What is the value of x?

What Is The Value Of X?

Answers

Answer 1

Answer:

x = 3

Step-by-step explanation:

CD is an angle bisector and divides the opposite side into segments that are proportional to the other 2 sides, that is

\(\frac{BD}{AD}\) = \(\frac{BC}{AC}\) ( substitute values )

\(\frac{x}{2.25}\) = \(\frac{4}{3}\) ( cross- multiply )

3x = 4 × 2.25 = 9 ( divide both sides by 3 )

x = 3


Related Questions

How many 9 digit numbers have their first and last digits even?

Answers

There are 900000000 nine-digits numbers and exactly half of them have an even sum of digits (because every number can be paired with another of the opposite parity by changing the last digit).

Answer:  200,000,000.

we have 9 spaces we need to fill in

There are 10 total numbers(0–9)

There are 5 even numbers(0,2,4,6,8)

fill from left to right

u cannot start with 0 so pick another number 2,4,6,8 any of those

4*10^7*5= 20*10^7 = 2*10^8

200,000,000.

HELP HELP HELP HELP HELP HELP HELP

HELP HELP HELP HELP HELP HELP HELP

Answers

Answer:

\(h(x)=\frac{1}{5}x\)

Step-by-step explanation:

\(6x+y=4x+11y\\\\6x-4x=11y-y\\\\2x=10y\\\\y=\frac{2x}{10}\\\\y=\frac{1}{5}x\)

so h(x) is

\(h(x)=\frac{1}{5}x\)

HURRY!!!!
The value of a baseball card can be represented by the equation y = 3 x + 39, where x represents the number of years that Robert has owned the card and y represents the total value, in dollars, of the card. What was the value of the card when Robert originally purchased it?
$3
$13
$36
$39

Answers

The value of the card was $13 when he originally purchased it.

Answer:

mark as brainliest plz...        it is $39

Step-by-step explanation:

ayeeeeeeeeeeeeeee

Find the value of x. Round to the nearest tenth.

Find the value of x. Round to the nearest tenth.

Answers

Answer:

x = 10.8

Step-by-step explanation:

Cos∅ = adj/hyp

Cos26 = x/12

Multiply both sides by 12

12 * cos26 = x

Use calculator

10.785528555590004 = x

Round

x = 10.8

Find the missing length

Find the missing length

Answers

Answer:

x = 16.64

option A

Step-by-step explanation:

Using the pythagoreom therom

Answer:

16.64

Step-by-step explanation:

Since it's a right angled triangle, we use Pythagoras theorem:

(Hypotenuse)² = (base)² + (perpendicular)²

x² = 14² + 9²

x² = 196 + 81

x² = 277

√x² = √277

x = 16.64

Express 1/10 cm as a fraction of 3 metres​

Answers

Answer:

1/3000

Step-by-step explanation:

3 meters to centimeters:

3 × 100 = 300

= 1/10 ÷ 300

= 1/10/300

= 1/(10×300)

= 1/3000

A certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales in 1997 were up 7 percent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 percent from 1996, what is the ratio of revenue from car sales in 1996 to revenue from truck sales in 1996

Answers

Answer:

The answer is "1:2"

Step-by-step explanation:

Let 96 car sales are X and 96 truck sales are Y  And income from 97 cars is 0.89X, income from 97 trucks is 1.07Y

\(\to \frac{(0.89X+1.07Y)}{(X+Y)}=1.01\\\\\frac{X}{Y}=?\\\\\to \frac{(0.89X+1.07Y)}{(X+Y)}\ \ \text{Divide by Y and get}\ \ \frac{( \frac{0.89X}{Y}+1.07)}{(\frac{X}{Y}+1)} =1.01\\\\\)

Then

\(\to \frac{X}{Y}=1:2\)

Evaluate the expression for b = 8
2b=?

