What is the surface area of this
rectangular prism?

A large t-statistic indicates a greater difference between the sample means and provides stronger evidence for a significant difference between the populations.

The t-statistic is a measure of the difference between two sample means relative to the variability within the samples. When the population means are different, the difference between the sample means will tend to be larger, which will result in a larger numerator in the t-statistic formula. The larger the difference between the sample means, the greater the evidence for a difference between the populations. In contrast, if the population means are similar, the difference between the sample means will be smaller, resulting in a smaller numerator and a weaker test of significance.

The denominator of the t-statistic formula is the standard error of the mean, which measures the variability of sample means around the population mean. If the sample size is large enough, the standard error of the mean will be small, resulting in a smaller denominator and a larger t-statistic. Therefore, when the population means are different, a larger t-statistic would be expected due to a combination of a larger numerator and a smaller denominator.

In summary, If the population means are different, a large t-statistic would be expected.

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Answer:

\(t1 {15y08 \frac{18 \gamma \gamma }{?} }^{2} \)

From the provided equations, the equation which has no solution is 3 4 x less-than-or-equal-to 2 +4x. Option 2 is correct.

Inequality equation is the equation in which the two expressions are compared with greater than, less than or other inequality signs.

From the given equations, the equation which has no solution has to be found out. When the value, does not equate for the expression, then the expression has no solution.

The first equation given in the problem is,

\(6 (x +2) > x-3\)

Solve it further,

\(6 x +12 > x-3\\6x-x > -3-12\\5x > -15\\x > -3\)

The second equation given in the problem is,

\(3+ 4x \leq 2 (1 +2x)\)

Solve it further,

\(3+ 4x \leq 2 +4x\\4x- 4x \leq 2-3\\0\leq-1\)

The value of 0 is greater than the number -1. Thus, this inequality has no solution.

The option 3 and 4 has a solution. Hence, from the provided equations, the equation which has no solution is 3 4 x less-than-or-equal-to 2 +4x. Option 2 is correct.

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Answer:

x=5

Step-by-step explanation:

-6 - 2(4x - 7) = -32

Distribute -2

-6 - 8x +14 = 32

Combine Like Terms

-8x + 8 = -32

Subtract 8 from both sides

-8x = -40

Divide each side by -8

- x - = +

So the final answer would be:

x = 5

Answer:

16

Step-by-step explanation:

((8/4)+ 6) x 2
(2 + 6) x 2      Divided 8 by 4
8 x 2         Added 2 and 6
16          Multiply

Step-by-step explanation:

R = x²/y

Substitute

R = (4.8×10⁵)²/2.8×10⁴

= 4.8²×10¹⁰/2.8×10⁴

= 23.04×10¹⁰/28000

can I see a picture of it

Answer:

x = 19, ARC MP = 104º

Step-by-step explanation:

9x-43 = 5x+33

4x = 76

x = 19

Arc MP = 360 - (9x-43 + 5x+33)

Arc MP = 360 - (9(19)-43 + 5(19)+33)

= 360 - 256

MP = 104º

Hello! First, let's remember what is Associative Property:

It is a mathematical rule who says that the order of the factors doesn't change the final result of a calculus.

We have the associative property in two mathematical operations, I'll show you some examples:

If we want to sum three numbers, 5, 10 and 15, how is the right way? We have some ways to do it:

(5+10)+15 = (15)+15 = 30

(5+15)+10 = (20)+10 = 30

5+(10+15) = 5+(25) = 30

So, no matter the order of the numbers, we will always get the same result.

An example with the other operation now:

If we want to multiply three numbers, 2, 3 and 5:

(2*3)*5 = (6)*5 = 30

(2*5)*3 = (10)*3 = 30

2*(3*5) = 2*(15) = 30

Also, no matter the order of the factors, we'll always obtain the same result.

However, in the subtraction and in the division we have to follow the right order, according to the precedence, so we can't use the Associative Property on these operations.

Right answer: C and D.

The value of side length w is 13.75 .

Given right angled triangle,

Perpendicular = w

Hypotenuse = 17

Angle of triangle = 54°

So,

According to the trigonometric ratios,

tanФ = p/b

cosФ = b/h

sinФ = p/h

By using sinФ,

sinФ = p/h

sin 54° =  w/ 17

0.809 = w/17

w = 13.75 .

Thus after correction w will be 13.75

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The area of the third side of the triangle is either 20 square unit or 12 square units.

Triangle:

in math, triangle refers a simple closed curve made of three line segments and it has three vertices, three sides and three angles.

Given,

Two sides of a right triangle measure 2 units and 4  units.

And we need to find the area of the square that shares a side with the third side of the triangle  ​

Let us consider is  Two sides of a right triangle measure 2 units and 4  units.

Here if sides are perpendicular sides, then by using Pythagorean theorem

=> third side² = 2² + 4²

When we simplify this one, then we get,

=> third side² = 4 + 16

So, the  third side² = 20

Then the area of the square that shares a side with the third side of the triangle =  third side² = 20 sq units

Similarly, if 4  units is hypotenuse side, then by using Pythagorean theorem, the third side is calculated as,

=> third side² = 4² - 2²

And when we simplify this one, then we get,

=> third side² = 16 - 4

Therefore, the third side² = 12

And the area of the square that shares a side with the third side of the triangle =  third side² = 12 sq units

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Answer:

3

Step-by-step explanation:

here is explain.

2*3+3 = 9

number 3 from the replacement set makes the equation

Answer:

Step-by-step explanation:

y=2x because

3x2 =6

10x2=20

12x2=24

17x2=34

I hope it's the right answer .

Answer:4

Step-by-step explanation:22-4=18-4=14-4=10-4=6=2

The statement that predicates \(∀x∀y∃z q(x, y, z)\) is true only for option b, where q(x, y, z) is defined as "xy = z." The correct option is B.

The statement for which \(∀x∀y∃z q(x, y, z)\) is true depends on the predicate q(x, y, z) provided in the options.

a. Let Q(x, y, z) be the statement "(x) = z = x = vz)." In this case,\(∀x∀y∃z\)\(Q(x, y, z)\) is false. It implies that for every x and y, there exists a unique z such that x = z = vz. However, this is not true for all real numbers since the equation implies that every real number is equal to its reciprocal, which is not the case.

b. Let O(x, y, z) be the statement "xy = z." Here, \(∀x∀y∃z O(x, y, z)\) is true. For any two real numbers x and y, we can always find a z such that z = xy. Therefore, the statement holds true for all real numbers.

c. Let Q(x, y, z) be the statement "xyz = x(yz)." In this case, \(∀x∀y∃z Q(x, y, z)\) is false. The equation implies that for all x and y, there exists a z such that the equality holds. However, this is not true for all real numbers, as the equation represents an associative property of multiplication that doesn't hold universally.

d. Let Q(x, y, z) be the statement "x = y = z." In this case, \(∀x∀y∃z Q(x, y, z)\) is false. The equation implies that for every x and y, there exists a unique z such that x = y = z. However, this is not true for all real numbers since not all real numbers are equal.

Therefore, the statement \(∀x∀y∃z q(x, y, z)\) is true only for option b, where q(x, y, z) is defined as "xy = z."

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The polynomials 1, 1-t, \(2-4t+t^2\) and \(6-18t+9t^2-t^3\) are linear independent and span \(P_3\). So the first four Laguerre polynomials forms a basis of \(P_3\).

We have the first four Laguerre polynomials. Here \(P_3\) is the space of all polynomials of degree at most 3.

i.e., \(P_3= \{ a+bx+cx^2+dx^3| a,b,c,d \in R\}\)

So the dimension of \(P_3\) is 4. Also there are 4 Laguerre polynomials.

Now to show that the first four Laguerre polynomials forms a basis, it remains to show that they are linear independent.

Consider the polynomials 1, 1-t, \(2-4t+t^2\) and \(6-18t+9t^2-t^3\). Write them into a matrix with the co-efficient of 1, t, \(t^2\) and \(t^3\) in each row.

