a survey of 100 high school students provided this frequency table on how students get to school: what is the probability that a randomly selected student either takes the bus or walks

The amount of money in Lucia's account after 5 years will be $1,105.5.

A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.

We know that the compound interest is given as

A = P(1 + r)ⁿ

Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.

Lucia opened a savings account and deposited $600.00 as principal. The account earns 13% interest, compounded annually. Then the amount of money after 5 years will be given as,

A = $600 × (1 + 0.13)⁵

A = $600 × (1.13)⁵

A = $600 × 1.84

A = $1,105.5

The amount of money in Lucia's account after 5 years will be $1,105.5.

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The average velocity between 3 and 6 seconds will be found with the following equation:

Answer:

1 and -4

Step-by-step explanation:

The vertical asymptote of a function is gotten by equating the denominator of such function to zero.

Given

f(x) = 4x+8/x^2+3x-4

The vertical asymptotes is expressed as;

x^2+3x-4 = 0

Factorize

x^2+4x-x-4 = 0

x(x+4) -1 (x+4) = 0

(x-1)(x+4) = 0

x-1 = 0 and x+4 = 0

x = 1 and x = -4

Hence the vertical asymptotes of the function are 1 and -4

By combinations, there are 210 10 bit strings which contains exactly 4 ones.

To find out how many 10-bit strings there are that contain exactly 4 ones, we can use the binomial coefficient formula.

The binomial coefficient formula is given by `C(n, k) = n! / (k! * (n-k)!)`,

where,

n is the total number of items, and k is the number of items

we want to choose from n. In this case, we want to choose 4 ones from 10 bits, so n = 10 and k = 4. Therefore, the number of 10-bit strings that contain exactly 4 ones is:

`C(10, 4) = 10! / (4! * (10-4)!) = 210`.

Hence, there are 210 10-bit strings that contain exactly 4 ones.

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It will take Sienna Rose 6 years and 3 months for her money to grow to $7000 at an annual interest rate of 3.60%, compounded monthly.

To remedy this hassle, we are able to use the formula for compound interest:

a = \(p(1 + r/n)^{(nt)\)

where a is the quantity of money after t years, p is the initial primary, r is the once-a-year hobby rate, n is the number of times the hobby is compounded in keeping with 12 months, and t is the time in years. In this example, we recognize that sienna rose invests $4000 at an annual interest charge of three. 60%, compounded monthly. So we've got:

P = $4000

r = 0.036

n = 12

A = $7000

we are able to remedy for t by plugging these values into the formula and fixing for t:

7000 = \($4000(1 + 0.036/12)^{(12t)}\)

7000/4000 = \((1 + 0.036/12)^{(12t)}\)

1.75 = \((1 + 0.003)^{12t}\)

ln(1.75) = 12t ln(1.003)

t = ln(1.75)/(12 ln(1.003))

t ≈ 6.25 years

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If the perimeter of the train ticket is 60 centimeters and it's length is 17 centimeter long it's height is 13 centimeter

A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length.

To find the perimeter of a rectangle we add all this sides together. This means that the perimeter of a rectangle is given as ;

P = l+l+w+w

P= 2(l+w)

60 = 2( 17+w)

60 = 2( 17+w)

17+w= 60/2

17+ w = 30

w = 30-17

w = 13cm

Therefore the height of the train ticket is 13cm

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Answer:

  see attached

Step-by-step explanation:

You want to use q=4 to show q×q³ = q⁴.

The attachment shows your calculator can help with this. It will compute and display the powers of values without requiring the intermediate calculations.

  4 × 4³ = 4 × 64 = 256

 4⁴ = 256 . . . . . . equivalent to 4 × 4³

An exponent signifies repeated multiplication in the same way a coefficient signifies repeated addition.

  4 × 4³ = 4 × (4·4·4) = 4·4·4·4 . . . . . using the associative property of multiplication

  4⁴ = 4·4·4·4 . . . . . . . equivalent to 4 × 4³

__

Additional comment

In literal terms, ...

  q×q³ = q·q·q·q = q⁴

Among the given options, an R-squared value of 0.5 is the most satisfactory as it indicates a moderate level of relationship between the variables. So, the correct option is b.

R-squared is a statistical measure that represents the proportion of the variance in the dependent variable that can be explained by the independent variable(s). It ranges from 0 to 1, with 1 indicating a perfect fit and 0 indicating no relationship between the variables.
In this case, an R-squared value of 0.5 means that 50% of the variance in the dependent variable can be explained by the independent variable(s). This is considered a moderate level of explanatory power.

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Answer:

22.05

Step-by-step explanation:

Answer:

22.05

Step-by-step explanation:

Using it's concept, the probability a person tests positive who does not actually have Tuberculosis is:

c. 49/148.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, there are 198 + 98 = 296 people who test positive, which is the number of total outcomes, and of those, 98 do not have the disease, which is the number of desired outcomes. Hence the probability is given by:

p = 98/296 = 49/148.

Which means that option c is correct.

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The probability a person tests positive who does not actually have Tuberculosis is 1/100

The probability is given as:

The probability a person tests positive who does not actually have Tuberculosis.

This is a conditional probability, and it can be calculated using

P = n(Tests positive | Does not have Tuberculosis)/n(Does not have Tuberculosis)

Using the given table of values, we have:

P = 98/9800

Evaluate the quotient

P = 1/100

Hence, the probability a person tests positive who does not actually have Tuberculosis is 1/100

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The slope of the line through (-2,3) and (1,-3) is -2.

Y = mx + b, where m is the line's slope and b is the y-intercept, is the slope-intercept form of a linear equation (the point where the line intersects the y-axis). This form is helpful because, given a line's equation, it enables us to quickly determine the slope and y-intercept. By charting the y-intercept and utilising the slope to identify additional points on the line, we can also use this technique to graph a line. We can also create an equation for a line given its slope and y-intercept using this approach.

The slope of the line is given as:

slope = (y2 - y1) / (x2 - x1)

Substituting the value of the given coordinates we have:

slope = (-3 - 3) / (1 - (-2))

slope = -6 / 3

slope = -2

Hence, the slope of the line through (-2,3) and (1,-3) is -2.

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The minimum yield value of the key material should be determined based on the yield stress of the shaft, which is 36 kg/m², the dimensions of the key, and the safety factor of 2.

To ensure that the key smoothly transmits the torque of the shaft, it is essential to choose a key material with a minimum yield value that can withstand the applied forces without exceeding the yield stress of the shaft.

The dimensions of the key given are 20x20x120 mm. To calculate the torque transmitted by the key, we need to consider the dimensions and the applied forces. However, the specific values for the applied forces are not provided in the question.

The safety factor of 2 indicates that the material should have a yield strength at least twice the expected yield stress on the key. This ensures a sufficient margin of safety to account for potential variations in the applied forces and other factors.

To determine the minimum yield value of the key material, we would need additional information such as the expected torque or the applied forces. With that information, we could calculate the maximum stress on the key and compare it to the yield stress of the shaft, considering the safety factor.

Please note that without the specific values for the applied forces or torque, we cannot provide a precise answer regarding the minimum yield value of the key material.

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The probability that a randomly chosen point within the square satisfies the condition is approximately 0.215.

Let's label the four corners of the square ABCD in the following way:

A---B

|   |

D---C

Assuming that the point is chosen uniformly at random within the square, we can approach this problem using geometry.

Let P be the randomly chosen point within the square. We want to find the probability that the distance from P to A and the distance from P to C are both no greater than 1.

Consider the circle centered at A with radius 1, and the circle centered at C with radius 1. These two circles intersect in two points, which we can label X and Y as shown below:

A---B

| X |

D---C Y

If P is inside the square ABCD and within the intersection of the two circles, then the distance from P to A and the distance from P to C are both no greater than 1. In other words, the region of points that satisfy the condition we're interested in is the intersection of the two circles.

To find the area of this intersection, we can use the formula for the area of a circular segment. Let r be the radius of the circles (in this case, r = 1), and let d be the distance between A and C (which is also the length of the diagonal of the square, so d = sqrt(2)). Then the area of the intersection of the two circles is:

2 * (area of circular segment) - (area of parallelogram)

where the factor of 2 comes from the fact that there are two circular segments (one from each circle). The area of a circular segment with angle theta and radius r is:

(r^2 / 2) * (theta - sin(theta))

where theta is the angle between the two radii that define the segment. In this case, since the two circles intersect at right angles, the angle between the radii is pi/2. So the area of a single circular segment is:

(1/2) * (pi/2 - sin(pi/2))

= (1/2) * (pi/2 - 1)

= (pi - 2) / 4

The area of the parallelogram is just d/2 times the distance from X to Y, which is also d/2. So the area of the parallelogram is (d/2)^2 = 1/2.

Putting everything together, we get:

2 * (area of circular segment) - (area of parallelogram)

= 2 * [(pi - 2) / 4] - 1/2

= (pi - 5) / 4

This is the area of the intersection of the two circles, which is the probability that the randomly chosen point P satisfies the condition we're interested in. So the answer to the problem is:

(pi - 5) / 4

≈ 0.215

Therefore, the probability that a randomly chosen point within the square satisfies the condition is approximately 0.215.

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Answer:

Step-by-step explanation:

Volume of a rectangular solid = l × w × h

where

l is the length

w is the width

h is the height

From the question

l = 12 feet

w = 3 feet

h = 4 feet

Volume = 12 × 3 × 4

= 144 feet

Hope this helps you.

It cannot be determined. At least one other point on the line is needed to determine if x is proportional to y

Given data ,

A point on a straight line has an x-coordinate of 3 and a y-coordinate of 6

Now , A single point on a straight line does not define the connection between x and y. We must evaluate the connection between x and y for several places on the line in order to establish if x is proportional to y.

As a result, the relationship between x and y cannot be inferred only from the supplied location (3, 6). To establish the proportionality between x and y, at least one more point on the line is required

Hence , the equation of line is solved

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Answer:

5.0 x 10^{4}

Step-by-step explanation:

To encrypt the message m = 892383 using Alice's RSA public key (n, e) = (2038667, 103), Bob computes the ciphertext c as c ≡ \(m^e\) (mod n).

Substituting the given values, we have c ≡ \(892383^103\) (mod 2038667). Calculating this congruence will yield the ciphertext c.

To find Alice's private key (n, d), we need to calculate d such that e⋅d ≡ 1 (mod ϕ(n)). Since p = 1301 divides n, we can determine the prime factorization of n as n = p⋅q, where q is the other prime factor. Then, ϕ(n) = (p - 1)(q - 1).

Next, we solve for d using the equation e⋅d ≡ 1 (mod ϕ(n)). In this case, e = 103, and we substitute the values of p, q, and ϕ(n) to find d.

To decrypt the ciphertext c = 317730 using Alice's private key (n, d), Alice computes the message m as m ≡ \(c^d\) (mod n). Substituting the given values, we have m ≡ \(317730^d\) (mod 2038667). Calculating this congruence will yield the original message m.

In summary, (a) Bob computes the ciphertext c using the public key, (b) Alice's private key (n, d) can be determined using the prime factorization and the equation e⋅d ≡ 1 (mod ϕ(n)), and (c) Alice decrypts the ciphertext c using her private key to obtain the original message m.

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Answer: 3.51

Step-by-step explanation:

Answer: The tip was 3.50$

Step-by-step explanation: Since the tip is 20% you would times the given amount by 20 then divide it by 100.

20 x 17.53 / 100 = 3.506

We're rounding to the nearest cent, so that would be 3.50.

There is no such vector-valued function r(t) that satisfies the given condition.

I. There is no such vector ū that satisfies u + ū = (1, 2) because if we add any vector to u, we change its direction and magnitude, but the vector ū should have the same magnitude and opposite direction to u.

II. Let v = (1, 3, -1). Then u + v = (2+1, 1+3, 3-1) = (3, 4, 2) and u x v = (-5, 7, -1). So u x v = u + v. Therefore, v satisfies the given condition.

III. There is no such vector-valued function r(t) because if r(t) = (x(t), y(t)) satisfies the condition that r'(t) = 2r(t), then we have:

x'(t) = 2x(t) and y'(t) = 2y(t)

These are two separate first-order differential equations, which have general solutions of the form:

x(t) = c1e^(2t) and y(t) = c2e^(2t)

where c1 and c2 are constants determined by the initial conditions. However, the vector-valued function r(t) = (x(t), y(t)) cannot have a constant magnitude because its components are functions of t that grow exponentially with time. Therefore, there is no such vector-valued function r(t) that satisfies the given condition.

