Chris bought 2.5 pounds of pears for $1.00
per pound. He also bought 1.3 pounds of
apples for $3.00 per pound. Tim gave the cashier
$20 for the pears and apples. How much change
did he receive?

Therefore, at the given point (1, 1, 2, 4), ∂u/∂t = (ln(2) / 2) × ∂t/∂u, and ∂t/∂u cannot be determined from the given equation.

To calculate the partial derivatives ∂u/∂t and ∂t/∂u using implicit differentiation of the given equation, we'll differentiate both sides of the equation with respect to the variables involved, treating the other variables as constants.

Let's break it down step by step:

Given equation: (-2ln(-x) = ln(2)(tx - v) × 2ln(w - uv) = ln(2)

We'll differentiate both sides of the equation with respect to u and t, treating x, v, and w as constants.

Differentiating with respect to u:

Differentiate the left-hand side:

d/dt (-2ln(-x)) = d/dt (ln(2)(tx - v))

-2(1/(-x)) × (-1) × dx/du = ln(2)(t × du/dt - 0) [using chain rule]

Simplifying the left-hand side:

2(1/x) × dx/du = ln(2)t × du/dt

Differentiating with respect to t:

2ln(w - uv) × d/dt (w - uv) = 0 × d/dt (ln(2))

2ln(w - uv) × (dw/dt - u × dv/dt) = 0

Since the second term on the right-hand side is zero, we can simplify the equation further:

2ln(w - uv) × dw/dt = 0

Now, we substitute the given values (1, 1, 2, 4) into the equations to find the partial derivatives at that point.

At (1, 1, 2, 4):

-2(1/(-1)) × dx/du = ln(2)(1 × du/dt - 0)

2 × dx/du = ln(2) × du/dt

dx/du = (ln(2) / 2) × du/dt

2ln(w - uv) × dw/dt = 0

Since the derivative is zero, it doesn't provide any information about ∂t/∂u.

Therefore, at the given point (1, 1, 2, 4):

∂u/∂t = (ln(2) / 2) × ∂t/∂u

∂t/∂u cannot be determined from the given equation.

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The test statistic is t = 24.135. (option d)

To perform the hypothesis test, we need to calculate a test statistic. In this case, we can use a two-sample t-test since we are comparing the means of two independent samples. The formula for the t-test is:

t = (x₁ - x₂) / (s_p * √(1/n₁ + 1/n₂))

where x₁ and x₂ are the sample means, s_p is the pooled standard deviation, n₁ and n₂ are the sample sizes.

Using the data provided, we can calculate the sample means and standard deviations for the two samples:

x₁ = 26.3%, s₁ = 0.37%, n₁ = 6

x₂ = 16.9%, s₂ = 0.57%, n₂ = 6

As per the percentage, we can then calculate the pooled standard deviation:

s_p = √(((n₁-1)*s₁² + (n₂-1)*s₂²) / (n₁+n₂-2))

s_p = √(((6-1)*0.37² + (6-1)*0.57²) / (6+6-2)) = 0.471%

Finally, we can calculate the t-statistic:

t = (26.3 - 16.9) / (0.471 * √(1/6 + 1/6)) = 24.135

Therefore, the test statistic is d) t = 24.135.

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Complete Question:

Solid fats are more likely to raise blood cholesterol levels than liquid fats. Suppose a nutritionist analyzed the percentage of saturated fat for a sample of 6 brands of stick margarine (solid fat) and for a sample of 6 brands of liquid margarine and obtained the following results:

Stick = [26.1, 26.5, 26.5, 25.8, 26.7, 26.2]

Liquid = [16.6, 16.5, 17.1, 17.5, 17.7, 16.3]

We want to determine if there a significant difference in the average amount of saturated fat in solid and liquid fats. What is the test statistic? (assume the population data is normally distributed)

a) t = 34.225

b) z = 34.225

c) z = 34.725

d) t = 24.135

e) t = 34.725

Are you sure you wrote the question corrcetly?

