find the missing number of each unit rate.
16/4=?/1

Answer:

75

Step-by-step explanation:

it will take 3 week for 3×25 and 5 week for 5×15. I hope this helps.

Answer:

there is no image

Step-by-step explanation:

Theres no image.........

Answer:

Step-by-step explanation:

The domain and range of the given function are [−3,∞) and [0,∞) respectively.

The given function is f(x)=2√(x+3).

Find the domain by finding where the function is defined. The range is the set of values that correspond with the domain.

The domain and range are defined for a relation and they are the sets of all the x-coordinates and all the y-coordinates of ordered pairs respectively.

Domain: [−3,∞),{x|x≥−3}

Range: [0,∞),{y|y≥0}

Therefore, the domain and range of the given function are [−3,∞) and [0,∞) respectively.

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Answer:

8 and one thirds

Step-by-step explanation:

5 times 5 is equal to 25 and 25 divided by 3 is 8.3333

Answer:

$8.33

Step-by-step explanation:

So, to figure out how much one mango costs, I did $5 divided by 3, which gave me 1.66.

I then multiplied that by 5 to see how much 5 mangos cost, and I got $8.33

Using the fundamental theorem of arithmetic, we have proven that (a, 6) [a, b] = ab for positive integers a and b.

To prove that (a, 6) [a, b] = ab for positive integers a and b using the fundamental theorem of arithmetic, we'll proceed as follows:

Step 1: Prime factorization of a and 6:

Using the fundamental theorem of arithmetic, we can write a and 6 as products of their prime factors:

a = p1^k1 * p2^k2 * ... * pn^kn,

6 = 2^1 * 3^1.

Step 2: Finding the greatest common divisor (a, 6):

To find the greatest common divisor (a, 6), we consider the common prime factors between a and 6 and take the minimum exponent for each prime factor. In this case, the common prime factor is 2 with an exponent of 1. Therefore, (a, 6) = 2^1.

Step 3: Prime factorization of [a, b]:

Using the fundamental theorem of arithmetic, we can write [a, b] as a product of its prime factors:

[a, b] = p1^m1 * p2^m2 * ... * pn^mn.

Step 4: Finding the least common multiple [a, b]:

To find the least common multiple [a, b], we consider the prime factors between a and b and take the maximum exponent for each prime factor. In this case, we have already determined that the common prime factor is 2 with an exponent of 1. Therefore, [a, b] = 2^1.

Step 5: (a, 6) [a, b] = ab:

Substituting the values we found, we have:

(a, 6) [a, b] = 2^1 * 2^1 = 2^2 = 4.

Since ab = 4, we have proven that (a, 6) [a, b] = ab for positive integers a and b using the fundamental theorem of arithmetic.

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Answer:

\(53\frac{1}{3}\)

Step-by-step explanation:

\(\frac{2}{3} * \frac{80}{1} = \frac{160}{3}=53\frac{1}{3}\)

hope this helps, good luck :)

Answer:

53.3 infinity

Step-by-step explanation:

Answer:

1) C

2) A

3) C

4) D

Step-by-step explanation:

1) n^2 = 16

n = 4 or n = -4

2) r^2 + 4 = 13

r = 3 or r = -3

3) 4n^2 + 3 = 19

n = 2 or n = -2

4) 2( x - 3 )^2 = 32

x = -1 or x = 1

Answer: A and D

Step-by-step explanation:

Hopefully, I am correct! =)

The inverse Laplace transform of \(L^{-1}\)(4s/(4s² + 1)) is \(e^{(-i/2t)\) + \(e^{(i/2t))/2\).

To find the inverse Laplace transform of \(L^{-1}\)(4s/(4s² + 1)), we can use partial fraction decomposition.

Step 1: Factorize the denominator of the Laplace transform.

4s² + 1 = (2s + i)(2s - i)

Step 2: Write the partial fraction decomposition.

4s/(4s² + 1) = A/(2s + i) + B/(2s - i)

Step 3: Clear the fractions.

4s = A(2s - i) + B(2s + i)

Step 4: Solve for A and B.

Comparing coefficients:

4 = 2A + 2B (coefficient of s terms)

0 = -Ai + Bi (constant terms)

From the second equation, we can see that A = B. Substituting this into the first equation:

4 = 4A

A = 1

So, B = 1 as well.

Step 5: Rewrite the partial fraction decomposition.

4s/(4s² + 1) = 1/(2s + i) + 1/(2s - i)

Step 6: Take the inverse Laplace transform.

\(L^{-1}\)(4s/(4s² + 1)) = \(L^{-1}\)(1/(2s + i)) + \(L^{-1}\)(1/(2s - i))

Using Theorem 7.2.1, the inverse Laplace transforms of the individual terms can be found:

\(L^{-1}\)(1/(2s + i)) = \(e^{(-i/2t)/2\)

\(L^{-1}\)(1/(2s - i)) = \(e^{(i/2t)/2\)

Therefore, the inverse Laplace transform of \(L^{-1}\)(4s/(4s² + 1)) is:

\(L^{-1}\)(4s/(4s² + 1)) = \(e^{(-i/2t)/2\) + \(e^{(i/2t)/2\).

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To test whether two or more population means are different, the critical value of the test is determined based on the significance level and the degrees of freedom.

In hypothesis testing, the critical value is the threshold value that determines whether the test statistic falls in the critical region, leading to the rejection of the null hypothesis. The critical value depends on the significance level chosen for the test and the degrees of freedom.

To calculate the critical value, we need to know the significance level, which represents the probability of making a Type I error (rejecting the null hypothesis when it is true). Common significance levels include 0.05 (5%) and 0.01 (1%).

Additionally, the degrees of freedom depend on the number of populations and the sample sizes. The degrees of freedom are usually calculated as the sum of the sample sizes minus the number of populations.

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The requried average rate of change is given as -7 dollars per hour. Option D is correct.

The association between two numerical variables measured for the same individuals is displayed in a scatterplot. One variable's values are displayed on the horizontal axis, and the other variable's values are displayed on the vertical axis.

here,
The average rate of change for the data from the 5th hour to the 8th hour is given as,
m = (y₂ - y₁) /  (x₂ - x₁)

m = 75 - 96 / 8 - 5
m = -21/3
m = -7 dollars per hour.

Thus, the requried average rate of change is given as -7 dollars per hour. Option D is correct.

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There are two correct statements regarding a 5 by 5 matrix with three eigenvalues, one of which has a three-dimensional eigenspace.

First, there must be at least two linearly independent eigenvectors associated with the eigenvalue that has a three-dimensional eigenspace. Second, the sum of the dimensions of the eigenspaces must be equal to the size of the matrix, which is 5 in this case.

To understand the first statement, recall that the dimension of an eigenspace is equal to the multiplicity of the associated eigenvalue, which is the number of times it appears as a root of the characteristic equation. Since one of the eigenvalues has a three-dimensional eigenspace, its multiplicity must be at least 3. This means there are at least 3 linearly independent eigenvectors associated with this eigenvalue, which is necessary to span a three-dimensional space. However, the sum of the multiplicities of all eigenvalues cannot exceed the size of the matrix, which is 5. Therefore, the remaining two eigenvalues must have a combined multiplicity of 2 at most, which implies that there are at most 2 linearly independent eigenvectors associated with each of them.

To understand the second statement, note that the sum of the dimensions of the eigenspaces is equal to the sum of the multiplicities of all eigenvalues. This follows from the fact that the eigenspaces associated with distinct eigenvalues are linearly independent. Since there are three distinct eigenvalues in this case, the sum of their multiplicities is at most 5, which means the sum of the dimensions of their eigenspaces is also at most 5. Since one of the eigenspaces has dimension 3, the sum of the dimensions of the other two eigenspaces must be at least 2, which means each of them has at least one linearly independent eigenvector.

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The area of the triangle is 3.535533, whose vertices are  (0,0,0), (1,3,−1), and (2,1,1) .

Explanation: -

To find the area of the triangle with vertices (0,0,0), (1,3,-1), and (2,1,1), you can use the formula for the area of a triangle in 3D space:

Area = 0.5 * ||AB x AC||

Here, AB and AC are the vectors representing the sides of the triangle, and "x" denotes the cross product.

STEP 1:- Find the vectors AB and AC:
AB = B - A = (1,3,-1) - (0,0,0)

     = (1,3,-1)
AC = C - A = (2,1,1) - (0,0,0)

     = (2,1,1)

STEP 2: - Compute the cross product AB x AC:
AB x AC = (3 * 1 - (-1) * 1, -(1 * 1 -(- 1 )* 2), 1 * 1 - 3 * 2)
AB x AC = (3 + 1, 3, 1 - 6)

              = (4, 2, -5)

STEP 3: - Compute the magnitude of the cross product ||AB x AC||:
||AB x AC|| = √(4² + (-3)² + (-5)²)

                  = √(16 + 9 + 25)

                  = √50

                  =7.071060

STEP 4: - Calculate the area of the triangle:
Area = 0.5 * ||AB x AC|| = 0.5 * (7.071060)

Therefore, the area of the triangle is 3.535533.

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Answer:

\(\textsf{Perpendicular to given line}:y=-3x+14\)

\(\textsf{Parallel to given line}: y=\dfrac13x-\dfrac83\)

Step-by-step explanation:

Rewrite the given equation to make y the subject:

\(\begin{aligned}-3x+9y &=5 \\ \implies 9y &=3x+5 \\ \implies y &=\dfrac13x+\dfrac59\end{aligned}\)

Therefore, the slope of the given equation is \(\frac13\).

If two lines are perpendicular to each other, the product of their slopes will be -1.  Therefore, the slope (m) of the line that is perpendicular to the given line is:

\(\begin{aligned}m \times \dfrac13 & =-1\\ \implies m & =-3\end{aligned}\)

To find the equation of the line, substitute the found slope (-3) and the point (5, -1) into the point-slope form of a linear equation:

\(\begin{aligned}y-y_1 & =m(x-x_1)\\ \implies y-(-1) &=-3(x-5) \\ y+1 & =-3x+15 \\ y &=-3x+14\end{aligned}\)

If two lines are parallel to each other, their slopes will be the same.  Therefore, the slope (m) of the line that is parallel to the given line is \(\frac13\)

To find the equation of the line, substitute the slope (\(\frac13\)) and the point (5, -1) into the point-slope form of a linear equation:

\(\begin{aligned}y-y_1 & =m(x-x_1)\\\\ \implies y-(-1) &=\dfrac13(x-5) \\\\ y+1 & =\dfrac13x-\dfrac53 \\\\ y &=\dfrac13x-\dfrac83\end{aligned}\)

Slope =m=1/3

Note that perpendicular lines have slopes negative reciprocal to each other .

Equation in point slope form

And

parallel lines have equal slope

Equation of parallel line

Answer:

So when we triple the value of "x" in that expression we also triple the value of "y". The corrrect answer is "x 3".

Step-by-step explanation:

For a given "x", y follows the expression: \(y = 8*x\). We have a new input to the function, which we will call "a", we know that this value is 3 times the value of the prior "x", so we can calculate what will happen to "y" as shown below:

\(y_1 = 8*x\)

For when the input is "a":

\(y_2 = 8*a\)

We know that "a" is 3 times x, therefore:

\(y_2 = 8*(3*x)\)

Due to the associative property of the product we can rewrite the above expression as:

\(y_2 = 3*(8*x)\)

Since "8*x" is the same as the prior "y", then we have:

\(y_2 = 3*y_1\)

So when we triple the value of "x" in that expression we also triple the value of "y". The corrrect answer is "x 3".

Answer:

x

Step-by-step explanation:

he domain of a quadratic function in standard form is always all real numbers, meaning you can substitute any real number for x. The range of a function is the set of all real values of y that you can get by plugging real numbers into x.

Answer:

The range is y \(\geq 1\).

Step-by-step explanation:

The graph is shifted up 1 unit, so the range will be everything positive after 1. Anything below 1 would not be in the range.

#teamtrees #WAP (Water And Plant)

Answer:

x = 1/3

Step-by-step explanation:

To solve the equation 9x - 1 = 2, we need to isolate the variable x on one side of the equation.

Adding 1 to both sides of the equation, we get:

9x - 1 + 1 = 2 + 1

Simplifying:

9x = 3

Dividing both sides by 9:

x = 3/9

Simplifying the fraction:

x = 1/3

Therefore, the solution to the equation 9x - 1 = 2 is x = 1/3.

Answer:

\(\displaystyle s(t)=\frac{3}{4}t^3+10t^3+5t+3\)

Step-by-step explanation:

Integrate v(t) with respect to time

\(\displaystyle \int(3t^3+30t^2+5)\,dt\\\\=\frac{3}{4}t^4+10t^3+5t+C\)

Plug-in initial condition to get C

\(\displaystyle s(0)=\frac{3}{4}(0)^3+10(0)^3+5(0)+C\\\\3=C\)

Thus, the position function is \(\displaystyle s(t)=\frac{3}{4}t^3+10t^3+5t+3\) given the velocity function and initial condition.

If the range on an X-bar-R chart suddenly and significantly increases, it indicates an increase in process variation. In this scenario, the mean (X-bar) may or may not be affected.

The mean represents the central tendency or average value of the process, while the range measures the dispersion or variation within the process.

If the mean remains stable and unaffected despite the increase in range, it suggests that the process average is still within control. However, if the range increase is accompanied by a significant shift in the mean, it indicates a potential shift in the process average.

To make a definitive determination, additional analysis and investigation are necessary to identify the underlying cause of the increased range and its impact on the process mean.

This could involve examining individual data points, performing hypothesis testing, or conducting further statistical analysis to assess the process stability and potential issues.

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From this proportion of days he does the activities, sometimes they will meet in one day.

He will do both in the same day when the day is a common factor of 3 and 4.

Since today he did both, the next time he will do so will be in the least common factor of 3 and 4.

To get the least common factor of these, we can identify the divisors of each and makes the divisions until both get to 1. If one of the divisiors is divisior for both, we don't repeat it.

So, from 3 and 4, we can start by the divisior of 2. 2 Is a divisior of 4, but not of 3, so we divide only the number for:

3, 4 | 2

3, 2 |

Now, we have 3 and 2, so we can divide for 2 again:

3, 4 | 2

3, 2 | 2

3, 1 |

Now, we have 3 and 1, so we can only divide by 3 now:

3, 4 | 2

3, 2 | 2

3, 1 | 3

1 , 1 |

So, in the end we have 2, 2 and 3, so the least common factor is 2*2*3 = 12.

Since the common factor of 3 and 4 is 12, Tyler will lift and jog on the same day 12 days after today.

The probability of a Type II error is represented by beta. Thus, the correct answer is option B.

Beta represents the probability of failing to reject the null hypothesis when it is false.

On the other hand, Type I error (alpha) represents the probability of rejecting the null hypothesis when it is true. A Type II error occurs when a false null hypothesis is not rejected. Hence, beta is the probability of making a Type II error.

The null hypothesis is rejected when the p-value is less than or equal to the level of significance, not exceeds it.

The p-value is the probability of obtaining a result as extreme as or more extreme than the observed result when the null hypothesis is true. If the p-value is less than the level of significance, the null hypothesis is rejected, and vice versa.

Hence, the statement "The null hypothesis is rejected when the p-value exceeds the level of significance" is false.

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Answer:

Step-by-step explanation:

17

Answer: Acute

Step-by-step explanation:

I don't know

Answer:

27 spoons of yellow paint

Step-by-step explanation:

Red paint : Yellow paint = 8 : 12

Let 'x' be the number of spoons of yellow paint.

8 : 12 :: 18 : x

Product of extremes = Product of means

8 * x = 12 * 18

     \(x = \frac{12*18}{8}\)

     x = 3 *9

     x = 27 spoons

Answer:27 is awser

Step-by-step explanation:

0.003 is the probability that the number of calls among the 25 that involve a fax transmission exceeds the expected number by more than 2 standard deviations

To calculate the probability that the number of calls among the 25 that involve a fax transmission exceeds the expected number by more than 2 standard deviations.The mean is the expected number of calls involving a fax transmission, while the standard deviation is the measure of variability in the distribution. We then use this information to calculate the probability of exceeding the expected number by more than 2 standard deviations, which can be done using the z-score formula. The z-score for values more than 2 standard deviations away from the mean is 2.33, which corresponds to a probability of 0.003. Thus, the probability that the number of calls among the 25 that involve a fax transmission exceeds the expected number by more than 2 standard deviations is 0.003.

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Answer:

infinitely many solution

Step-by-step explanation:

-8x + 8x + 7 = 7

7 = 7

Answer:

1, 5 and 6.

Step-by-step explanation:

The sides of this triangles has lengths in the ratio x : √3x : 2x where 2x is the hypotenuse.

When C = 30,  the side AB is the small leg  (=x).

When B = 90, the hypotenuse is  AC ( =2x).

When A =  60, the larger leg is BC (=√3x).

1.  AB = 4, BC = 4√3 :- Are possible legs.

5 AB = 7, AC = 14. :-  AB = small leg, AC = hypotenuse.

6. AB = 11, BC = 11√3:-   AB = small, BC = larger leg.

Answer:

1, 5, and 6

Hope this helps!

Step-by-step explanation:

Answer:

0.11

Step-by-step explanation: