painter was hired to design and draw a mural for a new restaurant. before he can design the mural, he needs to know the are of the wall. the restaurant manager informs the painter that the mural wall is 6-√2 feet tall by 12-√2 feet wide. what is the total area of the mural wall? (recall that the area of a rectangle is the width multiplied by the length)

a. 70-18√2 square feet
b. 74-18√2 square feet
c. 74-6√2 square feet
d. 74+18√2 square feet ...?

Answer:

7 7/8 pounds

Step-by-step explanation:

Given that a bag of oranges weighs 5 1/4 pounds and you want to know how much do 1 1/2 bags weigh, the next proportion must be satisfied:

(5 1/4 pounds)/(1 bag of oranges) = (x pounds)/(1 1/2 bag of oranges)

Isolating x:

x = (5 1/4)*(1 1/2)/1

x = 7 7/8 pounds

To calculate 75% of 90, convert the percentage to a decimal (0.75) and multiply it with 90, resulting in 67.5.

To find 75% of 90, we can use the concept that 'percent' means 'per hundred'. The calculation involves turning the percentage into a decimal by dividing by 100 and then multiplying by the number in question. Thus, 75% can be written as 0.75 (since 75 divided by 100 equals 0.75).

Therefore, to find 75% of 90, we multiply 90 by 0.75:

0.75 × 90 = 67.5

The correct answer is 67.5, not 6750, 675, or 6.75.

9 decimals with two decimal places that when rounded to the nearest tenth round to 8.7 are 8.65, 8.66, 8.67, 8.68, 8.69, 8.70, 8.71, 8.72 and 8.73.

Rounding a number means the process of making a number simpler such that its value remains close to what it was. The result obtained after rounding off a number is less accurate, but easier to use. While rounding a number, we consider the place value of digits in a number.

We need to write 9 decimals with two decimal places that when rounded to the nearest tenth round to 8.7

8.65, 8.66, 8.67, 8.68, 8.69, 8.70, 8.71, 8.72 and 8.73.

Therefore, 9 decimals with two decimal places that when rounded to the nearest tenth round to 8.7 are 8.65, 8.66, 8.67, 8.68, 8.69, 8.70, 8.71, 8.72 and 8.73.

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Answer: [tex]327[/tex] [tex]\text{ounce}[/tex]

Step-by-step explanation:

Given: On the way home from school, ross wears his [tex]20[/tex] pound backpack and carries his [tex]7[/tex] ounce lunchbox.

To Find: how many ounces does he carry in total.

Solution:

Weight of Ross's backpack [tex]=20[/tex] [tex]\text{pound}[/tex]

Weight of Ross's lunchbox [tex]=7[/tex] [tex]\text{ounce}[/tex]

Now,

As unit of weight of backpack and lunchbox is different, we need to convert it.

[tex]1[/tex] [tex]\text{pound}[/tex] [tex]=16[/tex] [tex]\text{ounce}[/tex]

Now weight of backpack is[tex]=\text{weight in pound}\times16[/tex]

                                 [tex]20\times16[/tex]

                                 [tex]320[/tex] [tex]\text{ounce}[/tex]

Total ounces carried by Ross [tex]=\text{weight of backpack}+\text{weight of lunchbox}[/tex]

                                                 [tex]320+7[/tex] [tex]\text{ounce}[/tex]

Hence Total ounce carried by Ross is [tex]320+7[/tex] [tex]\text{ounce}[/tex]

You need to use the midpoint formula of (x1+x2)/2,(y1+y2)/2

put in the actual points will look like this. (3x+5+x-1)/2,(3y-y)/2

now solve to get (4x+4)/2,(2y)/2

finish (2x+2,y)

Final answer:

The coordinates of the midpoint of the line segment with endpoints A(3x + 5, 3y) and B(x - 1, -y) are (2x + 2, y), using the midpoint formula.

Explanation:

To find the coordinates of the midpoint of a line segment with endpoints A and B, you can use the midpoint formula, which is ((x₁ + x₂)/2, (y₁ + y₂)/2). For the given endpoints A(3x + 5, 3y) and B(x - 1, -y), substituting the coordinates into the formula gives us the midpoint coordinates as follows:

Hence, the coordinates of the midpoint of AB are (2x + 2, y).

Answer: 35.86

Step-by-step explanation:

By applying the DayTimer and NightTimer plans' rules and doing the necessary calculations, the total payment on the NightTimer plan would be $33.26747.

The total power used from 7am-7pm is 275 KWH and from 7pm-7am is 265 KWH. In this case, you have used more power during the 7am-7pm period. As such, you qualify for the DayTimer plan's rate. Therefore, you pay $0.06831/KWH for the power used between 7am-7pm, which results in 275 KWH * $0.06831/KWH = $18.78575. However, since most of your power usage is from 7am-7pm, you receive a 20% discount on your night usage. The night rate, therefore, is 20% less than the DayTimer rate, which is $0.06831 * (1 - 20/100) = $0.054648/KWH. Hence, you will pay 265 KWH * $0.054648/KWH = $14.48172 for power used between 7pm-7am. By adding these two amounts together, your total payment on the NightTimer plan would be $18.78575 + $14.48172 = $33.26747.

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The employee earns a fixed salary of $340 plus a 6% commission on sales. In a week with $660 in sales, his total earnings would be $379.60.

The employee's weekly income is a combination of a fixed salary and a percentage of sales. His fixed salary is $340. From his sales, he earns a 6% commission. So for a week with $660 in sales, the commission would be 6/100 * 660, which equals $39.60. Adding this commission to the fixed salary: $340 + $39.6 = $379.60. So, the employee's overall earnings for the week would be $379.60.

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Applying the Pythagorean theorem, the length of diagonal DF is: C. 21 cm.

The sum of the squares of the two shorter legs of a right triangle equals the square of the length of the longest leg.

Let the point of intersection of the diagonals be O.

Diagonal FD bisects diagonal EG into equal segments EO and OG. EO = OG = 24/2 = 12 cm

Find the lengths of FO and OD using the Pythagorean theorem:

FO = √(20² - 12²) = 16 cm

OD = √(13² - 12²) = 5 cm

Length of diagonal DF = FO + OD = 16 + 5 = 21 cm.

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''90 feet in 2.5 hours'' have fastest speed.

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.

Given that;

There are some distances and time.

Now,

For Option A;

⇒  18 feet in 20 minutes

Since, We know that;

⇒ Speed = Distance / Time

               = 18/20

               = 0.9 feet per minutes

For Option B;

⇒  90 feet in 2.5 hours

⇒ 90 feet in 150 minutes

Since, We know that;

⇒ Speed = Distance / Time

               = 90/150

               = 0.6 feet per minutes

For Option C;

⇒  20 yards in 1.5 hours

Since, 1 yards = 3 feet

⇒ 60 feet in 90 minutes

Since, We know that;

⇒ Speed = Distance / Time

               = 60/90

               = 0.67 feet per minutes

For Option D;

⇒  3 2/3 yards in 15 minutes

Since, 1 yards = 3 feet

⇒ 11 feet in 15 minutes

Since, We know that;

⇒ Speed = Distance / Time

               = 11/15

               = 0.73 feet per minutes

Hence, Clearly ''90 feet in 2.5 hours'' have fastest speed.

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Final answer:

After converting each option to the same unit of speed, it's clear that Option A with a speed of 0.9 feet per minute is the fastest.

Explanation:

To determine which speed is the fastest, we need to convert each option into the same unit of speed, typically feet per minute or meters per second for consistency. Here, we'll choose feet per minute for simplicity.

Option A: 18 feet in 20 minutes = 0.9 feet/minute

Option B: 90 feet in 2.5 hours (150 minutes) = 0.6 feet/minute

Option C: 20 yards (60 feet) in 1.5 hours (90 minutes) = 0.67 feet/minute

Option D: 3 2/3 yards (11 feet) in 15 minutes = 0.73 feet/minute

Comparing these speeds, Option A is the fastest with 0.9 feet per minute.

Solution:

As, you can see that shape 1 and shape 2 are not congruent nor the shape 1 is dilated by any factor to get the shape 2.

Both the shapes are concave polygon.

The base length of two shapes are equal .

→2 ×  AB  =  P Q  →(approx)

→BC=QR

→2 × CD= RS→→→(approx)

If translation has taken place, all the vertices has been translated by same amount.

So, option (4) is true,which is Shape 1 is not congruent to shape 2 because a sequence of rigid transformations will not map shape 1 onto shape 2."

The correct expression of the solution set will be;

''All real numbers that are greater than negative three.''

What is Inequality?

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The solution set is,

m ≥ - 3

Now,

Here, The solution set is,

m ≥ - 3

Clearly, a number 'm' is greater than or equal to - 3.

Thus, We can formulate;

The correct expression of the solution will be;

''All real numbers that are greater than negative three.''

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Answer:

Option B is the correct answer.

Step-by-step explanation:

Refer the the figure below of the question given.

The height of radio tower = CD

CD = AD - AC

We have

       [tex]tan46=\frac{AD}{AB}\\\\AD=ABtan46=67tan46\\\\tan36=\frac{AC}{AB}\\\\AC=ABtan36=67tan36\\\\CD=67tan46-67tan36=20.70m[/tex]

Option B is the correct answer.

Answer:

15

7

Just to simplify the answer above.

Step-by-step explanation:

X = 24 ft Of Materials

Y = 2 ft Of Distance

X = (12,7)

Y = (0,2)

Using The Pythagoras Theorem

[tex]D=\sqrt{12^{2}+5^{2}}=13[/tex]

Total lenght is:

[tex]\left[\begin{array}{ccc}3*13+24+4=26\\26+28=54\end{array}\right][/tex]

Answer:

she spends 44 dollars per sister, 24 dollars per nephew

Step-by-step explanation:

180=3(20+x)+2x

180=60+3x+2x

120=5x

x=24

x+20=44

Answer:

c. 400 times more likely

Step-by-step explanation:

The non-permissible replacements for the variable x in the expression (x^2)/(2x-4) are x = 0 and x = 2.

An expression is undefined when its denominator is equal to zero. Therefore, we need to find the values of x that make the denominator, 2x-4, equal to zero.

Solve the equation for x: 2x - 4 = 0 2x = 4 x = 2

Therefore, x = 2 is a non-permissible replacement because it makes the denominator zero.

Additionally, the expression also includes x^2 in the numerator. Since any number multiplied by zero is still zero, dividing any non-zero number by zero results in undefined. Therefore, x = 0 is also a non-permissible replacement.

In conclusion, the non-permissible replacements for the variable x in the expression (x^2)/(2x-4) are x = 0 and x = 2.

Answer:

Angle of intersection is one half of the sum of measurements of intercepted arcs.

Step-by-step explanation:

An inscribed angle is the angle formed by the intersection of two chords having a common endpoint in a circle.

Also, by the angles of Intersecting Chords Theorem,

When two chords intersect inside a circle, then the measure of the angle formed is one half of sum of the measure of the arcs intercepted by the angle and its vertical angle.

Which is the relationship between the angle of intersection and the intercepted arcs.

Final answer:

The rule for the nth term of the arithmetic sequence is given by the formula a_n = 19 + (n - 1)×3, where a1 is the first term of the sequence and d is the common difference.

Explanation:

To write the rule for the nth term of an arithmetic sequence where the 10th term a10 is 46 and the common difference d is 3, we use the formula:

an = a1 + (n - 1)d

We have that:

a10 is the 10th term of the sequence which is 46.

The common difference d is 3.

Firstly, we need to find a1, the first term of the sequence. We can use the given a10 to find a1.

a10 = a1 + (10 - 1)×3

46 = a1 + 9×3

46 = a1 + 27

a1 = 46 - 27

a1 = 19

Now we can write the rule for the nth term:

an = 19 + (n - 1)×3

This formula allows us to calculate any term in the sequence by substituting the desired term number for n.