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Answer:

40 did it on edge

Step-by-step explanation:

The unit rate of calories per ounce will be 40 calories/ ounce

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

We are given that 4-ounce container of Greek yogurt contains 160 calories and it is to calculate for one ounce calories contain in Greek yogurt :

4-ounce = 160

1- ounce = 160/4

=40

Therefore, the unit rate of calories per ounce = 40 calories/ ounce.

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Answer:

b = 2 + sqrt13, 2 - sqrt13

v = 2, - 6

Sorry if you need to show work it's really hard to type it out since I don't have the symbols

The probability that the article will have no errors is approximately 0.0233.

To solve this problem, we can use the formula for the probability of an event, which is the number of favorable outcomes divided by the total number of outcomes.

Let's first find the probability that the article is typed by the first typist. Since the article is equally likely to be typed by either typist, this probability is 1/2.

Now, we need to find the probability that the article has no errors given that it is typed by the first typist. We know that the average number of errors per article typed by the first typist is 3.5, so the probability that an article typed by the first typist has no errors is given by the Poisson distribution with λ = 3.5:

P(X = 0) = e^(-λ) * λ^0 / 0! = e^(-3.5) * 3.5^0 / 1 = e^(-3.5) ≈ 0.0302

Similarly, we can find the probability that the article has no errors given that it is typed by the second typist. This probability is given by the Poisson distribution with λ = 4.1:

P(X = 0) = e^(-λ) * λ^0 / 0! = e^(-4.1) * 4.1^0 / 1 = e^(-4.1) ≈ 0.0164

Finally, we can use the law of total probability to find the probability that the article has no errors:

P(X = 0) = P(X = 0 | typed by first typist) * P(typed by first typist) + P(X = 0 | typed by second typist) * P(typed by second typist)

= 0.0302 * 1/2 + 0.0164 * 1/2

= 0.0233

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To determine if the given series converge or diverge, we can use various tests.

(a) Σk(ln(k))2: We can use the integral test. Let f(x) = (ln(x))^2, then f'(x) = 2ln(x)/x, which is positive and decreasing for x ≥ e. Thus, f(x) is decreasing for x ≥ e. Then, by the integral test, since ∫e^∞ (ln(x))^2 dx = lim t→∞ [(t ln(t) - t)/2] = ∞, the series diverges.

(b) Σ1/(k ln(k)): We can use the integral test. Let f(x) = 1/(x ln(x)), then f'(x) = -1/(x ln(x))^2, which is negative for x ≥ e. Thus, f(x) is decreasing for x ≥ e. Then, by the integral test, since ∫e^∞ 1/(x ln(x)) dx = lim t→∞ (ln(ln(t))) = ∞, the series diverges.

(c) Σk-1/e^k: We can use the ratio test. We have |(k/e^k+1)/(k-1/e^k)| = e/(1+k) → 0 as k → ∞, so the series converges.

(d) Σ1/(1+√k): We can use the limit comparison test with Σ1/√k. Let a_k = 1/(1+√k) and b_k = 1/√k, then lim k→∞ a_k/b_k = lim k→∞ √k/(1+√k) = 1, which is finite and positive. Since Σ1/√k converges (p-series with p=1/2), Σ1/(1+√k) also converges.

(e) Σk3+5e^24k2/k: We can use the ratio test. We have |((k+1)^3+5e^24(k+1)^2)/k+1)/(k^3+5e^24k^2)/k| = |(k+1)(k^2+3k+1)+5e^24(k+1)^2|/(k^3+5e^24k^2) → ∞ as k → ∞, so the series diverges.

(f) Σ1/k!: We can use the ratio test. We have |1/(k+1)!/1/k!| = 1/(k+1) → 0 as k → ∞, so the series converges.

Based on your input, I will provide you with the convergence or divergence of the given series.

(a) Σ (k(ln(k))^2): This series diverges as the terms do not approach zero and grow without bound due to the k factor.

(b) Σ (1/ln(k)): This series diverges using the integral test as the integral of 1/ln(x) from 2 to infinity is divergent.

(c) Σ (k^(-1)/((k^3)+5)): This series converges using the comparison test. The given series is smaller than the convergent p-series Σ (1/k^2) for all k.

(d) Σ (1/(1+√k)): This series diverges using the comparison test. The given series is larger than the divergent harmonic series Σ (1/k) for all k.

(e) Σ (e^(2k)/(k^2)): This series diverges as the terms do not approach zero and grow without bound due to the e^(2k) factor.

