HELPP ME
Some of the radicals below are like terms, while others are not: √2, − 3√2, 2√3, 5√2, 2√5, √32


List the Like Terms here


3b) Combine those like terms to write one single simplified radical (do not type!):


3c) Explain why the leftover terms are NOT like terms with the others.

Answer: 7

Step-by-step explanation: The average rate of change of a function f(x) over an interval [a,b] is defined as the ratio of “change in the function values” to the "change in the endpoints of the interval"1. In other words, it is the slope of the line that passes through two points on the graph of f(x)2.

To find the average rate of change of f(x) = x² + x + 4 from x = 2 to x = 4, we can use this formula:

Average rate of change = [f(4) - f(2)] / (4 - 2)

First, we need to plug in x = 4 and x = 2 into f(x) and simplify:

f(4) = (4)² + (4) + 4 f(4) = 16 + 8 f(4) = 24

f(2) = (2)² + (2) + 4 f(2) = 4 + 6 f(2) = 10

Next, we need to subtract f(2) from f(4), and divide by (4 - 2):

Average rate of change = [24 - 10] / (4 - 2) Average rate of change = 14 / 2 Average rate of change = 7

The solution to the equation 1/2 + 3y = y/5 is y = -3/14.

What is the linear equation in one variable?

A linear equation in one variable is an equation that can be written in the form:

ax + b = 0

where x is the variable, a and b are constants, and a is not equal to zero. The solution to the equation is the value of x that makes the equation true.

To solve for y in the equation 1/2 + 3y = y/5, we need to isolate y on one side of the equation.

First, we can simplify the left side of the equation by combining the like terms:

1/2 + 3y = (6/10) + (30y/10) = (6 + 30y)/10

Now we can rewrite the equation as:

(6 + 30y)/10 = y/5

To solve for y, we can start by multiplying both sides of the equation by 10, to eliminate the denominators:

6 + 30y = 2y

Next, we can simplify by subtracting 2y from both sides:

6 + 28y = 0

Finally, we can solve for y by subtracting 6 from both sides and then dividing by 28:

28y = -6

y = -6/28

Simplifying the fraction, we get:

y = -3/14

Therefore, the solution to the equation 1/2 + 3y = y/5 is y = -3/14.

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To create a graph and write an equation to represent the list of ordered pairs given, we need to plot each point on a coordinate system.

x | y

--|--

2 |-3

1 |-1

-1| 3

3 |-5

Plotting these points on a coordinate plane, we get:

![Graph of ordered pairs]

To write an equation to represent these ordered pairs in the form y = mx + b, we need to find the slope of the line and the y-intercept.

To find the slope:

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

Let's use the points (1, -1) and (3, -5) to find the slope:

m = (-5 - (-1)) / (3 - 1)

m = -4 / 2

m = -2

Now that we know the slope, we can use any point and the slope to find the y-intercept (b).

Using the point (1, -1):

y = mx + b

-1 = (-2)(1) + b

b = 1

So the equation that represents these ordered pairs in the form y = mx + b is:

y = -2x + 1

And the graph of this equation looks like:

![Graph of equation y = -2x + 1]

Answer:

C

Step-by-step explanation:

6x° and 60° form a right angle and sum to 90° , that is

6x + 60 = 90 ( subtract 60 from both sides )

6x = 30 ( divide both sides by 6 )

x = 5

For 15:
Sine: √2/2
Cosine: √2/2
Tangent: 1

For 17:
Sine: -1/2
Cosine: √3/2
Tangent: -1/√3

For 19:
Sine: (1+√3)/2
Cosine: (1-√3)/2
Tangent: √3

For 21:
Sine: -1/2
Cosine: -√3/2
Tangent: 1/√3

For 23:
Sine: √3/2
Cosine: 1/2
Tangent: √3

For 25:
Sine: -√2/2
Cosine: -√2/2
Tangent: -1

For 27:
Sine: (1-√3)/2
Cosine: (1+√3)/2
Tangent: -√3

For 29:
Sine: -(√3-1)/2
Cosine: (1+√3)/2
Tangent: -√3

For 16:
Sine: √3/2
Cosine: -1/2
Tangent: -√3

For 18:
Sine: -√2/2
Cosine: √2/2
Tangent: -1

For 20:
Sine: (√3-1)/2
Cosine: (1+√3)/2
Tangent: √3

For 22:
Sine: -(1+√3)/2
Cosine: (√3-1)/2
Tangent: -1/√3

For 24:
Sine: 1/2
Cosine: √3/2
Tangent: 1/√3

For 26:
Sine: √2/2
Cosine: -√2/2
Tangent: 1

For 28:
Sine: (√3+1)/2
Cosine: (1-√3)/2
Tangent: -1/√3

For 30:
Sine: -(1-√3)/2
Cosine: (√3+1)/2
Tangent: √3

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Answer:

Ans = (1.50 x 29 movies) + 16

Step-by-step explanation:

y represents total costs

x represents how many movie he rents

$1.50 is the rent of each movie

$16 is the fixed fee

thus

y = 1.50 x + 16

Ans = (1.50 x 29 movies) + 16

The table can be filled up accordingly:

1.  5 years compounded semi-annually:

b = (1 + 0.06/2)

y= 1800 (1 + 0.03)^10

x = 2

2. For the 5 years compounded quarterly:

b =  (1 + 0.06/4)

y =  1800 (1 + 0.015)^20

x =4

3. For the 5 years compounded monthly:

b = (1 + 0.06/12)

y = 1800 (1.005)^60

x = 12

4. For 10 years compounded annually:

b = (1 + 0.06/1)

x =  1800 (1.06)^10

y = 1

5. For 10 years compounded quarterly:

b =  (1 + 0.06/4)

y =1800 (1 + 0.005)^60

x = 4

6. For 10 years compounded monthly:

b = (1 + 0.06/12)

y = 1800 (1 + 0.005)^120

x = 12

To solve the compound interest we use the formula:

P(1+r/n)^(n*t).

For the 5 years compounded semi-annually:

A = 1800 (1 + 0.06/2)^2*5

A = 1800 (1 + 0.03)^10

A = 1800 (1.03)^10

A = 1800 (1.344)

A = 2419

For the 5 years compounded quarterly:

A = 1800 (1 + 0.06/4)^4*5

A = 1800 (1 + 0.015)^20

A = 1800 (1.015)^20

A= 1800 (1.3468)

A= 2424.24

For the 5 years compounded monthly:

A = 1800 (1 + 0.06/12)^12*5

A = 1800 (1 + 0.005)^60

A = 1800 (1.005)^60

A = 1800 (1.34885)

A = 2427.93

For 10 years compounded annually:

A= 1800 (1 + 0.06/1)^10

A = 1800 (1.06)^10

A = 1800 (1.7908)

A = 3223.53

For 10 years compounded semi-annually:

A = 1800 (1 + 0.06/2)^20

A = 1800 (1 + 0.03)^20

A = 1800 (1.03)^20

A =1800 (1.806)

A = 3251

For 10 years compounded quarterly:

A= 1800 (1 + 0.06/4)^4*10

A = 1800 (1 + 0.015)^40

A= 1800 (1.015)^40

A = 1800 (1.814)

A = 3265.23

For 10 years compounded monthly:

A= 1800 (1 + 0.06/12)^120

A = 1800 (1 + 0.005)^120

A = 1800 (1.005)^20

A= 1800 (1.8194)

A = 3274.9

The best pay period is that with the highest returns which is 10 years compounded monthly.

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The annual interest rate is 6.5%

The first step is to write out the parameters given in the question

Joseph places $5500 in a savings account for 30 months

He rans $893.75 in interest

The annual interest rate can be calculated by multiplying the amount in the savings by the number of months which is 30

= 5500 × 30y
= 165,000y

= 165,000y/12

= 13,750y

Equate 13,750y  with the amount of interest

13,750y= 898.75

y= 898.75/ 13,750

y= 0.065 × 100

= 6.5%

Hence the annual interest rate is 6.5%

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The point in which the line through the origin perpendicular to the plane 2x - y - z = 4 meets the plane 3x - 5y + 2z = 6 is (4/3, -2/3, -2/3).

To find the point in which the line through the origin perpendicular to the plane 2x - y - z = 4 meets the plane 3x - 5y + 2z = 6, we can use the following steps:

Find the normal vector of the plane 2x - y - z = 4. This is given by the coefficients of the x, y, and z terms, which are 2, -1, and -1, respectively. So the normal vector is (2, -1, -1).

Since the line through the origin is perpendicular to the plane, it must be parallel to the normal vector of the plane. Therefore, the direction vector of the line is (2, -1, -1).

The equation of the line through the origin with direction vector (2, -1, -1) is given by x = 2t, y = -t, and z = -t, where t is a parameter.

Substitute the equations of the line into the equation of the plane 3x - 5y + 2z = 6 to find the value of t:

3(2t) - 5(-t) + 2(-t) = 6

6t + 5t - 2t = 6

9t = 6

t = 2/3

Substitute the value of t back into the equations of the line to find the point of intersection:

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

y = -(2/3) = -2/3

z = -(2/3) = -2/3

Therefore, the point in which the line through the origin perpendicular to the plane 2x - y - z = 4 meets the plane 3x - 5y + 2z = 6 is (4/3, -2/3, -2/3).

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Correct statements are m∠C = m∠F, ΔABC ~ ΔDEF and 3/5 = y/z

Similar triangles are triangles that have the same shape but can be of different sizes. All equilateral triangles and squares of any length are examples of similar objects. That is, if two triangles are similar,  their corresponding angles are congruent and their corresponding sides have the same proportions. Here, triangle similarity is indicated by the symbol '~'.

Given,

two triangles ABC and DEF

m∠A = m∠D = 40°

m∠B = m∠E = 60°

Sum of all interior angles of a triangle is equal to 180°

m∠A + m∠B + m∠C = m∠D + m∠E + m∠F = 180°

40 + 60 + m∠C = 40 + 60 + m∠F

m∠C = m∠F

All three angles are congruent

By A-A-A rule

ΔABC ~ ΔDEF

ratio of corresponding sides will be equal

6/10 = y/z

3/5 = y/z

Hence, m∠C = m∠F, ΔABC ~ ΔDEF and 3/5 = y/z are the correct statement.

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No function exists in this relation. No, since there isn't always a single output for every input.

What is a function?

Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.

Here, we have

Given: The mapping diagram represents a relation where x represents the independent variable and y represents the dependent variable.

We have to show the relation between a function.

The x-values are entered into the function machine. The function machine generates the y-values after its operations are complete. Any internal function is possible.

A mapping diagram with arrows pointing from negative 3 to 0, negative 1 to 2, 1 to 0, 3 to 2, and 5 to 5, as well as two circles with the numbers 0, and labels for the x and y values, respectively

but according to the definition of y, it should give only one value

Hence, it is not a function.

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Answer:A

Step-by-step explanation:

because

The point E' will have a y-value of -1 instead of 3 and x-value of 6 instead of -6.

A polygon is a two-dimensional shape composed of straight line segments that close in a loop to form a single shape. Generally, polygons have three or more sides and angles. Depending on the number of sides, polygons can be classified as triangles, quadrilaterals, pentagons, hexagons, and so on.

A reflection across the x-axis of the graph of polygon ABCDE with point E at (-6,3) would result in the creation of a second polygon A'B'C'D'E' with E' at (-6,-1). This is because the reflection flips the points across the x-axis, meaning all of the y-values of the points will be converted to the opposite sign. Therefore, in the new polygon, point E' will have a y-value of -1 instead of 3. This is because the reflection across the x-axis will cause the y-values of each point to flip signs, with the y-value of E increasing from -3 to -1.

Similarly, a reflection across the y-axis of polygon ABCDE with point E at (-6,3) would result in the creation of polygon A'B'C'D'E' with E' at (6,1). This is because the reflection flips the points across the y-axis, meaning all of the x-values of the points will be converted to the opposite sign. Therefore, in the new polygon, point E' will have an x-value of 6 instead of -6. This is because the reflection across the y-axis will cause the x-values of each point to flip signs, with the x-value of E increasing from -6 to 6.

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Answer:

Reflection across y = 1

Step-by-step explanation:

i got this right on the flvs test!

By answering the above question, we may infer that So Kendra's water equation bottle holds 64 fluid ounces.

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.

The volume of a quart is 32 fluid ounces. Kendra's water bottle, which holds 2 quarts of water, therefore has:

64 fluid ounces are equal to 2 quarts when each is 32 fluid ounces.

So Kendra's water bottle holds 64 fluid ounces.

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Based on the calculation we know that

The value of x as 7− is 35.

The value of x as 7+ is 35.

Suppose that f( x ) = 7 x − 7. We can complete the following statements by plugging in the values of x and evaluating the function.

As x → 7 − , f ( x ) → 42 − 7 = 35
As x approaches 7 from the left, the function f(x) approaches 35.

As x → 7 + , f ( x ) → 42 − 7 = 35
As x approaches 7 from the right, the function f(x) also approaches 35.

Therefore, the function f(x) = 7x - 7 has a horizontal asymptote at y = 35 as x approaches 7 from both the left and the right.

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The contractor has 5.95 hours for the job if  $930 is spent by him.

The total cost for the job can be modeled by C = 42H + 680, where C is the total cost of the job, H is the number of hours of labor, and 680 is the cost of materials.

If the owner wants to spend $930 for the job, then the number of hours that the contractor has for the job can be found by solving the equation C = 42H + 680 for H.

Thus, 42H + 680 = 930. Subtracting 680 from both sides gives 42H = 250. Dividing both sides by 42 gives H = 250/42 = 5.95 hours.

Therefore, the contractor has 5.95 hours for the job if the owner wants to spend $930.

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Yes, it is better to use percentages to compare groups when making a graph. This is because percentages allow for a more accurate comparison of the data, as they take into account the relative size of each group. If we only use frequencies, we may get a skewed view of the data, as one group may be much larger than the other.

Here is the side by side bar graph showing the men's and women's responses to the question "Do you play sports?":

Gender Yes No

Male 9 7

Female 7 14

The graph indicates that a higher percentage of males play sports compared to females. However, it also shows that there are more females who do not play sports compared to males. This suggests that there may be a gender difference in the participation of sports among students.

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The cumulative distribution function for N when a coin is flipped 3 times with  P[H]=0. 3 is given by ,

F(N≤ 0) = 0.343 , F(N≤1) = 0.784 , F(N≤2) = 0.973 , F(N≤3) = 1.000.

Cumulative distribution function (CDF) of N,

Probability of getting n or fewer heads in three coin flips,

(All values of n from 0 to 3)

Probability of getting exactly n heads in three flips.

Apply binomial distribution,

P(N = n) = ³Cₙ ×(0.3)ⁿ × (0.7)³⁻ⁿ

For cumulative distribution function, add up the probabilities of getting 0, 1, 2, or 3 heads in three flips,

F(N≤ 0)

=P(N=0)

=³C₀ × (0.3)⁰ × (0.7)³

= 1 × 1 × 0.343

= 0.343

For F(N≤1) is equal to,

⇒F(N≤1)

= P(N=0) + P(N=1)

 =  ³C₀ × (0.3)⁰ × (0.7)³ + ³C₁ × (0.3)¹ × (0.7)²

= 0.343 + 0.441

= 0.784

F(N ≤ 2)

= P(N=0) + P(N=1) + P(N=2)

= ³C₀ × (0.3)⁰ × (0.7)³

+ ³C₁ × (0.3)¹ × (0.7)²

+³C₂ × (0.3)² × (0.7)¹

= 0.343 + 0.441 + 0.189

= 0.973

This implies CDF for N is equal to,

F(N ≤n) = [tex]\sum_{0}^{x}[/tex]³Cₓ × (0.3)ˣ × (0.7)³⁻ˣ

And F(N≤3) is equal to,

⇒F(N≤3)

= P(N=0) + P(N=1) + P(N=2) + P(N=3)

=  ³C₀ × (0.3)⁰ × (0.7)³

+ ³C₁ × (0.3)¹ × (0.7)²

+ ³C₂ × (0.3)² × (0.7)¹

+ ³C₃× (0.3)³ × (0.7)⁰

= 0.343 + 0.441 + 0.189 + 0.027

= 1.000

Therefore, the cumulative distribution function for N is equal to,

F(N≤ 0) = 0.343

F(N≤1) = 0.784

F(N≤2) = 0.973

F(N≤3) = 1.000

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The largest angle is [tex]\frac{7a}{4}[/tex] and the smallest angle is [tex]\frac{3a}{4}[/tex].

In this case, we have the angles [tex]\frac{5a}{2}, \frac{3a}{4}, and \frac{7a}{4}[/tex]. So we can set up the equation:

[tex]\frac{5a}{2} + \frac{3a}{4} + \frac{7a}{4} = 180[/tex]

To solve for "a", we can simplify the left side of the equation by finding a common denominator:

[tex]\frac{(10a + 3a + 7a)}{4} = 180[/tex]

Simplifying the left side gives:

[tex]\frac{20a}{4} = 180[/tex]

And further simplifying gives:

5a = 180

Dividing both sides by 5 gives:

a = 36

Now that we know the value of "a", we can substitute it back into each angle expression to find their actual values:

[tex]\frac{5a}{2} = \frac{5(36)}{2} = \frac{903a}{4} = \frac{3(36)}{4} = \frac{277a}{4} = \frac{7(36)}{4} = 63[/tex]

Therefore, [tex]\frac{7a}{4} = 63[/tex] is the largest angle and [tex]\frac{3a}{4} = 27[/tex] is the smallest angle.

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The simplified expression is x^(454)y^(584) * 2^(109).

To simplify the given expression, we need to use the laws of exponents. The laws of exponents are:

- (a^m)^n = a^(mn)
- a^m * a^n = a^(m+n)
- a^m / a^n = a^(m-n)

Using these laws, we can simplify the given expression as follows:

(x^3y^3)^31 * (32x^13y^18)^31 / (2xy^3)^2 * (2xy^3)^2 * (2x)^2 * (2x^3y^5)^3 * (4xy)^5 * (2x^3y^5)^3 * (4x)^5

= x^(3*31)y^(3*31) * 32^31x^(13*31)y^(18*31) / 2^2x^2y^(3*2) * 2^2x^2y^(3*2) * 2^2x^2 * 2^(3*2)x^(3*3)y^(5*3) * 4^5x^5y^(5*5) * 2^(3*2)x^(3*3)y^(5*3) * 4^5x^5

= x^(93)y^(93) * 32^31x^(403)y^(558) / 2^6x^6y^6 * 2^6x^6y^6 * 2^2x^2 * 2^6x^9y^15 * 4^5x^5y^25 * 2^6x^9y^15 * 4^5x^5

= x^(93+403)y^(93+558) * 32^31 / 2^6 * 2^6 * 2^2 * 2^6 * 4^5 * 2^6 * 4^5 * x^(6+6+2+9+5+9+5) * y^(6+6+15+25+15)

= x^(496)y^(651) * 32^31 / 2^(6+6+2+6+6) * 4^(5+5) * x^42 * y^67

= x^(496-42)y^(651-67) * 32^31 / 2^26 * 4^10

= x^(454)y^(584) * 32^31 / 2^26 * 4^10

= x^(454)y^(584) * 2^(5*31) / 2^26 * 2^(2*10)

= x^(454)y^(584) * 2^(155) / 2^(26+20)

= x^(454)y^(584) * 2^(155-46)

= x^(454)y^(584) * 2^(109)

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In response to the aforementioned query, we may say that D is equal to equation sqrt((3 - 3)2 + (-8 - 2)2 = sqrt(0 + (-10)2) = sqrt(100) = 10. As a result, it takes 10 units to get from position X to point Y.

A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.

The distance formula may be used to determine the separation between two points:

Sqrt((x2 - x1) + (y2 - y1)) = sqrt(d)

where d is the distance between the two locations, and (x1, y1) and (x2, y2) are the coordinates of the two points.

We may get the separation between points X at (3, 2) and Y at (3, -8), using the following formula:

D is equal to sqrt((3 - 3)2 + (-8 - 2)2 = sqrt(0 + (-10)2) = sqrt(100) = 10.

As a result, it takes 10 units to get from position X to point Y.

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The length of the arc intercepted by a central angle of \( \frac{\pi}{2} \) radians in a circle with a radius of \( 11 \mathrm{in} \) is \( \frac{11\pi}{2} \mathrm{in} \).

To find the length of the arc intercepted by a central angle of \( \frac{\pi}{2} \) radians in a circle with a radius of \( 11 \mathrm{in} \), we can use the formula for arc length: \( s = r\theta \), where \( s \) is the arc length, \( r \) is the radius of the circle, and \( \theta \) is the central angle in radians.

Plugging in the given values, we get:

\( s = (11 \mathrm{in})(\frac{\pi}{2}) \)

Simplifying, we get:

\( s = \frac{11\pi}{2} \mathrm{in} \)

Therefore, the length of the arc intercepted by a central angle of \( \frac{\pi}{2} \) radians in a circle with a radius of \( 11 \mathrm{in} \) is \( \frac{11\pi}{2} \mathrm{in} \).

Note: If the question asks for the answer to be rounded, you can use a calculator to find the approximate value of \( \frac{11\pi}{2} \) and round to the desired number of decimal places. For example, if the question asks for the answer to be rounded to the nearest tenth, the answer would be \( 17.3 \mathrm{in} \).

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5. The expression fοr the area of a rectangle with length l and width w is l × w.

What is a rectangle?

In Euclidean plane geοmetry, a rectangle is a quadrilateral with four right angles. It can also be defined as: an equiangular quadrilateral, since equiangular means that all οf its angles are equal.

5. The area of a rectangle is given by the prοduct of its length and width. Therefore, the expressiοn for the area of a rectangle with length l and width w is:

Area = l x w

6. Imagine dilating the rectangle with length & and width w by a factοr of k.

⇒ (l × k) × (w × k)

7. An expression fοr the area of the dilated rectangle.

⇒ l × w × k²

⇒ k²lw

8. Vοlume = l × w

Volume' = k²lw

Then we have

Volume/Volume'  = (l × w)/k²lw

Vk²lw = V'lw

Divide bοth sides by lw

Vk² = V'

Thus, The area ο a rectangle when it's dilated by a scale factor of k will be dilated k² times

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The p-value for our test is 0.0120, accurate to 4 decimal places.

We are conducting a study to see if the proportion of men over 50 who regularly have their prostate examined is significantly different from 0.49. We are performing a two-tailed test and our sample data produce the test statistic z=2.517.

To find the p-value, we need to use a standard normal distribution table or calculator. We will use the table for this answer.

The first step is to find the area to the left of the test statistic z=2.517 in the standard normal distribution table. This gives us the probability of obtaining a z-score less than or equal to 2.517. The closest value in the table is 2.51, which gives us an area of 0.9940.

Since we are conducting a two-tailed test, we need to find the area in both tails of the distribution. To do this, we subtract the area to the left of the test statistic from 1: 1-0.9940 = 0.0060. This gives us the area in the right tail of the distribution.

Finally, we multiply this value by 2 to get the p-value for our two-tailed test: 0.0060 * 2 = 0.0120.

Therefore, the p-value for our test is 0.0120, accurate to 4 decimal places.

p-value = 0.0120

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Answer:

x=5, y=-15

Step-by-step explanation:

7x+2y=5

3x+2y=-15

4x=20

 x=5

7(5)+2y=5

       2y=-30

         y=-15

Answer:

100°

Step-by-step explanation:

∠A and ∠B are supplementary angles, which means:

∠A° + ∠B° = 180°

[tex](2x) + (2x + 20) = 180[/tex]

Expand the parenthesis and solve for x:

[tex]2x + 2x + 20 = 180[/tex]

[tex]4x + 20 = 180[/tex]

[tex]4x = 180 - 20[/tex]

[tex]4x = 160[/tex]

[tex]x = \frac{160}{40}[/tex]

∴[tex]x = 40[/tex]

Substitute the value of x to determine the measurement of ∠B:

[tex]2(40) + 20[/tex]

[tex]80 + 20[/tex]

= 100°

The 42 grams of aluminum implies that the chemist has 0.06429ml of aluminum

The density of material shows the denseness of that material in a specific given area. A material’s density is defined as its mass per unit volume. Density is essentially a measurement of how tightly matter is packed together. It is a unique physical property of a particular object. The principle of density was discovered by the Greek scientist Archimedes. It is easy to calculate density if you know the formula and understand the related units The symbol ρ represents density or it can also be represented by the letter D.

How to determine the amount of aluminum?

The mass is given as:  Mass = 42 grams

The density of aluminum is: Density = 2.7 g/cm³

So, we have: Volume = Density/Mass

This gives, Volume = 2.7/42

Evaluate : Volume = 0.06429cm³

Convert to ml

Volume = 0.06429ml

Hence, the chemist has 0.06429ml of aluminum

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For Michael to pay cash for the tractor priced at R160,000 with the exchange rate as US$1 = R17.96, the amount he must change is US$8,908. 69.

An exchange rate is the unit rate at which one country's currency is exchanged for another.

Exchange rates are based on a country's economic performance or indices in comparison to other countries.

The price of the tractor = R160,000

Exchange Rate: US$ = R17.96

R160,000 = US$8,908. 69 (R160,000/R17.96)

Thus, Michael needs to exchange US$8,908. 69 to purchase the tractor costing R160,000.

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The rate of change of f(x) = 2(2) is equal to the rate of change of the function in the graph.

A function is a relation between two sets of values in mathematics. It is a mathematical process that takes an input and produces an output. It is represented as an equation which describes the relationship between the input and the output. A function can also be used to represent a mathematical rule or procedure that takes a set of inputs and produces a set of outputs.

The rate of change, or slope, is the measure of how quickly one variable changes when the other changes. In the graph, the rate of change is a constant, meaning that for every one unit the x-value increases the y-value increases by two. This is the same as the rate of change of f(x) = 2(2), as for every two units the x-value increases the y-value increases by four. Both the graph and the equation of the function have a constant rate of change which is equal to two, so the rate of change of f(x) = 2(2) is equal to the rate of change of the function in the graph.

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