For something to be parallel their slopes have to be equal but their y-intercepts need to be different.

since your equation equals y=3/4x+7 that would mean that 3/4 is the slope.

so an answer with a slope of 3/4x and a y-intercept not equal to 7 would be the correct answer.

Answer:

Second option 168= 18.X + 12.2X

Step-by-step explanation:

Area of the shape is in two parts,

Are of the larger rectangle is Lenght x width

Lenght is 12cm and width is x +2x

Area = 12 x 3x = 36x cm²

Area of the smaller rectangle = 6 x X = 6xcm²

Total area 36x + 6x = 168cm²

Another method

Find the area of the big rectangle including the cut off area

Lenght x width = 18 x (2x + X)

Area =18 x 3x or 18.3x

Calculate the white area

Length x width = 6 x 2x = 12x

Deduct the white area from the larger area

168= 18.3x - 12x

Third method

Divide the rectangle from top down

First rectangle length x width = 18x X or 18x

Second rectangle length x width = 12 x 2x

168= 18. x + 12 . 2x

The correct equation which can be used to find the value of x is,

⇒ 168 = 18 × x + 12 × 2x

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

The figure shown has a total area of 168 cm².

Now, We can find as;

Area of rectangle = Length x width

Hence, We can formulate;

⇒ 18 × x + 12 × 2x = 168

Thus, The correct equation which can be used to find the value of x is,

⇒ 168 = 18 × x + 12 × 2x

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To determine the assignment of employees to jobs that minimizes the total time required to perform the four jobs, we need to consider the time taken by each person to complete each job. Using the given Table 50, we can analyze the data and identify the optimal assignment.

By examining Table 50, we can identify the minimum time taken by each person for each job. Starting with Job 1, we see that Person 4 takes the least time of 16 hours. Moving to Job 2, Person 2 takes the least time of 18 hours. For Job 3, Person 1 takes the least time of 25 hours. Lastly, for Job 4, Person 4 takes the least time of 14 hours.

Therefore, the optimal assignment would be:

- Person 4 for Job 1 (16 hours)

- Person 2 for Job 2 (18 hours)

- Person 1 for Job 3 (25 hours)

- Person 4 for Job 4 (14 hours)

This assignment ensures that the minimum total time is required to perform the four jobs, resulting in a total time of 16 + 18 + 25 + 14 = 73 hours.

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false. The vertical axis is the y-axis, which is where x=0. In this equation, when x=0, we have: y=4(0)-5
y=-5

Therefore, the line produced by the equation Y=4X−5 crosses the vertical axis at y=-5, not y=5.

To further understand this concept, we can visualize the equation on a graph. When we plot the points (0,-5) and (1,-1) (which is found by substituting x=1 into the equation), we can draw a line that passes through both points. This line is the graph of the equation Y=4X−5. We can see that the line crosses the vertical axis (y-axis) at y=-5, which confirms that the answer is false.

In summary, the equation Y=4X−5 crosses the vertical axis (y-axis) at y=-5, not y=5.

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Answer:

Step-by-step explanation:

360 + 3*180 = -360 + 540 = 180

For four sides -360 + 180*4 = 360

n-2)*180

For a fifteen sided share the sum of angles = (15-2)*180 = 13*180

Answer:

180

Step-by-step explanation:

From the question, we can see that we have two box-and-whisker plots. One of them represents the test score for Jake and the other the test scores of Ryan.

In a box-and-whisker plot, we have the following information:

We can see the following information from Jake and Ryan as follows:

The interquartile range (IQR) is the difference between Q3 and Q1.

• Median = about 86

• First Quartile (Q1) = 80

• Third Quartile (Q3) = 90

• Interquartile range (IQR) = Q3 - Q1 = 90 - 80 = 10

• Median = 75

• First Quartile (Q1) = 70

• Third Quartile (Q3) = 85

• Interquartile range (IQR) = Q3 - Q1 = 85 - 70 = 15

Now, in summary, therefore, we can say that:

• Ryan's median test score (75) is ,less than, Jake's median test score (86).