(f) Σ (k!/k^2): This series diverges as the terms do not approach zero and grow without bound due to the k! factor.

Please let me know if you have any further questions!

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Answer:

true

Step-by-step explanation:

Answer:

true

Step-by-step explanation:

the square root of 9 is 3 and its a whole number

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Answer:

Step-by-step explanation:

find a number that can go into 30 and go and then what ever you get multiply it with five and X will be your answer

The vector in the plane of b and c whose projection on a has a magnitude of sqrt(2/3) is option C: 2i - j + 5k.

To find a vector in the plane of b and c whose projection on a has a magnitude of sqrt(2/3), we need to find the component of a that lies in the plane of b and c. This can be done by finding the orthogonal projection of a onto the plane of b and c.

The plane of b and c can be represented by the cross product of b and c:

n = b × c = (i + 2j - k) × (i + j - 2k)

  = i(j*(-2) - (-k)*1) - (i*(-2) - (-k)*1) + (i*(1) - (i)*(-2))

  = -3i + 5k

The projection of a onto the plane of b and c can be found using the dot product:

proj = (a · n) / |n|

    = ((2i - j + k) · (-3i + 5k)) / sqrt((-3)^2 + 5^2)

    = (-6 - 5) / sqrt(9 + 25)

    = -11 / sqrt(34)

Now, we can find the vector in the plane of b and c by scaling the normal vector n by the magnitude of the projection:

vector = (proj / |n|) * n

      = (-11 / sqrt(34)) * (-3i + 5k)

      = (33 / sqrt(34))i - (55 / sqrt(34))k

Simplifying this vector, we get:

vector = (33 / sqrt(34))i - (55 / sqrt(34))k

Comparing this with the given options, we see that the vector (33 / sqrt(34))i - (55 / sqrt(34))k matches option C: 2i - j + 5k.

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Complete Question

Let a=2i−j+k,b=i+2j−k and c=i+j−2k be three vectors. A vector in the plane of b and c whose projection on a is of magnitude  sqrt (2/3)  is what?

A 2i+3j-3k

B 2i+3j+3k

C 2i-j+5k

D 2i+j+5k

Answer:

The answer should be -7k

Step-by-step explanation:

here's how to do it

take the - from (-7) and put it here -k×7 because multiplying a positive and a negative equals a negative.

then when you put them in order you should get -7k

sorry if they doesn't explain well but I hope it helped!

Answer:

b=62

Step-by-step explanation:

3(2)^2+2(5)^2

3*4+2*25

12+50=62

Option (a) is correct. There is only a 2% chance that we would get a correlation coefficient as big as or bigger than the one observed if the null hypothesis were true.

If a correlation coefficient has an associated probability value of .02, it means that there is only a 2% chance that we would get a correlation coefficient this big (or bigger) if the null hypothesis were true.

This probability value, also known as the p-value, indicates the likelihood of observing the data or more extreme data if the null hypothesis were true. In this case, the null hypothesis would be that there is no correlation between the two variables being analyzed.

Therefore, option (a) is correct. There is only a 2% chance that we would get a correlation coefficient as big as or bigger than the one observed if the null hypothesis were true.

This means that the results are statistically significant, suggesting that there is a relationship between the variables being analyzed.

Option (b) is also correct. The results are important because they suggest that there is a significant relationship between the variables being analyzed.

This information can be used to inform decision-making and further research.

Option (c) is incorrect. We should not accept the null hypothesis because the p-value is less than the commonly used alpha level of 0.05.

This means that we reject the null hypothesis and conclude that there is a relationship between the variables.

Option (d) is also incorrect. The hypothesis has not been proven but is rather supported by the evidence.

Further research is needed to confirm the relationship between the variables and to determine the strength and direction of the relationship.

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Answer:

scientific notation = 2.226 * 10^8

Standard form = 222600000

As it is 22.26 * 10^7

Step-by-step explanation:

(5.3x10^4)(4.2x10^3)

Since all the numbers are being multiplied by each other, one can use the associative property to change the order in which they are multiplied.

5.3 x 10^4 x 4.2 x 10^3

= 5.3 * 4.2 * 10^4 * 10^3

= 22.26 * 10^7

Either convert back to scientific notation, standard form or keep as it is.

scientific notation = 2.226 * 10^8

Standard form = 222600000

As it is 22.26 * 10^7