Name all numbers between 67 and 113 that are a multiple of 4, 9 and 12.

A standard form equation representing the weightlifting situation is 45x + 10y = 260. If eight 10-pound plates are used, the number of 45-pound plates used is 4.

The situation given can be translated mathematically to an equation in standard form as follows: 45x + 10y = 260. This equation signifies that the total weight lifted (260 pounds) is equal to the sum of the weight of the 45

pound plates

(which each weighs 45 pounds multiplied by the number of plates, represented by x) and the 10 pound plates (which each weighs 10 pounds multiplied by the number of plates, represented by y). In the second part of the question, we're told that the weightlifter uses eight 10-pound weights, so y=8. Substituting y=8 into the equation from above, it simplifies to 45x + 80 = 260, which solves to x = 4. So, if the weightlifter uses eight 10 pound plates, then he uses four 45 pound plates.

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Nan and Soto used a total of 45 tiles. However, to cover a coffee table that has an area of 36 inches by 24 inches, they need 54 tiles, so they will need to acquire 9 more tiles.

1A. Nan uses 30 tiles and Soto uses half as many, which means Soto uses 15 tiles. So, they used a total of 45 tiles (30 + 15).1B. The area of the coffee table is 36 inches by 24 inches, which equals 864 square inches (36 x 24). Each tile is a four-inch square, so it covers an area of 16 square inches (4 x 4).

To find out how many tiles are needed, we divide the total area of the table by the area of one tile: 864/16 = 54 tiles. Since Nan and Soto have only 45 tiles, they need an additional 54 - 45 = 9 more tiles to cover the table.

Answer:

the third one its 100% verified

Step-by-step explanation:

Answer:

4.063 x 10*4

Step-by-step explanation:

take the big number and move it from the exponent then bwa

The question requires solving a system of linear equations which results from given conditions on three unknown numbers. The unknowns can be represented by the letters x, y, and z which need to be solved for by leveraging the knowledge of algebra.

The question given is a classic example of a system of linear equations. Let's represent the first number as x, the second number as y, and the third number as z. From the question, we have the following equations:

[tex]x + y + z = 12 \\2x + 5y + 6z = 59 \\8x - y = 23[/tex]

Solving this system, we can find the values for x, y, and z which represent the three numbers. One of the methods for solving such a system is substitution or elimination method. Nevertheless, the solving such system requires a strong understanding of basic algebra including addition, subtraction, multiplication, and division of numbers and algebraic expressions.

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Final answer:

The visible portion of the longitude line under the plane from an altitude of 5 miles is approximately 320.38 kilometers, using the formula D = 112.88 km √h where h is the altitude in kilometers.

Explanation:

The question asks how much of the longitude line directly under the plane is visible from an altitude of 5 miles high. To find this distance, we can use the formula given for horizon distance: D = 112.88 km √h, where h is the altitude in kilometers. Since 5 miles is approximately 8.05 kilometers, we can calculate the distance to the horizon by taking the square root of the altitude and multiplying by 112.88 kilometers.

First, calculate the square root of the altitude:
√8.05 ≈ 2.838.

Then, we multiply by the constant:
D ≈ 112.88 km × 2.838 ≈ 320.38 km.

Therefore, from an altitude of 5 miles, the visible portion of the longitude line directly under the plane is approximately 320.38 kilometers long.

We have been given that prices increase at a monthly rate of 0.5%.

Number of months in a year = 12

Let us suppose the item cost $1, then the percentage is given by

[tex]P=P_0(1+r)^n\\ \\ P=1(1+0.005)^{12}\\ \\ P=1.062[/tex]\\

Therefore, increase in a year is

[tex]1.062-1\\ =0.062[/tex]

Therefore, the required percentage in a year is 6.2%

Answer:

The slope of the line is [tex]-\frac{1}{2}[/tex]

Step-by-step explanation:

To know the slope of a line we can have the equation or to know points of the line. In this case from the graph we can get to points (-4,-1) and (0,-3). Having this and using the equation to calculate the slope, we have:

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

Defining:

[tex](x1=-4,y1=-1)[/tex] and [tex](x2=0,y2=-3)[/tex]

Replacing this values in the initial equation, this is:

[tex]m=\frac{-3-(-1)}{0-(-4)}[/tex]

[tex]m=\frac{-2}{4} =-\frac{1}{2}[/tex]

The slope of the line is [tex]-\frac{1}{2}[/tex]

We need to find the future value of annuity due with the following given values :-

Payment, Pm = 295 dollars.

N=4 (for quarterly)

Rate at 10%, r = 0.10/4 = .025

Time for 6 years, T = 6x4 = 24.

Future Value formula is :-

[tex]FV_{ad}=P_m*(1+r)*[\frac{(1+r)^T-1}{r} ] \\\\ FV_{ad}=295*(1+0.025)*[\frac{(1+0.025)^{24}-1}{0.025} ] \\\\ FV_{ad}=295*(1.025)*[\frac{(1.025)^{24}-1}{0.025} ] \\\\ FV_{ad}=295*(1.025)*[\frac{(1.80872595)-1}{0.025} ] \\\\ FV_{ad}=295*(1.025)*[\frac{0.80872595}{0.025} ] \\\\ FV_{ad}=295*(1.025)*(32.34903798) \\\\ FV_{ad}=9,781.54 \;dollars[/tex]

Hence, the final answer is 9,781.54 dollars.

Answer:

Option D [tex]\frac{b}{15}[/tex]

Step-by-step explanation:

Let

b-----> the number of bagels

we know that

To find the algebraic expression of "the bagels were divided equally into fifteen bags" , divided the number of bagels by fifteen

so

[tex]\frac{b}{15}[/tex]