Answers

2b=16 because 2(8) = 18 you have to replace b with 8

Answer: 16

2(8)

16

Step-by-step explanation:

b = 8

2(8)

= 16

Tri-Slope has warrants outstanding in addition to its common stock. There are 5 million shares of stock and 1 million warrants. The stock is selling for $43 each and with each warrant you can buy a new share for $40. Determine the new stock price if all warrants are exercised immediately. $42.5 $40.5 $43 $40 Can not be calculated.

Answers

If all 1 million warrants of Tri-Slope are exercised immediately, the new stock price would be approximately $42.5, resulting in a total market value of $255 million with 6 million shares.

To determine the new stock price if all warrants are exercised immediately, we need to calculate the total number of additional shares that would be created and then adjust the stock price accordingly.Given that there are 5 million shares of stock and 1 million warrants, if all warrants are exercised, an additional 1 million shares would be created. Each warrant allows the purchase of a new share for $40.To exercise all 1 million warrants, it would cost a total of 1 million * $40 = $40 million.

The total number of shares after exercising all warrants would be 5 million + 1 million = 6 million shares.The total market value of the company after exercising the warrants would be $40 million (cost of exercising warrants) + ($43 per share * 5 million shares) = $40 million + $215 million = $255 million.

Therefore, the new stock price would be the total market value of the company divided by the total number of shares: $255 million / 6 million shares ≈ $42.5.So, the new stock price if all warrants are exercised immediately would be approximately $42.5.

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the base of a pyrimid is one foot square and the hight of each face is 14 inches what is the surface area of the pyrmid?

Answers

Therefore, the total surface area of the pyramid is 312 square inches.

To find the surface area of a pyramid, we need to find the area of the base and the area of each triangular face and then add them together.

The area of the base is 1 square foot = 12 inches x 12 inches = 144 square inches.

To find the area of each face, we need to find the area of the corresponding triangle. We know that the height of each face is 14 inches and the base of each triangle is half the base of the pyramid, which is 6 inches. Therefore, the area of each face is:

(1/2) x base x height = (1/2) x 6 inches x 14 inches = 42 square inches.

Since there are four triangular faces, the total area of the faces is 4 x 42 square inches = 168 square inches.

Therefore, the total surface area of the pyramid is:

144 square inches (base) + 168 square inches (faces) = 312 square inches.

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pat designs a patio with a trapezoid shaped deck consisting of 16 rows of congruent slate tiles. the numbers of tiles in the rows form an arithmetic sequence. the first row contains 15 tiles and the last row contains 30 tiles. how many tiles are used in the deck?

Answers

The first row has 15 tiles and the last (16th) row has 30 tiles. The total number of rows is 16, which means there are 15 steps between the first and the last row.

Let d be the common difference between the rows. We can write the following equation:

15 + 15d = 30

Solving for d:

15d = 30 - 15
15d = 15
d = 1

Now that we know the common difference is 1, we can use the arithmetic series formula to find the total number of tiles used in the deck:

S = n * (a1 + an) / 2

Here,
S = total number of tiles
n = number of rows (16)
a1 = number of tiles in the first row (15)
an = number of tiles in the last row (30)

S = 16 * (15 + 30) / 2
S = 16 * 45 / 2
S = 16 * 22.5
S = 360

So, Pat used a total of 360 tiles for the trapezoid-shaped deck.

Answer:360

The number of tiles used in the deck is 525. This can be answered by the concept of arithmetic sequence.

Let x be the number of tiles in each row in the arithmetic sequence. Then, the sum of the number of tiles in all 16 rows can be expressed as the sum of an arithmetic series:

S = (n/2)(a + l),

where n is the number of terms, a is the first term, and l is the last term. In this case, n = 16, a = 15, l = 30, and x is the common difference, which can be found by using the formula:

x = (l - a) / (n - 1)

Substituting the values given, we get x = 1.25. Therefore,

S = (16/2)(15 + 30) = 525.

Therefore, the total number of tiles used in the deck is 525.

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​ TV and WY areparallellines. S T U V W X Y Z Which angles are corresponding angles?

Answers

Answer:

A picture provided would be better, but here's a picture to help you find an answer to your question.

Step-by-step explanation:

The two angles marked in red are corresponding angles on a pair of parallel lines. Corresponding angles are ALWAYS congruent to each other.

 TV and WY areparallellines. S T U V W X Y Z Which angles are corresponding angles?

Brianna solved a two-step equation, but she made a mistake along the way. 0. 1x 3 = 1. 7 (-3) 0. 1x 3 = 1. 7 (-3) Line 1 0. 1x = -1. 3 Line 2 (-0. 1) 0. 1x = -1. 3 (-0. 1) Line 3 x = -1. 4 Line 4 What mistake did Brianna make? On Line 1, Brianna should have subtracted 3 instead of adding -3. On Line 1, Brianna violated the addition property of equality. On Line 3, Brianna should have divided by 0. 1 instead of subtracting 0. 1. On Line 3, Brianna violated the addition property of equality.

Answers

Brianna made a mistake in solving the two-step equation. On Line 1, she incorrectly added -3 instead of subtracting 3. This violated the addition property of equality.

In the given equation, 0.1x + 3 = 1.7, Brianna attempted to isolate the variable 'x' by performing inverse operations. However, on Line 1, instead of subtracting 3 from both sides of the equation to eliminate the constant term, she mistakenly added -3. This error led to an incorrect expression: 0.1x + 3 - 3 = 1.7 - 3, which simplifies to 0.1x = -1.3.

The addition property of equality states that if the same value is added to both sides of an equation, the equality remains true. However, Brianna's addition of -3 violated this property since she should have subtracted 3. By mistakenly adding the negative value, she altered the equation's balance and arrived at an incorrect result.

Had Brianna subtracted 3 correctly on Line 1, the equation would have become 0.1x = -1.3. Continuing the steps, on Line 2, she could have divided both sides by 0.1 to isolate 'x'. However, the given prompt does not mention any mistake in Line 2.

Therefore, the mistake made by Brianna was on Line 1, where she should have subtracted 3 instead

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What is the solution for the system of linear equations shown in the graph?

a coordinate grid with one line that passes through the points 0 comma 0 and 1 comma 3 and another line that passes through the points 0 comma 2 and 1 comma 1

negative one half comma one half
one half comma three halves
three halves comma one half
three halves comma three halves

Answers

To find the solution for the system of linear equations shown in the graph, we need to find the point of intersection of the two lines.

The first line passes through the points (0,0) and (1,3). We can find the equation of this line using the slope-intercept form:

y = mx + b

where m is the slope and b is the y-intercept.

The slope of the line can be found using the two given points:

m = (y2 - y1) / (x2 - x1)

m = (3 - 0) / (1 - 0)

m = 3/1

m = 3

The y-intercept of the line is (0,0), so b = 0.

Therefore, the equation of the first line is:

y = 3x

The second line passes through the points (0,2) and (1,1). We can find the equation of this line using the slope-intercept form:

y = mx + b

where m is the slope and b is the y-intercept.

The slope of the line can be found using the two given points:

m = (y2 - y1) / (x2 - x1)

m = (1 - 2) / (1 - 0)

m = -1/1

m = -1

The y-intercept of the line is (0,2), so b = 2.

Therefore, the equation of the second line is:

y = -x + 2

To find the point of intersection of these two lines, we can set their equations equal to each other:

3x = -x + 2

Solving for x, we get:

4x = 2

x = 1/2

Substituting x=1/2 into either equation, we can find y:

y = 3x

y = 3(1/2)

y = 3/2

Therefore, the point of intersection of the two lines is (1/2, 3/2).

So, the solution for the system of linear equations shown in the graph is:

x = 1/2

y = 3/2

Therefore, the correct response is:

one half comma three halves

Please help me out on this

Please help me out on this

Answers

Answer:

just divide i believe

162÷9

15÷5

84÷14

24÷12

f(x)= {3x-6 if x<=3
{6x-2 if x>3


f(5)=

Answers

For the given function the value of F(5) is 28.

What is a function?

In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.

F(x) is a piecewise-defined function. This means that the value of F(x) depends on the value of x.

For x <= 3, F(x) = 3x - 6.

For x > 3, F(x) = 6x - 2.

To find the value of F(5), we need to determine which definition of F(x) applies. Since 5 is greater than 3, we use the second definition of F(x):

F(5) = 6(5) - 2 = 30 - 2 = 28

Hence, For the given function the value of F(5) is 28.

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Can someone solve this for me pls

Can someone solve this for me pls

Answers

Answer:

a= m<SQR

Step-by-step explanation:

The annual rate of return on stock indexes (which combine many individual stocks) is very roughly Normal. Since 1945, the Stand & Poor's 500 index has had a mean yearly return of 12.5%, with a standard deviation of 17.8%. Take this Normal distribution to be the distribution of yearly returns over a long period.
a) In what range do the middle 95% of all yearly returns lie?
b) The market is down for the year if the return on the index is less than zero. In what proportion of years is the market down?
c) In what proportion of years does the index gain 25% or more?

Answers

a) The range in which the middle 95% of all yearly returns lie is approximately from -23.1% to 48.1%.

b)  the proportion of years in which the market is down is approximately 24.2%.

C)  the proportion of years in which the index gains 25% or more is approximately 16.4%.

a) We can use the empirical rule for normal distributions to find the range in which the middle 95% of all yearly returns lie. According to the empirical rule, for a normal distribution with mean μ and standard deviation σ, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% falls within two standard deviations of the mean, and approximately 99.7% falls within three standard deviations of the mean.

In this case, the mean yearly return is 12.5% and the standard deviation is 17.8%. So, the middle 95% of all yearly returns lie within two standard deviations of the mean, which is:

12.5% ± 2(17.8%) = 12.5% ± 35.6%

Therefore, the range in which the middle 95% of all yearly returns lie is approximately from -23.1% to 48.1%.

b) To find the proportion of years in which the market is down, we need to find the area under the normal curve to the left of zero, since we are interested in the proportion of years with a return less than zero. We can use the standard normal distribution table or a calculator to find this area. Using a calculator, we get:

P(Z < -0.70) = 0.2420

where Z is the standard normal random variable with mean 0 and standard deviation 1, and -0.70 is the z-score corresponding to a return of zero, calculated as:

z = (0 - 12.5) / 17.8 = -0.70

Therefore, the proportion of years in which the market is down is approximately 24.2%.

c) To find the proportion of years in which the index gains 25% or more, we need to find the area under the normal curve to the right of 25%. Using a calculator, we get:

P(Z > 0.98) = 0.1635

where 0.98 is the z-score corresponding to a return of 25%, calculated as:

z = (25 - 12.5) / 17.8 = 0.98

Therefore, the proportion of years in which the index gains 25% or more is approximately 16.4%.

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pla shop mathematics ​

pla shop mathematics

Answers

The number of trees more than 10m tall but not more than 20m tall is 18 trees.

How many of the trees are more than 10m tall but not more than 20m tall?

0 < h ≤ 5 = 5

height greater than 0m less than or equal to 5m

5 < h ≤ 10 = 9

height greater than 5m less than or equal to 10m

10 < h ≤ 15 = 13

height greater than 10m less than or equal to 15m

15 < h ≤ 20 = 5

height greater than 15m less than or equal to 20m

20 < h ≤ 25 = 1

height greater than 20m less than or equal to 25m

The number of trees that are more than 10m tall but not more than 20m tall are;

10 < h ≤ 15 = 13

15 < h ≤ 20 = 5

So,

13 + 5 = 18 trees

Therefore, the total number of trees which are 10m tall but not more than 20m tall is 18 trees.

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When the survey results came back employees indicated that the lighting in the building is too low. There are 50 lights in the building it will cost 50 to replace each light the new lights are led lights that are brighter and more efficient and last 10 years it will save the company 305 per year in energy cost plus make a brighter more productive work space making employees happier how many years will it take for the new lights to pay for themselves round to the nearest year

Answers

Answer:

8 years

Step-by-step explanation:

There are 50 lights present in the building and each light cost $50. Therefore the cost of changing all the bulbs is:

Cost = number of lights * cost per light = 50 lights * $50 = $2500

Changing the lights in the building save the company $305 per year in energy cost. Therefore, the number of years required for the new lights to pay for themselves is:

number of years = cost of changing bulbs / money saved per year

number of years = $2500 / $305 per year = 8.2

number of years = 8 years to the nearest year

The area of this trapezoid is 25.5.
What is the height of the trapezoid? Show your work.​

The area of this trapezoid is 25.5. What is the height of the trapezoid? Show your work.

Answers

Answer:

22.4

Step-by-step explanation:

3.2 times 7 is 22.4

Hopes this helps

also please give me brainlest

Answer:

5 ft

Step-by-step explanation:

area = ½( 3.2 + 7)h = 25.5 → ½( 10.2 )h = 25.5 →

5.1 h = 25.5 → h = 25.5/5.1 = 5

at a certain truck manufacturing plant, 8 trucks were produced last week. unknown to the manufacturer, 3 of the trucks had defective transmissions. suppose that a certain local shipping company has just purchased 2 trucks from the manufacturer. what is the probability that: a. both trucks purchased had defective transmissions? b. only one of the trucks had a defective transmission? c. suppose the company purchases 3 trucks. what is the probability that all 3 had defective transmissions?

Answers

The probability that both trucks purchased had defective transmissions is 9/64 and if one truck has then 30/56

Total trucks = 8

Trucks having defective transmissions = 3

Trucks purchased = 2

Let the event that a truck has a defective transmission be = D

Let the event that a truck does not have a defective transmission = ND

a. Probability that both trucks purchased had defective transmissions:

P(D) = number of defective trucks / total number of trucks

= 3/8

As the likelihood of the second truck being defective is unaffected by the first truck's defect, therefore,

P(D and D) = (3/8) x (3/8)

= 9/64

b. Probability that only one of the trucks had a defective transmission:

P(D) = 3/8

P(ND) = 1 - P(D)

1 - 3/8 = 5/8

Given that one of the trucks is already known to be defective, there is a 5/7 chance that the second truck will not be as well (since there are 5 non-defective trucks left out of 7 total remaining trucks). The likelihood that the second truck will be flawed in this instance is 3/7. (since there are 3 defective trucks left out of 7 total remaining trucks)

Therefore,

P(D and ND) + P(ND and D)

= (3/8) x (5/7) + (5/8) x (3/7)

= 15/56 + 15/56

= 30/56

c. Probability that all 3 trucks had defective transmissions:

Given that the first two trucks had problematic transmissions, there is a chance that the third truck will as well. The likelihood of the third truck being defective is 2/6 because it is already known that two of the trucks are problematic (since there are 2 defective trucks left out of 6 total remaining trucks)

Therefore,

P(D and D and D)

= (3/8) x (3/8) x (2/6)

= 9/128

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find the distance between the points (7,23) and (3,-3), rounded to the hundredths place​

Answers

Answer:

26.31

Step-by-step explanation:

Use distance formula

d = \(\sqrt{(x_{2}-x_{1)^{2} + (y_{2}-y_ ^{1)^2} } }\)

substitute in points and solve

d =  \(\sqrt{(7-3)^2 + (23-(-3))^{2} }\)

d = \(\sqrt{4^{2}+26^{2} }\)

d = \(\sqrt{16 + 676}\)

d = \(\sqrt{692}\)

d = 26.30589288

d = 26.31 rounded

Please help someone, give me correct answer to these 2 problems.

I will mark you brainliest for the correct answer.

Please help!!!!!

I need the answer to both pictures!!!!!!!

Please help someone, give me correct answer to these 2 problems.I will mark you brainliest for the correct
Please help someone, give me correct answer to these 2 problems.I will mark you brainliest for the correct

Answers

Answer:

60° 60° 60°

60°

Step-by-step explanation:

In any triangle, the sum of its interior angles is 180°, and 60+60+60=180.

As for the other question, we can see that angle5=angle1, and angle6=angle2, due to the parallelism of the lines.

Angle5+angle6=180°, therefore

Angle6=180-120=60°=angle2

Help me with this question thingy plas

Help me with this question thingy plas

Answers

ANSWER:

x = -3

Step-by-step explanation:

55+54+x+74=180

109+x+74=180

183 + x = 180

x = -3

Answer:

Step-by-step explanation:

All triangles have 180 as the sum of the 3 interior angles.

x + 74 + 55 + 54 = 180            Combine

x + 183 = 180                           Subtract 183 from both sides.

x = 180 - 183                            Combine

x = - 3

You probably have been told that there is no such thing as a minus angle, and that's true. The angle isn't minus. Just x is. The size of the angle is

Angle size = 74 - 3 = 71

Now try adding them together

55 + 54 + 71 = 180 which is what it should come to  

ME NEEEEEEEED HE;LP NOOOOOOOOOW pls and swer even if u can only answer 1 it wud be appreciated, ty

ME NEEEEEEEED HE;LP NOOOOOOOOOW pls and swer even if u can only answer 1 it wud be appreciated, ty

Answers

Answer:

x ≤ -3/2 or x≥1/3

Step-by-step explanation:

-6x^2-7x+3≤0

-(3x-1)(2x+3)≤0

*-1                ≤ *-1

x ≤ -3/2 or x≥1/3

ME NEEEEEEEED HE;LP NOOOOOOOOOW pls and swer even if u can only answer 1 it wud be appreciated, ty

According to a U.S. news poll, 38% of students in the class of 2013 had done an internship during their time as an undergraduate student. Dana is interested in finding out whether students at her university had an internship rate that was higher than the national average. She obtained a list of 25 randomly selected students from the population of all students at her university by requesting this information from the university’s institutional research office. She collected the responses and calculated that the proportion for her university was 43%. Which one of the following statements about the z-test is correct?
It is not safe to use the z-test for p, since the sample is not a random sample from the entire population (or cannot be considered as one).
It is not safe to use the z-test for p, since n * (1 ? po) is not large enough.
It is safe to use the z-test for p.
It is not safe to use the z-test for p, since n * po is not large enough.
A national poll by the Institute for College Access and Success showed that in 69% of college graduates from public and nonprofit colleges in 2013 had student loan debt. Dr. Blackman wanted to find out if her public nonprofit university had a lower proportion of students who graduated with student loan debt in 2013.
For this survey, the null hypothesis was that the proportion of students with graduated with student loan debt equals 69% and the alternative hypothesis is that the proportion with student loan debt does not equal 69%. The significance level for this test was 0.05.
The results of the hypothesis test of the new survey showed a p-value of 0.039.
Which of the following statements is correct? Check all that apply.
The results were statistically significant.
The results were not statistically significant.
The null hypothesis should be rejected.
The null hypothesis should be accepted.
The null hypothesis cannot be rejected.

Answers

Answer: The null hypothesis should be accepted and The results were not statistically significant

Step-by-step explanation:

A sphere of radius 0.62 inches, a 1 inch cube, and a 1×0.5×2 inch box all have a volume of approximately 1 cubic inch. Given that the surface area of a sphere with radius r is 4πr2, rank these objects, from highest to lowest, based on their surface area to volume ratios.

Answers

Answer:

good morning is that has to go to the one that has to be done by the time to khow hasgot is a good idea to go

Step-by-step explanation:

Rhodes college football and I will be done by then to khow hasgot and I will send it out to me and decor is he still in the one I will send you the election results and

The ranking from highest to lowest surface area to volume ratio is: 1. Sphere 2. Box 3. Cube.

To rank the objects based on their surface area to volume ratios, we need to compare the ratios of surface area to volume for each object. Let's start with the sphere. The surface area of a sphere with radius r is given by the formula 4πr².

In this case, the radius is 0.62 inches. Therefore, the surface area of the sphere is approximately 4π(0.62)² square inches. The volume of the sphere is given by the formula (4/3)πr³.

Substituting the radius of 0.62 inches, we find that the volume of the sphere is approximately (4/3)π(0.62)³ cubic inches.

To calculate the surface area to volume ratio, we divide the surface area by the volume. In this case, we have (4π(0.62)^2) / [(4/3)π(0.62)^3] = 3 / 0.62. Next, let's consider the cube.

The surface area of a cube with side length s is given by the formula 6s²

In this case, the side length is 1 inch. Therefore, the surface area of the cube is 6(1)² square inches. The volume of the cube is given by the formula s³

Substituting the side length of 1 inch, we find that the volume of the cube is 1³ cubic inch. Dividing the surface area by the volume, we have (6(1)²) / 1 = 6.

Finally, let's look at the box. The surface area of a box with dimensions length, width, and height is given by the formula 2(length × width + width × height + height × length). In this case, the dimensions are 1 inch, 0.5 inch, and 2 inches respectively. Therefore, the surface area of the box is 2(1 × 0.5 + 0.5 × 2 + 2 × 1) square inches. The volume of the box is given by the formula length × width × height. Substituting the dimensions, we find that the volume of the box is 1 × 0.5 × 2 cubic inches. Dividing the surface area by the volume, we have [2(1 × 0.5 + 0.5 × 2 + 2 × 1)] / (1 × 0.5 × 2).

Comparing the surface area to volume ratios, we find that the sphere has the highest ratio, followed by the box, and then the cube. So, the ranking from highest to lowest surface area to volume ratio is: 1. Sphere 2. Box 3. Cube

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Determine the truth value of each conditional statement. If true, explain your reasoning. If false, give a counterexample.If two angles are congruent, then they are vertical angles.

Answers

The truth value of the conditional statement is false, and the counterexample of this statement is corresponding angles

How to determine the truth value of the conditional statement?

The conditional statement is given as:

If two angles are congruent, then they are vertical angles.

The above statement is false because not all congruent angles are vertical angles

A counterexample of this statement is a corresponding angle

i.e. corresponding angles are congruent angles, but they are not vertical angles

Hence, the truth value of the conditional statement is false, and the counterexample of this statement is a corresponding angle

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A researcher is interested in determining the practical significance of a statistically significant difference (p < .01) between the achievements of Grade 10 and Grade 11 learners in an emotional intelligence test.

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The researcher is interested in determining the practical significance of a statistically significant difference (p < .01) between the achievements of Grade 10 and Grade 11 learners in an emotional intelligence test.

To assess the practical significance of the statistically significant difference, the researcher should consider effect size measures. Effect size quantifies the magnitude of the difference between groups and provides information about the practical significance or real-world importance of the findings.

One commonly used effect size measure is Cohen's d, which indicates the standardized difference between two means. By calculating Cohen's d, the researcher can determine the magnitude of the difference in emotional intelligence scores between Grade 10 and Grade 11 learners.

Interpreting the effect size involves considering conventions or guidelines that suggest what values of Cohen's d are considered small, medium, or large. For example, a Cohen's d of 0.2 is often considered a small effect, 0.5 a medium effect, and 0.8 a large effect.

By calculating and interpreting Cohen's d, the researcher can determine if the statistically significant difference in emotional intelligence scores between Grade 10 and Grade 11 learners is practically significant. This information would provide insights into the meaningfulness and practical implications of the observed difference in achievement.

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