Probability and Statistics Question

Answer:

1.  x-intercept = (1, 0),   y-intercept = (0, -2)

7.  y + 4 = -6( x - 7)

Step-by-step explanation:

Given point-slope equation:

[tex]y-2=2(x-2)[/tex]

The x-intercept is when y = 0:

[tex]\begin{aligned}y=0\implies 0-2 &=2(x-2)\\-2&=2x-4\\2&=2x\\x&=1\end{aligned}[/tex]

The y-intercept is when x = 0:

[tex]\begin{aligned}x=0\implies y-2 &=2(0-2)\\y-2&=2(-2)\\y-2&=-4\\y&=-2\end{aligned}[/tex]

Therefore, the intercepts are:

To graph the equation, plot the intercepts and draw a straight line through them.  (See attachment 1).

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[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}[/tex]

Given:

Substitute the given slope and point (7, -4) into the formula to write the equation of the line in point-slope form:

[tex]\implies y-(-4)=-6(x-7)[/tex]

[tex]\implies y+4=-6(x-7)[/tex]

To graph the line, find the value of y when x = 6 and when x = 8:

[tex]\begin{aligned}x=6\implies y+4 &=-6(6-7)\\y+4 &=-6(-1)\\y+4&=6\\y&=2\end{aligned}[/tex]

[tex]\begin{aligned}x=8\implies y+4 &=-6(8-7)\\y+4 &=-6(1)\\y+4&=-6\\y&=-10\end{aligned}[/tex]

To graph the equation, plot the points (6, 2) and (8, -10) and draw a straight line through them.  (See attachment 2).

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Please note that I have drawn the graphs using the same size 7x7 grids as shown in your question paper.  If you wish to graph more of the line, please change the scale from those I have used.

The solution to the logarithmic expression log²x + log²(x + 10) = log²11 is;

x = -11 and 1

We are given the logarithmic expression as;

log²x + log²(x + 10) = log²11

By the power rule of logarithm, we know that; log²x = 2log x

Thus;

log²x + log²(x + 10) = log²11 can be expressed as;

2log x + 2log (x + 10) = 2log 11

Divide through by 2 to get;

log x + log (x + 10) = log 11

We know from product rule of logarithm that log (ab) = log a + log b. Thus; log x + log (x + 10) = log 11 is;

log x(x + 10) = log 11

Log cancels out to get;

x² + 10x - 11 = 0

Using quadratic equation calculator gives;

x = -11 and 1

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The most general antiderivative of the function is -7cosx-4secx+C on the interval (-π/2,π/2) is not defined.

Given that,

We have a function f(x)=7sinx -4secx tanx.

We have to find the most general antiderivative of the function on the interval (-π/2, π/2).

We know that,

Take the function,

f(x)=7sinx -4secx tanx.

The antiderivative is

= [tex]\int {7sinx-4secxtanx} \, dx[/tex]

= [tex]7\int{sinx} \, dx -4\int {secxtanx} \, dx[/tex]

= 7(-cosx)-4[tex]\int {sinx/cos^{2}(x) } \, dx[/tex]

Take cosx =u

-sinxdx=du

= -7cosx-4[tex]\int {-1/u^{2} } \, du[/tex]

= -7cosx-4(1/u)+C

=-7cosx-4(1/cosx)+C      ( since we know u=cosx)

= -7cosx-4secx+C

Now for the interval (-π/2,π/2)

= -7(cosπ/2-cos(-π/2))-4(secπ/2-sec(-π/2))+C

= -7(0-0)-4(∞-∞)+C

=not defined

Therefore, The most general antiderivative of the function is -7cosx-4secx+C on the interval (-π/2,π/2) is not defined.

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The length AE of the rhombus is √195 units

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

AD = 4x + 2

DC = 7x - 13

BD = 34

All the four sides of a rhombus are congruent

This means that

DC = AD

Substitute the known values in the above equation, so, we have the following representation

7x - 13 = 4x + 2

Evaluate the like terms

3x = 15

Divide both sides by 3

x = 5

Substitute x = 5 in AD = 4x + 2

So, we have

AD = 4 x 5 + 2

AD = 22

The length AE of the rhombus is then calculated as

AE² = AD² - (BD/2)²

Substitute the known values in the above equation, so, we have the following representation

AE² = 22² - (34/2)²

Evaluate

AE² = 195

Take the square roots

AE = √195

Hence, the length is √195 units

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Answer:

translation of 2 squares left and 1 square down

Step-by-step explanation:

consider the top vertex of both figures

S → T

then shape T is a translation of shape S

by moving 2 squares to the left and 1 square down

The Question is based on the concept of Linear Equations and its answer will vary as the values of x and y varies

What is Linear Equations?

A linear equation is an algebraic equation in which the unknown variable is represented by a linear combination of terms and constants. It is a mathematical expression that can be written in the form ax + b = c, where a, b, and c are constants, and x is an unknown variable. Linear equations can be used to describe and solve a variety of real-world problems, such as finding the cost of a product or the distance between two points. Linear equations are also used in the fields of calculus, geometry, and physics.

Here we will just take value of x = 1 and y = 2 to show how this works
putting these values in all 6 Linear Equations we will get that
2x+y = 2(1)+2= 2+2 = 4
similarly in other 5 Question.
3x+2y = 7
3y + 2x = 8
10x + 4y + 2x = 10 + 8 + 2 = 20
6y + 5x = 12 + 5 = 17
7x + 4y = 7 + 8 = 15

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The account balance of Bob Rowinski if he kept the money on deposit for 6 months is $4,032.00.

The compound interest formula can be expressed as;

A = P(1 + r/n)^(n*t)

Where A is accrued amount, P is principal, r is interest rate, t is time elapsed.

Given the data in the question;

Plug the given values into the above formula and solve for A.

A = P(1 + r/n)^(n*t)

A = $4000( 1 + 0.016/2 )^(2*0.5)

A = $4000( 1 + 0.008 )^(1)

A = $4000( 1.008 )

A = $4,032.00

Therefore, the accrued amount after half a year is $4,032.00

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Answer:

Step-by-step explanation:

1)11357*(105.7/100)^t

2)1 year 12000.121  2 year 12684  5 year 14979.1  10 years 19763.3

3)11357*(105.7/100)^t=22714 so t+12.5

The value of C using Pythagorean Theorem when a equal 5feet and b equals 18feet then, C = 18.68

In mathematics, the Pythagorean theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle and is written as a^2 + b^2 = C^2

Using the Pythagorean theorem a^2 + b^2 = C^2

from the question we are given 5 feet and 18feet respectively

to find c we substitute the value into the equation

a^2 + b^2 = C^2

a= 5feet and b= 18 feet

5^2 + 18^2 =C^2

25 + 324 = C^2

349 =C^2

Square root both side

C= [tex]\sqrt{349}[/tex]

C = 18.68

Therefore, C in the equation is C = 18.68

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Using Pythagoras theorem the value of c is 18.68 feet

Pythagoras theorem or Pythagorean theorem is an important topic in Mathematics, which explains the relation between the sides of a right-angled triangle. The sides of the right triangle are also called Pythagorean triples.

The value of c can easily be calculated using Pythagoras theorem which is given as;

c² = 5² + 18²

where;

c² = 25 + 324

c² = 349

c = √349

c = 18.68 feet

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Answer:

1/2

Step-by-step explanation:

The statements that are true for a translation are:
The distances between points on the polygon are preserved by the transformation.
The distance between corresponding points in the image and pre-image is constant.
These statements are true for a translation because when an object is translated, it is shifted a certain distance in a certain direction. This means that the distances between points on the polygon remain the same and the distance between the corresponding points in the image and pre-image is constant.

Translation is the process of converting written, spoken, or visual information from one language into another. It is a complex process involving both linguistic knowledge and cultural understanding. Professional translators use a range of techniques to accurately convey the meaning of a text, including knowledge of grammar, syntax, and idiomatic expressions. Translators also take into account the cultural context of the text, ensuring that the translation reflects the same cultural references and nuances as the original. Translation can also refer to the conversion of DNA sequences from one form to another, such as from RNA to protein.

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Option A is correct.

What is increasing and decreasing graphs?

Generally speaking, we are aware that if something is growing, it is moving upward, and if it is shrinking, it is moving downward. As a result, if we talk about a function's graph, an increasing function is one that is moving upward, and a decreasing function is one that is moving downward. 

From the graph, we infer that the sunlight, that is the shaded area increased in the given time. Which means that the sunlight was less.

From the milkweed population graph, we see that the milkweed population decreased over time.

Hence the most supportive hypothesis would be option A.

The milkweed population is a biotic factor that decreased as the amount of sunlight, an abiotic factor, decreases.

