Solve the equation 3x+5y=4
for y

The answer to this item is 23/32.

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty.

Given that the events are not mutually exclusive the union of the probability of the events is calculated through the equation,

P(Q or R) = P(Q) + P(R) - P(Q and R)

Substituting the known values,

P(Q or R) = 3/5 + 1/3 - 1/5

Simplifying,

P(Q or R) = 11/15

Hence the answer to this item is 23/32.

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Final answer:

The total area to be painted is 512 square feet, calculated by summing up the areas of the two longer walls (288 sq ft) and the two shorter walls (224 sq ft). For time estimation, the linear equation would be t = 4 + (512/1000), resulting in approximately 4.51 hours of painting time.

Explanation:

To calculate the area of the four walls in a room for painting, you will be finding the surface area of the sides not including the floor or ceiling. First, you need to calculate the area of the two longer walls and the two shorter walls separately.

For the longer walls, the area for one wall is 18 ft (length) times 8 ft (height), which gives you 144 square feet for one long wall. There are two such walls, so multiply by 2, which equals 288 square feet for both long walls.

For the shorter walls, the calculation is similar. The area for one short wall is 14 ft (width) times 8 ft (height), which gives 112 square feet for one short wall. With two short walls, the total is 224 square feet.

Add the area of the long walls and the area of the short walls together to get the total painting area: 288 sq ft + 224 sq ft = 512 square feet.

To express this as part of a linear equation for time estimation given in the scenario, if it takes one hour per 1,000 square feet, we would use the equation t = 4 + (A/1000), where t is the total time in hours and A is the area in square feet. Since the painting area is 512 square feet, the painting time is t = 4 + (512/1000), giving 4.512 hours, which rounds up to approximately 4.51 hours.

the answer is 8 and 16

Options: A

Key: 1|5 means 15

Options: B

Key: 1|5 means 15

Options: C

Key: 1|5 means 15

Options: D

Key: 1|5 means 15

Answer:

Options: D

Key: 1|5 means 15

Step-by-step explanation:

Given: 15, 16, 15, 48, 48, 63, 15, 29, 16, 30, 48

To plot a stem and leaf plot, first rearrange the observations in ascending order: 15, 15, 15, 16, 16, 29, 30, 48, 48, 48 , 63

Next, is to get the range of values

Low: 15

High = 63

Next, is to identify the stems

Using the range of 15 to 63, we need stems of 1, 2, 3, 4, 5 and 6

In tabular form, the stems are:

Stems ||

1  ||

2  ||

3  ||

4  ||

5  ||

6 ||

Next, is to fill in the leafs

Stem || Leaf

1 || 5 5 5 6 6

2 || 9

3 || 0

4 || 8 8 8

5 ||

6 || 3

Lastly, we write out our observations

1. The stem Value 1 has leaf values 5,5,5,6,6

2. The stem Value 2 has a leaf value 9

3. The stem Value 3 has a leaf value 0

4. The stem Value 4 has leaf Values 8,8,8

5. The stem Value 5 has no leaf

6. The stem Value 6 has leaf value 3

Comparing the observation with the options, option D represents the stem-and-leaf plot representation of 15, 16, 15, 48, 48, 63, 15, 29, 16, 30, 48  

Answer:

$806

Step-by-step explanation:

The regular earning of a cashier = $10.20 per hour

over 35 hours per week he gets = $10.20 + $1.30 per hour

                                                      = $11.50 per hour

He worked 40 hours in first week and 38 hours the second week.

His earnings in first week  = (35 × 10.20) + (5 × 11.50)

                                           = $357 + $57.5

                                           = $414.50

His earnings in second week = (35 × 10.20) + (3 × 11.50)

                                                 = $357 + $34.50

                                                 = $391.50

His total earnings in this two weeks = $391.50 + $414.50

                                                            = $806

His total earning was $806.

ANSWER

Component form:

[tex]\binom{ - 16}{2} [/tex]

2. Magnitude

[tex]2\sqrt{65} [/tex]

EXPLANATION

Given that P = (-5, 5) and Q = (-13, 6),

Vector PQ

[tex] = \binom{ - 13}{6} - \binom{ - 5}{5} [/tex]

[tex] = \binom{ - 13 + 5}{6 - 5} [/tex]

[tex] = \binom{ - 8}{1} [/tex]

2 vector PQ

[tex] = 2 \binom{ - 8}{1} [/tex]

[tex] = \binom{ - 16}{2} [/tex]

This is the component form.

The magnitude is given by

[tex] = \sqrt{ {x}^{2} + {y}^{2} } [/tex]

[tex] = \sqrt{ {( - 16)}^{2} + {2}^{2} } [/tex]

[tex] = \sqrt{256 + 4} [/tex]

[tex] = \sqrt{260} [/tex]

[tex] = 2\sqrt{65} [/tex]

The quadratic function with vertex (0, 0) and passing through the point (-2, 2) is y = 0.5x^2. This is a transformation of the parent quadratic function y = x^2 with a vertical stretch by a factor of 0.5.

The quadratic function with the given vertex (0, 0) and going through the point (-2, 2) can be written in the form of the vertex form of a quadratic function i.e. y = a(x - h)² + k, where (h, k) is the vertex of the parabola. Since the vertex given is (0,0), the function becomes y = ax².

Now, to find the value of 'a', we can substitute the x and y coordinates of the given point (-2,2) into the equation. So, 2 = a(-2)², this simplifies to 2 = 4a. Solving for 'a', we get a = 0.5. So, the function is y = 0.5x².

This function is a transformation of the parent function y=x². The 0.5 in front of x² means that the graph of the function stretches vertically by a factor of 0.5. Thus, the parabola opens upwards and is narrower than the parent function.

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The student's question asked for finding the percentage increase in an item's price. This can be calculated by subtracting the initial price from the final price, dividing that difference by the initial price, and then multiplying the result by 100. In this case, the price of the item has increased by 140% from yesterday to today.

To find the percentage increase of the price of an item, we subtract the initial price from the final price, then divide that number by the initial price, finally multiply that result by 100 to obtain the percentage. In this case, the initial price of the item was $115, and the final price is $276.

Here's how the calculation works:

Therefore, the price of the item has increased by 140% from yesterday to today.

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This question is nasty. It sounds like you should be finding area of the figure you see. I'll do that first, although I don't think it's the right answer. (But it might be).

Area Trapezoid = (b1 + b2) * h / 2

b1 = 8

b2 = 12

h = 5

Area Trapezoid = (8 + 12 ) * 5 / 2

Area Trapezoid = 20 * 5/2

Area = 50 square feet.

The problem is that no lumber yard will cut that for you without charging you. The practical answer is 12 * 5  = 60 square feet is what you will have to buy. Then you cut out the triangles for yourself.

Final answer:

To maximize the profit from selling Boombotix speakers, the company should sell 0.75 thousand speakers, or 750 speakers, which is determined by finding the vertex of the profit function p(x) = 8 + 6x - 4x2.

Explanation:

The function p(x) = 8 + 6x - 4x^2 represents the profit from selling x thousand Boombotix speakers. To find the number of speakers that should be sold to maximize profit, we need to find the vertex of the parabola represented by this quadratic function, which is a downwards opening parabola because the coefficient of x^2 is negative (-4).

The vertex form of a quadratic function is p(x) = a(x-h)2 + k, where (h, k) is the vertex of the parabola. The x-coordinate of the vertex (h) can also be found using the formula h = -b/(2a) where a is the coefficient of x2 and b is the coefficient of x in the standard form of the quadratic function. In this case, a = -4 and b = 6. Applying the formula:

h = -b/(2a) = -6/(2 * -4) = -6 / -8 = 0.75

Hence, the company should sell 0.75 thousand speakers, or 750 speakers, to maximize profit.

The Greatest Common Divisor (GCD) of 100 and 254 can be found using Prime Factorization and the Euclidean Algorithm. Both methods produce a GCD of 2.

The student is asking for how to find the Greatest Common Divisor (GCD) of 100 and 254 using two different methods: Prime Factorization and the Euclidean Algorithm.

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Answer:

d

Step-by-step explanation: