O MEASUREMENT AND DATA
Introduction to the probability of an event
A spinner with 12 equally sized slices has 5 red slices, 3 blue slices, and 4 yellow slices. The dial is spun and stops on a slice at random. What is the probabili
that the dial stops on a slice that is not red?
Write your answer as a fraction in simplest form.
Explanation
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Dec

The degree to turn before walking 673 paces is 59 degrees

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

Lengths = 989 paces, 673 paces and 861 paces

These paces can be represented as

x = 989

y = 673

z = 861

The measure of the required angle (angle Z) i.e.  the degree to walk can be calculated using the following cosine rule

z² = x² + y² - 2xy * cos(Z)

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

861² = 989² + 673² - 2 * 989 * 673 * cos(Z)

Evaluate the exponents, the products and the summation

So, we have the following representation

741321 = 1431050 - 1331194 * cos(Z)

Evaluate the like terms

- 1331194 * cos(Z) = -689729

Divide both sides by  - 1331194

cos(Z) = 0.51812808651

Take the arc-cos of both sides

Z = 58.7

Approximate

Z= 59 degrees

Hence, the measure of the angle is 59 degrees

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Answer:

A

Step-by-step explanation:

as the graphic suggests : reflect (mirror) ABD across the line BD, and CBD is a mirrored but otherwise equal copy of ABD, which also makes angle C equal to angle A.

all the other answer options are creating new triangle that do not map to CBD.

The price of a 10-year $100 par value bond bearing a 10% coupon rate payable semiannually, and redeemable at 105, bought to yield 8% convertible semiannually, is its present value of $115.87.

The price of a bond is its present value.

The present value can be computed by setting the following parameters:

This can be done using an online finance calculator with the results as follows:

N (# of periods) = 20 semiannual periods (10 years x 2)

I/Y (Interest per year) = 8%

PMT (Periodic Payment) = $5 ($100 x 10% x 1/2)

FV (Future Value) = $105

Results:

Present Value (PV) = $115.87

Sum of all periodic payments = $100 ($5 x 20)

Total Interest = $89.13

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Answer: 115.87 (If you don't get this answer then the solution is incorrect.)

From the 5-number summary table, the answers came out as a) 60 students b) 90 students c) 20 students d) 40 students

What are quartile ranges?

The interquartile range in descriptive statistics reveals the spread of your distribution's middle half.

Any distribution that is sorted from low to high is divided into four equal portions using quartiles. The interquartile range (IQR) contains the second and third quartiles, or the middle half of your data set.

Median marks is the marks secured by 50% of students.

Hence, if there 120 students and the median marks is 73, the number of students who got more than 73 is 50% of 120, which is 60.

Q1 or the first quartile range is the marks obtained by 25% of students.

Hence, 25% of 120 students scored 55 and 75% of 120 students scored more than 55, which is 90.

For the 80 students in evening classes, 25% of the secured grade less than 45, the first quartile, which is 25% of 80, that is 20.

Similarly 50% of 80 students scored grade more than between 45 and 82, which is 40.

From the 5-number summary table, the answers came out as a) 60 students b) 90 students c) 20 students d) 40 students

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By graphing, the solution to the system, y = 5x + 2 and y = x - 2 is: A. (-1, -3)

The solution to a system of equations is the coordinates of an ordered pair that will make both of the equations to be true. This coordinates is determined by graphing.

To do this, plot both lines on a coordinate plane, then determine the coordinates of the point of intersection of both lines.

Given the system of equations,

y = 5x + 2

y = x - 2

The graph that shows both equations are attached below where the red line is y = 5x + 2, and y = x - 2 is the blue line.

The point of intersection is at (-1, -3). Therefore, the solution is:

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The if-then statement is:

If angles are vertical angles then their measure is equal.

and converse of the implication is:

If the measure of angles is equal then they are vertical angles.

What is the Converse Statement?

That sort of reversal is called a converse. Definition: The converse of a conditional statement is created when the hypothesis and conclusion are reversed. In Geometry, the conditional statement is referred to as p → q. The Converse is referred to as q → p.

We have given the statement:

Vertical angles are equal in measure.

A). Rewrite the statement as an if-then statement.

If angles are vertical angles then their measure is equal.

B). Write the converse of the implication

If the measure of angles is equal then they are vertical angles.

Hence, the if-then statement is:

If angles are vertical angles then their measure is equal.

and converse of the implication is:

If the measure of angles is equal then they are vertical angles.

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Answer:

x = - 3

Step-by-step explanation:

2(x - 6) + 2 = 4x - 4 ← distribute parenthesis on left side and simplify

2x - 12 + 2 = 4x - 4

2x - 10 = 4x - 4 ( subtract 4x from both sides )

- 2x - 10 = 4x - 4 ( add 10 to both sides )

- 2x = 6 ( divide both sides by - 2 )

x = - 3

Answer:

SOLUTION

2(X-6)+2=4X-4

open the blanket by multiplication

2x-12+2=4x-4

2x-10=4x-4

collect like term

2x+4x=-4+10

6x=6

divide both side by 6

x=1

The z-scores correspond to the oldest and youngest senators of ages 87 and 44 are 2.57 and -1.17. The z-score corresponding to the oldest senator of age 85 is 2.39.

A Z-score is a metric that quantifies how closely a value relates to the mean of a set of values. The formula to calculate this score [tex]z=\frac{x-\mu}{\sigma}[/tex].  Where z is the z-score, x is the observed value, μ is the sample mean, and σ is the sample standard deviation.

Given μ = 57.5 and σ = 11.5.

When x = 87, the z-score value is,

[tex]\begin{aligned}z&=\frac{87-57.5}{11.5}\\&=2.57\end{aligned}[/tex]

When x = 44, the z-score value is,

[tex]\begin{aligned}z&=\frac{44-57.5}{11.5}\\&=-1.17\end{aligned}[/tex]

When x = 85, the z-score value is,

[tex]\begin{aligned}z&=\frac{85-57.5}{11.5}\\&=2.39\end{aligned}[/tex]

The required answers are 2.57, -1.17, and 2.39.

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Answer:

  new triangle is similar to and 2 times the size of the original

Step-by-step explanation:

You want to construct a new triangle with the sides of the existing one being midsegments of the new one. Then you want to know the relationship between the triangles.

The attachment shows the described construction.

The sides of the original triangle are midsegments of the new triangle, so the new triangle is ...

If the position of a moving object at a time t the curvature of the earth would be 1/4t.

A curved path having various radii of curvature is known as a variable-curvature path. from: 2020 Control Systems Design of Bio-Robotics and Bio-mechatronics with Advanced Applications.

A straight line has zero curvature. In contrast to the tangent, which is a vector quantity, the curvature at a point is often a scalar quantity or one that can be described by a single real integer.

|| r (t) || = 3[tex]t^{2}[/tex], || r' (t) || = 2t, || T (t) || = 1

|| T' || = 1/2

Curvature K = || T' (t) || / || r' (t)  || = (1/2) / 2t

K = 1/4t

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Answer: She needs to ride 13.9 more kilometers on her bike to finish the race.

Step-by-step explanation:

==> 30 = 3.75 + 12.35 + x

Take 16.1 from both sides:

==> 30 = 16.1 + x

==> 30 = 13.9km

Answer:

Step-by-step explanation:

The answer would be 13.9, if you add 12.35 to 3.75 you get 16.1, then 16.1 added to 13.9 equals 30

The equation of slope intercept form is y = 3/2x + 12 if a line passes through the point (-6,3) and has a slope of 3/2.

The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation. The slope, m, is a measure of how steep a line is. The equation of a straight line that passes through a particular point and is inclined at a specific angle to the x-axis can be found using the point slope form. Every point on a line must satisfy the equation for the line in order for it to exist. This implies that a line is represented by a linear equation in two variables.

Given

A line passes through the point (-6,3)

and has a slope of 3/2

Slope intercept form

y = mx + b

Equation,

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

y - 3 = 3/2(x+6)

2y - 6 = 3x + 18

2y = 3x + 24

y = 3/2x + 12

The equation of slope intercept form is y = 3/2x + 12 if a line passes through the point (-6,3) and has a slope of 3/2.

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The option b "The index for any quarter must be between 0 and 2" is correct.

In the given question, we have to find the incorrect statement about a company has computed a seasonal index for its quarterly sales.

For its quarterly sales, the corporation has created a seasonal indicator.

Consequently, it is correct that the four quarterly seasonal index figures add up to 4.

True, the average index is 1.

In this situation, an index of 0.75 for the first quarter's sales implies that they were 25% below average, while an index of 1.10 shows that they were 10% over average.

Hence, the incorrect statement of the option b "The index for any quarter must be between 0 and 2" is correct.

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3) The tire diameter using the aspect ratio is; 29 inches

4) The aspect ratio of a standard print paper is; 22:17

The aspect ratio is defined as the relationship between the width and height.

Now, in this case, the aspect ratio must be in whole numbers and not decimals and as such we can solve as follows;

3) We are told that the aspect ratio of a tire is 50%.

Thus, the aspect ratio is; 50/100 = 1/2 or 1:2.

Now, we are told that width 10 inches, and the rim diameter is 19 inches, then it means that the tire diameter = 10/2 + 19 + 10/2 = 29 inches

4) The standard print paper is 11" by 8.5. This can also be written as;

11 by 17/2 or 11 * 2 : 17

= 22:17

This then gives us the aspect ratio.

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The values for the given data set is as follows 120 , 720 , 8 ,40320 , 6720 ,3628800 respectively.

The formula to calculate the permutation is , P = n! / (  n - r )!. Using this formula we get the result as,

P(6,3) = 6! / (6−3)!

​= 6! /  3!

​ = 120

P(8,1) = 8! / (8 - 1)!

​= 8! /  7!

​ = 8

P(6,5) = 6! / (6-5)!

6! / 1!

720

Similarly ,

P(8,8)= 40320

P(8,5) = 6720

P(10,9) = 3628800

A permutation is a specific arrangement of items. Set members or elements are arranged in a sequence or linear order here.

For example, the permutation of set A=1,6 is 2, as in 1,6,1.

There are no alternative ways to arrange the items in set A, as you can see.

In permutation, the elements must be organised in a specific sequence, whereas in combination, the order of the elements is irrelevant. Read also: Permutation And Combination

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Answer: 160 inches

Step-by-step explanation:

To put lights around the window, you will need a total of 32 + 48 + 32 + 48 = <<32+48+32+48=160>>160 inches of lights. You will need this much light to go completely around the window.

The solution of the inequality is greater than or equal to 18. The number of fruit snacks that were in the bag is 18.

What is the inequality?

In mathematics, inequalities specify the relationship between two non-equal values. Equal does not imply inequality. Typically, we use the "not equal sign (≠)" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

Given inequality is

X÷3  ≥  6

Rewrite left side expression:

X/3 ≥  6

Multiply both sides by 3:

X ≥  6 × 3

X ≥ 18

The value X is greater than or equal to 18.

Therefore the number of fruit snacks that were in the bag is 18.

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(a) Using y the manufacture can find the required diameter of the hole.

(b) The mean of the random variable y is 0.003.

(c) The standard deviation of the y is 0.0063.

(d) It is reasonable to assume that x1 and x2 are independent since peg and hole are made of different wood.

(e)  We can see that mean of y is greater than standard deviation of y, So mostly the peg maybe bigger than hole.

Given that x1 be the peg diameter with mean 0.25 in. and standard deviation 0.0006 in.and x2 be the hole diameter with mean 0.253in. and deviation 0.002 in.

a) y=x2-x1 denote the difference between hole and peg diameter

if y<0 , the peg won’t go inside the hole and

if y>0 ,the peg be loose to the hole

So using y the manufacture can find the required diameter of the hole.

b)Now, we have to find the mean of the random variable y

μ(y) = μ(x2) - μ(x1)

μ(y) = 0.253-0.25

μ(y) = 0.003

c) Now we have to find the standard deviation of the y

σ(y) = √{var(x1)+ var(x2)}(x1 and x2 are independent)

σ(y) = √0.000036+0.000004

σ(y) = √0.00004

σ(y) = 0.0063

d) It is reasonable to assume that x1 and x2 are independent since peg and hole are made of different wood.

e) With a standard deviation larger than the mean , it would be fairly likely to observe a negative value of y, so it would be a relatively common occurrence to find a peg that was too big to fit in the predrilled hole. We can see that mean of y is greater than standard deviation of y, So mostly the peg maybe bigger than hole.

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For an independent-measures t test, the option that describes the estimated standard error of the difference in sample means is D. an estimate of standard distance between the difference in the sample mean and the difference in the corresponding population mean.

A statistical test called a t test is employed to compare the means of two groups. It is frequently employed in hypothesis testing to establish whether a procedure or treatment actually affects the population of interest or whether two groups differ from one another.

The Independent Samples t Test compares the means of two separate groups to see if there is statistical support that the population mean values are statistically significantly different. A parametric test is called the Independent Samples t Test. For instance, you could determine whether first-year graduate salaries varied by gender using an independent t-test.

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Complete question

for the independent-measures t test, which of the following describes the estimated standard error of the difference in sample means (whose symbol is

a. a weighted average of the two sample

b. the difference between the standard deviationa

c. The variance

d. an estimate of standard distance between the difference in the sample mean and the difference in the corresponding population mean.

Answer:

Step-by-step explanation:

w

Answer:

x is 44 Hope that helps.

Answer:

[tex] \sqrt{176} [/tex]

[tex] \sqrt{16 + 11} [/tex]

[tex]4 \sqrt{11} [/tex]

Step-by-step explanation:

The answer is

[tex]4 \sqrt{11} [/tex]

We

need to express 176 as the product of its prime factors i.e. 176 = 2 × 2 × 2 × 2 × 11. Therefore, √176 = √2 × 2 × 2 × 2 × 11 = 4 √11 . Thus, the square root of 176 in the lowest radical form is 4 √11.

i hope this helped

The procedure is correct is  1 + tan²(theta) = sec²(theta)

What is  Fraction?

Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.

And

cos²(theta) = 1 - sin²(theta)

Are both valid identities

Keisha and the David.

As per the question Kisha and the David found the same value of the cosine theta as given by the  Sine theta = Negative Start Fraction 8 Over 17 End Fraction. The Keisha solution and the Davis solution for the solution were tan-squared (theta) + 1 = sec-squared (theta).

Thus the answer is both procedures are correct.

As they both wanted to find the solutions to the numerical problems they made two different methods.

Such as the Sine theta = Negative Start Fraction and the tan-squared (theta) + 1 = sec-squared (theta).

Hence both options are the same and true.

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The product of -2/7 x 7/4 to the simplest form in fraction is -1/2.

In arithmetic, a number expressed as a quotient, in which a numerator is divided by a denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator.

[tex]\frac{-2}{7} x \frac{7}{4}[/tex]

Solving this we multiply the fraction by multiply the numerator by numerator and also Denominator by Denominator  

= [tex]\frac{-14}{28}[/tex]

Simplify further  by dividing the numerator by denominator we have:

= [tex]\frac{-1}{2}[/tex]

Therefore, the the product of the fraction to the simplest form is -1/2 and this can also be written in decimal; -0.5

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The two polynomials whose difference is 2x^2 + x + 4 are

6x² + 3x + 5 and 4x² + 2x + 1.

Polynomial is an equation written as the sum of terms of the form kx^n.

where k and n are positive integers.

We have,

The difference between the two polynomials is 2x² + x + 4.

The two polynomials are:

6x² + 3x + 5 _____(1)

4x² + 2x + 1 ______(2)

The difference between (1) and (2)

6x² + 3x + 5 - 4x² - 2x - 1

2x² + x + 4

Thus,

The two polynomials are 6x² + 3x + 5 and 4x² + 2x + 1.

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Answer: After eight seconds, the bug can be at any point on the number line that is at a distance of at most 8 units from the origin. This includes all the integers from -8 to 8, inclusive, for a total of 17 possible positions. The probability of the bug being at any particular position is the same for all positions, which is 1/17.

After nine seconds, the bug can be at any point on the number line that is at a distance of at most 9 units from the origin. This includes all the integers from -9 to 9, inclusive, for a total of 19 possible positions. The probability of the bug being at any particular position is the same for all positions, which is 1/19.

The volume of the pentagonal prism as per the given values is obtained as 2.5 cm³.

A pentagonal prism has two pentagonal surfaces on the top and the bottom. It has ten vertices, 15 edges and 7 faces. The number of rectangular surfaces are five.

The expression for the volume of a regular pentagon is given as V =  5/2 × abh

Where h is the height and a and b are the length of the sides.

Now, the value of a, b and h as per the question is given as,

a = b = h = 1.

Then, the volume can be calculated as,

V = 5/2 × 1 ×1 × 1
   = 2.5

Hence, the volume of the regular pentagonal prism  is given as 2.5 cm³.

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If the perimeter of the  rectangle is 56m with length 18m the breadth is 10m

You should know that the breath of the rectangle is the two shorter sides of the rectangle.

The perimeter of the rectangle is the distance round the rectangle

In every rectangle, there are 2 Lengths and 2 breadths

This implies that the perimeter is

P= L+B+L+B

P=2L+2B

This implies that

56=2(18)+2B

⇒56=36+2B

56-36=2B

20=2B

Making B the subject of the relation we have

B=20/2

B=10m

Therefore the breadth of the rectangle is 10m

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