Write a linear function f with f(-10) = 4.5 and f(-2)=4.5.

The solution to the equations is y = -7

From the question, we have the equation to be given as

3x - 2y = 5

The above equation is a linear equation

The domain or the replacement set is given as

{-3}

Rewrite properly as

Domain  = {-3}

or

x = -3

So, we replace the variables using the elements in the replacement set

When x = -3, we have

3 x -3 - 2y = 5

Evaluate the products

This gives

-9 - 2y = 5

Add 9 to both sides

-2y = 14

Divide both sides by -2

y = -7

So, we have

x = -3 and y = -7

Hence, the solution to the equation is y = -7

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The probability that shooting stars are there in the fall is 0.5904.

The probability of not seeing any falling star in that time period of 15 minutes is 1 - 0.2 = 0.8.

In this way, the combined probability of not seeing any of the falling stars in the four-time period is: 0.8 * 0.8 * 0.8 * 0.8 = 0.8⁴ = 0.4096

= 1 - 0.4096 = 0.5904

=P(X = x) = μˣ * e^-μ / x!

Here, the span is of 15 minutes. In this way, the typical number of events in the span is 15λ. The probability of witnessing 0 occasions (i.e X = 0) is:

P(X = 0) = μ⁰ * e^-(15λ) / 0! = 1 / e^(15λ) — — (1)

(1) is equal to 80% as the probability of at least one event happening is 20%.

So, 1 / e^(15λ) = 0.8

or, e^(15λ) = 1.25

or, 15λ = ln(1.25) = 0.2231

= λ = 0.0149 / min

In this way, the typical number of occasions (falling stars) is 0.0149 per minute.

Presently, the typical number of occasions in an hour is:

0.0149 * 60 = 0.8926 / hour

So, the Poisson distribution expression becomes:

P(X = x) = 0.8926ˣ * e^-0.8926 / x! — — (2)

Here, the time span is 60 minutes.

Presently, we should find the probability of not having even a solitary occasion in 60 minutes:

P(X = 0) = 0.8926⁰ * e^-0.8926 / 0! = 0.4096

So, the probability of having at least one event is the complement of the above probability.

So, P(X≥1) = 1 - P(X=0) = 1 - 0.4096 = 0.5904

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The ordered pairs that are a solution to the given linear equation -5x + 3y > 12 are:

In order to determine which ordered pairs are true solutions based on the given linear equation, we would have to test each of the ordered pairs by substituting their values into the linear equation as follows;

For ordered pair (3, 9), we have:

-5x + 3y > 12

-5(3) + 3(9) > 12

-15 + 27 > 12

12 > 12 (False).

For ordered pair (-5, 5), we have:

-5x + 3y > 12

-5(-5) + 3(5) > 12

25 + 15 > 12

40 > 12 (True).

For ordered pair (3, -6), we have:

-5x + 3y > 12

-5(3) + 3(-6) > 12

-15 - 18 > 12

-33 > 12 (False).

For ordered pair (-2, -5), we have:

-5x + 3y > 12

-5(-2) + 3(-5) > 12

10 - 15 > 12

-5 > 12 (False).

For ordered pair (2, 8), we have:

-5x + 3y > 12

-5(2) + 3(8) > 12

-10 + 24 > 12

14 > 12 (True).

For ordered pair (-6, 0), we have:

-5x + 3y > 12

-5(-6) + 3(0) > 12

30 + 0 > 12

30-5 > 12 (True).

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The statement "The median and altitude of an isosceles triangle can be same", is verified by drawing diagram

The statement is  

"The median and altitude of an isosceles triangle can be same"

Draw an isosceles triangle ABC with BD = CD,

Draw a line segment AD perpendicular to the side BD

Here AD is the height of the triangle which is the altitude of the triangle

From the figure we can see that the length of BD = length of CD

Where D is the mid point of the line BD.

Therefore the line AD is the median of the triangle

Hence, The statement "The median and altitude of an isosceles triangle can be same", is verified by drawing diagram

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The z-observed value for the test of average number of times that a typical american says a word that is considered to be profane is -0.41.

The formula for calculating the z-score is-

z = (x - μ)/s

in which,

n = sample size (= 15)

μ = mean (= 4)

σ = standard deviation (= 5.6)

s = σ/√n

s = 5.6/√15

s = 1.44

Put the value in z score;

z = (3.4 - 4)/1.44

z = -0.41

Because of how near to zero this test statistic is, we will not be able to rule out the null hypothesis. Seven.

There isn't enough proof to claim that there is a mean difference or that it exists in your circumstance.

Thus, they're basically arguing that we can't rule out the null hypothesis.

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Answer:

See below

Step-by-step explanation:

Find slope using two convenient integer coordinates

(-1,4)  and (1, -8) are convenient

  slope = (y1-y2) / (x1-x2) = (4 - -8) / ( -1 -1) =  12/-2 = -6

the y-axis intercept is -2  ( by looking at the graph)

y = -6x -2      Done.

The equation of line [L] would be y = (1/6)x + 9.

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

We have a equation of line [k] is y + 2 = -6(x - 7). Line [L] includes the point (-6,8) and is perpendicular to line k.

We have the equation of line [K] as -

y + 2 = - 6(x - 7)

y = - 6(x - 7) - 2

y = - 6x + 42 - 2

y = - 6x + 40

Slope of line [L] will be -

m[L] = 1/6

Assume the equation to be -

y = (1/6)x + c

Line [L] includes the point (-6, 8), so we can write -

8 = (1/6) x (- 6) + c

8 + 1 = c

c = 9

So, the equation will be -

y = (1/6)x + 9

Therefore, the equation of line [L] would be y = (1/6)x + 9.

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The expression that represents the change in April's score from the start to the end of the game is 355 - 150 = 205.

April played a game. The score at the beginning of the game was 150 points. After twenty minutes, her score was 355 points. We have to determine the change in her score from the beginning of the game to the end of the game.

Let the change in the score be represented by the variable "C". The change in her score is calculated below. The change in the score is the difference between the final and the initial score of April.

C = 355 - 150

C = 205

Hence, the change in her score from the beginning of the game to the end of the game is 205 points.

The complete question is given below.

At the beginning of the game, April had a score of 150 points. April played for another 20 minutes, and her final score was 355. Write and then evaluate a subtraction expression to determine the change of her score from the beginning of the game to the end of the game.

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Answer:

gradient:

y2-y1/x2-x1

1-1/9-3

0/-6

= 0

The value of r is -10 for line with slope 2/5 .

What is slope?

A line's slope, often known as its gradient, is a numerical representation of the line's steepness and direction.

Main Body:

We know that the slope of line in two point form is

(y₂-y₁)/(x₂-x₁) = m where m = slope

given points are (-3,r) and (7,-6) m= 2/5

(-6-r)/(7+3)= 2/5

(-6-r)/10 =2/5

therefore value of r= -10

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The height of the electric pole is 12 m

When an electric wire falls, its one end touches the ground at P, 5 m away from the base of the pole,

base = 5

length of the wire from the top of the pole to the ground is 13 m

Height of the plant can be calculated by pythagoras theorem

h² = p² + b²

13² = p² + 5²

p² = 169 - 25

p = √144

p = 12m

Therefore, the height of the electric pole is 12 m

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Answer:

30%

Step-by-step explanation:

To calculate the percent of change, you find the amount of change and divide that my the original amount

[tex]\frac{3-2.1}{3}[/tex] = [tex]\frac{.9}{3}[/tex] = .3  As a percent, this would be 30%

The expression that shows the distance you would drive from the library to the grocery store along this road is; |-5|+|7|

An absolute value inequality is defined as an expression that has absolute functions as well as inequality signs. For example, the expression |x + 5| > 1 is an absolute value inequality that contains a greater than symbol.

Now, from the inequality line graph attached, we see that the point of the library is at -5 on the line graph.

Similarly, we also see that the point of the grocery store which i will liken to the maths class is at the point 7.

Thus, the distance between both points when we take absolute values into consideration is; |-5|+|7|

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The equation using the absolute value function is x+2y-8=0.

In the given graph, we have:

(h, k) ∈ (4, 2) and a = -1/2

In the general absolute value function, substitute these values:

Let's f(x) be y:

Therefore, the equation using the absolute value function is x+2y-8=0.

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The radical form of each of the given expressions are;

1) 2^(2/3) =  ∛(2²)

2) 3^(1/3) = ∛3

3) 3^(3/2) = √3³

4) 2^(1/2) = √2

The radical form of the expression [tex]a^{\frac{x}{y} }[/tex] is; [tex]\sqrt[y]{a^{x} }[/tex]

Thus, we can solve each of the given expressions;

1) We are given the expression as 2^(2/3).

Thus;

x = 2 and y = 3 and we have; ∛(2²)

2) We are given the expression as 3^(1/3).

Thus, x = 1 and y = 3 and so we have;

∛3

3) We are given the expression as 3^(3/2). Thus;

x = 3 and y = 2 and so we now have; √3³

4) We are given the expression as 2^(1/2). Thus;

x = 1 and y = 2 and so we now have; √2

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After rotation, the coordinates of the vertex of the rhombus become:

We know ,  when a point (x,y) rotates 270° counterclockwise about the origin, our point (x,y) becomes (y,-x)

From the graph the coordinates of the vertex of the rhombus are:

Therefore after rotation, the coordinates of the vertex of the rhombus become:

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Answer:

Step-by-step explanation:

The slope of the line y = -5x-4 is -5 or -5/1 so the slope of the perpendicular line is +1/5 eg…

y = x/5 + c

To find c we substitute x=15, y=-2

-2 = 15/5 + c

-2 = 3 + c

C = -5

So the equation is

Y = x/5 - 5

The graph of the function f(z) = - 0.25z + 4 is drawn.

Drawing the graph (curve) of the appropriate function is the process of graphing a function. Although graphing simple functions like linear, quadratic, cubic, etc. is very straightforward, complicated functions like rational, logarithmic, etc. need some expertise and an understanding of certain mathematical principles.

Drawing a function's representation as a curve on a coordinate plane is known as graphing. Every point on a curve (or graph) that represents a function satisfies the function equation.

A collection of edges that are ordered pairings of vertices (also known as directed edges, directed links, directed lines, arrows, or arcs) is displayed

The graph of the function is drawn. On the x-axis, the z-variable variables and on the y-axis the f(z) values are shown.

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Answer: 1/12

Step-by-step explanation: If the candy jar is only 1/4 full, and there's 3 brothers, they would each receive 1/3 of 1/4. THis would be 1/12 of the jar.

The evaluation of the expression (2.4) · (1.3) gives 3.12

From the question, we have the following expression that can be used in our computation:

(2.4) · (1.3)

Express as products

This gives

(2.4) * (1.3)

Remove the brackets

So, we have the following representation

2.4 * 1.3

Evaluate the product

3.12

Hence, the solution is 3.12

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Answer:

H = 30 ft

Step-by-step explanation:

Since the triangle is 90 degrees and we have to find out how tall the streetlight is we have to subtract 90 and 40 degrees. Which we get 50 degrees, after we subtract 20 from the 50 degrees. So we get 30 ft or 30 degrees.

The diagonal of the rectangle is 14.87 units.

A rectangle is a two-dimensional shape where the length and width are different.

The area of a rectangle is given as:

Area = Length x width

We have,

Area of rectangle = 110 square units

Length = 11 units

Area of a rectangle = Length x Wide.

110 square units = Length x Wide

110 = 11 x Wide

Wide = 110/11

Wide = 10

Now,

The diagonal of a rectangle.

Using the Pythagorean theorem we get,

Diagonal² = Wide² + Length²

Diagonal² = 10² + 11²

Diagonal² = 100 + 121

Diagonal² = 221

Diagonal = √221

Diagonal = 14.87 units.

Thus,

The diagonal of the rectangle is 14.87 units.

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Answer:

one is 203

two is 87

Step-by-step explanation:

We use Inferential Statistics is used to estimate how likely it is that a statistical result based on data from a random sample is representative of the population.

Given that;

What kind of statistics is used to gauge the likelihood that a statistical finding based on information from a random sample is representative of the population the sample is presumed to have been drawn from?

Inferential Statistics:

You attempt to conclude using inferential statistics that go beyond the immediate facts alone. For instance, we use inferential statistics to try to infer what the population would think from the sample data. Alternately, we utilize inferential statistics to assess the likelihood that an observed difference between groups in this study is a reliable one or one that may have occurred by chance. Descriptive statistics are used to simply describe what's happening in our data, while inferential statistics are used to conclude more general conditions from our data.

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90° is the least angle measure by which this figure can be rotated so that it maps onto itself.

The correct option is (B)

From the figure,

As the figure has two axis of symmetry, placing x and y axis such that the origin lies on its centroid.

Angle between x axis and y axis is 90°.

So rotating any degree which is a multiple of 90 i.e., 90°, 180°, 270°, 360°...… would yield the original figure.

Therefore, 90° is the least angle measure by which this figure can be rotated so that it maps onto itself.

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Alexi will not like the drink because the ratio of liquid to ice is 1/1.

Alexi likes her drink to have a liquid-to-ice ratio of about 1/3. A fast food restaurant put 16 ounces of ice in her 32-ounce cup. We need to find out if Alexi will like her drink or not, and if not, why not.

Let the ratio of the liquid to the ice in the drink be represented by the variable "R". The total volume of the cup is 32 ounces. The amount of ice in the cup is 16 ounces. So the amount of liquid in the drink is the difference between these two amounts. Hence, the amount of liquid in the cup is 32 - 16 = 16 ounces.

The ratio of the amount of liquid to the amount of ice in the drink is calculated below.

R = 16/16

R = 1/1

Hence, the ratio of the amount of liquid to the ice in the drink is 1/1. So, Alexi will not like her drink.

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The value of x in the given triangle is x = 12  .

Angle Sum Property of the Triangle states that the sum of measure of all three sides of the triangle is 180° .

In the question ,

a triangular figure is given

in which , the measure of angle A is (6x - 19)°

the measure of angle B is [tex]=[/tex] 84°

the measure of angle C is [tex]=[/tex] (3x + 7)°

So , By Angle sum property ,

we get

∠A + ∠B + ∠C [tex]=[/tex] 180°

substituting the values of angle A, B and C ,

we get

(6x - 19)° [tex]+[/tex] 84° + (3x + 7)° [tex]=[/tex] 180°

6x - 19 [tex]+[/tex] 84 [tex]+[/tex] 3x + 7 [tex]=[/tex] 180

9x + 72 = 180

9x = 180 - 72

9x = 108

x = 108/9

x = 12

Therefore , the value of x is [tex]=[/tex] 12

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