• The interquartile range of Ryan's test score (15) is ,greater than, the interquartile range of Jake's test scores (10).

[Hence, we have to select less than in the first part of the question, and greater than in the second part of the question.]

An equation that mode the relationship between thee two variable is y=2x+3 .

Let x represent the number of 6-month period worked

Let y represent the total number of paid vacation day

According to the question,

When he started work, he was given three paid day of vacation. For each six-month period he pay at the job, his vacation is increased by two day.

Each year has 2 six-month periods. After 4.4 years Roberto will have worked 8.8 six-month periods. He will have been given vacation days for each of the 8 whole working periods he has completed. x=8 y=2*8+3 y=19

An equation that mode the relationship between thee two variable is y=2x+3 (Total vacation time equals 2 days times x plus the 3 days he was given at the start).

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Answer:

The narrator checks the old man at every night at midnight

Step-by-step explanation:

Answer: y = 2(x + 2)² - 5

Step-by-step explanation:

          We are going to use the completing the square method to transform this quadratic equation from standard form to vertex form.

Given:

     y = 2x² + 8x + 3

Factor the 2 out of the first two terms:

     y = 2(x² + 4x) + 3

Add and subtract \(\frac{b}{2} ^2\):

     y = 2(x² + 4x + 4 - 4) + 3

Distribute the 2 into -4 and combine with the 3:

     y = 2(x² + 4x + 4) - 5

Factor (x² + 4x + 4):

     y = 2(x + 2)² - 5

A random variable Y has a uniform distribution over the interval (θ1, θ2). The variance of Y is (θ2 - θ1)^2 / 12.

The variance of a uniform distribution is given by:

\(Var(Y) = (θ2 - θ1)^2 / 12\)

To derive this, we can use the standard formula for variance:

\(Var(Y) = E(Y^2) - [E(Y)]^2\)

where E(Y) is the expected value of Y.

Since Y is uniformly distributed over the interval (θ1, θ2), we have:

\(E(Y) = (θ1 + θ2) / 2\)

To compute E(Y^2), we have:

\(E(Y^2) = ∫θ1^θ2 y^2 f(y) dy\)

where f(y) is the probability density function of Y, which is constant over the interval (θ1, θ2) and zero elsewhere. Therefore:

\(E(Y^2) = ∫θ1^θ2 y^2 (1 / (θ2 - θ1)) dy\)

\(= [(y^3 / 3) * (1 / (θ2 - θ1))] from θ1 to θ2\)

\(= (θ2^3 - θ1^3) / (3 (θ2 - θ1))\)

Now, we can compute the variance:

\(Var(Y) = E(Y^2) - [E(Y)]^2\)

\(= (θ2^3 - θ1^3) / (3 (θ2 - θ1)) - [(θ1 + θ2) / 2]^2\)

\(= (θ2 - θ1)^2 / 12\)

Therefore, the variance of Y is (θ2 - θ1)^2 / 12.

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We can start by placing the center at (-5,1).

The radius of the circle will be the distance between the center and the point (-2,-3).

If we graph this two points, we can use an angle protractor to draw the circle passing through point P(-2,-3) and centered at (C(-5,1):

Answer:

Todos los lados de un cuadrado son iguales. Hay 4 lados en un cuadrado. Entonces, para encontrar un lado, debemos dividir el área por 4.

432/4 = 108, Un lado del cuadrado mide 108 metros.

Answer:

D

Step-by-step explanation:

1.5% of 55,000 is 825

add 825 to 500 it totals to 1325

The total amount of interest paid over the life of the loan is $1863.45.

The present value of the loan.

Since there are 12 months in a year, and the loan has n-years, there are 12n monthly payments.

Let's use the formula for the present value of an annuity due:

\(PV = PMT \times ((1 - (1 + r) ^(-n)) / r) \times (1 + r)\)

PV is the present value of the loan, PMT is the monthly payment, r is the monthly interest rate, and n is the number of months.

