Find the distance from the point $\left(1,\ 2\right)$ to the line $y=\frac{1}{2}x-3$
. Round your answer to the nearest tenth.

Answer:

  ∠A = 64°

Step-by-step explanation:

You have a triangle inscribed in a semicircle with acute angles marked A=(5x-1)° and C=(2x)°.

A triangle inscribed in a semicircle is a right triangle. (You know that because angle B is half the measure of 180° arc AC.) That means the two marked angles total 90°:

  (5x -1) +(2x) = 90

  7x = 91

  x = 13

Then angle A is ...

  A = (5·13 -1)° = (65 -1)° = 64°

The measure of angle A is 64°.

__

Check:

  C = (2x)° = (2·13)° = 26°

Then A+C = 64° +26° = 90°, as required.

At a 5% level of significance, the claims that a shipment of goods contains at most 2% defective items is accepted.

To investigate the claim that the shipment contains at most 2% defective items, we can use the 5% level of significance. The claim is that the population proportion of defective items is at most 2%, or p0 ≤ 0.02. The sample size is n = 200, and the sample proportion of defective items is pobs = 10/200 = 0.05.

The test statistic is then:

z = (pobs - p0) / √(p0(1-p0) / n)

= (0.05 - 0.02) / √(0.02(1-0.02)/200)

= 1.02.

With a 5% level of significance, we can look up the critical value for a one-tailed z-test and find that it is zα/2 = 1.645. Because 1.02 < 1.645, the test statistic is not greater than the critical value, and thus we fail to reject the null hypothesis that the population proportion of defective items is at most 2%.

In conclusion, with a 5% level of significance, the claim that the shipment contains at most 2% defective items is accepted.

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The declaration made indicates that Mabel left a $15.80 gratuity.

Percent, which is a relative number used to denote hundredths of any amount. Since one percent is equal to one tenth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified. percentage.

To find the amount of the tip that Mabel left, we can multiply the bill amount by the tip percentage, which is 20% or 0.2 in decimal form.

The amount of the tip is:

Tip = Bill Amount x Tip Percentage

Tip = $79 x 0.2

Tip = $15.80

Therefore, the tip that Mabel left was $15.80.

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The sine of angle C is √30/10.

Trigonometric ratios are mathematical expressions used to relate the angles and sides of a right-angled triangle.

Sine = Opposite / Hypotenuse

Cosine  = Adjacent / Hypotenuse

Tangent = Opposite / Adjacent  

are the fundamental ratios in a right-angle triangle  

where

"Opposite" refers to the side opposite to the angle.

"Adjacent" refers to the side adjacent to the angle.

"Hypotenuse" refers to the longest side of the right-angled triangle

Here we have  

A right-angle triangle DCB  

Where DC = 10 units, CB = √70  

From trigonometric ratios,

Sin θ =  Opposite side/ Hypotenuse

Sin C = DB/CD

By the Pythagorean theorem  

=> DC² = CB² + DB²  

=> (10)² = (√70)² + DB²

=> 100 = 70 + DB²

=> DB² = 100 - 70

=> DB = √30

Sin C = √30/10

Therefore,

The sine of angle C is √30/10.

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Answer:

[tex]x=1.6[/tex]

Step-by-step explanation:

To solve, first cross-multiply:

[tex]\frac{x}{4} = \frac{2}{5}[/tex]

[tex]5x = (4)(2)[/tex]

Then, solve the equation:

[tex]5x=8[/tex]

[tex]x=\frac{8}{5}[/tex]

[tex]\frac{8}{5} = 1.6[/tex]

[tex]x=1.6[/tex]

Therefore, x = 1.6.

I hope this helps!

Answer:

Step-by-step explanation:

the diameter of the circle is approximately 1.2 kilometers.

We can use the formula for the area of a circle:

Area = pi x (diameter/2)^2

where pi is a constant approximately equal to 3.14, and diameter is the distance across the circle passing through its center.

We are given the area of the circle as 1.1304 square kilometers, so we can substitute this value into the formula and solve for diameter:

1.1304 = 3.14 x (d/2)^2

1.1304 = 0.785d^2

d^2 = 1.1304/0.785

d^2 = 1.440

d = sqrt(1.440)

d ≈ 1.2

Therefore, the diameter of the circle is approximately 1.2 kilometers.

The system of equations shown models the total costs for taking 10 classes at each.

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

Given that Toe Tappers charges a rate for each class plus a one-time registration fee.

Dance World, y = 15x

Toe Tappers, y = 25 + 12.5x

Where x = number of classes

Now Equate the total cost at both dance studios;

15x = 25 + 12.5x

Collect like terms;

15x - 12.5x = 25

2.5x = 25

Divide both sides by 2.5;

2.5x / 2.5 = 25 / 2.5

x = 10 classes

Thus, x = number of classes = 10

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The coordinates of the reflected polygon F'G'H'I' are as follows:

F'(-2, -1), G'(5, -4), H'(8, -5), and I'(6, -2).

In mathematics, reflection is defined as the mirror image of a figure crossing a line (drawn or imagined), known as the line of reflection.

The vertices of the polygon FGHI are as follows:

F(2, -1)

G(5, 2)

H(8, 3)

I(6, 0)

To reflect the polygon FGHI across the line y = -1, we need to flip the points over the line.

Now we can reflect each of the points of the polygon across the line y = -1 to get the image:

F(2, -1) stays in the same place because it lies on the line of reflection.

G(5, 2) is reflected to G'(5, -4) by flipping it vertically across the line y = -1.

H(8, 3) is reflected to H'(8, -5), and

I(6, 0) is reflected to I'(6, -2).

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Answer:

a) -5x, 3x y 7x son monomios semejantes a -3x¹.

b) Verdadero, ya que ambos tienen coeficiente -12 y la misma parte literal ab.

c) Falso, ya que el primer monomio tiene exponente 2 en la variable x y exponente 1 en la variable y, mientras que el segundo monomio tiene exponente 1 en x y exponente 2 en y.

d) 3x²y³ y 2x²y³ son dos monomios semejantes de grado 5 y cuya parte literal consta de las variables x e y elevadas a exponentes 2 y 3 respectivamente.

The maximum value of the objective function is 73 when x=4 and y=17 and minimum value  is 21 when x=1 and y=5.

To find the maximum and minimum values of the objective function F=5y−4x, we need to use the constraints given in the question and solve for x and y. The constraints are y≤4x+1, y≥−4x+5, and x≤4.

First, we need to graph the constraints to find the feasible region. The feasible region is the area on the graph where all the constraints are satisfied.

Next, we need to find the corner points of the feasible region. The corner points are where the constraints intersect. The corner points are (1, 5), (4, 17), and (4, 11).

Finally, we need to plug in the corner points into the objective function to find the maximum and minimum values.

F(1, 5) = 5(5) - 4(1) = 21
F(4, 17) = 5(17) - 4(4) = 73
F(4, 11) = 5(11) - 4(4) = 47

The maximum value of the objective function is 73 when x=4 and y=17. The minimum value of the objective function is 21 when x=1 and y=5.

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The response to the given question would be that The slope of the line is the constant of proportionality if the graph is a straight line through the origin.

Partnerships that have the same ratio across time are said to be proportional. For instance, how many trees there are in an orchard and how many apples there are in a harvest of apples are determined by the average number of apples per tree. Proportional in mathematics refers to a linear connection between two numbers or variables. As the first quantity doubles, so does the other. When one of the variables drops to 1/100th of its previous value, the other also decreases. When two quantities are proportional, it means that as one rises, the other rises as well, and the ratio between the two quantities stays the same at all levels. As an example, consider the diameter and circumference of a circle.  

It is difficult to estimate the constant of proportionality between two variables, y and x, without first viewing the graph.

Nevertheless, the constant of proportionality may be calculated by dividing any y-value by its corresponding x-value if the two variables are directly proportional, which means that when x rises, y rises as well at a consistent pace.

If y = kx, where k is the proportionality constant, then mathematically, k = y/x at every point on the graph.

The slope of the line is the constant of proportionality if the graph is a straight line through the origin.

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Answer:

$32

Step-by-step explanation:

Since the coats are discounted by 60%, we need to find 100-60=40% of the original price.

We need to find 40% of 80.

We can use proportional relationships.

100%=80

10%=8

40%=32

Step-by-step explanation:

The given function is a quadratic function with a positive leading coefficient, therefore it opens upwards and has a minimum value. To find the minimum value of the function, we can use the formula:

x = -b/2a

where a = 1 and b = 6 are the coefficients of the quadratic function.

x = -6/2(1) = -3

Substitute x = -3 into the function to find the minimum value:

f(-3) = (-3)^2 + 6(-3) + 11 = 2

Therefore, the minimum value of the function is 2.

Answer:

Step-by-step explanation:

When writing the equation for a circle on a plane, we use the format:

[tex](x-x_{1})^2+(y-y_{1})^2=r^2[/tex]

x1 and y1 is the point of the center of the circle, which in this case is (1,-2)

r represents the radius, which is the distance from the center to the edge of the circle, which is (4,-2) - (1,-2) = 3

Our equation is now:

[tex](x-1)^2+(y+2)^2=9[/tex]

the reason why its y+2 is because (y-(-2) = (y+2)

r is squared, which is why it's 9 instead of 3. Hope this helps!

Answer:

  75 seconds

Step-by-step explanation:

You want to know how long it took Sean to drink his slushy, given a graph of amount remaining versus time.

Sean will have finished his slushy when the amount remaining is zero. That point on the graph occurs when the time is 75 seconds.

It takes 75 seconds for Sean to finish the slushy.

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f(x) = x^2 - 9
f(-x) = (-x)^2 - 9

y1 = 2√(x + 5) - 3
y2 = √(2(x - 5)) + 3

For the second question:
f(x) = x^2 - 9
f(-x) = (-x)^2 - 9
f(-x) = x^2 - 9

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The expression -5 + 6x + 3y2 has three terms, and the expression (x+2)(y-4) is a product of two factors, not a sum or difference of terms.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

An algebraic expression is a combination of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division, without the use of equal sign (=). It can include one or more terms, which are separated by addition or subtraction operators.

The expressions that contain exactly two terms are:

7 - 9x

8x2 + 5x

Therefore, The expression -5 + 6x + 3y2 has three terms, and the expression (x+2)(y-4) is a product of two factors, not a sum or difference of terms.

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The expression will be 5 + 11x.

What is an expression?

An expression in mathematics is a combination of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.)

It is possible to compare expressions to phrases. In English, a phrase by itself may contain an action, but it does not constitute a whole sentence.

Explanation: 3 + 7

Let the number to be "x"

Step 1 : the number is multiplied by - 8

           So, -8 x

Step 2 : subtracted from the sum of 5 and 3 times the number

       So,  (5 +3x) - (-8x)

           = 5+3x + 8x

           = 5 + 11x

Hence, The final expression will be 5 + 11x.

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The graph that represents the solution for the open sentence 3|p|−5<7 is:

a diagram (such as a series of one or more points, lines, line segments, curves, or areas) that represents the variation of a variable in comparison with that of one or more other variables

: the collection of all points whose coordinates satisfy a given relation (such as a function)

: a collection of vertices and edges that join pairs of vertices

Number line ranging from negative five to five. A line begins with an open point at negative four and ends with an open point at four.

Image with alt text: Number line ranging from negative five to five. A line begins with an open point at negative four and ends with an open point at four.

In this graph, the open points at -4 and 4 indicate that the values of p that make the inequality true do not include -4.

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Since the two hexagons are similar, their corresponding sides are in the same ratio as the scale factor.

Let x be the length of a side of the smaller hexagon, then the corresponding length of a side of the larger hexagon can be expressed as (3/7)x.

The area of a hexagon can be calculated using the formula: A = (3√3/2)s², where s is the length of a side.

Since the area of the smaller hexagon is 18 m², we can solve for x as follows:

18 = (3√3/2)x²

x² = 12/√3

x = 2√3

Now we can calculate the area of the larger hexagon:

Area of the larger hexagon = (3√3/2)(3/7x)² = (3√3/2)(3/7(2√3))² = 54/49 m²

Finally, we can calculate the volume of the larger hexagon, assuming it is a regular hexagonal prism:

Volume of the larger hexagon = Area of hexagon x Height

The height of the hexagonal prism is the same as the length of the side of the larger hexagon, which is (3/7)x:

Volume of the larger hexagon = (54/49) x (3/7)x = 54/343 x² ≈ 0.212 x²

Substituting the value of x, we get:

Volume of the larger hexagon ≈ 0.212 x (2√3)² = 1.272 m³

Therefore, the volume of the larger hexagon is approximately 1.272 m³.

Well, I'm not sure if it's correct but I got 42.

I got this by doing something along the lines of:

1) 18/x = 3/7

2) Cross multiply

3) 3x = 126

4) Divide both sides by 3

5) x = 42

A function is given. g(x)=3−4/5x; x=−5 ,x=4 the net change between the given values of the variable is -7.2. The average rate of change between the given values of the variable is -0.8.

(a) To determine the net change between the given values of the variable, we need to find the difference between the function values at x = -5 and x = 4.

g(-5) = 3 - 4/5(-5) = 3 + 4 = 7
g(4) = 3 - 4/5(4) = 3 - 3.2 = -0.2

Net change = g(4) - g(-5) = -0.2 - 7 = -7.2

(b) To determine the average rate of change between the given values of the variable, we need to find the slope of the secant line between the points (-5, 7) and (4, -0.2).

Average rate of change = (g(4) - g(-5))/(4 - (-5)) = (-7.2)/(9) = -0.8

Therefore, the average rate of change between the given values of the variable is -0.8.

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a) The appropriate hypothesis test for this situation is an independent samples t-test. The test statistic is the t-value, which is 0.824 b) the above hypothesis test, compute and comment on The effect size is 0.074,

The null hypothesis is that there is no difference in stress level between full-time and part-time volunteers, and the alternative hypothesis is that there is a difference in stress level between full-time and part-time volunteers.

The test statistic is the t-value, which is 0.824. The degrees of freedom is 529, which is calculated by adding the sample sizes of the two groups (336 + 195) and subtracting 2. The p-value is 0.411, which is greater than the significance level of 0.05.

This means that we fail to reject the null hypothesis and conclude that there is no significant difference in stress level between full-time and part-time volunteers.

b) The effect size for this hypothesis test can be calculated using Cohen's d, which is the difference between the two group means divided by the pooled standard deviation.

The effect size is 0.074, which is considered a small effect. This means that the difference in stress level between full-time and part-time volunteers is small and may not be practically significant.

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Answer:

75%

Step-by-step explanation:

Starting value: 12

Final Value: 21

Subtract final value minus starting value

Divide that amount by the absolute value of the starting value

Multiply by 100 to get percent increase

If the percentage is negative, it means there was a decrease and not an increase.

answer:

4.6 kilograms of pears

question:

I don't know if you meant 2.5 or 25 but ill assume you meant 2.5

A horizontal change of 96ft, there will be a vertical change of 3072ft.

The slope of a line is the ratio of the vertical change to the horizontal change between two points on the line. In other words, the slope is the rise over the run.

If the slope of a line is 32, that means that for every 1 unit of horizontal change, there is a 32 unit vertical change.

So, if the horizontal change is 96ft, we can use the slope formula to find the vertical change:

Vertical change = slope × horizontal change

Vertical change = 32 × 96

Vertical change = 3072

Therefore, for a horizontal change of 96ft, there will be a vertical change of 3072ft.

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If Emma needs to travel a distance of 15 miles or less, she should choose the red cab company because it has a lower cost. If she needs to travel more than 15 miles, she should choose the yellow cab company  

From the question, we are to determine which company Emma should use when she wants to minimize cost.

Let's assume that Emma needs to travel a distance of d miles to get to the airport.

The cost C of taking the red cab company can be represented by the function:

Cred(d) = 3.50 + 1.25d

Similarly, the cost C of taking the yellow cab company can be represented by the function:

Cyellow(d) = 5.00 + 1.15d

To determine which company Emma should use to minimize cost, we need to find the value of d that makes the cost of each company equal. In other words, we need to solve the equation:

Cred(d) = Cyellow(d)

Substituting the expressions for Cred(d) and Cyellow(d), we get:

3.50 + 1.25d = 5.00 + 1.15d

Simplifying and solving for d, we get:

0.10d = 1.50

d = 15

Hence, if Emma needs to travel a distance of 15 miles or less, she should choose the red cab company because it has a lower cost. If she needs to travel more than 15 miles, she should choose the yellow cab company.

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Answer:

144x^3+9

Step-by-step explanation:

First of all multiply 8x^2 and 18x then it is 144

By answering the above question, we may infer that The input value 0 equation represents the height at sea level, making it an inappropriate value for this function.

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.

For the predicament, the following input values would be suitable:

B) 1

C) 2

D) 3

E) 4

As the temperature drops by around 5°F for every 1,000 feet of height, we must utilise altitude numbers in thousands of feet to obtain the function's proper input values. Hence, we would utilise a value of 1 as an input for every 1,000 feet of height rise. Consequently, 1, 2, 3, and 4 would be the proper input values, which correspond to altitudes of 1,000, 2,000, 3,000, and 4,000 feet, respectively. The input value 0 represents the height at sea level, making it an inappropriate value for this function.

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The expected value of the game in which you have a (1/20) chance of winning  is $1.50.  The probability of a student scoring between 75 and 89 is 0.5536. The probability of a student scoring above 85 is 0.4562.

1. To find the expected value of the game, we need to multiply the probability of each outcome by the value of that outcome and then add them together.

E(X) = (1/20)($300 + $15) + (19/20)(-$15)

E(X) = $315/20 - $285/20

E(X) = $30/20

E(X) = $1.50

So the expected value of the game is $1.50.

2. To find the probability of a student scoring between 75 and 89, we need to use the z-score formula:

z = (x - μ)/σ

For x = 75, z = (75 - 84)/9 = -1

For x = 89, z = (89 - 84)/9 = 0.56

Using a z-table, we can find the probability of a student scoring between these two z-scores:

P(-1 < z < 0.56) = P(z < 0.56) - P(z < -1)

P(-1 < z < 0.56) = 0.7123 - 0.1587

P(-1 < z < 0.56) = 0.5536

So the probability of a student scoring between 75 and 89 is 0.5536.

3. To find the probability of a student scoring above 85, we need to use the z-score formula:

z = (x - μ)/σ

For x = 85, z = (85 - 84)/9 = 0.11

Using a z-table, we can find the probability of a student scoring above this z-score:

P(z > 0.11) = 1 - P(z < 0.11)

P(z > 0.11) = 1 - 0.5438

P(z > 0.11) = 0.4562

So the probability of a student scoring above 85 is 0.4562.

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