Use the information below to find EF such that triangle ABC is congruent to triangle DEF

AB=36 BC=24 DE=48 m<B=110 m<E=110 EF=?

Jason needs 4L of blue paint to paint a bedroom. At 500mL per tin costing $11.50 each, he will need 8 tins, totaling $92.00 for the paint.

The question asks to calculate the total cost of blue paint Jason needs to paint a bedroom. Jason requires 4L (4000mL) of paint and one 500mL tin costs $11.50. Since 4000mL is eight times 500mL, we will need eight tins of paint. To find the total cost, we multiply the cost of one tin by the number of tins needed:

Cost of one tin of paint = $11.50
Number of tins needed = Total volume required / Volume of one tin = 8

Total cost = Cost of one tin  times Number of tins = $11.50  times 8 = $92.00.

Therefore, it will cost Jason $92.00 to buy the blue paint needed to paint the bedroom.

part 1 of the book took 19 days

The World Lottery's grand prize is approximately 209,701 times larger than Charlotte's annual salary when dividing the grand prize amount by her annual salary.

To determine approximately how many times larger the World Lottery's grand prize is compared to Charlotte's annual salary, we perform a division of the two amounts. Charlotte's annual salary is $29,354, and the World Lottery grand prize is $6,156,782,221.

To find out how many times larger the lottery prize is than Charlotte's salary, we use the following calculation:

Lottery Prize to Salary Ratio = World Lottery Grand Prize / Charlotte's Annual Salary

Lottery Prize to Salary Ratio = $6,156,782,221 / $29,354 ≈ 209,701

This means that the World Lottery's grand prize is approximately 209,701 times larger than Charlotte's annual salary.

Note: This is a simplified approximation and does not take into account any deductions or taxes that would be applied to either the grand prize or the salary.

Answer:

[tex]34z+6=34(z+\frac{3}{17})[/tex]

Step-by-step explanation:

To find : Factor 34 out of [tex]34z+6[/tex] ?

Solution :

Factor out means taking common term from the given expression.

Expression is given as [tex]34z+6[/tex]

Taking 34 common from 34z is left with z.

Taking 34 common from 6 is left with [tex]\frac{6}{34}[/tex].

So, [tex]34z+6=34(z+\frac{6}{34})[/tex]

[tex]34z+6=34(z+\frac{3}{17})[/tex]

Therefore, The required expression is [tex]34z+6=34(z+\frac{3}{17})[/tex]

For the function f(x, y) = 9 + xy - x - 2y in the triangular region, the maximum value is 9 at point (1,0), and the minimum value is 1 at point (1,4). The critical point does not lie within the triangle region.

To find the absolute maximum and minimum values of the multivariate function f(x, y) = 9 + xy − x − 2y on the triangular region with vertices (1, 0), (5, 0), and (1, 4), we first locate the critical points within the region by solving the system of first order partial derivative equations.

Notice that (2,1) is not in the triangle region, so there's no critical point in the interior of the triangle. The maximum and minimum must occur somewhere on the boundary, i.e., the lines connecting (1, 0), (5, 0), and (1, 4).

After using these points in the function, we get the following:

The maximum value is 9 when (x,y) are (1,0) and the minimum value is 1 when (x,y) are (1,4).

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The probability that the marble is blue on the second draw, given that the first marble was replaced and had the number 6 on it, is 4 out of 7.

The probability that the marble is blue on the second draw, given that the first marble was replaced and had the number 6 on it, can be found using conditional probability.

The probability of drawing a blue marble on the first draw is 4 out of 7 (4 blue marbles out of a total of 7 marbles). Since the first marble was replaced, the probability of drawing a blue marble on the second draw is still 4 out of 7. Therefore, the probability that the marble is blue on the second draw, given that the first marble had the number 6 on it, is also 4 out of 7.

Solution:

Given that, Milton got a paperweight like the one shown in the figure.

The Paper Weight is in the shape of a cuboid and a cube.

Length and breadth of cuboid is a and height of the cuboid is 2a, whereas side of cube is a.

The volume of sand required to fill in the Paper Weight , is equal to the volume of the Paper weight,

Volume of Paper Weight = Volume of cube + Volume of cuboid

We know that, Volume of cube =[tex] (side)^{3} [/tex]

and , Volume of Cuboid = [tex] length \times breadth \times height [/tex]

Volume of Paper Weight = [tex] a^{3}+ (a\times a \times2a)= a^{3} +2a^{3} = 3a^{3} [/tex]

Given that , a = 2 inches , then Volume of Paper Weight = [tex] 3 \times (2)^{3}= 3\times 8 = 24 [/tex]

[tex] 24 \: in^{3} [/tex] is the volume of the paperweight.

Option A is the correct solution.

Answer:

[tex]\frac{2}{3}[/tex]

Step-by-step explanation:

We have that:

Lynne owns 12 games.

Of those

5 are sports games

3 are educational

What fraction of the games are either sport games or educational games?

[tex]f = \frac{5}{12} + \frac{3}{12} = \frac{8}{12} = \frac{2}{3}[/tex]

Introducing vehicles costing less than $5,000 will alter the supply curve by adding a new segment for lower-priced cars, likely leading to an increase in the quantity supplied for this market segment. This reflects market segmentation and aligns with the demand for cheaper vehicles.

The introduction of cars less than $5,000 into the salesman's inventory may affect the distribution of car sales. When discussing economic models, a supply curve (such as curve So) indicates the quantity of goods that sellers are willing to supply at various prices. According to the scenario provided, Point J on the supply curve So shows that if the price is $20,000, the quantity supplied will be 18 million cars. However, if the price drops to below $5,000, this will most likely introduce a new segment on the supply curve, as the current supply data relates to higher-priced vehicles.

Introducing lower-cost cars will attract a different consumer base, often overlooked in premium markets. This could lead to an increase in the quantity supplied of cheaper cars, as the demand for this segment is likely to be different from premium cars. If the projection of selling 200 cars in 10 years holds true, it will introduce a new point on the supply curve, which will represent cars at a lower price point and possibly a higher quantity compared to the original supply curve for higher-priced cars.

It cannot be determined from the given information whether the overall effect will pull market equilibrium towards the lower end, but it introduces the concept of market segmentation where different products and prices can co-exist, catering to different consumer needs and preferences.

Answer:

2,3,5,8

Step-by-step explanation:

edge 22

The cost of the cell phone plan over x months is represented by the equation y = 35x + 43.85. For 9 months, the total cost is $359.85, and for a 1-year contract, the total annual cost is $463.85.

The total monthly cost of the cell phone plan for x months of service can be represented by the linear equation y = 35x + 18.85 + 25. Here, y represents the total cost, x represents the number of months, 35 is the cost per month, 18.85 is the cost of the cell phone, and 25 is the one-time activation fee. The equation simplifies to y = 35x + 43.85, since the cost of the phone and the activation fee is a one-time charge, independent of the number of months.

For x = 9 months of service, the ordered pair is (9, y), where y = 35(9) + 43.85. Therefore, the ordered pair associated with x = 9 is (9, 359.85).

If you sign a 1-year contract, which is 12 months, you will pay y = 35(12) + 43.85, which results in a total cost of $463.85 for the year.

Answer:

Vertex form:

[tex]f(x)=8(x+\frac{1}{4})^2-\frac{1}{2}[/tex]  

Step-by-step explanation:

Given: [tex]f(x)=8x^2+4x[/tex]

We need to write in vertex form.

Vertex form:

[tex]y=a(x-h)^2+k[/tex]

vertex: (h,k)

[tex]f(x)=8x^2+4x[/tex]

Step 1: Take out 8 common from each term

[tex]f(x)=8(x^2+\frac{1}{2}x)[/tex]

Step 2:  Add and subtract square of half of coefficient of x

[tex]f(x)=8(x^2+\frac{1}{2}x+\frac{1}{16}-\frac{1}{16})[/tex]

Step 3: Factor the term inside parentheses

[tex]f(x)=8(x^2+2\cdot \frac{1}{4}\cdot x+(\frac{1}{4})^2)-8\cdot \frac{1}{16})[/tex]

[tex]f(x)=8(x+\frac{1}{4})^2-\frac{1}{2}[/tex]                   [tex]\because (a^2+2ab+b^2)=(a+b)^2[/tex]

Hence, The vertex form of f(x)

[tex]f(x)=8(x+\frac{1}{4})^2-\frac{1}{2}[/tex]