A giant rectangular sheet of cardboard, 20 m x 10 m, is made into a lidless box by cutting squares out of the corners. The volume this box can hold is 96 m3. What are the possible dimensions of the squares that were cut out of the corners to create this box?

The equation of the linear function in slope intercept form is;

y = -0.5x + (-5)

The equation of a line in slope intercept form is expressed as;

y = mx + c

where;

m is slope

c is y-intercept

From the given table, we can see that the slope is;

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

m = (-4.5 - (-4))/(-1 - (-2))

m = -0.5/1

m = -0.5

At x = 0, y = -5 and so the y-intercept is -5. Thus the equation is;

y = -0.5x + (-5)

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Answer:

O up to the left, down to the right

Step-by-step explanation:

See attached graph.  As x becomes negative, x^3 will always be negative.  But the minus sign in -x^3 mean it will go in the positive direction as x gets smaller (below 0).  The same logic tells us that when x is positive, the -x^3 term will always be negative,  As x increases, the term -x^3 rapidly decreases.

The value of x based on the information given in the triangle will be 11.

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a singular triangle and a singular plane.

It should be noted that based on the information given, the value of x will be calculated thus:

24 / x + 5 = 54 / 36

Cross multiply

24 / x + 5 = 3 / 2

3(x + 5) = 24 × 2

3x + 15 = 48

Collect the like terms

3x = 48 - 15

3x = 33

Divide

x = 33 / 3

x = 11

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To prove that two triangles are similar, we must show that they have the same shape, but not necessarily the same size. This can be done by showing that the corresponding angles of the two triangles are equal and that the corresponding sides are in proportion.

To do this, we can use the Side-Side-Side (SSS) Similarity Theorem. This theorem states that if all three pairs of corresponding sides of two triangles are in proportion, then the two triangles are similar. To prove this, we must show that the ratio of each pair of corresponding sides is equal.

For example, let's say we have two triangles ABC and DEF. To prove that these two triangles are similar, we must show that the ratio of AB to DE is equal to the ratio of BC to EF. We can do this by solving the following equation:

AB/DE = BC/EF

If the equation is true, then the two triangles are similar.

We can also use the Angle-Angle-Angle (AAA) Similarity Theorem to prove that two triangles are similar. This theorem states that if all three pairs of corresponding angles of two triangles are equal, then the two triangles are similar. To prove this, we must show that the measure of each pair of corresponding angles is equal.

For example, let's say we have two triangles ABC and DEF. To prove that these two triangles are similar, we must show that the measure of angle A is equal to the measure of angle D, the measure of angle B is equal to the measure of angle E, and the measure of angle C is equal to the measure of angle F.

If the measures of the corresponding angles are equal, then the two triangles are similar.

Therefore, to prove that two triangles are similar, we must show that either the corresponding sides are in proportion (using the SSS Similarity Theorem) or the corresponding angles are equal (using the AAA Similarity Theorem).

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A child's ticket cost is  $12.50 and an adult's ticket cost $25.00.

Two or more expressions with an Equal sign is called as Equation.

Given that Mr and Mrs Tan and their three children bought tickets for a 'Holiday- On-Ice' show.

Let x be the cost of a child's ticket, 2x be the cost of adult's ticket

The cost of all three children's tickets would be 3x and total cost of Mr. and Mrs. Tan's tickets would be 4x

So the total cost of all five tickets would be 3x + 4x = 7x.

We know that the total cost was $87.50

7x = 87.50

Divide both sides by 7

x = 87.50 / 7

x=12.50

Hence, a child's ticket cost is  $12.50 and an adult's ticket cost $25.00.

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According to the graph, it can be inferred that the average height of the students is 63 inches.

To find the height of the seventh grade soccer players we must analyze the graph. In this case we have a height range from 60 inches to 65 inches. However, we do not know what the individual heights of each of the players are.

In the graph, an intermediate line is also shown in the height segment that signifies the average height of soccer players. In this case it would be 63 inches. Based on the above, the average height would be 63 inches.

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No, we cannot conclude that there is a difference in the mean number of surgeries performed by hospital or by day of the week.

The data provided would need to be further analyzed to determine if there is a statistically significant difference between the means. A t-test or ANOVA could be used to test for differences between the means.

1. The data provided shows the number of outpatient surgeries performed at three hospitals in the Tulsa, Oklahoma, area on each day of the week.

2. To determine if there is a difference in the mean number of surgeries performed by hospital or by day of the week, a statistical test needs to be conducted.

