Ben says this system of equations has one solution. Is he correct? Explain

Number of cubes with edge length 1/2cm that fit in the prism is 11160 and the volume of the prism is 1395 cubic centimeter

Dimensions of the rectangular prism = [tex]7\frac{1}{2}[/tex] cm × 12 cm × [tex]15\frac{1}{2}[/tex] cm

Convert the mixed fraction to the simple fraction

The dimensions of the rectangular prism = 15/2 cm × 12 cm × 31/2 cm

The volume of the rectangular prism = w × l × h

Where

w is the width

l is the length

h is the height

The volume of the rectangular prim = 15/2 × 12 × 31/2

= 1395 cubic centimeter

The side off the cube = 1/2 cm

Volume of the cube = a^3

= (1/2)^3

= 0.125 cubic centimeter

Number of cubes will fit in rectangular prism = Volume of rectangular prism /  Volume of the cube

= 1395 / 0.125

Divide the terms

= 11160 cubes

Therefore, 11160 cubes will fit in the rectangular prism and the volume of the prism is 1395 cubic centimeter

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The corresponding p-value for this test statistic is 0.005, which is smaller than our significance level of α=0.05.

To begin, we define the population proportion of people who shop for groceries online in region A as p₁ and the population proportion of people who shop for groceries online in region B as p₂.

Our null hypothesis is that there is no difference in these proportions, which we can write as H0=> p₁ = p₂. Our alternative hypothesis is that there is a difference, which we can write as H1=> p₁ ≠ p₂.

Next, we need to calculate the sample proportions and standard errors for each region. We can do this using the formulas:

p₁ = x₁/n₁, p₂ = x₂/n₂

where x₁ and x₂ are the number of people in each sample who shop for groceries online, and n₁ and n₂ are the sample sizes. The standard errors are given by:

=> SE₁ = √(p₁(1-p₁)/n₁),

=> SE₂ = √(p₂(1-p₂)/n₂)

Using the given data, we find that p₁ = 0.16, p₂ = 0.24, SE₁ = 0.037 and SE₂ = 0.042.

We can now calculate the test statistic, which measures the difference between the sample proportions under the assumption that the null hypothesis is true. We use the formula:

z = (p₁ - p₂) / √(SE₁² + SE₂²)

Substituting the values we calculated, we get:

z = (0.16 - 0.24) / √(0.037² + 0.042²) = -2.83

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Complete Question:

A random sample of 100 people from region A and a random sample of 100 people from region B were surveyed about their grocery-shopping habits. From the region A sample, 16 percent of the people indicated that they shop for groceries online. From the region B sample, 24 percent of the people indicated that they shop for groceries online. At the significance level of α=0.05, do the data provide convincing statistical evidence that there is a difference between the two regions for the population proportions of people who shop online for groceries? Complete the appropriate inference procedure to support your answer.

Answer:

-19 > k

Step-by-step explanation:

-4 > k + 15

Subtract 15 from each side.

-4-15 > k + 15-15

-19 > k

Any value less than -19 would make this statement true

Answer:

- 19 > k

Step-by-step explanation:

- 4 > k + 15

Subtract 15 from both sides.

- 4 - 15 > k

- 19 > k

The roots of the equation, f (x) = ( x - 6 )²( x + 2 )² are 6 and - 2.

The root of the function is calculated by setting the function equal to zero.

The given function is f (x) = ( x - 6 )²( x + 2 )²

we will separate the two equation and set them equal to zero.

( x - 6 )² = 0  ----  equation  ( 1 )

or

( x + 2 )² = 0 -------- equation ( 2 )

from the first equation, x = 6

from the second equation, x = - 2

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The complete question is below:

Find the roots of f(x) = (x - 6)² (x + 2)²

Answer:

Step-by-step explanation:

4 x 6= 24

24+2=26

Answer:

  about 2.43 seconds

Step-by-step explanation:

You want the time when the height described by h = -16t² +36t +7 is equal to zero.

The quadratic equation ...

  -16t² +36t +7 = 0

can be solved using the quadratic formula. It tells you the solution to ...

  ax² +bx +c = 0 is ...

  [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Then the solutions to the given quadratic are ...

  [tex]x = \dfrac{-36\pm\sqrt{36^2-4(-16)(7)}}{2(-16)}=\dfrac{9\pm\sqrt{109}}{8}\approx\{-0.180,2.430\}[/tex]

The ball will hit the ground after about 2.43 seconds.

Answer:

n = (3/8)x+(45/8)

Step-by-step explanation:

3x+5 = 4(n-5)*(6/3)

Is this written correctly?

3x+5 = 4(n-5)*(6/3)

3x+5 = 8(n-5)      [Simplify: {4*(6/3) = 8)]

3x+5 = 8n-40      [Expand the parentheses]

8n-40 = 3x+5      [Rearrange]

8n = 3x+5 + 40    [Rearrange]

8n = 3x+45          [Simplify]

n = (3x+45)/8       [Divide both sides by 8]

n = (3/8)x+(45/8)    [Rearrange]

Answer: 20

Step-by-step explanation:

30-60-90 triangles are special: Their side lengths fall in a ratio of 1:2:[tex]\sqrt{3}[/tex], in order of Shortleg : hypotenuse : longleg

Since we know the short leg is 10, the hypotenuse must be double, or 20.

Ashton has 4.5 bags of pecans. since you can't have half a bag, he might need to round up to 5 bags

A fraction represents a part of a whole.

If Ashton used 1/4 of the pecans in a soup recipe, he has 3/4 of the pecans left.

To find out how many pounds of pecans he has left.

we can multiply the original amount of pecans by 3/4:

3/4 x 6 pounds = 4.5 pounds

So Ashton has 4.5 pounds of pecans left to split into bags.

If he splits the remaining pecans into 1-pound bags, then he has:

4.5 pounds ÷ 1 pound/bag = 4.5 bags

Therefore, Ashton has 4.5 bags of pecans. However, since you can't have half a bag, he might need to round up to 5 bags

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The complete question

Ashton picked 6 pounds of pecans. He used 1/3 of the pecans in a soup recipe. Ashton puts the pecans that are left in 1/4 pound bags. How many bags of pecans does he have

Yes, the product of (x - 3)^2 is a perfect square trinomial because it can be written as the square of the binomial (x - 3).

A perfect square trinomial is a trinomial of the form a^2 + 2ab + b^2, where a and b are terms that can be squared. When we expand the square of a binomial, we get a perfect square trinomial.

In this case, the binomial is (x - 3), and its square is (x - 3)^2. When we expand this expression, we get:

(x - 3)^2 = (x - 3)(x - 3) = x^2 - 6x + 9

This is a perfect square trinomial, because it can be written as the square of the binomial (x - 3). Specifically, we can write:

(x - 3)^2 = (x - 3)(x - 3) = (x - 3)^2

Therefore, the product of (x - 3)^2 is a perfect square trinomial.

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The total amount of money Mario, Giana, and Allan split was $2160. Giana received $640 less than Allan did.

Let x represent the sum of money Mario got.

Giana got three times

Allan got seven times

Total: 2x, 3x, 7x, or 12x.

Allan received $640 more than Giana, therefore

7x = 640 + 3x

4x = 640

x = 160

Total amount split is 12x, or 12 * 160, or $2160.

The total amount of money Mario, Giana, and Allan split was $2160. To determine the overall amount, we must first determine how much money each person received. We know that Giana received three times as much as Mario did, while Allan received seven times as much. So, using 2x, 3x, and 7x, respectively, where x is the amount of money Mario received, we can express how much each person earned.

We may draw up an equation to determine how much money Mario received by taking into account the fact that Allan received $640 more than Giana. It goes like this: 7x = 640 + 3x. x = 160 is the result of solving this equation. Mario thus received $160 whereas Giana received $480 after multiplying 3x by 3 * 160. Allan received $1120 since he was paid $640 more than Giana (7x = 7 * 160). Mario, Giana, and Allan divided the total amount of money as follows: 2x + 3x + 7x = 12x = 12 * 160 = $2160.

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The area of the right triangle with side lengths of 15cm and 12cm is 90 cm².

The area of triangle can be determined using the equation;

Area = 1/2 × base × height.

The angle described forms a right-triangle.

Area = 1/2 × base × height

Area = 1/2 × 12cm × 15cm

Area = 6cm × 15cm

Area = 90 cm²

Therefore, the area of the triangle is 90 cm².

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By using a statistical method called regression to model the relationship between the number of earthquakes and various factors that may influence them, such as geological features or human activities.

To answer this question, we need to use a statistical concept called variance. In simple terms, variance measures how spread out a set of data is from its mean or average value.

In the case of earthquakes, we can use historical data to calculate the average number of large earthquakes that occur in the US per year, and then calculate the variance to see how much variation there is in the actual number of earthquakes from year to year.

By doing so, we can make predictions about the expected number of earthquakes in the future and estimate their variance.

In mathematical terms, the variance of a random variable X can be calculated as follows:

Var(X) = E[(X - μ)²]

Where E is the expected value operator, μ is the mean or average value of X, and ² means "squared." This formula tells us to subtract the mean from each value of X, square the result, take the average of these squared differences, and that gives us the variance of X.

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Answer:

Based on these observations, the inequality represented by the graph is y > mx + b, where m is a positive number and b is a negative number.

Step-by-step explanation:

The graph represents a linear function. To find the inequality, we can find the equation of the line in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.

From the graph, it can be seen that the slope of the line is positive, which means that as x increases, y also increases. Also, the y-intercept is negative, which means that the line crosses the y-axis at a negative value.

Based on these observations, the inequality represented by the graph is y > mx + b, where m is a positive number and b is a negative number.

Note that the exact values of m and b can be found by using two points on the line and solving for the slope and y-intercept using the formula for a line.

The value of x in the triangle is 6√5

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

The triangle

Using the above as a guide, we have the following:

x/20 = 9/x

Cross multiply the equation

so, we have the following representation

x^2 = 180

TAke the square root of hoth sides

This gives

x = 6√5

Hence, the solution of x is  6√5

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Answer:

Step-by-step explanation:

The average rate of change of a function over an interval is equal to the total change in the function's output divided by the total change in the input over the interval. In other words, it is the slope of the secant line that connects the two points on the function defined by the interval.

If the function is represented by y = f(x), the average rate of change of the function over the interval [-4, -3] can be calculated as:

Δy / Δx = (f(-3) - f(-4)) / (-3 - (-4))

So, to calculate the average rate of change, you would need to know the values of the function f(x) at x = -3 and x = -4. If you provide the equation for the function f(x), I can help you find the average rate of change.

If on the following Tuesday, Terry fills out scale again and receives a score of 28 , then Terry's scores on the Self-Monitoring Scale do not appear to be Reliable .

The Terry's scores on the Self-Monitoring Scale do not appear to be reliable, because there is a significant difference between his score on Friday and his score on the following Tuesday.

The Reliability is defined as the consistency of measurement over time or across different conditions.

In this case, if Terry's scores on the Self-Monitoring Scale were reliable, we would expect them to be consistent or stable over time.

However, his score on Tuesday is significantly lower than his score on Friday suggests that there may be some inconsistency in his responses .

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The value of x and y are not specified, but the result of the multiplication is 24x^2 + 76x + 50.

What do you mean by Expression?

In mathematics, an expression is a mathematical phrase that can contain numbers, variables, and operators. Expressions can be combined and simplified to solve problems, find relationships, and evaluate the truth of statements. For example, the expression "3 + 4" is a simple expression that represents the value 7 when evaluated.

Expressions can also be more complex, involving multiple operations, variables, and functions. For example, the expression "2x + 3y - z" is a more complex expression that involves three variables and three different operations.

Given the expression (3x + 5)(8x + 10), to find the value of x and y, we have to multiply the two expressions inside the parentheses and simplify the result.

Multiplication of the expressions:

(3x + 5)(8x + 10) = 24x^2 + 76x + 50

So, the value of x and y are not specified, but the result of the multiplication is 24x^2 + 76x + 50.

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Increase the accuracy of your measurements by using a more precise instrument or tool, such as a protractor or ruler.

The accuracy of the intersection of your three circles may not have been exact due to imprecise measurements taken. To improve the results, you could use a more precise instrument or tool, such as a protractor or ruler. With a protractor , you can measure the angle of the intersection of the circles more accurately. If a ruler is used, make sure that it is a straight edge, and measure the distance between the circles to ensure they intersect at the same point . Once the measurement is taken, draw the circles and their intersection accordingly. Doing this will help improve the accuracy of the intersection of the three circles and yield better results.

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By induction, it can be concluded that if we remove the root of a k-th order binomial tree, it results in k binomial trees of the smaller orders.

1. To prove by induction that if we remove the root of a k-th order binomial tree, it results in k binomial trees of the smaller orders, we can use the following steps:

2. Base case: For k = 1, we have a single node, and if we remove the root, there is no tree left.

3. Inductive hypothesis: Suppose that the result holds for some k = n, that is, if we remove the root of an n-th order binomial tree, it results in n binomial trees of the smaller orders.

4. Inductive step: We need to prove that the result also holds for k = n + 1. To do this, we consider a (n + 1)-th order binomial tree. According to the definition, this tree is formed by joining two n-th order binomial trees. Let's call them T1 and T2. If we remove the root of this tree, the two subtrees T1 and T2 will become the n binomial trees of the smaller orders. These n binomial trees are all distinct because they correspond to the different possible combinations of nodes in the two subtrees T1 and T2.

Therefore, by induction, it can be concluded that if we remove the root of a k-th order binomial tree, it results in k binomial trees of the smaller orders.

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The inequality represented by the graph is given as follows:

y < 4x - 2.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The graph crosses the y-axis at y = -2, hence the intercept b is given as follows:

b = -2.

When x increases by 1, y increases by 4, hence the slope m is given as follows:

m = 4.

The values to the left of the line are shaded, hence the inequality represented by the graph is given as follows:

y < 4x - 2.

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For the given matrix A, a 3x2 matrix B such that AB=I, where I is the 2x2 matrix B =  [tex]\left[\begin{array}{ccc}a&b\\c&d\\e&f\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}-2&1\\1&-1\\1&1\end{array}\right][/tex] when AB=I

Given matrix A = [tex]\left[\begin{array}{ccc}1&2&1\\1&1&1\\\end{array}\right][/tex]₂ₓ₃

B = [tex]\left[\begin{array}{ccc}1&2&1\\1&1&1\\\end{array}\right][/tex]₃ₓ₂

In such a way we know that, that AB = I ₂ₓ₂

therefore = [tex]\left[\begin{array}{ccc}1&2&1\\1&1&1\\\end{array}\right][/tex] [tex]\left[\begin{array}{ccc}a&b\\c&d\\e&f\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right][/tex]

we can say that [tex]\left[\begin{array}{ccc}a+2c+e&b+2d+f\\a+c+e&b+d+f\\\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right][/tex]

then, a+2c+e=1

then, when elaborated we get, a+2(-a-e)+e=1

a-2a-2e+e=1

-a-e=1

a+e = -1

2c-c = 1, c = 1 hence we get the value for c

similarly we can do the same steps for the other values

b+2d+f=0

1-d+2d=0

1+d = 0

d = -1

we get the value of d as well now for the value of a and e we can proceed as shown below:

a+c+e=0

c= -a-e

a+e= -c

a+e= -1

a= -2, e=1

similarly we can proceed as shownfor the values of b and f

b+d+f=1

b+f=1-d

b+f=2

b=1, f=1

when we put these values in the correct order and place we get the value for matrix b such as shown below,

therefore, matrix B =  [tex]\left[\begin{array}{ccc}a&b\\c&d\\e&f\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}-2&1\\1&-1\\1&1\end{array}\right][/tex]

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Answer:

The value of the investment in 5 years.

Step-by-step explanation:

The description of the function states that it tells us the value of an investment at some point in the future (t), measured in years.  In other words, f(t).  When the time is 5 years, it would be written as f(5), and the t term in the function will be set to 5 for the calculation, which will yield the value of the investment at that time.

Answer:

x = 2.0909090

Step-by-step explanation:

Here is my solution.

Answer:

Area = 15a^3b^6

Perimeter: 10a^2b^4+6ab^2

Step-by-step explanation:

Formula For Area: L*W

Input The Numbers: 5a^2b^4 * 3ab^2

5a^2b^4 * 3ab^2 = 15a^3b^6

Area = 15a^3b^6

Formula for perimeter: P=2(l+w)

Input the Numbers: P = 2(5a^2b^4 + 3ab^2)

2(5a^2b^4 + 3ab^2) = 10a^2b^4+6ab^2

Perimeter: 10a^2b^4+6ab^2

Hope this helped!

On solving the provided question, we cans ay that  in this triangle by Pythagorean theorem [tex]A^2 = B^2 + C^2[/tex] => AC = [tex]\sqrt{115}[/tex]

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

here, in this triangle by Pythagorean theorem

[tex]A^2 = B^2 + C^2[/tex]

AC = [tex]\sqrt{14^2 - 9^2}[/tex]

AC  = [tex]\sqrt{196 - 81}[/tex]

AC = [tex]\sqrt{115}[/tex]

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