Kim wants to buy art supplies that normally costs $50, but are on sale for 20% off. What is the sale price for the art supplies?​

Answer:

The answer is: K = 14.

Answer:

Answers and explanations below

Step-by-step explanation:

1. Not congruent (no justification needed)

2. FGH by SSS

3. VLM by SAS

4. Not sufficient information (not similar)

In a case whereby Adam traveled out of town for a regional basketball tournament. He drove at a steady speed of 72.4 miles per hour for 4.62 hours. The exact distance Adam traveled was miles Adam traveled a distance of about 335 miles.

The distance traveled in a unit of time is called speed. It refers to a thing's rate of movement. The scalar quantity known as speed is the velocity vector's magnitude. It has no clear direction.

Speed = Distance/ time

speed =72.4 miles

time=4.62 hours

Distance =speed * time

= 72.4 *4.62

Distance = 334.488 miles

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complete question;

Adam traveled out of town for a regional basketball tournament. He drove at a steady speed of 72.4 miles per hour for 4.62 hours. The exact distance Adam traveled was miles. Rounding decimals to the nearest whole number, Adam traveled a distance of about miles.

Answer:

x = 2/3

Step-by-step explanation:

The last two digit of postal code here is 12

We multiply this by x

so we have x * 12 = 12x

The number of family members is 6 ; and we are to equate it to my age which is 14

thus, we have the equation as;

12x + 6 = 14

12x = 14-6

12x = 8

x = 8/12

x = 2/3

Answer: 1

\((\frac{x^{a+b} }{x^{c} }) ^{a-b}.(\frac{x^{b+c} }{x^{a} }) ^{b-c} .(\frac{x^{c+a} }{x^{b} })^{c-a}\\\\= \frac{x^{(a+b)(a-b)} }{x^{c(a-b)} }.\frac{x^{(b+c)(b-c)} }{x^{a(b-c)} }.\frac{x^{(c+a)(c-a)} }{x^{b(c-a)} }\\\\=\frac{x^{a^{2}-b^{2} } }{x^{ac-bc} }.\frac{x^{b^{2}-c^{2} } }{x^{ab-ac} }.\frac{x^{c^{2}-a^{2} } }{x^{bc-ab} } \\\\=\frac{x^{a^{2}-b^{2}+b^{2}-c^{2}+c^{2}-a^{2} } }{x^{ac-bc+ab-ac+bc-ab} }\\\\=\frac{x^{0} }{x^{0} }=1\)

Step-by-step explanation:

The critical path is the path with the longest duration, which in this case is A -> B -> D -> E with a duration of 11 days.

To determine the critical path of the project, we need to find the longest path of activities that must be completed in order to finish the project on time. This is done by calculating the earliest start time (ES) and earliest finish time (EF) for each activity.

Starting with activity A, ES = 0 and EF = 4. Activity B can start immediately after A is complete, so ES = 4 and EF = 7. Activity C can start after A is complete, so ES = 4 and EF = 6. Activity D can start after B is complete, so ES = 7 and EF = 9. Finally, activity E can start after C and D are complete, so ES = 9 and EF = 11.

The variance for each activity is also given, which allows us to calculate the standard deviation and determine the probability of completing the project on time. The critical path is the path with the longest duration, which in this case is A -> B -> D -> E with a duration of 11 days.

Using the expected durations and variances, we can calculate the standard deviation of the critical path. This information can be used to determine the probability of completing the project on time.

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1) To find the optimum quantities of X and Y that the consumer will purchase, we need to consider two conditions: the budget constraint and the utility maximization. The budget constraint can be expressed as Px*X + Py*Y = Income. Given that Px = 1, Py = 2, and Income = 300, the budget constraint becomes X + 2Y = 300. To maximize utility, we need to find the combination of X and Y that maximizes the utility function U = X*Y^2  Taking the derivative of U with respect to X and Y, we get dU/dX = Y^2 and dU/dY = 2XY. Setting dU/dX equal to the marginal rate of substitution (MRS), which is the ratio of prices (MRS = Px/Py), we have Y^2 = 1/2. Rearranging, we get Y = 1/sqrt(2). Setting dU/dY equal to the MRS, we have 2XY = 1/2. Substituting Y = 1/sqrt(2), we get X*(1/sqrt(2)) = 1/2. Solving for X, we find X = sqrt(2)/2. Therefore, the optimum quantities of X and Y that the consumer will purchase are X = sqrt(2)/2 and Y = 1/sqrt(2). 2) This combination of X and Y is an equilibrium in the sense that it maximizes the consumer's utility given the budget constraint and the prices of the goods. It represents the point where the consumer allocates their income between X and Y in a way that maximizes their overall satisfaction, taking into account the relative prices of the goods.

3) To find the maximum satisfaction, we substitute the optimum quantities of X and Y into the utility function. The maximum satisfaction is given by U = X*Y^2 = (sqrt(2)/2) * (1/sqrt(2))^2 = 1/2. Therefore, the maximum satisfaction that this utility-maximizing consumer can achieve is 1/2. 4) On the diagram, we can plot X on the x-axis and Y on the y-axis. The budget constraint can be represented by the line X + 2Y = 300. The optimum combination of X and Y, given by X = sqrt(2)/2 and Y = 1/sqrt(2), can be shown as a point on the diagram. Note: Unfortunately, as a text-based AI, I am unable to provide a visual diagram.

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Answer:

105 = a

Step-by-step explanation:

L = a + (n-1)*d

n = 65

d = -2

L = u21 = 65

65 = a + (21 - 1)*(-2)        Divide by - 2

65 = a + 20*-2               Multiply 20 times - 2

65 = a  - 40                    Add 40 to both sides

65+40 = a                      Combine

105 = a

The value of the first term is 105

The nth term of an arithmetic sequence is gotten by using the formula:

= a + (n - 1)d

The value of the 21st term which has been given in the question is 65 and the common difference is -2. This will be:

a + (n - 1)d = 65

a + (21 - 1)d = 65

a + 20d = 65

Since d, common difference = -2

a + 20d = 65

a + 20(-2) = 65

a - 40 = 65

a = 60 + 45

a = 105

In conclusion, the value of the first term is 105

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The rank of matrix A can be determined based on the given information in the question is as follows.

The rank of a matrix refers to the maximum number of linearly independent columns (or rows) in the matrix. From the given information:

a. Since A has linearly independent columns, the rank is equal to n, where n is the number of columns.

b. If Null(A)={0}, it means that the only solution to the homogeneous equation Ax=0 is the trivial solution (where x=0). This implies that the columns of A are linearly independent. Since A is a 6-by-4 matrix, the rank is equal to the number of columns, which is 4.

c. The dimension of the null space (denoted as dim(Null(A))) is equal to the number of linearly independent solutions to the homogeneous equation Ax=0. In this case, dim(Null(A))=3, which means that there are 3 linearly independent solutions. Since A is a 5-by-6 matrix, the rank can be found by subtracting the dimension of the null space from the number of columns: rank(A) = 6 - dim(Null(A)) = 6 - 3 = 3.

d. The determinant of a square matrix measures its invertibility. If det(A) is non-zero, it means that A is invertible, and an invertible matrix has full rank. Therefore, the rank of A is equal to the number of columns, which is 3.

e. The dimension of the row space (denoted as dim(Row(A))) represents the number of linearly independent rows in A. Since dim(Row(A))=3, it means that there are 3 linearly independent rows. Thus, the rank of A is 3.

f. An invertible matrix is non-singular and has full rank. Therefore, if A is a 4-by-4 invertible matrix, its rank is equal to the number of columns, which is 4.

g. If the system Ax=b has either a unique solution or no solution, it means that the column space of A has dimension 3. Hence, the rank of A is 3.

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Time taken by Miguel car to drive is, 1.6 hour.

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

We have to given that;

Miguel went for a drive in his new car. He drove at a speed of 53 miles per hour for 84.8 miles.