3. A t-test or ANOVA could be used to test for differences between the means.

4. The results of the test would need to be examined to determine if there is a statistically significant difference between the means.

5. At the 0.05 significance level, we cannot conclude there is a difference in the mean number of surgeries performed by hospital or by day of the week.

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The probability that it will have distinct even digits is 6/1000.

The first digit can take on 5 values (0,2,4,6,8).

The second digit could take on 4 values (one less than 5 to be unique).

The third digit could take on 3 values (two less than 5 to be unique).

So that makes,

N=5.4.3

N=60

P= 60/1000

P=3/50

So there are 60 unique three digit even numbers.

There are 1000 possible outcomes.

Probability and statistics are two fundamental concepts in mathematics. Probability is about the probability of an event, whereas statistics are about how different techniques are used to process different data.

Probability and statistics allow us to process complex data in a very understandable way.

Probability is one of the most popular topics in statistics. The reason is that this one theory is often used when trying to predict something. For example, figuring out what comes out of a random series of events. For simplicity, probability is also called chance or probability. 

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The probability that the hand contains exactly 3 face cards is 0.1503.

Combinations of 7 cards out of a choice of 52.

52!/(45! *7!)= 52*51*50*49*48*47*46/7*6*5*4*3*2 = 133,784,560

Combinations of 3 face cards out of 12

12*11*10/3*2 = 220

Combinations of 4 non-face cards out of 40

40*39*38*37/4*3*2 = 91,390

Combinations of 5 face cards and 2 non-face cards

220 * 91,390 = 20,105,800

So the probability is 20,105,800/133,784,560 or 0.1503

Probability theory is the theory used to model uncertainty. Probability value o events show how likely it is the event will occur with an interval of values between zero up to one. However, probability theory can only used for events that have information that complete.

For events that have no information complete can be represented by imprecise probability. One model of imprecise probability is the set-valued probability. Probability worth the set is the non-empty set with every the elements are the results of the probability selector mapping.

Then a set-valued measure is constructed which is constructed by set-valued probabilities.

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To construct and interpret 95% confidence intervals for the outcomes of each simulation, then option C. The confidence interval from the first simulation is (0.564, 0.616), and the confidence interval from the second simulation is (0.615, 0.665). For the first trial, we are 95% confident the true proportion of wins with the new game strategy is between 0.564 and 0.616. For the second trial, we are 95% confident the true proportion of wins with the new game strategy is between 0.615 and 0.665 is correct.

To calculate the confidence interval, we can use the formula for a normal approximation to the binomial distribution.

The standard error of the proportion is given by the formula SE = sqrt(p(1-p)/n), where p is the proportion of wins, and n is the number of games played. The 95% confidence interval is given by p +/- 1.96 * SE.

Plugging in the values from the first simulation, we have p = 590/1000 = 0.59, and n = 1000. So, SE = sqrt(0.59(1-0.59)/1000) = 0.0242. The 95% confidence interval is 0.59 +/- 1.96 * 0.0242 = (0.564, 0.616).

Similarly, for the second simulation, p = 640/1000 = 0.64, and n = 1000. So, SE = sqrt(0.64(1-0.64)/1000) = 0.0244. The 95% confidence interval is 0.64 +/- 1.96 * 0.0244 = (0.615, 0.665).

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Expanded form of the expression - 1/3 (y - x) is,

⇒ - 1/3y + 1/3x

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The expression is,

⇒ - 1/3 (y - x)

Now, We can expand the expression as;

⇒ - 1/3 (y - x)

⇒ - 1/3 × y - 1/3 × - x

⇒ - 1/3y + 1/3x

Thus, Expanded form of the expression - 1/3 (y - x) is,

⇒ - 1/3y + 1/3x

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The Number of sodas sold: 174,

The number of hot dogs sold: 58.

Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.

Both linear equations with one variable and those with two variables exist.

Given a vendor sold a combined total of 232 sodas and hot dogs.

let S for the number of sodas sold and H for the number of hot dogs sold,

S + H = 232

The number of sodas sold was three times the number of hot dogs sold

S = 3H

substitute the values,

S + H = 232

3H + H = 232

4H = 232

H = 232/4

H = 58

and the number of sodas sold

S = 3H

S = 3*58

S = 174

Hence the number of sodas sold = 174,

and the number of hot dogs sold = 58.

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The probability that none are mechanical engineering majors is 0.51.

The number of students who are not mechanical engineering majors is 100 - 49 = 51. The probability of choosing a student who is not a mechanical engineering major in one draw is 51/100. The probability of choosing five students in a row who are not mechanical engineering majors is (51/100)^5. Thus, the answer is (51/100)^5 = 0.1517816.

Probability refers to potential. From 0 to 1 is used to express the value. To determine how likely an event is to occur, probability has been introduced in mathematics. This is the fundamental theory of probability, which is also applied to the probability distribution, and from which you will discover the likelihood of results for a random experiment. The complete number of possibilities that can occur should be known before calculating the likelihood that a certain event will occur.

The complete question is:-

In a class of 100 students, 30 are computer science majors, 49 are mechaincal engineering majors, 13 are civil engineers and the rest are general engineering majors. Assume students only have one major.Suppose five students from the class are chosen at random what is the probability none are mechanical engineering majors?My info I know: The mechanical engineers account for 49% of the students, making 51% not mechanical engineers? Do I take five out of the 51, so 0.05 X 0.51?

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Answer:

(- 1, 1 )

Step-by-step explanation:

the solution to a system of equations given graphically is at the point of intersection of the lines.

the lines intersect at (- 1, 1 ) , then

the solution is (- 1, 1 )

Answer:

88%, 88%, 85%

Step-by-step explanation:

You can check these by multiplying the first number given by the percentages below. (or finding how much the 2nd number is of the first number)

150 × .88 = 132

275 × .88 = 242

300 × .85 = 255

The probability of the sample having a average gas mileage between 27 and 29 miles per gallon will be 0.0116.

What is a normal distribution?

The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.

The z-score is a statistical evaluation of a value's correlation to the mean of a collection of values, expressed in terms of standard deviation.

In 2015, new cars had an average fuel efficiency of 27.9 miles per gallon with a standard deviation of 6.8 miles per gallon. a sample of 30 new cars is taken.

Then the probability the sample has a mean gas mileage between 27 and 29 miles per gallon will be

The value of the z-score at x = 27, we have average as

The value of the z-score at x = 29, we have

z= 0.16

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Ratio of carnations to all flowers

= 4/13 or 4:13 or 4 carnations to 13 flowers.

A ratio can be defined as the relationship or comparison between two numbers of the same unit to check how bigger is one number than the other one.

Given,

There are 6 roses 8 carnations and 12 tulips

Total flowers = 6 + 8 + 12 = 26

Ratio of carnations to all flowers

= 8/26

= 4/13

or 4:13

or 4 carnations to 13 flowers.

Hence,

4/13 or 4:13 or 4 carnations to 13 flowers

is the ratio of carnations to all flowers.

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Taking into account the definition of a system of linear equations, Celia has 58 coins in her bank, 13 dimes and 45 quarters.

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

In the systems of equations, the values of the unknowns must be found, with which, when replaced, they must give the solution proposed in both equations.

In this case, a system of linear equations must be proposed taking into account that:

You know:

So, the system of equations to be solved is

d + q= 58

0.10d + 0.25q= 12.55

It is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, Isolating the variable "d" from the first equation, we obtain:

d= 58 -q

Substituting in the second equation you get:

0.10× (58-q) + 0.25q= 12.55

Solving:

0.10×58 - 0.10q + 0.25q= 12.55

5.8 - 0.10q + 0.25q= 12.55

- 0.10q + 0.25q= 12.55 -5.8

0.15q= 6.75

q= 6.75÷ 0.15

q= 45

Remembering that d=58 - q, you get:

d= 58 - 45

d= 13

Finally, she has 13 dimes and 45 quarters.

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Therefore , the solution of the given problem of unitary method comes out to be $1.5 one apple cost.

To finish a work using the unitary strategy, multiply the quantity by two after computing the size of a small slice. The unit variable technique, which is just an expression, helps to distinguish a coded item from a specific group or collection of groups. For example, 40 pens would cost Rs. 400 (or $1.01 or 400 pounds). There is a chance that one nation will have complete control over the technique used to do this. Almost all living things have a unique trait.

Here,
Given :

=> 3 pound bag of apples cost $16

=> 8 apples in a pound

So,

In 3 pounds there are 3*8 = 24 apples

=> 24/16

=> 12/8

=> 3/2

=> 1.5

Therefore , the solution of the given problem of unitary method comes out to be $1.5 one apple cost.

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Answer:

19.6666666667

Step-by-step explanation:

The expression which is equivalent to 3x² - 10x - 8 is (x - 4)(3x + 2).

The correct answer option is option C

3x² - 10x - 8

check all that applies:

(3x - 2)(x - 4)

= 3x² - 12x - 2x + 8

= 3x² - 14x + 8

(3x - 4)(x - 2)

= 3x² - 6x - 4x + 8

= 3x² - 10x + 8

(x - 4)(3x + 2)

open parenthesis

= 3x² + 2x - 12x - 8

= 3x² - 10x - 8

(3x - 4)(x + 2)

= 3x² + 6x - 4x - 8.

collect like terms

= 3x² + 2x - 8

Therefore, (x - 4)(3x + 2) is equivalent to the expression 3x² - 10x - 8

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The value of {x} would be 11.872.

Cosine of the angle is defined as the ratio of base and hypotenuse. Mathematically -

cosθ = (base)/(hypotenuse)

Given is a right angled triangle as shown in the figure.

We can write the value of {x} as -

cos{32} = x/14

{x} = 14 cos (32)

{x} = 14 x 0.848

{x} = 11.872

Therefore, the value of {x} would be 11.872.

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The wechsler intelligence scale has a mean of 100 and a standard deviation of 15.  the z score that corresponds to an iq score of 115 is 1.

To calculate the Z score, you subtract the mean from the score and divide it by the standard deviation. In this case, 115-100=15, and 15/15=1.  A Z score of 1 indicates that the score is one standard deviation above the mean. This means that a score of 115 is higher than 84% of the population. It is in the top 16% of scores.

This score is considered to be in the high average range on the Wechsler Intelligence Scale.  The Z score can be interpreted in a variety of ways. It can be used to compare scores or to see how far a score is from the mean. It also can be used to compare scores across different tests. For example, a Z score of 1 on the Wechsler Intelligence Scale could be compared to a Z score of 1 on another test to see how the scores compare.

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No, as the confidence intervals for the two groups overlap.

From the given data,

The poll has an error of 34% of the people say they will vote for Bugs Bunny

⇒(34 ± 6)% ≈ 28% to 40%

⇒26% say they will vote for Baby Shark.

The confidence interval for the percentage of people supporting Baby Shark is

⇒(26 ± 6)% ≈ 20% to 32%

No, it is not possible to say with certainty that more people in the population support Bugs Bunny over Baby Shark based on this poll.

Since the confidence intervals for the two groups overlap , we cannot  say that in population, more people clearly support Bugs Bunny over Baby Shark.

Hence, the correct answer is: no, as the confidence intervals for the two groups overlap.

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Answer:

12+16x-8

Step-by-step explanation:

The outside factor of the average property price of the local neighborhood would bias bexp in a positive direction.

This is because an increase in average property price will increase the value of the dependent variable (bexp). If the average property price of the local neighborhood increases, it will likely lead to an increase in the value of bexp.

This is because the increase in average property price will lead to an increase in the value of properties in the local neighborhood, which will in turn increase the value of bexp. Therefore, an increase in the average property price of the local neighborhood will lead to an increase in the value of bexp.

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Answer:

150

Step-by-step explanation:

(5)(5)=25

(25)(5)=125

add: =150

[tex]5\times5+25\times5[/tex]

[tex]5\times5=25\\25\times5=125[/tex]

[tex]25+125[/tex]

[tex]=\fbox{150}[/tex]

We need to calculate the total  of the rectangular prism and divide it with the volume of single 1/3 cubes to get the number of cubes. It takes almost 25 cubes to fill the rectangular prism of given dimension.

The rectangular prism has 2.5 m length, 5 m tall and 0.75 m wide.

The total volume of the rectangular prism will be 2.5 m × 5 m × 0.75 m = 8.25 m³.

The volume of single cube will be (1/3) m³ = 0.33 m³

Now to find the number of cubes to fill the rectangular prism, we can divide the volume of the prism with the volume of single cube.

8.25 m³ / 0.33 m³ = 25 cubes.

It takes almost 25 cubes to fill the rectangular prism of dimension 2.5 m length, 5 m tall and 0.75 m wide.

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Answer:

21

Step-by-step explanation:

We can use Pythagorean theorem a^2 + b^2 = c^2

a = 20

b = x

c = 29

20^2+b^2=29^2

resulting our b value being 21

The expression as a terminating decimal is 0.2499999....

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

-4/-16

Evaluate the expression by dividing 4 and 16 by 4

So, we have the following representation

1/4

Next, we divide 1 by 4

This gives

0.25

As a repeating decimal, we have

0.2499999....

Hence, the solution is 0.2499999....

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