In the rectangle shown below, tan x=1/4
the ratio of AB to BC is 10:3
work out the length of AC in cm

Answer: 1.5

Explanation: Searched enough until all sources said 1.5

Hope this helps!

Answer: C

Step-by-step explanation:

if x is less than or equal to -3 then the color on the number line would have to go to the left and cover the lower numbers and the circle on the -3 has to be filled in to be equal to x.

Answer:

Divide each term in the problem by 3 and simplify.

Step-by-step explanation:

Exact Form: [tex]x= \frac{8}{375}[/tex]

Decimal Form: [tex]x= 0.0213[/tex]

Hope this helps!

Answer:

s ≤ 9

Step-by-step explanation:

Let's call the number of miles Eugene needs to ride in the next 3 hours "x". Then, to meet his goal of riding at least 40 miles today, the total number of miles he will ride can be expressed as:

13 + x

Since he has 3 more hours to ride, he needs to ride at a certain average speed (in miles per hour) to cover the remaining distance "x" within these 3 hours. Let's call this speed "s".

Then, we can write an inequality to represent this situation as:

x/s ≤ 3

This inequality says that the distance "x" divided by the speed "s" should be less than or equal to 3 hours. Multiplying both sides by "s", we get:

x ≤ 3s

Now, we can combine this inequality with the expression for the total distance Eugene needs to ride:

13 + x ≥ 40

This inequality says that the sum of the distance Eugene already rode (13 miles) and the remaining distance he needs to ride ("x") should be greater than or equal to 40 miles.

Substituting x ≤ 3s into this inequality, we get:

13 + 3s ≤ 40

Solving for s, we get:

3s ≤ 27

s ≤ 9

Therefore, Eugene needs to ride at a speed of at least 9 miles per hour in the next 3 hours to meet his goal of riding at least 40 miles today.

Ric was slightly faster than Tom with a speed of 13.54 km/h compared to Tom's speed of 13.33 km/h.

The speed of an object, also known as v in kinematics, is the size of the change in that object's position over time or the size of the change in that object's position per unit of time, making it a scalar number.

To calculate the speed of Tom and Ric, we can use the formula:

Speed = Distance / Time

For Tom:

Speed = 10 km / (45 minutes / 60 minutes per hour) = 13.33 km/h

For Ric, first translate 1 hour and 2 minutes into hours as follows:

1 hour 2 minutes = 1.0333 hours (since 1 minute is 1/60 of an hour)

Speed = 14 km / 1.0333 hours = 13.54 km/h

So, with a speed of 13.54 km/h as opposed to Tom's 13.33 km/h, Ric was just a little bit quicker than Tom.

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The Princeton Playhouse sold 60 adult tickets and 90 child tickets were sold if the playhouse sold $2940 worth of tickets.

Let's solve the issue with an equation method.

Let a represent the quantity of adult tickets sold and c represent the quantity of kid tickets sold. As a result of our knowledge that 150 passes were sold altogether, we have:

a + c = 150

We also know that $2940 in total was raised from the selling of tickets. One adult ticket costs $20.50, while one minor ticket costs $15.50. These amounts are the totals. Consequently, we have:

20.50*a + 15.50*c = 2940

Our system of two equations now has two factors. We have two options for resolving it: substitution and removal. Here, we'll employ the replacement approach.

The first solution for a can be solved as follows:

a = 150 - c

By replacing an in the second equation with this formula, we obtain:

20.50(150 - c) + 15.50*c = 2940

By enlarging and condensing, we obtain:

3075 - 5*a = 2940

Restoring for a results in:

3075 - 5(150 - c) = 2940

By enlarging and condensing, we obtain:

c = 90

As a result, 90 children's tickets were distributed. By applying the first equation, we can determine the quantity of adult passes sold:

a + c = 150

a + 90 = 150

a = 60

Consequently, 60 adult tickets were distributed.

In conclusion, the Princeton Playhouse sold 60 seats for adults and 90 for children.

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The answer is (-5,3), since both Point F and Line D are 5 units away from point (-5,3).

Answer:

11x - 5y

Step-by-step explanation:

group 1 : 5x + 6x = 11x

group 2 : -2y -3y = -5y

starting with x terms

11x - 5y

Answer:

5

Step-by-step explanation:

Sketch the diagram

AE is equal to the other half of the diagonal EC

3x + 12 = 27

Subtact 12 from both sides

3x = 15

Divide both sides by 3

X = 5

let the ratio be given by x : 2x : 3x.

[tex]\longrightarrow \: x + 2x + 3x = 360[/tex]

[tex]\longrightarrow \: 6x = 360[/tex]

[tex]\longrightarrow \: x = \frac{360}{6} [/tex]

[tex]\longrightarrow \: x = 60[/tex]

The smallest no. is 60.

The exact value of the cosine of the angle BAC is 1 / √10.

The length of the sides of a triangle can be found using the distance formula:

d = √[(x2 - x1)² + (y2 - y1)² + (z2 - z1)²]

To find the length of the side AB, we plug in the coordinates of A and B into the distance formula:

AB = √[(4 - 2)² + (2 - 2)² + (1 - 2)²] = √[4 + 0 + 1] = √5

Similarly, we can find the length of the other two sides:

BC = √[(2 - 4)² + (3 - 2)² + (1 - 1)²] = √[4 + 1 + 0] = √5

CA = √[(2 - 2)² + (3 - 2)² + (1 - 2)²] = √[0 + 1 + 1] = √2

The shortest side of the triangle S is CA, with a length of √2 units.

To find the cosine of the angle BAC, we can use the law of cosines:

cos(BAC) = (AB² + CA² - BC²) / (2 * AB * CA)

Plugging in the values we found for the lengths of the sides:

cos(BAC) = (√5² + √2² - √5²) / (2 * √5 * √2) = (5 + 2 - 5) / (2 * √10) = 2 / (2 * √10) = 1 / √10

Therefore, it can be stated that the precise value of the cosine of angle BAC is 1 /√10.

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Exercise 11.14 states that we must prove Theorem 11.7, given that the polynomial ring Fp[x] has irreducible polynomials of arbitrarily high degree for every prime number p. It means that there is no positive integer n such that all the irreducible polynomials of F[x] have degree less than or equal to n.

Theorem 9.4 states that the ring of polynomials K[x] with coefficients in a field K contains infinitely many irreducible monic polynomials. These two theorems will be used in the following proof of Theorem 11.7.Proof :
Let Fp[x] be a polynomial ring with p as a prime number.

The number of polynomials of degree at most n in Fp[x] can be expressed as follows:{n + 1 + p − 1\choose p − 1} = {n + p \choose p},where we have applied Theorem 9.4 to determine the number of monic irreducible polynomials of degree n over Fp. For every prime number p and any positive integer n, the number of irreducible polynomials in Fp[x] of degree at most n is less than or equal to {n + p \choose p}.'

Now, suppose there exists an integer N such that all irreducible polynomials of Fp[x] have degree less than or equal to N. Then the number of irreducible polynomials of Fp[x] with degree at most N is {N + p \choose p}.Since Theorem 9.4 shows that there are infinitely many irreducible polynomials in K[x] for any field K, there exists a prime p and a monic irreducible polynomial of degree greater than N in Fp[x].

Hence, this contradicts the previous assumption that there is an N that bounds the degree of all irreducible polynomials in Fp[x].Therefore, we have proved that for every prime number p, the polynomial ring Fp[x] has irreducible polynomials of arbitrarily high degree, and this is Theorem 11.7.

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The correlation coefficient, denoted by r, can take values between -1 and 1 inclusive.

If r = -1, this indicates a perfect negative correlation, meaning that as one variable increases, the other variable decreases in a perfectly linear fashion.

If r = 0, this indicates no correlation or a very weak correlation between the two variables.

If r = 1, this indicates a perfect positive correlation, meaning that as one variable increases, the other variable increases in a perfectly linear fashion.

For all other values of r between -1 and 1, the strength and direction of the correlation vary. Values of r closer to -1 or 1 indicate a stronger correlation, while values of r closer to 0 indicate a weaker correlation. The sign of r indicates the direction of the correlation: a positive sign indicates a positive correlation, while a negative sign indicates a negative correlation.

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Step-by-step explanation:

I'm sorry, but the driving distance between Buffalo, NY, and Rochester, NY, is not 117,456 kilometers. In fact, it is approximately 112 kilometers (69.5 miles) via the New York State Thruway (I-90).

To round this distance to the nearest tenth, we would round to one decimal place, which gives us:

112 kilometers rounded to the nearest tenth = 112.0 kilometers.

a) P(te < 23) = 0 and (b) P(te < 32) = 4.02 and The probability of 95% that the project will be completed is 16 days.

The probability of an event is a number that indicates the probability of the event occurring. Expressed as a number between 0 and 1 or as a percent sign between 0% and 100%. The more likely an event is to occur, the greater its probability. The probability of an impossible event is 0; the probability of a certain event occurring is 1. The probabilities of two complementary events A and B - either A occurring or B occurring - add up to 1.

According to the Question:

Value of probability 95% = 3

   Z =  Tₐ-Tₙ/σ

⇒ 3 = Tₐ - 10/2

⇒ Tₐ = 16 days.

Therefore, the probability 95 percent that the project will be completed is 16 days.

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The given function rule is:

f(x) = 2x - 5. Therefore, the finished function table will end at 5.

We must assess the function f(x) for each value of x given in order to finish the function table:

For x = -3:

f(-3) = 2(-3) - 5 = -6 - 5 = -11

For x = 0:

f(0) = 2(0) - 5 = -5

For x = 1:

f(1) = 2(1) - 5 = -3

For x = 4:

f(4) = 2(4) - 5 = 3

For x = 5:

f(5) = 2(5) - 5 = 5

The finished function table is as follows:

x f(x)

-3 -11

0 -5

1 -3

4 3

5 5

ending at variable 5.

The function rule that is provided is:

f(x) = 2x - 5

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Answer: You save $25.00

Step-by-step explanation:

4.49 minus 3.99 = .50 cents

4.49 times 50 = 224.50

.50 cents times 50 = 25.00

224.50 - 25.00 =199.50

Three boys share R2100 in ratio 3:5:7 and the first boy will get R420, the second boy will get R700, and the third boy will get R980.

To determine how much each boy will receive, we must add up the ratios, which equals 3 + 5 + 7 = 15

To determine how much each boy will receive, we must add up the ratio, which equals 

In other words, the R2100 is split into 15 equal parts.

We can divide the overall amount by 15 to determine the value of each component:

R2100 ÷ 15 = R140

Accordingly, each component is valued R140.

We can multiply their ratio by R140 to determine the amount that each guy will receive:

First boy's share:

3 parts × R140 = R420

Second boy's share:

5 parts × R140 = R700

Third boy's share:

7 parts × R140 = R980

The first boy will receive R420, the second boy R700, and the third boy R980 as a result.

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Yes, the system is consistent. This is because the number of pivot columns (3) is equal to the number of unknowns in the system (3).

This means that the system has a unique solution that can be determined by performing Gaussian Elimination or other linear algebra techniques.

If the coefficient matrix for a system has n columns, and there are only n pivots, then the system is consistent because every equation has a pivot column.

In this case, the matrix has three pivot columns, therefore the system is consistent because each equation has a pivot column.

Therefore, the system is consistent.

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Answer: that would have been £21

Step-by-step explanation: have a good day

Answer:

21

Step-by-step explanation:

30% of 70 is 70% of 30

0% of 30 can be found by 30/10 which is 3

we need 70 percent, so 3*7 will get us 70%, which is 21

(0, 7) adding ordered pairs to the set {(0, 1), (2, 4), (3, 5)} would make it not a function.

A function is a relationship between a number of inputs and outputs. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. There is a range, codomain, and domain for every function. The graph is a function if any vertical line drawn can cross it at no more than one point. The graph is not a function if there is any location where a vertical line can cross it at two or more points. The relationship between the input or domain and the output or range is known as the function rule. A relation is a functional if and only if each subdomain value has a single value in the range.

Determine whether {(0, 1), (2, 4), (3, 5)} is a function.

True.

(0, 7) adding ordered pairs to the set {(0, 1), (2, 4), (3, 5)} .

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Answer:

x > 3   or   3 < x < infinity

Step-by-step explanation:

Since the circle over 3 is "open" (not filled in), this means that the symbol we use for the inequality is simply "greater than" rather than "greater than/equal to".

Additionally, there is no point on the right side; it is an infinite arrow. This means that x is equivalent to anything above 3.

Therefore, x is greater than 3 is the correct inequality. Depending on the answer your teacher is looking for, however, it could also be 3 < x < infinity. this is because there is no visible end to the arrow.

*As I don't know what you're focusing on, I cannot tell you which answer your teacher is looking for. Base your answer off the form of the answers of the lesson you are focusing on.

The "standard error" (SE) of the sample mean is equal to p/√n, approximately normally distributed, and represents the shape of the sample distribution.

The mean of the binomial distribution is np.

p is the population standard deviation and √(p(1-p)/n) is the standard error (SE) of the "sampling distribution" of the sampling proportion.

The "sampling distribution" of the "sampling mean" has an approximately normal distribution with mean mu and standard error sigma/sqrt(n) as long as n is greater than or equal to 30 or X follows a normal distribution.

Therefore, p/√n approximates the shape of the sample distribution with the sample mean (n).

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Answer:

Let's assume the number of people called is "x".

The ratio of successful signups to the number of people called is 0.125, which can also be written as 1/8. Therefore, the number of successful signups can be expressed as (1/8)x.

We know that the salesperson has 25 signups this month, so we can write the equation as:

(1/8)x = 25

To solve for x, we can multiply both sides by 8:

x = 200

Therefore, the salesperson called 200 people this month.

|-86| = 86 The Badwater Basin, which is 282 feet (86 metres) below sea level, is the lowest place in North America.

The absolute value is always positive. The elevation of the shoreline, or the ocean-land boundary, is referred to as sea level. Land above this altitude is above sea level, whereas land below it is below sea level. When we visit the shoreline, the small strip of land that separates the land from the water, we experience relative sea level. When we observe the shoreline, we can see that it fluctuates throughout the day. Tides and winds affect how the shoreline narrows and widens, but they do not determine the sea level. To eliminate these effects from the calculations, we use mean sea level (MSL). In a specific location, MSL represents the halfway point between mean high tide and mean low tide.

-86 has an absolute value of 86.

Advice: The absolute value is consistently positive.

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Answer:

The graph represents a linear function because there is a constant rate of change.

Step-by-step explanation:

Linear functions have constant rate of change,

For any two points (x1, y1) and (x1, y2), rate of change remains constant, it also represents a straight line.

We know this constant as the slope of line passing through these points

[tex]\dfrac{y_2 - y_1}{x_2 - x_1} = m[/tex]

Therefore, we can say that The graph represents a linear function because there is a constant rate of change.

Hopefully this answer helped you!!

a) The probability that we both lose when you bet on red and I bet on black is 0.463.
b) The probability that at least one of us wins is 0.537.
c) The probability that at least one of us loses is 1.


a) When you bet on red, the probability of losing is 18/38 because the roulette wheel has 18 red spaces out of 38 total spaces. Similarly, the probability of losing when I bet on black is 18/38. Since these are independent events, the probability of both losing is (18/38) × (18/38) = 0.221 or 0.22 (rounded to two decimal places).

Therefore, the probability that we both lose is 0.22 or 22%.

b) The probability that at least one of us wins is equal to the complement of the probability that we both lose. The complement rule states that if P(A) is the probability of event A, then P(not A) = 1 – P(A). In this case, P(both lose) = 0.22, so P(at least one wins) = 1 – P(both lose) = 1 – 0.22 = 0.78 or 78%.

c) The probability that at least one of us loses is 1 because it is impossible for both of us to win at the same time. In other words, the events "you lose" and "I lose" are complementary and exhaustive, which means that their probabilities add up to 1.

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Logn 2logn nlog(n2) nn logn nn2 23n log(log(nn)) is the proper arrangement of the functions under the O notation using just (equivalent) or (strict subset of).

The O notation is used to classify functions according to their growth rates. It is a way of measuring the complexity of an algorithm. The functions are arranged in ascending order of growth rates, with the slowest growing function at the beginning and the fastest growing function at the end.

The function logn has the slowest growth rate, followed by 2logn, which is a constant multiple of logn. The function nlog(n2) has a higher growth rate than 2logn, but is still slower than nn logn. The function nn² has a higher growth rate than nn logn, but is still slower than 23n. The function log(log(nn)) has the highest growth rate of all the functions.

Therefore, the correct arrangement of the functions under the O notation is: logn ⊂ 2logn ⊂ nlog(n2) ⊂ nn logn ⊂ nn² ⊂ 23n ⊂log(log(nn)).

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The cross product of (2i -3j + 4k) and (i + j -7k) is -9i + 18j - 11k.

To calculate this,

use the formula for the cross product, which is:
AxBy - AyBx

The cross product of (2i -3j + 4k) and (i + j -7k) is

(2 × -7) - (-3 × 1)i + (2 × 1) - (4 × -7)j + (3 × -7) - (2 × 1)k

Simplifying the above expression yields -9i + 18j - 11k.

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