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The experimental probability of selecting the name Alex would be  40 % or 2 / 5

The experimental probability of selecting the name Alex can be found by the formula :

= Number of times Alex is drawn / Number of total draws x 100 %

Number of times Alex is drawn = 4 times

Number of total draws = 10 draws

The experimental probability of selecting Alex would therefore be :

= 4 / 10 x 100 %

= 0. 4 x 100 %

= 40 % or 2 / 5

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Answer:The answer is B

Step-by-step explanation:

The formal is A = a+b/2 time h

You just substitute the variables and get the answer

The price of new Tv is 107,990 including VAT .The percentage increase in price of tv is 8% in rate.

The current price of the plasma TV including VAT at 5% is 99,990 naira.

If the government raises VAT to 8%, the new price of the TV including VAT can be calculated as follows:

New price = current price * (1 + new VAT rate)

New price = 99,990 * (1 + 0.08)

New price = 107,992.2

Rounding the new price to the nearest 10 naira gives: 107,990 naira.

The increase in price of the TV can be calculated as follows:

Price increase = new price - current price

Price increase = 107,990 - 99,990

Price increase = 8,000

The percentage increase in price of the TV can be calculated as follows:

Percentage increase = (price increase / current price) * 100%

Percentage increase = (8,000 / 99,990) * 100%

Percentage increase = 8.0%

Therefore, the new price of the TV including VAT at 8% is 107,990 naira, and there is a 8.0% increase in price.

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____The given question is incomplete, the complete question is given below:

The advertised price of a plasma tv is 99,990 naira including vat at 5%. If the government raises vat to 8%,calculate the new price of the tv ,(to the nearest 10 naira) what is the percentage increase in price of the tv?

Answer:

Step-by-step explanation:

The vertex of the equation y = |x - 2 + 1| is (2, 1). The range of the equation depends on the value of x. When x < 2, the equation becomes y = -x + 1, which gives us a line with a slope of -1 that intersects the y-axis at (0,1) and has a minimum value of 1. When x >= 2, the equation becomes y = x - 1, which gives us a line with a slope of 1 that intersects the y-axis at (0,-1) and has no minimum value. Therefore, the range of the equation y = |x - 2 + 1| is [1, infinity).

Based on the information provided, the number of guests was 8 guests and the equation to represent this situation is 3/8 x + 2 = 5.

The first step to get to know the number of guests is to write an equation, this will help us discover the number of x  or guests. To write the equation, let's include the variable and values given:

3/8 x + 2 = 5

Now, let's solve this equation:

0.375x + 2 = 5

x = 5 -2/ 0.375

x = 3 / 0.375

x = 8 guests

Based on the above, it can be concluded that the number of guests, in this case, was 8.

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Which quantity is unknown?

the number of guest

_____________________________________

Write an equation that represents the situation.

3/8g + 2 = 5

_____________________________________

How many guests does David have?

g = 8

The length of the diagonal of an isosceles trapezoid is 2.83 cm

An isosceles trapezoid is a quadrilateral with two parallel sides and two non-parallel sides of different lengths.

In this case, the non-parallel sides are the bases, which are 3cm and 7cm long. The height is the perpendicular distance between the two bases and is given as 4cm. To find the length of the diagonals, we can use the Pythagorean theorem, which states that the sum of the squares of the two shorter sides of a right triangle is equal to the square of the hypotenuse (the longest side).

In an isosceles trapezoid, the diagonals are equal in length and bisect each other. Let's call the length of the diagonal d. We can draw a right triangle with one leg being half of the trapezoid's height (2cm), the other leg being half of the difference between the two bases (2cm), and the hypotenuse being the length of the diagonal d. Using the Pythagorean theorem, we get:

(2cm)² + (2cm)² = d²

4cm² + 4cm² = d²

8cm² = d²

d = √(8cm²)

d = 2√(2)cm

d = 2.83cm

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The two lines have the same slope and different y-intercepts, thus, the lines are parallel.