\(\left[\begin{array}{cccc}1&1&2&6\\0&-1&-4&-18\\0&0&1&9\\0&0&0&-1\end{array}\right]\)

This matrix is already in its echelon form with all its pivots occupied. The pivot of first row is 1. The pivot of 2nd row is -1. The pivot of 3rd row is 1 and the pivot of 4th row is -1.

Hence the polynomials are linearly independent since the columns of the above matrix are linearly independent.

In conclusion, the first four Laguerre polynomials 1, 1-t, \(2-4t+t^2\) and \(6-18t+9t^2-t^3\)  forms a basis for \(P_3\).

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Replace t with the months given as choices to see which one gives a positive value as an answer.

P(1) = 1^4-9(1)^3 + 24(1)^2-20(1) = -4

P(2) = 2^4-9(2)^3+24(2)^2-20(2) = 0

P(3) = 3^4 -9(3)^3+24(3)^2-20(3) = -6

P(5) = 5^4-9(5)^3+24(5)^2-20(5) = 0

P(6) = 6^4-9(6)^3+24(6)^2-20(6) = 96

It shows a profit in month 6 so it would start showing a profit in month 5.

The answer is 5 months

Answer:  max capacity is 1625 gallons.

Diagram is shown below.

=========================================================

Explanation:

We'll draw two horizontal number lines to help make a comparison or connection between percentages and tank capacity.

For the top number line, make 5 sections with the labels: 0%, 20%, 40%, 60%, 100%. The reason I'm picking 5 is because 40% = 40/100 = 2/5. So having 40% capacity means we're 2/5 full. That denominator 5 tells us how to subdivide each number line.

The bottom number line will also have 5 sections. We only know one label for this bottom portion right now. That label is 650. Place this directly under the "40%". This visually is one way to represent that 650 gallons is 40% filled. See the diagram below.

Cut the 650 in half to get 325. This corresponds to 40% cut in half to get 20%. Therefore, 325 will go under the 20%. Being 20% full means we have 325 gallons of water.

To figure out the 60% portion, we will multiply 325 by 3. This is because 3*20% = 60%, so 3*325 = 975. We'll write "975 gallons" under the "60%"

Then we have 1300 gallons under the 80% since 4*325 = 1300. Note how 4*20% = 80%, so that's where the '4' multiplier comes from.

Finally, we multiply 325 by 5 to get 1625 and that represents the full tank's capacity. Technically we could have just jumped to this directly without having to find the 60% or 80% capacity values, but it's good practice I think.

Again the diagram is shown below. The answer we're after is at the very bottom right corner. It's under the 100% to indicate the tank is completely full, or has reached max capacity.

-----------------------

Here's a way to find the answer without a double number line. This method involves setting up a proportion.

(40% full)/(650 gallons) = (100% full)/(x gallons)

40/650 = 100/x

40x = 650*100

40x = 65000

x = 65000/40

x = 1625

We confirm that the tank's max capacity is 1625 gallons.

Answer:

see explanation

Step-by-step explanation:

Using the trigonometric identities

sin²x + cos²x = 1 ⇒ 1 - sin²x = cos²x

cot x = \(\frac{cosx}{sinx}\)

Consider the left side

\(\frac{(1-sin0)(1+sin0)}{sin^20}\) ← expand numerator using FOIL

= \(\frac{1-sin^20}{sin^20}\)

= \(\frac{cos^20}{sin^20}\)

= cot²Θ = right side

Answer:

Yes, that is unusual as the problem is given.

Step-by-step explanation:

If the mean is 9.5 and the standard deviation is 0.55, then anything within the normal curve of 10.05 on the high end and 8.45 on the low end is normal. 12 is more than several standard deviations or an outlier if this makes sense.

So, it is unusual as the problem is stated, but if it's a weekend, 12 hours is normal. LOL

Good luck!  

Based on the normal distribution parameters given, the probability of a student getting atleast 12 hours of sleep ls 0. Hence, it is abnormal.