Substituting the given values, we get:

\(PV = \$800 \times ((1 - (1 + 0.12/12) ^(-12n)) / (0.12/12)) \times (1 + 0.12/12)\)

\(PV = \$800 \times ((1 - (1.01)^(-12n)) / 0.01) \times 1.01\)

\(PV = \$800 \times ((1 - 1.01^(-12n)) / 0.01) \times 1.01\)

\(PV = \$800 \times ((1 - 0.887^(-n)) / 0.01) \times 1.01\)

The formula for the interest paid in any given month of an annuity due:

\(I = PV \times r \times (1 + r) ^(m - 1)\)

I is the interest paid in the 45th month, PV is the present value of the loan, r is the monthly interest rate, and m is the month.

Substituting the given values for the 45th month, we get:

\(\$424.45 = PV \times 0.01 \times (1 + 0.01 )^(45 - 1)\)

\(\$424.45 = PV \times 0.01 \times (1.01)^4^4\)

\(PV = \$424.45 / (0.01 \times (1.01)^4^4)\)

PV =\(\$75799.45\)

Now that we know the present value of the loan, we can calculate the total amount of interest paid over the life of the loan.

Let's use the formula for the total interest paid in an annuity due:

\(Total interest = (PMT \times n \times (n + 1) / 2) - PV\)

Substituting the given values, we get:

Total interest = \((\$800 \times 12n \times (12n + 1) / 2) - \$75799.45\)

Total interest = \(\$9600n^2 + \$4800n - \$75799.45\)

We can solve for n by using the fact that the interest paid in the 45th month is $424.45:

\(\$424.45 = \$800 \times (n \times 12 - 44) \times 0.01 \times (1 + 0.01)^(45 - 1)\)

\(\$424.45 = \$800 \times (n \times 12 - 44) \times 0.01 \times (1.01)^4^4\)

n = 4.5

Substituting n = 4.5 into the formula for total interest, we get:

Total interest =\(\$9600 \times (4.5)^2 + \$4800 \times 4.5 - \$75799.45\)

Total interest = $1863.45

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Answer:

$10.80 and $43.20

Let A be a symmetric matrix that is invertible. This means that there exists a matrix B such that AB = BA = I, where I is the identity matrix. We want to show that B is also symmetric, that is, \(B = B^{T}\)

To prove this, we can use the definition of matrix inversion. We know that AB = I, so we can take the transpose of both sides:

\(AB^{T} = I^{T}\)

Using the transpose rules, we can rewrite this as:

\(B^{T} * A^{T}\) = I

Now, we can multiply both sides of this equation by A:

\(B^{T} * A^{T}\)* A = A

Since A is invertible, we can multiply both sides by A⁻¹ to get:

\(B^{T}\) = A⁻¹

Therefore, we have shown that the inverse of a symmetric matrix A, which we denote as A⁻¹, is also symmetric, since A⁻¹ = \(B^{T}\), which is the transpose of the matrix B.

Hence, we have proved that if a symmetric matrix is invertible, then its inverse is symmetric as well.

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Answer:

84

Step-by-step explanation:

Answer:

positive 84

Step-by-step explanation:

when you multiply a negative by a negative it becomes a positive

Answer:

The rule DO,0.25 (x, y) → (0.25x, 0.25y) is applied to the segment LM to make an image of segment L'M', not shown.

The coordinates of L' in the image are  

✔ (–1, 2)

.

The coordinates of M' in the image are  

✔ (1, 2)

.

The length, L'M', is  

✔ 2

.

The slope of the original segment and dilated segment are  

✔ both zero

.

Step-by-step explanation:

The question is incomplete. The complete question is:

On a coordinate plane, a line is drawn from point L to point M. Point L is at (negative 4, 8) and point M is at (4, 8). The rule DO,0.25 (x, y) → (0.25x, 0.25y) is applied to the segment LM to make an image of segment L'M', not shown. The coordinates of L' in the image are ??. The coordinates of M' in the image are ??. The length, L'M', is ??. The slope of the original segment and dilated segment are ??.

The coordinates of L' in the image are (-1, 2). The coordinates of M' in the image are (1, 2). The length, L'M', is 2. The slope of the original segment and dilated segment are both zero.

