 4r\)
\( \sf = \frac{4}{3} \pi {r}^{3} \: \green✓ \)
spearman's rho describes a linear relationship between two quantitative variables. group of answer choices true false
Answers
The given statement "spearman's rho describes a linear relationship between two quantitative variables." is False, because it is a correlation coefficient that measures the strength of a monotonic relationship.
In particular, Spearman's rho is used to measure the degree of association between two variables when the relationship between them is not linear. It works by ranking the values of the two variables and then computing the correlation between the ranks.
If the variables have a monotonic relationship, the Spearman's rho will be close to 1 or -1, depending on the direction of the relationship. If there is no relationship, the Spearman's rho will be close to 0.
For example, consider a dataset where the number of hours studied and the grade obtained in an exam are recorded for a group of students.
If the relationship between the two variables is non-linear, such as a U-shaped or inverted U-shaped curve, then the Spearman's rho would be more appropriate than the Pearson correlation coefficient, which measures the strength of a linear relationship.
In summary, Spearman's rho is used to measure the strength of a monotonic relationship between two variables, which can be non-linear.
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find the x value 7x-1+6x-1=180
Answers
Answer:
14
Step-by-step explanation:
Let's take it step-by-step
7x-1+6x-1=180
We move all terms to the left:
7x-1+6x-1-(180)=0
We add all the numbers together, and all the variables
13x-182=0
We move all terms containing x to the left, and all other terms to the right
13x=182
x=182/13
x=14
So remember, we move all terms to the left. We add all the numbers together, and all the variables. And we move all terms containing x to the left, and all other terms to the right.
Jason stands on a scale with two 2,5 kg hand weight, one in each hand The scale shows 98kg. Calculate jasons weight.
Answers
Jason's weight is 93 kg.
To calculate Jason's weight, we need to subtract the combined weight of the hand weights (2.5 kg + 2.5 kg = 5 kg) from the reading on the scale (98 kg).
Weight on the scale = Jason's weight + Weight of hand weights
98 kg = Jason's weight + 5 kg
Subtracting 5 kg from both sides of the equation:
Jason's weight = 98 kg - 5 kg
Jason's weight = 93 kg
Therefore, Jason's weight is 93 kg.
Based on the information provided, Jason's weight is calculated to be 93 kg.
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The simplified form of the expression-3jk33isAj* kWBm2k2 m3What is the value of A?What is the value of B?-278k16What is the value of a?What is the value of y?39What is the value of z?9
Answers
The expression is equal to:
\((\frac{-3jk^3}{2k^2m^3})^3=(\frac{-3jk^{(3-2)}}{2m^3})^3=(\frac{-3jk}{2m^3})^3\)\((\frac{-3jk^3}{2k^2m^3})^3=\frac{(-3)^3\cdot j^3\cdot k^3}{2^3\cdot(m^3)^3}=\frac{-27j^3k^3}{8m^{(3\cdot3)}}=\frac{-27j^3k^3}{8m^9}\)So:
\(\frac{Aj^xk^y}{Bm^z}=\frac{-27j^3k^3}{8m^9}\)Answer: A = -27
B = 8
x = 3
y = 3
z = 9
Answer this question plz
Answers
The measure of angle EDF from the given figure is 23°.
From the given figure, ∠EGF=23°.
What is and angles in the same segment theorem?The angles at the circumference subtended by the same arc are equal. More simply, angles in the same segment are equal.
By using angles in the same segment theorem, we get
∠EGF = ∠EDF = 23°
Therefore, the measure of angle EDF from the given figure is 23°.
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Solve.
13) Peter borrows $5000 at a rate of 9% compounded monthly. Find how much Peter owes at the end of 3 years.
Use: A=P(1+r/n)^nt
Round to two decimal places.
Answers
The final amount is higher than the principal amount because of the effect of Compounding interest. The interest is calculated monthly and added to the principal, resulting in a higher amount at the end of the term.
We are given:
Principal amount (P) = $5000
Rate of interest (r) = 9% per annum
Compounding frequency (n) = 12 (monthly)
Time period (t) = 3 years
Using the formula for compound interest:
A = P(1 + r/n)^(nt)
Substituting the given values, we get:
A = $5000(1 + 0.09/12)^(12*3)
A = $5000(1.0075)^36
A = $6817.60
Therefore, Peter owes $6817.60 at the end of 3 years.
the final amount is higher than the principal amount because of the effect of compounding interest. The interest is calculated monthly and added to the principal, resulting in a higher amount at the end of the term.
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Due in 1 hour, plz help
Answers
Answer:
1. 12/1= rate of change
Step-by-step explanation:
1.
1 mile= 30 seconds
(1,30)
6 miles= 1 1/2 minutes
6 miles=90seconds
(6,90)
Formula: y2-y1/x2-x1
90-30/6-1
60/5
12/1= rate of change
hope its right
What is mean particle velocity?
Answers
Mean particle velocity is the average speed at which the particles in a substance are moving.
Mean particle velocity is a measure of the motion of particles in a substance, such as a gas or a liquid. It is defined as the average speed of the particles in the substance, taking into account the speed and direction of each particle.
In a gas, the particles move randomly in all directions, while in a liquid, they move more chaotically due to the intermolecular forces between them. The mean particle velocity of a substance is influenced by various factors such as temperature, pressure, and the mass of the particles.
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find the selling price if
cost price is R720 with a profit of 40%
Answers
Answer:
R1008
Step-by-step explanation:
720 X 1.4 = R1008
I used 1.4 because there is a 40 percent profit
A spinner with 8 sections is shown below. If you were to spin the spinner 200 times, how many times can you expect to land on yellow or purple?
Answers
Answer:
125 times out of 200 spins or 125/200
Step-by-step explanation:
Set up your equation:
5/8 = x/200
Cross Multiply:
1000 = 8x
x = 125
slove the equation 4c + 7 = 23
Answers
We need to solve the expression:
\(4c+7=23\)The first step is to subtract "7" on both sides.
\(\begin{gathered} 4c+7-7=23-7 \\ 4c=16 \end{gathered}\)Then we need to divide both sides by 4.
\(\begin{gathered} \frac{4c}{4}=\frac{16}{4} \\ c=4 \end{gathered}\)The result of the equation is "c=4".
If the equations below are true, find the value of x + z.
(4x + 2y + 8z = 30
(3x +2y + 7z = 24
Answers
If the given equations are true, then the value of x + z is 6.
Simultaneous equations or systems of equations are two or more equations in algebra that must be solved jointly. The number of equations must match the number of unknowns for a system to have a singular solution.
Consider the equations are true,
4x + 2y + 8z = 30 ------------(1)
3x + 2y + 7z = 24 ------------(2)
Now,
By subtracting equation (2) from equation (1) we get:
eq(1) - eq(2)
4x + 2y + 8z - ( 3x + 2y + 7z ) = 30 -24
4x + 2y + 8z - 3x - 2y - 7z = 6
( 4x - 3x ) + ( 2y - 2y ) + ( 8z - 7z ) = 6
x + 0 + z = 6
x + z =6
Therefore, assuming the equations to be true the value of x + z is equal to 6.
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What is (5⁴) (5³) simplified
Answers
Answer:
5^7 or 78125
Step-by-step explanation:
An airline claims that it rarely loses a passenger's checked luggage, and, if checked luggage is lost, 90% of the luggage is recovered and returned to the owner within 24 hours. A consumer group believes the 24-hour recovery rate of lost luggage is actually lower (worse) than the airline's claim. They surveyed a large random sample of the airline's customers and found that 103 of 122 people who had lost luggage were reunited with the missing items within 24 hours. Is this enough evidence to claim the proportion of people who lost luggage with this airline a
Answers
The number that corresponds to the null hypothesis and the alternative hypothesis will be 3 and 6 respectively.
What is a null hypothesis?Specify the correct number from the list below that corresponds to the appropriate null and alternative hypotheses for this problem.
It should be noted that the null hypothesis suggests that there's no statistical relationship between the variables.
The alternative hypothesis is different from the null hypothesis as it's the statement that the researcher is testing.
In this case, the number that corresponds to the null hypothesis and the alternative hypothesis will be 3 and 6 respectively.
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. given a sphere, a great circle of the sphere is a circle on the sphere whose diameter is also a diameter of the sphere. for a given positive integer n, the surface of a sphere is divided into several regions by n great circles, and each region is colored black or white. we say that a coloring is good if any two adjacent regions (that share an arc as boundary, not just a finite number of points) have different colors. find, with proof, all positive integers n such that in every good coloring with n great circles, the sum of the areas of the black regions is equal to the sum of the areas of the white regions.
Answers
The only positive integers n that satisfy the condition for every good coloring of a sphere with n great circles, where the sum of the areas of black regions is equal to the sum of the areas of white regions, are powers of 2.
Let's consider the case where n is not a power of 2. If n has an odd prime factor p, then the coloring of the sphere can be arranged in a way that creates a contradiction. We can divide the sphere into p equal parts using p great circles. In each part, we can color half of it black and the other half white. Since p is odd, we will have a larger number of black regions than white regions, leading to an imbalance in their areas.
On the other hand, if n is a power of 2, we can prove by induction that it satisfies the condition. For n = 2, we can divide the sphere into two equal hemispheres and color them differently. Now, assume that for some k, the condition holds for n = \(2^k\). To prove it for n = \(2^{(k+1)}\), we can take the sphere divided by \(2^k\) great circles and replicate it k times, creating a larger sphere divided by \(2^{(k+1)}\) great circles. By alternating the colors of the replicated regions, we ensure that adjacent regions have different colors, and the areas of black and white regions remain balanced.
Hence, the only positive integers n that satisfy the condition are powers of 2.
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