Given the Parameters :

Using the Zscore formula, the probability of getting a atleast 12 hours of sleep can be expressed thus :

Zscore = (Score - Mean) / standard deviation

For X ≥ 12 :

The probability using a normal distribution table :

P(Z ≥ 4.54) = 1 - P(Z ≤ 4.54)

P(Z ≤ 4.54) = 1 ( normal distribution table)

P(Z ≥ 4.54) = 1 - 1 = 0

Since, the probability is 0 ; hence, it is unlikely and therefore, abnormal.

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The Paired samples t-test is the most suitable statistical technique for comparing the mean span of the dominant and non-dominant hands in this study.

To investigate whether the span of a person's dominant hand is greater than that of their non-dominant hand, the most appropriate statistical technique would be the Paired samples t-test.

The Paired samples t-test is used when comparing the means of two related groups or conditions. In this case, the dominant and non-dominant hands are related because they belong to the same individuals in the study. By comparing the means of the dominant and non-dominant hand spans, we can determine if there is a significant difference between the two.

The other options listed, ANOVA (Analysis of Variance), Independent samples t-test, Wilcoxon's matched-pairs signed rank test, and Mann-Whitney U test, are not suitable for this scenario because they are designed for different types of comparisons:

- ANOVA is used when comparing the means of three or more independent groups, which is not the case here.

- Independent samples t-test is used when comparing the means of two independent groups, which is not the case here as the measurements are paired.

- Wilcoxon's matched-pairs signed rank test and Mann-Whitney U test are non-parametric tests that are used when the data do not meet the assumptions of parametric tests. However, in this case, we have paired measurements, and the paired samples t-test is the appropriate parametric test.

Therefore, the Paired samples t-test is the most suitable statistical technique for comparing the mean span of the dominant and non-dominant hands in this study.

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Answer:63.75 :)

Step-by-step explanation:

Answer:

$63.75

Step-by-step explanation:

85 x 75/100

85/1 x 3/4

255/4 - > $63.75

- You should already know how to do this yourself as this is very easy and basic question.

Step-by-step explanation:

Area of a square = side X side      but the sides are the same length

area of square = s^2

   144      = s^2

    s = 12  m  

Answer:

B

Step-by-step explanation:

The answers of the expression is ,

1)55

2)21

3)160

4)6(2x+3)

5)13(x+3y)

6)width=3x+4

7)35b+56

8)28m+24f

9)-25

10)27c+36d.

What is expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Unknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it.

Here the given expressions , we need to simplifying them . Then,

1) 30+25

=> 30+25=55

2) 35-14

=> 35-14=21

3)60+100

=> 60+100= 160

4)12x+18

=> 6.2x+6.3

=>6(2x+3)

5)13x+39y

=> 13x+13.3y

=>13(x+3y)

6) Length of rectangle = 6 in

Area of rectangle = 18x+24

=> 18x+24 = 6*width

=> width = 3x+4

7)7(5b+8)

=>7.5b+7.8

=>35b+56

8)4(7m + 6f)

=> 4.7m+4.6f

=> 28m+24f

9). 5(3 – 8)

=> 5(-5) = -25

10)9(3c + 4d)

=> 9.3c+9.4d

=>27c+36d.

Hence the answers of the expression is ,

1)55

2)21

3)160

4)6(2x+3)

5)13(x+3y)

6)width=3x+4

7)35b+56

8)28m+24f

9)-25

10)27c+36d.

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Answer: 1. x = 32, 2. x = 16, 3. x = 77

Step-by-step explanation: All of these angles are 90 degree angles, therefore by subtracting the known term from 90, you are able to find the value of x. I hope that this helps :)

The term used to describe an error that occurs when numbers are moved to the right or left in an amount column is "Slide".

Slide:

An accounting slide is a mistake that happens when the decimal point of a number is moved to the left or right of where it should be.

For instance, a bookkeeper would enter $1,200.50 in place of $12,005 in the revenue account or $250.75 in place of $2,507.50 in the monthly insurance expenses. In general, bookkeeping mistakes and accounting blunders lead to financial record misstatements.

"Slide" is the name for a mistake that happens when numbers are moved to the right or left in an amount column.

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Answer:

4/41

Step-by-step explanation: