what is the value of x

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Zelda can swim at a speed of 75 meters per minute in still water and the rate of the water current is 25 meters per minute.

Let's call Zelda's speed in still water "s" and the rate of the water current "c".

When swimming upstream, Zelda's speed relative to the ground is s - c. When swimming downstream, her speed relative to the ground is s + c.

We're told that Zelda can swim 50 meters per minute upstream, so we can write the equation:

s - c = 50

We're also told that she can swim twice as fast downstream, so:

s + c = 2(50) = 100

Now we have two equations with two variables. We can solve for s by adding the two equations together:

s - c = 50

s + c = 100

(s - c) + (s + c) = 50 + 100

2s = 150

s = 75

So Zelda can swim at a speed of 75 meters per minute in still water.

To find the rate of the water current, we can substitute s = 75 into either of the two equations we wrote earlier. Let's use the first one:

s - c = 50

75 - c = 50

c = 25

So the rate of the water current is 25 meters per minute.

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1)The expression 4x^2-16x+12/x^2-9 is undefined when the denominator, x^2-9, equals zero because division by zero is undefined.

x^2-9 equals zero when x equals 3 or x equals -3. Therefore, the expression is undefined at x = 3 and x = -3. In all other cases, the expression is defined.

2) The given expression is:

(5-2x)/(x+2) + x^2/(x^2-4) - 5

To simplify this expression, we need to first find the LCD (least common denominator) of the two fractions. The denominator of the first fraction is x+2, and the denominator of the second fraction is x^2-4, which can be factored as (x+2)(x-2). So the LCD is (x+2)(x-2). Now we can rewrite the expression with this common denominator:

[(5-2x)(x-2) + x^2(x+2) - 5(x+2)(x-2)] / [(x+2)(x-2)]

Expanding the brackets and simplifying, we get:

(-x^3 - 3x^2 - 3x + 5) / [(x+2)(x-2)]

This expression is undefined when the denominator, (x+2)(x-2), equals zero because division by zero is undefined.

(x+2)(x-2) equals zero when x equals -2 or x equals 2. Therefore, the expression is undefined at x = -2 and x = 2. In all other cases, the expression is defined.

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The population of the country will be twice what it was in 1980 approximately 67.8 years after 1980, which would be around 2047.

To find out when the population will be twice what it was in 1980, we need to set up an equation and solve for t.

Let's first determine the population in 1980:

N(0) = 217e0.0102(0) = 217

So, the population in 1980 was 217 million.

Now, we want to find out when the population will be twice that amount:

2(217) = 434

We can set up an equation:

434 = 217e0.0102t

Divide both sides by 217:

2 = e0.0102t

Take the natural logarithm of both sides:

ln(2) = 0.0102t

Solve for t:

t = ln(2)/0.0102

t ≈ 67.8

Therefore, the population of the country will be twice what it was in 1980 approximately 67.8 years after 1980, which would be around 2047.

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Answer:

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

= (3 - 7) / (4 - (-2))

= -4 / 6

= -2/3

Therefore, the value of the parameter m is -2/3.

The equation of a circle with center (-3, -5) and radius 4 is (x+3)^2+(y+5)^2=16.

In the given equation we have to find the equation of circle with center and radius.

The given center is (-3, -5).

Radius = 4

The standard equation of a circle with center and radius.

(x−a)^2+(y−b)^2=r^2

where a and b represent a point of center and r represent a radius.

So a=-3, b=-5 and r=4.

Putting the value in the standard equation.

(x−(-3))^2+(y−(-5))^2=(4)^2

Simplifying

(x+3)^2+(y+5)^2=16

Hence, the equation of a circle with center (-3, -5) and radius 4 is (x+3)^2+(y+5)^2=16.

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The number of degrees of​ freedom is 19 when the sample size is 20.

Given:

Sample size of the first sample, n₁ = 20

Sample size of the second sample, n₂ = 20

Utilizing counts of differences between paired observations from the two groups, one can determine the degrees of freedom of two related populations.

In paired data, each group has an equal number of observations (n = n1 = n2).

Here we have n = n₁ = n₂= 20

The degree of freedom is,

df = n - 1

    = 20 - 1

    = 19

So, the number of degrees of​ freedom is 19 when the sample size is 20.

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Using the slope concept, it is found that the rate of download of the file is of 1920 MB/s.

The slope of a linear function is given by the change in the output divided by the change in the input.

In this problem:

\(m  = \frac{3840}{2} = 1920\)

The rate of download of the file is of 1920 MB/s.

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The term "Objective Function" refers to a mathematical model in linear programming which maximizes as well as minimizes some quantity.

Thus, in either a mathematical optimization problem, the objective function is the real-valued function for whom value must be minimized or maximized well over set of feasible alternatives.

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The bicycles produced from the beginning of week 2 to the end of week 3 are 2926.

To find the number of bicycles produced from the beginning of week 2 to the end of week 3, we will use the given production function P(t) = 95 + 588t^2 - 14t, where t is the number of weeks.

First, we need to find the number of bicycles produced by the end of week 2 and week 3.

To do this, we'll plug in t = 2 and t = 3 into the production function:

P(2) = 95 + \(588(2)^{2}\) - 14(2) = 95 + 588(4) - 28 = 95 + 2352 - 28 = 2419 bicycles

P(3) = 95 + \(588(3)^{2}\) - 14(3) = 95 + 588(9) - 42 = 95 + 5292 - 42 = 5345 bicycles

Now we need to find the difference between the bicycles produced by the end of week 3 and those produced by the end of week 2:

Number of bicycles produced from the beginning of week 2 to the end of week 3 = P(3) - P(2) = 5345 - 2419 = 2926 bicycles

So, the factory produced 2926 bicycles from the beginning of week 2 to the end of week 3.

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Answer:

1/6

Step-by-step explanation:

Out of these four card choices, for the first pick there are two even cards and four cards in total. This means that on the first pick there is a 2/4=1/2 chance that you pick an even card. On the second pick, if you do not replace the card, then there is 1 even card remaining, and 3 cards in total, leaving a probability of 1/3. Multiplying these two probabilities together, you get an overall chance of 1/6. Hope this helps!

The number of names that the teacher can draw is 22! / 17!. The Option D.

Permutation means the mathematical calculation of the number of ways a particular set can be arranged.

The number of permutations of 5 names drawn from 22 will be derived using permutations \(n!/(n-r)!\) where n is total number of items (22) and r is the number of items being selected (5).

= 22! / (22! - 5!)

= 22! / 17!

Therefore, the number of names that the teacher can draw is 22! / 17!.

Full question:

Assume that 22 kids have their names all different put in a hat. The teacher is drawing five names to see who will speak for first, second etc. for the day. How many PERMUTATIONS names can the teacher draw?

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Answer:

22!/17!

Step-by-step explanation:

If we set m = 4 and n = 1, we get a = 15 and c = 17, which means (15, 60, 17) is a primitive Pythagorean triple with b = 4T5. Also, we can find primitive Pythagorean triples with b = 4T6 and b = 4T7 by using the same method. We get (21, 84, 87) for b = 4T6 and (28, 112, 113) for b = 4T7. Therefore, it is clear that for every triangular number Tn, there is a primitive Pythagorean triple (a, b, c) with b = 4Tn

A Pythagorean triple is a set of three integers that satisfy the Pythagorean theorem, which states that the sum of the squares of the lengths of the two shorter sides of a right triangle is equal to the square of the length of the longest side, or hypotenuse. For example, the triple (3, 4, 5) is a Pythagorean triple because 3^2 + 4^2 = 5^2.

Now let's talk about triangular numbers. A triangular number is the sum of the first n positive integers, and it can be represented by the formula Tn = 1 + 2 + 3 + ... + n = (n(n+1))/2. The first few triangular numbers are 1, 3, 6, and 10.

Interestingly, in the list of the first few Pythagorean triples, we can observe a pattern where the value of b is four times a triangular number. For example, in the Pythagorean triple (3, 4, 5), we have b = 4T1. In (5, 12, 13), b = 4T2. In (7, 24, 25), b = 4T3. And in (9, 40, 41), b = 4T4.

So the question is: is this pattern true for all triangular numbers? Let's investigate further.

a) To find a primitive Pythagorean triple (a, b, c) with b = 4T5, we need to find a value of a and c such that a^2 + b^2 = c^2 and b = 4T5. Using the formula for T5, we get T5 = (5(5+1))/2 = 15. Therefore, b = 4T5 = 60. We can use the Euclid's formula for generating Pythagorean triples, which states that for any two positive integers m and n with m > n, a Pythagorean triple (a, b, c) can be generated by a = m^2 - n^2, b = 2mn, and c = m^2 + n^2.

If we set m = 4 and n = 1, we get a = 15 and c = 17, which means (15, 60, 17) is a primitive Pythagorean triple with b = 4T5.

Similarly, we can find primitive Pythagorean triples with b = 4T6 and b = 4T7 by using the same method. We get (21, 84, 87) for b = 4T6 and (28, 112, 113) for b = 4T7.

b) Now, the question is whether there is a primitive Pythagorean triple (a, b, c) with b = 4Tn for any triangular number Tn. Let's assume this is true and try to prove it.

Using the same Euclid's formula, we can generate a primitive Pythagorean triple (a, b, c) with b = 4Tn by setting m = 2Tn+1 and n = Tn. This gives us a = 4Tn^2 + 1 and c = 4Tn^2 + 2Tn + 1, and we can verify that b = 4Tn using the formula for Tn.

Therefore, we have proven that for every triangular number Tn, there is a primitive Pythagorean triple (a, b, c) with b = 4Tn

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Answer:

The annual percent increase in this model is 67%.

Step-by-step explanation:

The given function Y = 4.56(1.67)^x represents an exponential growth model, where x represents the number of years and Y is the value after x years. The base of the exponent, 1.67, represents the growth factor.

To find the annual percent increase, we can convert the growth factor to a percentage increase. Subtract 1 from the growth factor and multiply the result by 100:

(1.67 - 1) * 100 = 0.67 * 100 = 67%

So, the annual percent increase in this model is 67%.

The derivative of F(x) is \(F'(x) = x^{(1/3)\).

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.

To find the derivative of the given function F(x), we will apply the fundamental theorem of calculus and differentiate the integral with respect to x.

Let's compute F'(x):

F(x) = ∫[0 to x] \(t^{(1/3)} dt\)

To differentiate the integral with respect to x, we'll use the Leibniz integral rule:

F'(x) = d/dx ∫[0 to x] \(t^{(1/3)} dt\)

According to the Leibniz integral rule, we have to apply the chain rule to the upper limit of the integral.

\(F'(x) = x^{(1/3)} d(x)/dx - 0^{(1/3)} d(0)/dx\)   [applying the chain rule to the upper limit]

Since the upper limit of the integral is x, the derivative of x with respect to x is 1, and the derivative of 0 with respect to x is 0.

\(F'(x) = x^{(1/3)} (1) - 0^{(1/3)} (0)\)

\(F'(x) = x^{(1/3)\)

Therefore, the derivative of F(x) is \(F'(x) = x^{(1/3)\).

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Answer:

The scale drawing of the pool should be 3 x 8 inches.

Since a rectangular pool in your friend’s yard is 150 ft. × 400 ft, to create a scale drawing with a scale factor of 1 to 600, the following calculation must be performed:

150/600 = 1/4 = 0.25

400/600 = 2/3 = 0.66

1 foot = 12 inches

12 x 0.25 = 3

12 x 0.666 = 8

Therefore, the scale drawing of the pool should be 3 x 8 inches.

Answer:

It may take 20 to 30 seconds.

Step-by-step explanation: Hope this helped

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The average time it took for a tablet to dissolve in water that was 22 °C in temperature was 28.3 seconds.

Any substance that, when consumed, alters the physiology or psychology of an organism qualifies as a drug.

The properties of the API (active pharmaceutical ingredient) such as

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The probability that a customer purchases a biography book given that they purchase cooking and BobVilla books is 0.08.

To calculate this probability, we need to consider the following components:

1. The total number of customers purchasing cooking and BobVilla books: This is the denominator of our equation, and it represents the total number of customers who purchased the two books.

2. The number of customers purchasing the biography book: This is the numerator of our equation, and it represents the number of customers who purchased the biography book.

3. The probability that a customer purchases a biography book given that they purchase cooking and BobVilla books: This is the fraction of customers who purchased the biography book over the total number of customers who purchased the two books.

To calculate the probability that a customer purchases a biography book given that they purchase cooking and BobVilla books, we need to divide the numerator (the number of customers purchasing the biography book) by the denominator (the total number of customers purchasing the two books).

This probability can be expressed as a decimal, which is 0.08. This value can also be rounded to two decimal places, which is 0.08.

In conclusion, the probability that a customer purchases a biography book given that they purchase cooking and BobVilla books is 0.08.

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Answer:

domain should be(-infinty, -infinity), and range should be [3,-infinity)

Step-by-step explanation

its been a while since ive done these, but i think thats the answer.

For the quadratic function in the graph

A quadratic function is a polynomial in which the highest power of the unknown is 2.

Given the graph of a quadratic function with vertex (-2, 3) is shown in the figure below. To find the domain and the range, we proceed as follows

From the graph, we see that the x-values go from -∞ to +∞. This is its domain.

So, its domain is -∞ ≤ x ≤ +∞.

From the graph, we see that the maximum value of y is 3 and the graph tends towards -∞. The y-values is the range of the graph.

So, the range is 3 ≤ y ≤ +∞

So,

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The two inequalities are -1 ≤ 2x+7 AND 2x+7 < 21. The value of  x = 3 is the part of the solution set of this compound inequality.

The given inequality is

-1 ≤ 2x+7 < 21

First we have to split the given equality

-1 ≤ 2x+7 AND 2x+7 < 21

Solve each term of the inequality

-1 ≤ 2x+7

Subtract 7 from both side

-1-7 ≤ 2x+7 - 7

-8 ≤ 2x

Divide the both side by 2

-4 ≤ x

The second inequality part is

2x+7 < 21

Subtract 7 from both side

2x+7-7 < 21 - 7

2x < 14

Divide the both side by 2

x < 7

That means,

-4 ≤ x < 7

Therefore x = 3 is the part of the solution set of this compound inequality

Hence, the two inequalities are -1 ≤ 2x+7 AND 2x+7 < 21.The value of  x = 3 is the part of the solution set of this compound inequality.

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The value of P(1≤x≤3)  is 0.84

What is Probability ?

Probability can be defined as ratio of number of favourable outcomes and total number of outcomes.

P(1≤x≤3) defined the probability that the result is between 1 and 3, included. You can answer this question in two ways:

1. Sum the probabilities of good events:

From the graph, we have

P ( x= 1 ) = 0.32

P ( x = 2 ) = 0.24

P ( x= 3 ) = 0.28

So,

P ( 1 <= X <= 3 ) = 0.32 + 0.24 + 0.28

= 0.84

2. Use complementary probabilities

Asking that the result is 1, 2 or 3 is the same as asking that the result is not 4. The probability that the result is 4 is 0.16, so the probability that the result is not 4 will be

P ( x not equal to 4 ) = 1 - P ( x = 4 )

= 1- 0.16

= 0.84

Therefore, The value of P(1≤x≤3)  is 0.84

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Answer:

The equation that models how far from the tip of the saw is from the wood in terms of time is x(t) = 10×cos(2×π×t) + 17

Step-by-step explanation:

The given parameters are;

Length of the saw blade = 40 cm

Thickness of the wood across = 8 cm

Length of blade between wood saw handle with hand extended = 5 cm

Length of the tip from the wood at the above time = 40 - 8 - 5 = 27 cm

Length of blade between wood saw handle with saw pulled inwards = 25 cm

Length of the tip from the wood at the above time = 40 - 8 - 25 = 7 cm

Time for one complete cycle = 1 second

We note that the basic equation for oscillatory motion is of the form;

x(t) = A·cos(ωt) + d

Where:

A = Amplitude of the motion = (27 - 7)/2 = 10 cm

ω = Angular frequency = 2·π/T

ωt = Motion's phase

t = Time of the motion

d = The middle location = 27 - 10 = 17 cm

T = The time to complete a cycle = 1 s

Therefore;

ω = 2·π

Given that he stars with his arm extended out, we have;

27 = 10×cos(2×π×0) + 17

Therefore, the equation that models how far from the tip of the saw is from the wood in terms of time is x(t) = 10×cos(2×π×t) + 17.

Answer:

X=6

Y=5

Z=14.5

Step-by-step explanation:

the other side of the line is the exact same triangle.

To find X, 24 ÷4=6, therefore x=6

To find Y, 15÷3=5, therefore y=5

To find Z, 28+1=29 29÷2=14.5, therefore z=14.5

If z is not correct then it is probably 14, but the first on should be correc.

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Your answer is option b)

The time at which a star rises shifts approximately 4 minutes earlier each day, due to Earth's orbit around the Sun. Since there are roughly 30 days in a month, we can calculate the change in the rise time of Aldebaran over the course of a month.

Step 1: Calculate the time change over one month
30 days * 4 minutes per day = 120 minutes

Step 2: Convert minutes to hours
120 minutes ÷ 60 minutes per hour = 2 hours

Step 3: Subtract the time change from the current rise time
2:00 am - 2 hours = 12:00 am (midnight)

Therefore, you can expect Aldebaran to rise next month at midnight. The correct answer is b) midnight.

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The set of ordered pairs that is a function is (d) (0, 0), (1, 1), (4, 2), (9, 3)

The list of options represents the given parameter

As a general rule, for an ordered pair to be a function;

The y values on the ordered pair must point to different x values

In (a) the y values 4, 5, 6 and 7 have the same x value of 3

So, it is not a function

In (b) the y values 5 and 8 have the same x value of 2

So, it is not a function

In (c) the y values -1 and 1 have the same x value of 1

So, it is not a function

In (d) all the y values have different x values

So, it is a function

Hence, the ordered pair that is a function is  (d)

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Option D is the correct answer. if the residuals from a fitted regression violate the assumption of homoscedasticity their variance is not constant.

Homoscedasticity: It is an assumption of equal or similar variances in different groups are being compared. It is a condition in which the variance of the residual, or error term, in a regression model, is constant.

This is one of the most important assumptions of parametric statistical tests because they are sensitive to any dissimilarities. It is valid when X and Y are independent.

To deal with this First, we have attempted to transform your target using square root, log, reciprocal square root, or reciprocal transformations.

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Step-by-step explanation:

Using cosine rule,

f² = g² + e² - 2(g)(e)(cosF) = 6.7² + 5.9² - 2(6.7)(5.9)(cos70°)

= 52.6598 in²

Hence f = 7.3 in.

The length of f in the triangle EFG is 7.3 inches.

The law of cosine states that the square of any one side of a triangle is equal to the difference between the sum of squares of the other two sides and double the product of other sides and cosine angle included between them. The law of cosine states that: a² = b² + c² − 2bc·cosA.

Given that, in ΔEFG, g = 6.7 inches, e = 5.9 inches and ∠F=70°.

By using cosine rule in ΔEFG, we get

f² = e² + g² − 2eg·cos70°

= 5.9²+6.7²-2×5.9×6.7×0.342

= 79.7-27.03852

f² = 52.66148

f = 7.3 inches

Therefore, the length of f is 7.3 inches.

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Step-by-step explanation:

use quadratic formula to solve it and the answer is x=11/2 or -13/2

We know The formula of \(\tan\) is

\( \sf \longmapsto\tan(x) = \frac{Opposite}{Adjacent} \)

\(\sf \longmapsto \: \tan(x) = \frac{12}{5} \)

\(\sf \longmapsto \: \tan(x) = 2.4\)

\(\sf \longmapsto \: \tan(x) ≈2.44\)

\(\\ \sf\longmapsto tanX=\dfrac{Perpendicular}{Base}\)

\(\\ \sf\longmapsto tanX=\dfrac{YW}{WX}\)

\(\\ \sf\longmapsto tanX=\dfrac{12}{5}\)