The dilation of a segment to its image is the following of a given rule for every point on the segment to create an image.

We are given a line segment LM, with coordinates of L being (-4, 8) and that of M being (4, 8).

We are given a rule  \(D_{O, 0.25} (x,y) \rightarrow (0.25x,0.25y)\) which implies that every point on the line segment LM (x, y) is dilated to the point on the image L'M' as (0.25x, 0.25y).

The coordinates of L' in the image = (0.25*(-4), 0.25*8) = (-1, 2).

The coordinates of M' in the image = (0.25*(4), 0.25*8) = (1, 2).

The length of L'M' can be calculated using the distance formula between the points L' and M'.

Length = √((2 - 2)² + (1 - (-1))²) = √(0² + 2²) = √4 =  2 units.

∴ The length of L'M' = 2 units.

The slope of both LM and L'M' is 0, as they both are parallel to the x-axis and don't intersect with it.

∴ The coordinates of L' in the image are (-1, 2). The coordinates of M' in the image are (1, 2). The length, L'M', is 2. The slope of the original segment and dilated segment are both zero.

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Answer:

principle amount=$4500

interest=8%

now

a) interest amount= 8/100*4500

\( \frac{8}{100} \times 4500 \\ = 360\)

hence interest amount is $360

b) total amount (with interest)=$4500+ interest =$4500 +$360=$4860

hence the bank pays $4860 in total

The probability of coin landing with heads is an independent event.

The probability of winning 1st and 2nd prize is a dependent event.

Independents events are events whose occurrence do not depend on each other. They are random events. The probability of a coin landing on heads is a random event.

Dependent events are events that are not random. The outcome of one event depends on the outcome of another event.

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This question is about the probability of an event.

Probability of an Event is the opportunitiy of possibility, theoretically means the comparison between the number of events with the number of all possibilities that occur. Generally, we can write the probability formula like this;

P(A) = n(A)/ n(S)

Note: P(A) is probability of an Event

n(A) is the number of favorable results.

n(S) is the total number of events in the sample area.

In this question, we have to find the chance that the number we drew from list A is larger than the number we drew from list B. bellow is the Steps:

First of all, we have to list each table of numbers:

A { 10, 20, 30} which means n(A) is 3

B {10, 20, 30, 40} which means n(b) is 4

For example :

A represents the number taken from the list A

B represent the number taken from the list B

The question: P(A>B)

The result:

A B

20 10

30 10,20

N(A>B) = 1 + 2

= 3 probability

n(S) = n(A) x n(B)

= 3 x 4

= 12

Therefore, P(A>B) = n (A>B)/ n(S)

= 3/12

= ¼ or 0.25 probability

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The coordinates of Point A are (2, -7). To find the coordinates of Point B, we need to reflect Point A across the y-axis.

When we reflect a point across the y-axis, the x-coordinate changes its sign while the y-coordinate remains the same. So, the x-coordinate of Point B will be the opposite of the x-coordinate of Point A, and the y-coordinate of Point B will be the same as the y-coordinate of Point A.

Therefore, the coordinates of Point B will be (-2, -7). Point B is located 2 units to the left of the y-axis, with the same y-coordinate as Point A.

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Answer:

the probability of drawing a green marble is 4/25 (16% or 0.16)

Step-by-step explanation:

Total: 16+8+9+12+5= 50

# of green marbles: 8

Event G, such that a green marble is drawn:

P(G)= 8/50

= 4/25 (16% or 0.16)

I think this is the answer but sorry if just 4 I answer

Step-by-step explanation:

8k - 12 = 3

8k = 3 +12

8k = 15

k = 15/8

k = 1.875

Answer:

8k-12=3

8k=3+12 [we equate the negative 12 from LHS and take it to RHS and its value becomes positive there fore 3 +12 is possible]

8k=15

k=15/8[algebraic rule of there is no sign between number and variable there is ment to be multiplication and when the multiply is taken to next sign it becomes division and becomes a denominator]

k=1.875