Here we want to find the relation between the two lines:

8x = 3y + 3

-24x + 9y = 3

First, we need to write these two as lines in the slope-intercept form. We will get:

3y = 8x - 3

y = (8/3)*x - 3/3

y = (8/3)*x - 1

And the other one:

9y = 3 + 24x

y = (3/9) + (24/9)*x

y = (1/3) + (8/3)*x

So, we can see that both lines have the same slope (and different y-intercept), thus, the lines are parallel lines.

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The diameter of a circle is 10 feet.

The circumference of a circle is the perimeter of the circle. It is the total length of the boundary of the circle. The circumference of a circle is the product of the constant π and the diameter of the circle.

Given that, the circumference of a circle is 31.4 ft.

We know that, circumference of a circle is 2πr

Now, 2πr=31.4

2×3.14×r=31.4

6.28r=31.4

r=31.4/6.28

r=5 feet

Then, diameter=2×radius =10 feet

Therefore, the diameter is 10 feet.

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the sum of each infinite geometric series sum is 36

If the ratio between any two consecutive terms in a series of numbers is always the same, the progression is said to be geometric. The ratio of any two successive terms in the sequence (common difference) must be the same for the sequence 2, 4, 8, or 16 to be a general prime.

S = a/1-r is a general formula for calculating the sum of an infinite geometric series, where s stands for the sum, a1 is the series first term, and r is the common ratio.

a = first term = 18

r = common ratio = 1/2

sum of Geometric progression

r< 1

S∞ = a/(1-r)

S∞ = 18/(1-1/2) =36

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If you were to  graph a sine function from the data listed in the table the days since Jan 8 is an independent variable and amount of moon visible is dependent variable

Given that, we have to graph a sine function from the data listed in the table

From the table we can see that there a two types of variables, The days since the Jan 8 and the amount of moon visible

The independent variable is defined as the variables that does not depends on any other variables

The dependent variable is defined as the variables that depends on other variables

Here the days since the Jan 8 does not depends on any other variables, so it is an independent variable. similarly the amount of moon visible depends on the days since Jan 8 value, so it is a dependent variable

Therefore, the days since Jan 8 is an independent variable and amount of moon light visible is dependent variable

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The given question is incomplete, the complete question is :

if you were to graph a sine function from the data listed in the table above, what values would be represented by the dependent variable and what would be represented by the independent variable?

Answer:

3 students are probably planning on taking orchestra as their next elective.

Step-by-step explanation:

Russell's results of the 16 surveyed students tells us that (4/16), or 25%, of the students planned on taking orchestra as their next elective.  If we assume this sampling is valid for other students (i.e., the sampled students were chosen at random and are believed to be representative of the rest of the students), we may use the same percentage for the next 12 students:

 (12 students)*(25%) = 3 students are probably planning on taking  orchestra as an elective.

The empirical rule tells us that for a normal distribution with mean μ and standard deviation σ, approximately 99.7% of the observations fall between 98 and 122.

Since the distribution is bell-shaped, we can use the empirical rule (also known as the 68-95-99.7 rule) to estimate the percentage of observations that fall within certain ranges.

According to the empirical rule, for a normal distribution with mean μ and standard deviation σ:

About 68% of the observations fall within one standard deviation of the mean, i.e., between μ - σ and μ + σ.

About 95% of the observations fall within two standard deviations of the mean, i.e., between μ - 2σ and μ + 2σ.

About 99.7% of the observations fall within three standard deviations of the mean, i.e., between μ - 3σ and μ + 3σ.

In this case, the mean is 110 and the standard deviation is 4. Therefore:

About 68% of the observations fall between 110 - 4 = 106 and 110 + 4 = 114.

About 95% of the observations fall between 110 - 2(4) = 102 and 110 + 2(4) = 118.

About 99.7% of the observations fall between 110 - 3(4) = 98 and 110 + 3(4) = 122.

So approximately 99.7% of the observations fall between 98 and 122.

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The 8.4% compounded quarterly is the better investment because it gives a good return.

Compound interest is “interest-on-interest”, or the ability of a financial instrument to generate earnings on its earnings.  Compound interest, can be calculated using the formula :

[tex]A = P(1 + \frac{r}{n} )^{nt}[/tex]

where A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

(i)S = P

S = P(1.0854) (1.0854)

AP(1) = 1.0846 - 1

AP(1)= 0.08546 or 8.546%

(ii)r = 0.084/4

AP(2) = (1 + 0.084/4)⁴ -1

AP(2) = 1.08688 - 1

AP(2) = 8.668%

The 8.4% compounded quarterly investment is therefore preferable.

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Answer:

x=-2log10(12)

Step-by-step explanation:

12x10^x/2=1/12

x/2=-log10(12)

x=-2log10(12)

The volume of the composite solid with cube and hemisphere is equal to 646.0 cubic centimeters ( nearest tenth ).

In the attached figure:

Composite figure consists of two figures:

Cube and hemisphere

Side length of the cube = 8cm

Diameter of the hemisphere = 8cm

Radius of the hemisphere 'r' = 8cm / 2

                                           = 4cm

Volume of the cube = ( side length )³

⇒ Volume of the cube = (8)³

⇒ Volume of the cube = 512 cubic centimeters

Volume of the hemisphere = ( 2/3 )πr³

⇒ Volume of the hemisphere = ( 2/3 ) × 3.14 × ( 4 )³

⇒ Volume of the hemisphere = 133.97 cubic centimeters

Volume of the composite figure

= Volume of the cube  + volume of the hemisphere

= 512 + 133.97

= 645.97 cubic centimeters

= 646.0cubic centimeters

Therefore, the volume of the composite solid is equal to  646.0cubic centimeters ( nearest tenth ).

The above question is incomplete, the complete question is:

Find the volume of the composite solid. Round your answer to the nearest tenth. The volume is about cubic centimeters.

Figure is attached.

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The factored form of 12x²y - 6x² is  6x²(2y - 1).

The expression to be factorise is as follows: 12x²y - 6x²​.

Factorisation is the is defined as the breaking down of an entity . Factorisation simply implies we decompose the expression.

Therefore,

12x²y - 6x²

let's find the factors of 12x²y  and 6x².

Hence, the factors are 6x²

12x²y - 6x² = 6x²(2y - 1)

Therefore, the factored form is 6x²(2y - 1)

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The coordinates of the fourth vertex of the parallelogram are (1, -3).

A parallelogram is defined as a special type of quadrilateral that has both pairs of opposite sides parallel and equal.

Three vertices are located at these coordinates: (-1, 2), (1, 2), and (-1,-3).

we have three points in the coordinate plane, we can use the concept of vector addition to find the fourth point.

The vectors connecting the first and second points, and the first and third points can be determined as follows:

v₁ = (1,2) - (-1,2) = (2,0)

v₂ = (-1,-3) - (-1,2) = (0,-5)

The fourth point will be located at the vector sum of the first point and the vector formed by adding v₁ and v₂.

v₃ = v₁ + v₂ = (2,0) + (0,-5) = (2,-5)

So, the fourth point will be located at:

(-1,2) + (2,-5) = (1,-3)

Thus, the coordinates are (1, -3).

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(i) none of these ailments, 26

(ii) arthritis but neither of the other two ailments, 17

(iii) exactly one of these ailments, 102

(iv) arteriosclerosis and loss of hearing but not arthritis, 16

We can use a Venn diagram to solve this problem.

Let A, B, and C represent the events of having arthritis, arteriosclerosis, and loss of hearing, respectively. Then, the given information can be represented as:

A = 70

B = 60

C = 80

A ∩ B = 35

A ∩ C = 33

B ∩ C = 31

A ∩ B ∩ C = 15

Using these values, we can find the answers to the questions:

(i) The number of senior citizens with none of these ailments is the complement of the union of A, B, and C. That is:

n(A ∪ B ∪ C)' = n(S) - n(A ∪ B ∪ C)

                      = 200 - (70 + 60 + 80 - 35 - 33 - 31 + 15)

                      = 26

Therefore, 26 senior citizens had none of these ailments.

(ii) The number of senior citizens with arthritis but neither of the other two ailments is:

n(A) - n(A ∩ B) - n(A ∩ C) + n(A ∩ B ∩ C)' = 70 - 35 - 33 + 15

                                                                   = 17

Therefore, 17 senior citizens had arthritis but neither of the other two ailments.

(iii) The number of senior citizens with exactly one of these ailments is the sum of the complements of the intersections of the events. That is:

n(A' ∩ B ∩ C') + n(A ∩ B' ∩ C') + n(A' ∩ B' ∩ C) = (200 - 60 - 31 - 15 - 33) + (200 - 70 - 31 - 15 - 33) + (200 - 70 - 60 - 15 - 35) = 102

Therefore, 102 senior citizens had exactly one of these ailments.

(iv) The number of senior citizens with arteriosclerosis and loss of hearing but not arthritis is:

n(B ∩ C) - n(A ∩ B ∩ C) = 31 - 15 = 16

Therefore, 16 senior citizens had arteriosclerosis and loss of hearing but not arthritis.

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If both bound trains leave together at 8, they will also start together at 11:45 the next time.

The LCM of two numbers is the smallest possible number that is divisible by both of those two numbers. The prime factorization and the division methods are generally used to find the LCM.

An eastbound train leaves the station every 25 minutes whereas a westbound train leaves the station every 45 minutes.

These two types of trains will leave the station together if the time is divisible by both 25 and 45, that is, the LCM of them.

Find the LCM of 25 and 45 using the prime factorization method.

25=5×5

45=3×3×5

LCM(25,45)=3×3×5×5

=225

As 1 hour equals 60 minutes, it follows that 225 minutes equals 3 hours and 45 minutes.

If 3 hours 45 minutes is added to 8 hours, it will be 11 hours 45 minutes.

Therefore, the two trains leave the station together at 11 hours 45 minutes.

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Answer:

12 red marbles.

Step-by-step explanation:

No step by step explanation.

Based on the given data set, the following statements are true:

The other statements are false because:

Lastly, The interquartile range is not 10. As calculated above, Q1 is 46 and Q3 is 52, so the IQR is 52-46=6.

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See transcribed text below

Use the following data set to answer the question.

(54, 45, 48, 51, 53, 44, 52}

Which statements about the data set are true? Select all that apply.

The standard deviation is approximately 3.7.

The interquartile range is 10.

There are no outliers.

The outlier is 54.

The standard deviation is approximately 49.6.

The interquartile range is 8.

The approximate length of arc CB is given as follows:

14.17 cm.

The circumference of a circle of radius r is given by the multiplication of 2 by the number π = 3.14 and the radius r, as follows, hence the equation is given as follows:

C = 6.28r.

The radius for this problem is given as follows:

r = 7 cm.

The angle relative to arc CB is given as follows:

2 x 58º = 116º.

As an entire circumference has an angle of 360º, the approximate length of arc CB is obtained as follows:

116/360 x 6.28 x 7 = 14.17 cm.

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Answer:

62 Feet

Step-by-step explanation:

26+36=62

6 + 6 = 12

20 + 30 = 50

12 + 50 = 62

Answer:

The scuba diver is 62 feet deep.

Step-by-step explanation:

We know the scuba diver has dived 36 feet. When he stops to look at the school of fish, he doesn't dive down any further and stays at 36 feet. He then dives down another 26 feet

All we would need to do is add 36 and 26, which would give you your answer of 62.

The equivalent expression to 14^6 is given as follows:

[(14^5)^3]/14^9.

When two terms with the same base and different exponents are divided, we keep the base and subtract the exponents.

The power of power exponential rule states that when a single base is elevated to multiple powers, the powers are multiplied.

Then the expression with the desired value of 14^6 is obtained as follows:

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Answer: 3x+7+4x-2

Step-by-step explanation: 3x+4=7x

7-2=5

so the answer should be 7x+5

The statement "Before using census data, researchers need to consider the timeliness of the data." is true because census data is only accurate and useful when it is up to date.

The United States Census Bureau updates the data every ten years, so the most recent data will be from 2010. Additionally, researchers should be aware of any changes to the census information over time and make sure they are using the most up-to-date version. Furthermore, researchers need to understand the scope of the census data and what it is designed to measure.

The United States Census covers the entire population of the United States, but it is important to know the specific topics covered by each census and what population groups are included. Finally, researchers should be aware of how the census data is collected and the potential for error or bias in the data.

If the data is outdated, it could lead to inaccurate results or conclusions. Therefore, researchers must consider the timeliness of the data before using it in any research project.

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The complete question is:

True or False: Before using census data, researchers need to consider the timeliness of the data.

The function for the Pakistani Rupee (y) in terms of UAE Dirhams (x) can be represented as, y = 71.59 x.

A function is defined as a relation from a set A to a set B for which an element in set A maps to one and only one image in set B.

Usually the set A consists of the independent variable and set B consists of dependent variable.

We have to find a function relating the conversion of Pakistani rupees and UAE dirhams.

Let y denotes Pakistani Rupees and x denotes the UAE dirhams.

We know that,

1 UAE dirham = 71.59 Pakistani Rupees

So,

2 dirhams = 2 × 71.59 = 143.18 rupees

In this way,

x dirhams = 71.59 x rupees

So, we can write this as,

y = 71.59 x

Hence the required function is y = 71.59 x.

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The slope of the line is 9.75 and the y-intercept is -25.

Two distinct but related concepts are referred tο by the phrase "linear function": A polynomial function of degree zero οr one that has a straight line as its graph is referred tο as a linear function in calculus and related fields.

Given: Yvette is saving mοney to buy holiday gifts. She will save the money she makes at her part-time job. Hοwever, she borrowed $25 from her sister which she has to pay back befοre she can start saving.

Let the linear functiοn that models the given situation be y = ax + b. Here, a and b are constants.  We can use this infοrmation to find the values of a and b.

We put x = 0 & y = -25 into y = ax + b

b = -25

Substitute the value of b intο y = ax + b

y = ax -25...(1)

Nοw we put x = 4 and y = 14 in equatiοn(1) and we get

14 = 4a - 25

4a = 39

a = 9.75

Substitute the value of a in equatiοn (1):

y = 9.75x - 25

Cοmpare the above function with the slοpe-intercept form of a line y = mx + c

m = 9.75, c = -25

Hence, the slοpe οf the line is 9.75 and the y-intercept is -25.

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The inequality representing the situation is w >= 15, where w represents the weight of a can of tomatoes and the inequality states that it must be greater than or equal to 15 ounces.

The inequality that represents the situation is w >= 15, where w represents the weight of a can of tomatoes. This inequality states that the weight of a can of tomatoes is greater than or equal to 15 ounces, meaning that every can of tomatoes weighs at least 15 ounces.

This inequality represents a constraint or a condition on the weight of a can of tomatoes. In mathematical terms, the inequality w >= 15 says that the value of w, which represents the weight of a can of tomatoes, must be greater than or equal to 15 ounces. Any value that satisfies this inequality is considered a valid solution for the weight of a can of tomatoes. For example, 15 ounces, 16 ounces, 17 ounces, and so on are all valid weights for a can of tomatoes that meet the requirement of weighing at least 15 ounces.

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The complete question is:

At a supermarket, Each tomato can in a store weighs at least 15 ounces.

Let w stand in for the can of tomatoes' weight.

Which inequality best captures the circumstances?

[tex]w < 15 w < 15 W > 15 w > 15[/tex]