A collector has a box of 32 figurines. The value of each figurine increased by $2.32 over the past year. The box of figurines is now worth $114.24. What was the original cost, x, of one figurine? The original cost of one figurine was . Convince Me! Can the equation 32x + 2.32 = 114.24 be used to find the original cost of each figurine in the problem above? Explain.

Answer:

140 liters will remain after 10 mins

Step-by-step explanation:

The easy way is just multiply the amount lost per min by the number of mins.

(i × j) × k = 0, is the vector, not with determinants, but by using properties of cross products.

The procedure for multiplying two vectors is called the cross product of the two vectors. The sign(×) of multiplication between two vectors indicates a cross product. It is a three-dimensional system-defined binary vector operation.

A cross product in three dimensions is a binary operation on two vectors. It generates a vector that is parallel to both vectors. A and B together form a vector product, which is represented by the symbol a b. The vector that results from it is parallel to both a and b. Cross products and vector products are similar terms.

As we know,

i × j = | i | × | j | × sin 90° × k

or, i × j = 1 × 1 × 1 × k

or, i × j = k

thus,  (i × j) × k = k × k

or,  (i × j) × k = 0

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Answer:

  D) A″ (3, 2), B″ (3, 0), C″ (−1, 0), D″ (−1, 2)

Step-by-step explanation:

You want the coordinates of points A", B", C", D" after A(-5, 1), B(-5, 3), C(-1, 3), and D(-1, 1) have been translated by <2, -3> and reflected across the origin.

The translation transformation is given in the problem statement:

  (x, y) ⇒ (x +2, y -3)

The reflection transformation is ...

  (x, y) ⇒ (-x, -y) . . . . . . . reflection across the origin

The composition of these transformations is ...

  (x, y) ⇒ (-(x +2), -(y -3))

  (x, y) ⇒ (-x-2, -y+3)

Using this transformation on the given points, we find ...

  A(-5, 1) ⇒ A"(-(-5)-2, -1+3) = A"(3, 2)

  B(-5, 3) ⇒ B"(-(-5)-2, -3+3) = B"(3, 0)

  C(-1, 3) ⇒ C"(-(-1)-2, -3+3) = C"(-1, 0)

  D(-1, 1) ⇒ D"(-(-1)-2, -1+3) = D"(-1, 2)

Answer:

y = 5x - 3, so M = 5 and C = -3.

Answer:

The masimum height of 144 feet is reached at 3 second. The ball is in the air for 6second.

The deepest to highest creatures are in order flounder, bluefish, clam, hermit crab according to sea level.

What is sea level?

The average surface level of one or more of the coastal bodies of water on Earth is known as mean sea level, and it can be used to measure heights like elevation.

Main Body:

a) As the value for flounder is most negative , so we can say that it is found at the greatest depth .

after which bluefish is found .

the  value of clam is less positive than hermit crab so it is found after bluefish and at last hermit crab

Hence the order is like :  Flounder > bluefish > clam > hermit crab .

b)The difference between the depth at which bluefish and hermit crab are found is 5ft.

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Answer:

12x^2+4

Step-by-step explanation:

4(3x^2+1)

Therefore, the volume of the paper cone to the nearest tenth is 418.7 inches cubed.

The volume of the paper cone that Gretchen made to hold a gift for a friend is given by;V= (1/3)πr²hWhere;r = radius of the paper coneh = height of the paper coneπ = 3.14

Given that;Height of the paper cone (h) = 16 inches Radius of the paper cone (r) = 5 inchesWe are to find the volume (V) of the paper cone to the nearest tenth of an inch.

To obtain the volume of the paper cone, we can substitute the values of r and h in the formula above to obtain;

\(V= (1/3)\pir^2hV\)= \((\frac{1}{3} ) \times 3.14\times5^2 \times16V = (\frac{1}{3} ) \times 3.14\times25\times16V = (\frac{1}{3}) \times 1256V=418.7\)

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The x- and y-intercepts of the function g ( x ) = ( x + 1 ) ( x^2 - 10x + 24 ) are x-intercepts = -1 , 4 , 6 and y-intercepts = 24 .

Given :

Function

g ( x ) = ( x + 1 ) ( x^2 - 10x + 24 )

x + 1 = 0

x = -1 is one of the x - intercept .

factorize  x^2 - 10x + 24 so that we get a roots , roots are nothing but the x - intercepts.

= x^2 - 6x - 4x + 24

Take x as common  and -4 as common

= x ( x - 6 ) - 4 ( x - 6 )

( x - 6 ) has common

( x - 4 ) ( x - 6 ) = 0

x = 4 , 6

so x - intercepts = -1 , 4 , 6

y - intercepts = 24 .

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Answer:

             The x intercept:    (1.5, 0)

The slope intercept form:   y = 2x - 3

                      The slope:    m = 2

Step-by-step explanation:

x intercept means y=0

4x - 2y = 6

4x - 2·0 = 6

4x = 6

x = 1.5

The slope intercept form is:  y = mx + b

4x - 2y = 6            {subtract 4x from both sides}

- 2y = - 4x + 6       {dividing both sides by (-2)}

y = 2x - 3            ← slope intercept form

Slope is the number by x, in slope intercept form of line's equation

Answer: 5.79

36

16 cost

Step-by-step explanation:

Given, $X_1, . . . , X_n$ is a random sample from $N(θ, 1)$.

The least squares estimator of $θ$ is$$\hat{θ}=\frac{\sum_{i=1}^{n} X_i}{n}$$(1)

The likelihood function for

$θ$ is$$L(θ) = \prod_{i=1}^{n} \frac{1}{\sqrt{2π}}e^{-\frac{(X_i-θ)^2}{2}} = \frac{1}{(\sqrt{2π})^n}e^{-\frac{\sum_{i=1}^{n}(X_i-θ)^2}{2}}$$

Let us consider the negative log of the likelihood function of

$θ$ is$$\begin{aligned} -\ln L(θ) & = -\ln \frac{1}{(\sqrt{2π})^n} - \frac{\sum_{i=1}^{n}(X_i-θ)^2}{2}\\ & = -n \ln(\sqrt{2π}) - \frac{\sum_{i=1}^{n}(X_i-θ)^2}{2} \end{aligned}$$

Differentiating the above equation wrt $θ$

and setting the result to zero, we get

$$\frac{d}{dθ} \left(-\ln L(θ) \right) = \frac{\sum_{i=1}^{n}(X_i-θ)}{2}=0$$$$\implies \sum_{i=1}^{n}X_i=nθ$$Solving the above equation for $θ$, we get$$\hat{θ}=\frac{\sum_{i=1}^{n} X_i}{n}$$

Thus, we have shown that the least squares estimator of $θ$ is same as the maximum likelihood estimator of $θ$ for the normal distribution $N(θ, 1)$.

Hence, we have proved that the least square estimator of $θ$ is the same as the maximum likelihood estimator of $θ$.

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We have shown that the least square estimator of θ and the MLE of μ are the same in the case of a random sample from N(μ, σ²).

To prove that the least square estimator (LSE) of θ is the same as the maximum likelihood estimator (MLE) of μ in the case of a random sample X1, ..., Xn from N(μ, σ²) with μ ∈ ℝ, we need to show that they yield the same estimates.

The LSE of θ, denoted as ŜLSE, is obtained by minimizing the sum of squared differences between the observed values Xi and the estimated values θ:

ŜLSE = arg min θ Σ(Xi - θ)²

On the other hand, the MLE of μ, denoted as ŜMLE, is obtained by maximizing the likelihood function, which is the joint probability density function of the sample X1, ..., Xn, given the parameters μ and σ²:

ŜMLE = arg max μ Π f(Xi; μ, σ²)

In the case of a random sample from N(μ, σ²), the likelihood function can be written as:

L(μ, σ²) = Π (1/√(2πσ²)) * exp(-(Xi - μ)² / (2σ²))

Taking the natural logarithm of the likelihood function (log-likelihood), we have:

log L(μ, σ²) = Σ (-1/2) * log(2πσ²) - (Xi - μ)² / (2σ²)

To find the MLE of μ, we differentiate the log-likelihood with respect to μ and set it equal to zero:

d/dμ log L(μ, σ²) = Σ (Xi - μ) / σ² = 0

Simplifying, we have:

Σ (Xi - μ) = 0

Dividing by n, we obtain:

(Σ Xi - nμ) = 0

Solving for μ, we have:

ŜMLE = (1/n) * Σ Xi

Now, let's compare this with the LSE of θ:

ŜLSE = arg min θ Σ(Xi - θ)²

Taking the derivative with respect to θ and setting it equal to zero, we have:

d/dθ Σ(Xi - θ)² = -2Σ(Xi - θ) = 0

Simplifying, we have:

Σ Xi - nθ = 0

Solving for θ, we have:

ŜLSE = (1/n) * Σ Xi

Comparing the expressions for ŜMLE and ŜLSE, we can see that they are identical:

ŜMLE = ŜLSE = (1/n) * Σ Xi

Therefore, we have shown that the least square estimator of θ and the MLE of μ are the same in the case of a random sample from N(μ, σ²).