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4/10 is the fraction that is equivalent to the given fraction model

What is an equivalent fraction ?

According to equivalent fractions, two or more fractions are considered to be equal if, following simplification, both provide the same fraction. Let's imagine that a/b and c/d are two fractions. If these fractions are simplified to produce comparable fractions, such as e/f, they are then equal to one another.

For instance, if we simplify 5/15, the resulting fraction is the same as 1/3, hence that is the equivalent fraction of 1/3.

The fractions with distinct numerators and denominators but the same value are said to be equivalent fractions. For instance, since 2/4 and 3/6 both equal the 12, they are identical fractions. An element of a whole is a fraction. The same amount of the whole is represented by equivalent fractions.

As in the given model 2 out of 5 blocks are in red color which means the equivalent fraction to the given model is 2/5 which is equal to 4/10

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Answer:

2

Step-by-step explanation:

2x-1 = __x-1

Make both sides match to make the statement true.

2x-1 = 2x-1

Answer:

1/8, 1/8, 1/4, 1/4, 1/16, 1/16, 1/16, 1/16 = 1

1/2, 1/2 = 1

Step-by-step explanation:

from left to right

is this music class or math class lol?

Based on the provided information, Jerry's Z score will be negative, while Corey's Z score will be positive.

A Z-score refers to a numerical measurement that defines the raw value's relationship to the mean of a group of values. It is measured in terms of standard deviations from the mean. If a Z-score is 0, it means that the data point's score is identical to the mean score. A negative z-score indicates that the data point is below average or mean and a positive z-score indicates that the data point is above average or mean. Consider the formula for z score which is given by:

z = (x - µ)/σ where x is the given data value, µ is the mean, and σ is the standard deviation.

Hence, if the x < µ, the z score will be negative while if x > µ, the z score will be positive. As Corey scored higher than the mean on his SAT, his z score will be positive, and Jerry scored lower than the mean on his SAT, his z score will be negative.

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a)  minimum of nine hikers might have covered the distance between 6 and 17 miles because it falls within the standard interval of 10 ≤ x ≤ 15.

b) The maximum no. of hikers who might have covered the distance between 6 and 17 miles is 19.

What do minimum and maximum value mean?

Rearrange the function using fundamental algebraic concepts to get the value of x when the derivative equals 0. This response gives the x-coordinate of the function's vertex, which is where the maximum or minimum will occur. To find the minimum or maximum, rewrite the solution into the original function.

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Answer:

x = ± [tex]\sqrt{5}[/tex] x = 3

Step-by-step explanation:

to find the zeros set f(x) = 0 , that is

x³ - 3x² - 5x + 15 = 0 ( factor the first/second and third/fourth terms )

x²(x - 3) - 5(x - 3) = 0 ← factor out (x - 3) from each term

(x - 3)(x² - 5) = 0

equate each factor to zero and solve for x

x - 3 = 0 ⇒ x = 3

x² - 5 = 0 ( add 5 to both sides )

x² = 5 ( take square root of both sides )

x = ± [tex]\sqrt{5}[/tex]

the zeros of f(x) are then

x = - [tex]\sqrt{5}[/tex] , x = [tex]\sqrt{5}[/tex] , x = 3

The scale drawing's representation of the rectangle floor's circumference is 68 inches.

Area is the total amount of space that an object's shape or a flat (2-D) surface occupy.

Create a square on paper by using a pencil. Two dimensions make it up. A shape's area on paper is the space it takes up.

Imagine that your square is made up of smaller unit squares.

The area of a figure is equal to the number of unit squares required to completely cover the surface area of a particular 2-D shape. Square cms, square feet, square inches, square meters, etc. are a few common units for measuring area.

To get the area of the square figures presented below, draw unit squares with 1-centimeter sides. Therefore, the shape will be measured.

According to our question-

P = 2L + 2W

W = 5

P = 2L + 2(5) = 16

2L + 10 = 16

2L = 6

L = 3 ft

Hence, The scale drawing's representation of the rectangle floor's circumference is 68 inches.

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The equation of the transformed graph will be y = -3(2ˣ) + 2.

Transformation is rearranging a graph by a given rule it could be either increment of coordinate or decrement or reflection.

If we reflect any graph about y = x then the coordinate will interchange it that (x,y) → (y,x).

Suppose the equation of the given graph is y = A 2ˣ + k.

Substitute,(0,-1)

-1 = A 2⁰ + k

A + k = -1                (1)

Substitute, (1,-4)

-4 = A 2¹ + k

2A + k = -4            

A + k/2 = -2            (2)

Subtract 1 - 2 as

k - k/2 = -1 + 2

k/2 = 1

k = 2

And, A = -2 - 2/2

A = -3

Thus y = -3(2ˣ) + 2

Hence "The equation of the transformed graph will be y = -3(2ˣ) + 2 ".

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Answer:

Below

Step-by-step explanation:

x,y => ( +4 , -3)      because it is shifted 4 units to the right and down 3 units

In the given triangle, the angle between the two sides 5 and 6 is nearest 41°.

The term triangle means the polygon which has three sides and three angles and three vertices,

Here we have given that three  sides of a triangle have lengths 4, 5, and 6.

And here we need to find the angle between the two sides 5 and 6

According to the given values, let us consider a = 4, b = 5 and c = 6

So, the angle between 5 and 6 can be written as ∠b

And it can be calculated as the following is one way to perform the calculation and it may not be the best way.

∠B = arc cos(a² + c² - b²)/2ac

When we apply the values one the formula, then we get

=> 0.72273 rad

The approximate degree is written as

=> 41.41°

When we round off it then we get the resulting value,

=> 41°

Therefore, option (c) is correct.

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Answer:

408

Step-by-step explanation:

1+1+10 equals 12, then do 12 x 34, which equals 408

The required equation of the polynomial is p(x) = 4(x - 2 )⁵(x+5).

A polynomial in mathematics is an expression made up of coefficients and indeterminates and involves only the operations of multiplication, addition, subtraction, and non-negative integer exponentiation of variables.

Given the following properties: fifth degree, 2 is a zero of multiplicity 4, −5 is the only other zero, and the leading coefficient is 4.

The general form of the polynomial will be written as,

p(x) =  4(x - 2 )⁵(x+5).

Therefore, the required equation of the polynomial is p(x) = 4(x - 2 )⁵(x+5).

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Answer:

(25,-5)

Step-by-step explanation:

Option 3 and 4 are the operations involving complex numbers have solutions represented by (-6, 7).

Find the attachment answer

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The Class limit of the data is shown below.

Frequency tables or charts are used to represent frequency distributions. Frequency distributions can display the proportion of observations or the actual number of observations that fall inside each range. The distribution is known as a relative frequency distribution in the latter case.

Given:

From the data the class limit will be

45  - 54

55  -  64

65  -  74

75  -  84

85  -  94

95  -  104

105  -  114

class Boundary

44.5  - 54.5

54.5  -  64.5

64.5  -  74.5

74.5  -  84.5

84.5  -  94.5

94.5  -  104.5

104.5  -  114.5

Midpoint

49.5

59.5

69.5

79.5

89.5

99.5

109.5

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Answer:

The answer is 26.47.

Step-by-step explanation:

To get this answer, you simply need to subtract $105.66, by $79.19. You would get the answer of 26.47.

Step 1.       [tex]$105.66 x 5 = 528.3[/tex]

Step 2.      [tex]$79.19 x 5 = 395.95[/tex]

Step 3.     [tex]528.3 - 395.95 = 132.35[/tex]

Thus, with all these steps it would cost $132.35 more to go to the jets game than to go to the lions game.

The chart that could be used to display the data is given as follows:

Box plot; because the data is numerical.

A data-set can be classified as either numerical or categorical, depending on the values assumed by the data, as follows:

The correct charts for each type of data are given as follows:

The grade point average assumes numeric values, hence it is a numeric data and should be shown on a box plot, meaning that the last option is correct.

The box plot will show the number of grades in each range of the grade point averages, for example, how many grades between 0 and 1, how many between 1 and 2, and so on.

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The number of tiles must she purchase for the expense to be something similar at the two stores will be 30.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Margo can buy tile at a store for $0.79 per tile and lease a tile saw for $15. At one more store, she can acquire the tile saw free of charge assuming she purchases tiles there for $1.29 per tile.

Let 'y' be the total cost and 'x' be the number of tiles. Then the equation is given as,

y = 0.79x + 15       ...1

y = 1.29x               ...2

From equations 1 and 2, then we have

1.29x = 0.79x + 15

0.5x = 15

x = 30

The number of tiles must she purchase for the expense to be something similar at the two stores will be 30.

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