We know that;

⇒ Speed = Distance / Time

⇒ Time = Distance / Speed

Here, Speed = 53 miles per hour

Distance = 84.8 miles

Hence, We get;

⇒ Time = 84.8 / 53

⇒ Time = 1.6 hour

Thus, Time taken by Miguel car to drive is, 1.6 hour.

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Answer:A and b

Step-by-step explanation:

The dimensions of cylinders that have a volume under 220 cubic inches per serving are:

3-inch radius and 4-inch height
4-inch diameter and 4-inch height
4-inch diameter and 9-inch height

Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.

Here,
We can use the formula V = πr²h to find the volume of each cylinder.

For a cylinder with a 3-inch radius and 4-inch height:

V = π(3)²(4) ≈ 113.1 cubic inches

For a cylinder with a 4-inch radius and 4-inch height:

V = π(4)²(4) ≈ 200.96 cubic inches

For a cylinder with a 9-inch radius and 9-inch height:

V = π(9)²(9) ≈ 2289.0 cubic inches

For a cylinder with a 4-inch diameter and 9-inch height (radius is 2 inches):

V = π(2)²(9) ≈ 113.04 cubic inches

For a cylinder with a 6-inch diameter and 9-inch height (radius is 3 inches):

V = π(3)²(9) ≈ 254.5 cubic inches

For a cylinder with a 9-inch diameter and 4-inch height (radius is 4.5 inches):

V = π(4.5)²(4) ≈ 254.5 cubic inches

Therefore, the dimensions of cylinders that have a volume under 220 cubic inches per serving are:

3-inch radius and 4-inch height
4-inch diameter and 4-inch height
4-inch diameter and 9-inch height

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Answer:

4.46 m^2

Step-by-step explanation:

Sabemos que para un círculo de radio R, el área es:

A = pi*R^2

mientras que para un cuadrado de lado L, el área es:

A = L^2

Ahora queremos calcular los metros cuadrados de área que tiene que sacar el carpintero, esto será simplemente igual a la diferencia entre el área original de la mesa (cuando es circular) y el área final de la mesa (cuando es cuadrada).

Originalmente, la mesa es circular y tiene un radio de 2m.

Entonces el área original es:

A = 3.14*(2m)^2 = 12.56 m^2

Al final, la mesa será un cuadrado de tal forma que sus lados deben medir 2.83m, entonces el área final de la mesa será:

A' = (2.83m)^2 = 8.01m^2

La diferencia nos da:

A - A' = 12.56 m^2 - 8.01m^2 = 4.46m^2

Esto nos dice que se deben eliminar 4.46 m^2 para que la mesa quede cuadrada.

Yes, the given function y = g(x) in the attached graph is invertible as each input value of x has unique output y.

As given in the question,

Graph of the function y = g(x) is attached.

Invertible function are defined as when each input value of the function has unique output or for each input there is only one and only one output.

In the given graph of the function y = g(x)

Each input value of x there is only one and only one output.

Given graph y = g(x) is representing the straight line.

Therefore, the given graph of the function y = g(x) represent it is an invertible function as each input as one and only one output.

The above question is incomplete, the complete question is :

Does function g appear to be invertible? Use complete sentence to explain you reasoning?

Graph of the function g(x) is attached.

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Answer:

80 degrees

Step-by-step explanation:

a line is always 180 degrees

one side of that line is 100

so, just subtract 100 from 180

you get 80

180 - 100 = 80

Answer: x is greater than or equal to 18

Step-by-step explanation:

Answer:

x ≤ - 2

Step-by-step explanation:

- x/6 ≤ 3

- x/2 ≤ 1

- x ≤ 2

x ≤ - 2

Based on the sample data and the hypothesis test, there is sufficient evidence to support the claim that the population mean μ is greater than 29 at the significance level of 0.05.

What is the mean and standard deviation?

The standard deviation is a summary measure of the differences of each observation from the mean. If the differences themselves were added up, the positive would exactly balance the negative and so their sum would be zero. Consequently, the squares of the differences are added.

To test the claim about the population mean μ at the level of significance α, we can perform a one-sample t-test.

Given:

Claim: μ > 29 (right-tailed test)

α = 0.05

σ = 1.2 (population standard deviation)

Sample statistics: x = 29.3 (sample mean), n = 50 (sample size)

We can follow these steps to conduct the hypothesis test:

Step 1: Formulate the null and alternative hypotheses.

The null hypothesis (H₀): μ ≤ 29

The alternative hypothesis (Hₐ): μ > 29

Step 2: Determine the significance level.

The significance level α is given as 0.05. This represents the maximum probability of rejecting the null hypothesis when it is actually true.

Step 3: Calculate the test statistic.

For a one-sample t-test, the test statistic is given by:

t = (x - μ) / (σ / √(n))

In this case, x = 29.3, μ = 29, σ = 1.2, and n = 50. Plugging in the values, we get:

t = (29.3 - 29) / (1.2 / √(50))

= 0.3 / (1.2 / 7.07)

= 0.3 / 0.17

≈ 1.76

Step 4: Determine the critical value.

Since it is a right-tailed test, we need to find the critical value that corresponds to the given significance level α and the degrees of freedom (df = n - 1).

Looking up the critical value in a t-table with df = 49 and α = 0.05, we find the critical value to be approximately 1.684.

Step 5: Make a decision and interpret the results.

If the test statistic (t-value) is greater than the critical value, we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.

In this case, the calculated t-value is approximately 1.76, which is greater than the critical value of 1.684. Therefore, we reject the null hypothesis.

hence, Based on the sample data and the hypothesis test, there is sufficient evidence to support the claim that the population mean μ is greater than 29 at the significance level of 0.05.

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Answer: 7= D, 26 units

Step-by-step explanation:

Take the length. 0,0 to 0,9  the length is 9  Next take the width 0,9 to 4,9 the width is 4  L+Wx2 13x2=26

Answer:

Reflection. Hope this helps you :)

Step-by-step explanation:

Weakly decreasing sequences that are between p and q are in bijection with sequences of 0's and 1's of length q-p+N, where the sequences have exactly N ones. It's obvious that the number of such sequences is choose(q-p+N, N) because that's the number of ways of choosing N things from q-p+N things.

A sequence or function is weakly decreasing if the value of each term or point is less than or equal to the previous term or point.

In other words, a weakly decreasing sequence or function does not increase. It can stay the same or decrease, but it cannot go up. For example, the sequence 5, 4, 4, 3, 2, 2, 1 is weakly decreasing because each term is either less than or equal to the previous term. is weakly decreasing because each term in the sequence is either equal to or less than the previous term. However, the sequence {5, 3, 6, 1, 2} is not weakly decreasing because the third term (6) is greater than the second term (3).

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To calculate the hip length of a roof, measure the length of the hip rafter, calculate the run and rise of the hip rafter, and add them together.

Calculating the hip length of a roof requires some measurements of the roof's dimensions. The hip length is the distance from the outside corner of the building to the center of the roof ridge along the outside edge of the hip rafter.

To calculate the hip length, you'll need to know the pitch of the roof and the run and rise of the hip rafter. The run is the horizontal distance from the outside corner of the building to the center of the ridge, and the rise is the vertical distance from the outside corner to the top of the ridge.

It's important to note that the pitch of the roof and the dimensions of the hip rafter may vary depending on the design of the roof. Additionally, the hip length is just one measurement used to calculate the overall size and dimensions of a roof.

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29$ 16% of 25 is 4, so add it, and theres the answer

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Answer:

2/5

Step-by-step explanation:

Answer:

1/6

Step-by-step explanation:

Out of these four card choices, for the first pick there are two even cards and four cards in total. This means that on the first pick there is a 2/4=1/2 chance that you pick an even card. On the second pick, if you do not replace the card, then there is 1 even card remaining, and 3 cards in total, leaving a probability of 1/3. Multiplying these two probabilities together, you get an overall chance of 1/6. Hope this helps!

Answer:

Yes

Step-by-step explanation:

Answer:

yup its correct

Step-by-step explanation:

The length of the entire tunnel is 127.88 meters by using cosine law or formulae.

Here we can use the formulae of cosine when two sides a and b and angle between then is given we can apply it.

\(c^{2} =a^{2} +b^{2} -2ab cos (\alpha )\)

Let us take surveyor as point A

one end of the tunnel denoted by point B

other end of the tunnel denoted by point C.

The length of AB is 101 meters

length of AC is 120 meters.

Measure of angle at point A = 42° + 28° =70°

Now lets find the length of tunnel

=\(\sqrt{(120^{2})+(101^{2})-2.(120)(101) cos (70) }\)

=\(\sqrt{14400+10201-24240(0.34)}\)

=\(\sqrt{24601-8246}\)

\(\sqrt{16355}\)

=127.88 meters.

Hence the length of the entire tunnel is 127.88 meters.

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Answer:

p = 1/8

Step-by-step explanation:

Step 1: Write out equation

-3p + 1/8 = -1/4

Step 2: Subtract 1/8 on both sides

-3p = -3/8

Step 3: Divide both sides by -3

p = 1/8

By using unitary method, we found that the cost of 5m cloth is Rs. 1050.

According to the unitary method, the cost of 1 meter of cloth is equal to the total cost of 7 meters of cloth divided by 7. That is,

Cost of 1m cloth = Total cost of 7m cloth/7

We know that the total cost of 7m cloth is Rs. 1470. Therefore,

Cost of 1m cloth = 1470/7

Cost of 1m cloth = Rs. 210

This means that the cost of 1 meter of cloth is Rs. 210. Now, we need to find the cost of 5m cloth. To do that, we can use the unitary method again.

Cost of 5m cloth = Cost of 1m cloth x 5

Cost of 5m cloth = Rs. 210 x 5

Cost of 5m cloth = Rs. 1050

Therefore, the cost of 5m cloth is Rs. 1050.

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The solution of the given problem of equation comes out to be the quadratic function's expression is  \(y = -2x² + 8x + 3\)

Variable words are commonly used in complex algorithms to show uniformity between two incompatible claims.

Academic expressions called equations are used to show the equality of various academic numbers. Instead of a unique formula that splits 12 into two parts and can be used to analyse data received from \(y + 7\)  , normalization in this case yields b + 7.

Here,

A quadratic function's curve is shown in the provided illustration. The quadratic function's expression is

=> \(y = -2x² + 8x + 3\)

We can use the knowledge that a quadratic function's standard form is

=>  \(y = ax² + bx + c\)  , where a, b, and c are constants, to see this.

When y =  \(-2x² + 8x + 3\) is provided,

we can see that a = -2, b = 8, and c = 3 by comparing it to the standard form.

Therefore, the quadratic function's expression is \(y = -2x² + 8x + 3\)

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Answer:

$97.2

Step-by-step explanation:

The expression p + 0.08p

y=p + 0.08p

for p=$90

y=90+0.08*90

y=90+7.2

y=$97.2

Answer:

Step-by-step explanation:

f(x) = 5x + 1

Given these two points on the graph of g(x), we must determine the slope, m, of the line.  Going from (-4, 2) to (2, 14), x (the run) increases by 6 and y (the rise) increases by 12, so the slope is m = rise/run = 12/6, or m = 2.  Adapting the slope-intercept form y = mx + b, we find b as follows:

14 = 2(2) + b, or 14 = 4 + b, or b = 10.  Then g(x) is 2x + 10.

Comparing f(x) = 5x + 1, we determine whether each of the four statements is true or false:

A is false; the respective y-intercepts of f and g are 1 and 10.

B is true:  the respective y-intercepts of g and f are 10 and 1.

C is false; neither y-intercept is 7.

D is false.  1