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The amount of juice the cup can hold given that the cup has diameter of 8 centimeters and a height of 12 centimeters is 602.88 cm³

To know the amount of juice the cup can hold, we shall obtain the volume of the cup.

We shall use the formula for obtaining volume of cylinder to obtain the volume of the cup. Details below:

Volume = πr²h

Volume = 3.14 × 4² × 12

Volume = 3.14 × 16 × 12

Volume = 602.88 cm³

Thus, we can conclude from the above calculation that the amount of juice the cup can hold is 602.88 cm³

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Answer: 75.4

Step-by-step explanation:

Answer:

Factoring w2-16w+19

The first term is, w2 its coefficient is 1 .

The middle term is, -16w its coefficient is -16 .

The last term, "the constant", is +19

Step-1 : Multiply the coefficient of the first term by the constant 1 • 19 = 19

Step-2 : Find two factors of 19 whose sum equals the coefficient of the middle term, which is -16 .

-19 + -1 = -20

-1 + -19 = -20

1 + 19 = 20

19 + 1 = 20

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

w2 - 16w + 19 = 0

hope it helps

"Financial" as it is not an effectiveness MIS metric.

To determine which one is not an effectiveness MIS metric, we need to understand the purpose of these metrics. Effectiveness MIS metrics measure how well a system is achieving its intended goals and objectives.

Customer satisfaction is a common metric used to assess the effectiveness of a system. It measures how satisfied customers are with the product or service provided.

Conversion rates refer to the percentage of website visitors who complete a desired action, such as making a purchase. This metric is often used to assess the effectiveness of marketing efforts.

Financial metrics, such as revenue and profit, are crucial indicators of a system's effectiveness in generating financial returns.

Response time measures the speed at which a system responds to user requests, which is an important metric for evaluating system performance.

Therefore, based on the given options, "Financial" is not a type of effectiveness MIS metric. It is a separate category of metrics that focuses on financial performance rather than the overall effectiveness of a system.

In summary, the answer is "Financial" as it is not an effectiveness MIS metric.

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Answer:

49÷7=7-4=3

Step-by-step explanation:

Answer:

F

Step-by-step explanation:

Answer:

  F

Step-by-step explanation:

You only need to read as far as ...

  y ≤

to choose the correct graph. The values in the solution will be less than or equal to those on the boundary line. That means the graph will be shaded below the line, and the line will be solid (because it is part of the solution).

The graph with a solid line and shading below is graph F.

Answer:

below 15 times

Step-by-step explanation:

If the numbers on the spinner are 1, 2, 3, 4, 5, 6 (six numbers) the even numbers are 2, 4, 6 ( three numbers) than 3 out of 6 numbers on the spinner are even.

If Jane will spin the spinner below 30 times the is expected that less than half of the time 30/2 = 15 times will be an even number.

Answer:

0 ≤ y ≤ 7

Step-by-step explanation:

Hey there! :)

Please see an explanation for better understanding, and let me know if you have any questions!

Range in Function means set of all y-values. We know by the graph that y-value is a vertical value while x-value is horizontal value. From the graph, we have y-axis which is vertical line and x-axis which is horizontal line.

For this question, I would like you to focus on y-value instead, at best, only. That is because we are finding the range, as said above that range is the set of all y-values.

To find the range in graph, first, you must understand that range starts from minimum point/value to maximum point/value. Therefore, we will have to find y-values for both points and combine the interval.

From the graph, we see that there are two points given which are (-6,0) and (9,7). Since (-6,0) is the minimum point because below y = 0, there exists no values. On the other hand, (9,7) is our maximum point because above y = 7, there exists no values.

Focus only y-values, for both points, we have y = 0 and y = 7. Since range is minimum < y < maximum - for opened dots of both points or minimum ≤ y ≤ maximum - for closed dots for both points.

In case if you don’t know what opened dots and closed dots are. Opened dots are white dots while closed dots are colored dots, usually dark ones.

Thus, from the y-values of both point, our range is 0 ≤ y ≤ 7

a) The upfront fee is $0.

b) It will cost $3.3 to travel 11 miles.

c) The new upfront fee is $1.4.

d) It will cost $5.6 to travel 14 miles.

To solve this problem, we can set up a system of equations based on the given information.

Let's denote the upfront fee as "f" and the cost per mile as "c".

From the first scenario:

We know that the total cost for riding 4 miles is $3.2. This can be expressed as:

f + 4c = 3.2   -- Equation 1

From the second scenario:

We are told that only the upfront fee has changed. The total cost for riding 7 miles is $5.6. This can be expressed as:

f + 7c = 5.6   -- Equation 2

To solve for the upfront fee and cost per mile, we can solve this system of equations.

Solving the system of equations:

Equation 1: f + 4c = 3.2

Equation 2: f + 7c = 5.6

Subtracting Equation 1 from Equation 2 to eliminate "f":

(f + 7c) - (f + 4c) = 5.6 - 3.2

7c - 4c = 2.4

3c = 2.4

c = 0.8

Substituting the value of c into Equation 1 to find "f":

f + 4(0.8) = 3.2

f + 3.2 = 3.2

f = 3.2 - 3.2

f = 0

a) The upfront fee is $0.

b) To travel 11 miles, the cost would be: 0 + 11(0.3) = $3.3

c) The new upfront fee is still unknown.

d) To travel 14 miles, we can use the same cost per mile of 0.3:

New upfront fee (let's call it "f2") + 14(0.3) = Total cost

f2 + 4.2 = Total cost

We are given that the total cost is $5.6, so we can substitute this value:

f2 + 4.2 = 5.6

f2 = 5.6 - 4.2

f2 = 1.4

c) The new upfront fee is $1.4.

d) To travel 14 miles, the cost would be: 1.4 + 14(0.3) = $5.6.

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2. Using proportion, the value of x = 38, the length of FC = 36 in.

3. Applying the angle bisection theorem, the value of x = 13. The length of CD = 39 cm.

The Angle Bisector Theorem states that in a triangle, an angle bisector divides the opposite side into segments that are proportional to the lengths of the other two sides of the triangle.

2. The proportion we would set up to find x is:

(x - 2) / 4 = 27 / 3

Solve for x:

3 * (x - 2) = 4 * 27

3x - 6 = 108

3x = 108 + 6

Simplifying:

3x = 114

x = 114 / 3

x = 38

Length of FC = x - 2 = 38 - 2

FC = 36 in.

3. The proportion we would set up to find x based on the angle bisector theorem is:

13 / 3x = 7 / (2x - 5)

Cross multiply:

13 * (2x - 5) = 7 * 3x

26x - 65 = 21x

26x - 21x - 65 = 0

5x - 65 = 0

5x = 65

x = 65 / 5

x = 13

Length of CD = 3x = 3(13)

CD = 39 cm

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Answer:

0.83

Step-by-step explanation:

\( \frac{45}{54} \\ \)

Use 3 to divide through

\( \frac{5}{6 } = 0.8333333\)

The Australia to Britain, decreasing the interest rate in Britain and increasing the interest rate in Australia.

The equilibrium real interest rate is the short-term rate that is consistent with aggregate production at potential and stable inflation in the long run.

We have:

The equilibrium real interest rate in Britain increases to 8 percent, while the equilibrium real interest rate in Australia remains at 4 percent.

From the above data, we can say,

Australia to Britain, decreasing the interest rate in Britain and increasing the interest rate in Australia.

Thus, the Australia to Britain, decreasing the interest rate in Britain and increasing the interest rate in Australia.

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Answer:

2/100=0.02

0.02*15=33.3

111+33.3

144.3

Step-by-step explanation:

6/4 + 2/3 (taking LCM between denominators)

=> 6*3/4*3 + 2*4/3*4

=> 18/12 + 8/12

=> (18 + 8)/12

=> 26/12

=> 13/6

Answer:

Step-by-step explanation:

Answer:

19 is a prime number. 40 is a composite number

Step-by-step explanation:

40 can be divided by number other than 1 and its self

19 can only be divided by 1 and itself

Answer:

19 is composition 40 is prime number

In order to find the number of distinguishable permutations of the group of letters A, A, G, E, E, E, M, we can use the following formula:

The number of permutations = n! / (n1! n2! ... nk!), where n is the total number of objects to be arranged, and n1, n2, ..., nk are the numbers of objects that are identical to one another.

For this problem, we have 7 letters with 2 A's, 3 E's, and 1 G and 1 M letter.

Using the formula above, we can find the number of distinguishable permutations: 7! / (2! 3! 1! 1!) = (7 × 6 × 5 × 4 × 3 × 2 × 1) / [(2 × 1) × (3 × 2 × 1) × (1 × 1) × (1 × 1)] = 2520

Therefore, there are 2520 distinguishable permutations of the group of letters A, A, G, E, E, E, M.

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