Select which of the following are surds
√17
√36
B
√100
C
A
√15
D
√30
E

Answer:

choice 1) x = 2,3

Step-by-step explanation:

2x/(x - 2) - (x + 3)/(x - 4) = -4x/(x² - 6x + 8)

Factor x² - 6x + 8 into (x - 2)(x - 4):

2x/(x - 2) - (x + 3)/(x - 4) = -4x/(x - 2)(x - 4)

multiply both sides of the equation by (x - 2)(x - 4):

2x(x - 4) - (x + 3)(x - 2) = -4x

simplify:

2x² - 8x - x² + 2x - 3x + 6 = -4x

combine like terms:

x² -9x + 6 = -4x

add 4x to each side:

x² -5x + 6 = 0

factor:

(x - 3)(x - 2) = 0

x = 2, x = 3

The coordinates of Q(6, -4) under a reflection in the x-axis is Q'(6,4)

The coordinates of x will remain the same for reflection in the X axis, while y will change with the opposite sign.

From the question, we have

The coordinates of Q(6, -4) under a reflection in the x-axis is Q'(6,4).

Reflection:

A reflection is referred to as a flip in geometry. A reflection is the shape's mirror image. A line, called the line of reflection, will allow an image to reflect through it. Every point in a figure is said to reflect the other figure when they are all equally spaced apart from one another. The reflected picture should have the same size and shape as the original, but it faces the opposite way. Changes in position during contemplation may also result in translation. Pre-image and image are terms used to refer to the same thing in this context. ABC and A'B'C are used to represent the pre-image and image, respectively. The coordinate system may be referred to by the reflection transformation (X and Y-axis).

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Answer: 1/2 + 3/4

1/2 + 3/4

---Find a common denominator

2/4 + 3/4

5/4

---Convert improper fraction to a mixed number

5/4 = 1 1/4

Answer: 1 1/4 miles

Hope this helps!

By using  1-PsiTarget(H15, 500) we compute the probability of cell H15's value exceeding 500 in a spreadsheet simulation.

PsiTarget is a function commonly used in spreadsheet simulation software to calculate probabilities.

The first argument (H15) specifies the cell you want to calculate the probability for.

The second argument (500) represents the target value you want to compare against.

The PsiTarget function returns the probability of the cell's value being less than or equal to the target value.

By subtracting this probability from 1, you get the probability of the cell's value exceeding the target value.

Therefore, the correct formula to compute the probability of cell H15's value exceeding 500 is 1-PsiTarget(H15, 500).

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Both c. f is continuous on the interval [-2,3], where f(-2)=0 and f(3)=20 and d. f is continuous on the interval [-2,3], where f(-2)=15 and f(3)=30 options are correct. given below is the explanation of the result.

using Intermediate value theorem:(statement: suppose that f∈c[a,b] and f(a)≠f(b) then given a number λ lies between f(a) and f(b) there exist a point c ∈(a,b) such that f(c)=λ)

know according to the Intermediate value theorem both option c and d are correct here because either f(a)<f(b) for a number λ lies between f(a) and f(b) there exist a point c ∈(a,b) such that f(c)=λ) here if we take  interval [-2,3], where f(-2)=0 and f(3)=20 the theorem is applicable. if we have f(a)>f(b) for a number λ lies between f(a) and f(b) there exist a point c ∈(a,b) such that f(c)=λ so if we take the interval [-2,3], where f(-2)=15 and f(3)=30,the above stated theorem is applicable.

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a. The probability of success (hitting the target) is constant for each trial (88% or 0.88).

b. The probability of hitting the 6th target is:

P(X = 1) = C(1, 1) * 0.88^1 * (1 - 0.88)^(1 - 1) = 0.88

c. Using the binomial probability formula as before, with p = 0.88 and n = 3:

P(X = 1) = C(3, 1) * 0.88^1 * (1 - 0.88)^(3 - 1)

P(X = 2) = C(3, 2) * 0.88^2 * (1 - 0.88)^(3 - 2)

P(X = 3) = C(3, 3) * 0.88^3 * (1 - 0.88)^(3 - 3)

a) The three characteristics of this scenario that indicate we are working with Bernoulli trials are:

The experiment consists of a fixed number of trials (eight shots).

Each trial (shot) has two possible outcomes: hitting the target or missing the target.

The probability of success (hitting the target) is constant for each trial (88% or 0.88).

b) To find the probability of hitting the 6th target (considered as a single trial), we can use the binomial probability formula:

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

where:

P(X = k) is the probability of getting exactly k successes,

C(n, k) is the binomial coefficient or number of ways to choose k successes out of n trials,

p is the probability of success in a single trial, and

n is the total number of trials.

In this case, k = 1 (hitting the target once), p = 0.88, and n = 1. Therefore, the probability of hitting the 6th target is:

P(X = 1) = C(1, 1) * 0.88^1 * (1 - 0.88)^(1 - 1) = 0.88

c) To find the probability that the first time hitting the target is not until the 4th shot, we need to consider the complementary event. The complementary event is hitting the target before the 4th shot.

P(not hitting until the 4th shot) = P(hitting on the 4th shot or later) = 1 - P(hitting on or before the 3rd shot)

The probability of hitting on or before the 3rd shot is the sum of the probabilities of hitting on the 1st, 2nd, and 3rd shots:

P(hitting on or before the 3rd shot) = P(X ≤ 3) = P(X = 1) + P(X = 2) + P(X = 3)

Using the binomial probability formula as before, with p = 0.88 and n = 3:

P(X = 1) = C(3, 1) * 0.88^1 * (1 - 0.88)^(3 - 1)

P(X = 2) = C(3, 2) * 0.88^2 * (1 - 0.88)^(3 - 2)

P(X = 3) = C(3, 3) * 0.88^3 * (1 - 0.88)^(3 - 3)

Calculate these probabilities and sum them up to find P(hitting on or before the 3rd shot), and then subtract from 1 to find the desired probability.

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a) The mean weight of pineapples grown in the field this year is different from the mean weight of pineapples grown last year. b) The power to detect an increase of 2 ounces in the mean weight of pineapples (μa = 33 ounces) is approximately 0.932, and the probability of making a Type 2 error with a true mean of 33 ounces is approximately 0.068.

(a) The null hypothesis (H0) and alternative hypothesis (Ha) can be written as follows:

Null Hypothesis (H0): The mean weight of pineapples grown in the field this year is equal to the mean weight of pineapples grown last year (μ = 31 ounces).

Alternative Hypothesis (Ha): The mean weight of pineapples grown in the field this year is different from the mean weight of pineapples grown last year (μ ≠ 31 ounces).

(b) To calculate the power and the probability of making a Type 2 error, we need to assume the population mean weight of pineapples this year (μa) is 33 ounces. We also need to determine the critical value for the given significance level (α) of 0.05.

Given that the sample size (n) is 30, the population standard deviation (σ) is 4 ounces, and the mean weight under the alternative hypothesis (μa) is 33 ounces, we can calculate the test statistic (z) using the formula:

z = (\(\bar x\) - μa) / (σ / √n)

where \(\bar x\) is the sample mean.

With \(\bar x\) = 31 ounces, σ = 4 ounces, μa = 33 ounces, and n = 30, we can calculate the test statistic:

z = (31 - 33) / (4 / √30)

z = -2 / (4 / √30)

z = -2 / (4 / 5.477)

z = -2 / 1.0954

z ≈ -1.825

Using a standard normal distribution table or calculator, we can find the corresponding p-value for this z-value. Let's assume it is approximately 0.034 (one-tailed test).

The power of the test can be calculated as 1 minus the probability of a Type 2 error. Since the alternative hypothesis is two-sided, we divide the significance level (α) by 2 and find the corresponding critical z-value. Let's assume it is approximately 1.96 (two-tailed test).

Now we can calculate the power using the formula:

Power = 1 - P(Type 2 Error) = 1 - P(z < -1.96 or z > 1.96)

P(Type 2 Error) = P(z < -1.96 or z > 1.96) ≈ 2 * P(z < -1.96) (assuming symmetry)

P(Type 2 Error) ≈ 2 * 0.034 ≈ 0.068

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Step-by-step explanation:

A) Given the initial height of plant = 20cm

Percent increase monthly = 4%

increment after x month = (4% of 20)x

increment after x month = (0.04*20)x

increment after x month = 0.8x

The height after x month = initial height + increment

The height after x month = 20 + 0.8x

Hence an equation that model the growth of the plant is 20+0.8x

B) To get the height of the plant after 5 months, we will substitute x = 5 into the modeled equation in A as shown;

H(x) = 20+0.8x

H(5) = 20 +0.8(5)

H(5) = 20+4

H(5) = 24cm

hence the height of the plant after 5minths is 24cm

The final speed v2 is √6 times the initial speed v1, when the net force is 2f1 and the object moves the same distance d while the force is being applied.

We can use the work-energy theorem to solve this problem, which states that the work done on an object by a net force is equal to the change in its kinetic energy.

When the force has magnitude f1 and the object moves a distance d, the work done is:

W = f1 * d

This work changes the kinetic energy of the object from zero to (1/2) * m * v1^2, where m is the mass of the object. Therefore, we have:

f1 * d = (1/2) * m * v1^2

Solving for v1, we get:

v1 = sqrt((2 * f1 * d) / m)

Now, when the net force has magnitude f2 = 2f1 and the object moves the same distance d, the work done is:

W = f2 * d = 2f1 * d

This work changes the kinetic energy of the object from (1/2) * m * v1^2 to (1/2) * m * v2^2, where v2 is the final speed of the object. Therefore, we have:

2f1 * d = (1/2) * m * (v2^2 - v1^2)

Solving for v2, we get:

v2 = sqrt(v1^2 + (4 * f1 * d) / m)

Substituting the expression for v1, we get:

v2 = sqrt((4 * f1 * d) / m + (2 * f1 * d) / m)

Simplifying, we get:

v2 = sqrt(6) * v1

Therefore, the final speed v2 is sqrt(6) times the initial speed v1.

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Answer:

it's A.

Step-by-step explanation:

a vertical translation, in the name, means you are moving the graph up or down the y axis. a horizontal translation is moving the graph left or right on the x axis. a reflection across the x axis is all the x values *-1. 180 counterclockwise rotation is rotating the graph top to bottom.

Answer:

A. Vertical translation

Step-by-step explanation:

A vertical translation means the object moves up or down without changing anything else of itself, such as size, rotation, reflection, etc.  Only movement up and down.

Reflection is where the object moves as though the axis is a mirror, where the object translates the same distance from the axis, but also flips across the axis, so if it is an x-axis, it flips upside down, and at a y-axis, flips left and right.

A rotation in any direction that is 180 degrees means that the object appears to be flipped opposite of what it started as.  For example, if A is at the top point, after rotation, A would be the bottom point.

A horizontal translation is the same as with a vertical translation, except the object moves left or right.

From each of these analyses I provided on each of the answer choices, we can clearly see that the correct answer is the first option, "A. Vertical translation," as the object did exactly as I described what a vertical translation is.

If I helped (and more clearly explained, hopefully, than the other answer), please make this answer brainliest ;)

Answer:

3dfg

Step-by-step explanation:

The box-and-whisker plot that illustrates the given data set is shown in the image below (see attachment).

A box-and-whisker plot consists of the following values of a data set: min, max, lower quartile, median, and upper quartile.

Here, Given the data set,

30, 22, 22, 27, 28, 23, 24, 25, 26, 23

the five-number summary for the box-and-whisker plot would be:

Minimum: 22

Quartile Q1: 22.75

Median: 24.5

Quartile Q3: 27.25

Maximum: 30

Thus, the box-and-whisker plot that illustrates the given data set is shown in the image below (see attachment).

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The windows of house are 8 feet apart distance.

As we are provided with the the total width of house is 33 feet and 4 feet distance between the edge of the house and the end windows

So the space available for the windows is total width of the house minus the  distance between the edge of the house and the windows from both the sides = 33 - 2(4) = 33-8 = 25 feet

The length of the windows to be inserted is the product of number of windows  and their side = 3 × 3 = 9 feet

The total distance between the windows can be find out by reducing the distance covered by windows from the area available for windows = 25feet - 9 feet = 16 feet

There are three windows, so there will be only 2 gaps whose length is 16 feet / 2 = 8 feets

Hence, the windows of the house are 8 feet  apart

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The variable for the number of wraps and the number of gift bags are x and y.

A linear function can be used to depict a straight line on the coordinate plane. The equation y = 3x - 2 serves as an illustration of a linear function since it represents a straight line in the coordinate plane.

Nonlinear functions are those whose graphs do not follow a straight line. A graph of it can be any curve other than a straight line.

A quadratic function is an illustration of a non-linear function.

Let, The number of wraps be 'x' and the number of gift bags be 'y'.

Therefore, From the given information x + y = 25 and 6x + 2y = 110.

Solving this linear system graphically we have an intersection (x, y)

at (15, 10).

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Answer:

  F = 3x +(2.7×10^7)/x

Step-by-step explanation:

The formulas for area and perimeter of a rectangle can be used to find the desired function.

The area of the rectangle will be the product of its dimensions:

  A = LW

Using the given values, we have ...

  13.5×10^6 = xy

Solving for y gives ...

  y = (13.5×10^6)/x

The perimeter of the rectangle is the sum of the side lengths:

  P = 2(L+W) = 2(x+y)

The total amount of fence required is the perimeter plus one more section that is x feet long.

  F = 2(x +y) +x = 3x +2y

Substituting for y, we have a function of x:

  F = 3x +(2.7×10^7)/x

__

Additional comment

The length of fence required is minimized for x=3000. The overall size of that fenced area is x=3000 ft by y=4500 ft. Each half is 3000 ft by 2250 ft. Half of the total 18000 ft of fence is used for each of the perpendicular directions: 3x=2y=9000 ft.

It is true that the slope of the horizontal tangent line to the parametric curve at a point (x(t), y(t)) is given by dy/dx = (dy/dt)/(dx/dt).

The statement is saying that if f(g(t)) has a horizontal tangent at t = 1, then the curve has a well-defined tangent line at that point, which is also a horizontal tangent. Let's break this down step by step:

f(g'(1)) = 0: This means that the derivative of f with respect to its input g(t) is equal to zero at t = 1. In other words, the slope of the tangent line of f(g(t)) at t = 1 is zero.

dx/dt is not zero at t = 1: This means that the curve g(t) has a well-defined tangent line at t = 1, because the slope of the tangent line of g(t) is not infinite (i.e., the derivative dx/dt is defined and finite).

Setting dy/dx = 0 gives dy/dt / dx/dt = 0: This is using the chain rule of differentiation to relate the derivative of f with respect to t (i.e., dy/dt) to the derivative of f with respect to x (i.e., dy/dx) and the derivative of g with respect to t (i.e., dx/dt).

dy/dt = 0 when dx/dt is not zero: Since dy/dx = 0 and dx/dt is not zero, we can conclude that dy/dt must also be zero at t = 1. This means that the slope of the tangent line of f(g(t)) is also zero at t = 1.

Therefore, the curve has a horizontal tangent at t = 1: Since both g(t) and f(g(t)) have horizontal tangents at t = 1, we can conclude that the curve f(x) also has a horizontal tangent at x = g(1). This means that the tangent line to the curve at that point is horizontal.

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Answer:

y= 12x^3-5x

y=2x^2+x+6

Step-by-step explanation:

To build an equation system, make both sides of the given equation equal to the same variable.

Let y be the variable. The equation 12x^3 - 5x = 2x^2 + x + 6 thus becomes 12x^3 - 5x = y = 2x^2 + x + 6.

As a result, the equation system becomes

Let's form two

Keep cube root on one side and shift rest to right

Form equations

The derivative limit is used to find the rate of change of a function at a specific point by taking the limit of the difference quotient as the change in the input variable approaches zero.

The derivative of a function at a specific point is the rate at which the function changes at that point. More specifically, it is the slope of the tangent line to the graph of the function at that point.

The derivative limit refers to the process of finding the derivative of a function at a particular point by taking the limit of the difference quotient as the change in the input variable approaches zero.

In mathematical notation, the derivative of a function f(x) at a point x=a is denoted as f'(a), and is defined as:

f'(a) = lim h→0 (f(a+h) - f(a))/h

Here, h represents the change in the input value, and as h approaches zero, the quotient (f(a+h) - f(a))/h approaches the slope of the tangent line to the graph of the function at the point x=a.

The concept of the derivative limit is essential to calculus and is used in many areas of mathematics, science, and engineering to model and analyze real-world phenomena.

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Answer:

Step-by-step explanation:

Substitute (x, y) value in 5x -  4y and if you get 17 then (x , y) is the solution.

If you are getting 17, then (x, y) is not a solution.

1) (1 , -3)

5x - 4y = 5*1 - 4*(-3)

            = 5 + 12

            = 17

(1, - 3) is a solution.

2) (-6, 2)

5x - 4y = 5*(-6) - 4*2

           = -30 - 8

          = -38   ≠ 17

So, (-6 , 2) is not a solution.

3) (-3 , -8)

5x - 4y = 5*(-3) - 4* (-8)

           = -15 + 32

           = 17

So, (-3 , -8) is a solution.

4) (2 , 9)

5x - 4y = 5*2 - 4 *9

           = 10 - 36

           =  -16 ≠ 17

So, (2 , 9) is not a solution

Sometimes. p ⇒ q is true if both p and q are true, or whenever p is false.

Always. ¬ p ⇒ ¬q is true if ¬p and ¬q are both true (which means p and q are both false), or whenever ¬p is false (p is true).

The value of the limit is:

lim(x→a) (5x^2 - 1) / (x + 10)

The limit of a function as x approaches some value. Here's a step-by-step explanation using the given terms:

1. Identify the function: It appears that the function is f(x) = (5x^2 - 1) / (x + 10).

2. Determine the value x is approaching: Since it's unclear what value x is approaching, let's use the symbol 'a' to represent it. We want to find lim(x→a) f(x).

3. Substitute the value of 'a' into the function: Since we don't have a specific value for 'a', let's find the general limit expression:

lim(x→a) (5x^2 - 1) / (x + 10)

4. Analyze the function: As x approaches 'a', we need to check if the function is continuous at that point. If it is continuous, we can directly substitute the value of 'a' into the function.

5. If there is no specific value of 'a' provided, the answer will be expressed in terms of 'a'. In this case, the limit of the function as x approaches 'a' is:

lim(x→a) (5x^2 - 1) / (x + 10)

Without knowing the specific value of 'a', this is the most concise answer I can provide. If you can clarify the question, I'd be happy to help further!

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Answer:

The new angles are in color

Answer:

The measure of the missing angle is 25 degrees.

Answer:

S.I = (P × R × T)/100

where;

P - principal

R - rate

T - time

Your answer would be 2(x+1)

Answer:

30-60-90

Step-by-step explanation:

It is still the same no matter how it is rotated or translated.

Answer:

Step-by-step explanation:

In the diagram BC=9. Find ABOUT and AC

Answer:

Solutions: x = 7, y = 9;  or (7, 9)

Step-by-step explanation:

Given the following systems of linear equations:

7x - 8y = -23

7x - 7y = -14

Since the coefficients of x in the given system have the same sign, we could use the process of elimination by subtracting the two equations.

    7x - 8y = -23

-   7x - 7y = -14    

             -y = -9  

Divide both sides by -1 to solve for y:

\(\frac{-y}{-1} = \frac{-9}{-1}\)

y = 9

Substitute the value of y into either one of the given equations to solve for x:

7x - 7y = -14

7x - 7(9) = -14

7x - 63 = -14

Add 63 to both sides:

7x - 63 + 63 = -14 + 63

7x = 49

Divide both sides by 7 to solve for x:

\(\frac{7x}{7} = \frac{49}{7}\)

x = 7

Double-check whether x = 7 and y = 9 are valid solutions to the given system:

x = 7, y = 9:

7(7) - 8(9) = -23

49 - 72 = -23

-23 = -23 (True statement).

7(7) - 7(9) = -14

49 - 63 = -14

-14 = -14 (True statement).

Therefore, the solution to the given systems of linear equations are x = 7, and y = 9, or (7, 9).