Two mechanics worked on a car. The first mechanic worked for 5 hours, and the second mechanic worked for 15 hours. Together they charged a total of $1400. What was the rate charged per hour by mechanic if the sum of the two rates was $130 per hour

Answer:

Step-by-step explanation:

A. 1). Area of the rectangle = length×width = 11×8 = 88 cm²

Perimeter = 2(18+11) = 58 cm

2).Area of a parallelogram = length×height = 24×16 = 384 ft²

Perimeter = 2(19+24) = 2×43 = 86 ft

3). Area of a right angle triangle = (1/2)×base×height = (1/2)×12×9 = 54 in²

Perimeter = (9+12+15) = 36 in

4). Area of a triangle = (1/2)×Base×height = (1/2)×21×19 = 199.5 m²

Perimeter = (20+21+23) = 64 m

5). Area of an obtuse angle triangle = (1/2)×height×base = (1/2)×2.9×2.4 = 2.9×1.2 = 3.48 cm²

Perimeter = (2.9+2.4+4.5) = 9.8 cm

6). Area of a parallelogram = base × height = 56×90= 5040 ft²

Perimeter = 2(56+100) = 2×156 = 312 ft

B. 7). Area of the shaded area = (27×27 - 12×12) = 729-144 = 585 in²

8). Area of the shaded area = 10(9+7) - (1/2)×10×9 = 160 - 45 = 115 cm²

9). Area of the shaded area = 50×53 - 25×23 = 2650 - 575 =2075 ft²

10). Area of the shaded area = 10×13 - (1/2)×6×8 = 130 - 24 = 106 m²

11). Area of the shaded area = 18×18 - (1/2)×18×9 = 324 - 81 =243 in²

12). Area of the shaded area = 11×17 - (1/2)×11×17 = (1/2)×11×17 = 93.5 cm²

To approximate the weight of a cone-shaped pile of sand, find the volume of the cone using the formula V = (1/3)πr²h. Multiply the volume by the weight of one cubic foot of sand (100 pounds) to find the weight of the pile. Round to the nearest hundred pounds.

To approximate the weight of a cone-shaped pile of sand, we first need to find the volume of the cone.

The formula for the volume of a cone is V = (1/3)πr²h, where r is the radius of the base and h is the height.

Let's say the radius is 2 feet and the height is 5 feet.

Plugging these values into the formula, we get V = (1/3)π(2²)(5) = 20π.

Now, since one cubic foot of sand weighs about 100 pounds, we can multiply the volume of the cone by 100 to find the approximate weight.

Therefore, the weight of the cone-shaped pile of sand is approximately 20π × 100 = 2000π pounds.

Rounding to the nearest hundred pounds, the weight is approximately 6283 pounds.

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Starting from -4 and applying a series of moves (+3, -2, +6, -5) sequentially on the number line, the final position of Point x is -2.

The question involves finding the final position of Point x after a series of moves on a number line. Starting from -4, we apply the moves in sequence: adding 3, subtracting 2, adding 6, and finally subtracting 5. The operations are as follows:

Therefore, the final position of Point x on the number line is -2.

Answer:

Belinda will get $25 from her insurance company when she files her claim.

Step-by-step explanation:

Comprehensive insurance covers your car from damage from fire, theft or falling objects like trees etc.

To get the claim, the company will check the worth of the GPS system in the market minus the deductible amount.

So, the cost of GPS system was $400. And comprehensive deductible is $375.

So, Belinda will receive [tex]400-375=25[/tex] dollars

The answer is: Belinda will get $25 from her insurance company when she files her claim.

Answer:

1/3

Step-by-step explanation:

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Final answer:

The average distance for all segments of the flower shop deliveries trip is calculated to be 14.5 miles.

Explanation:

To calculate the average distance travelled for all segments of the trip, we first convert each distance to an improper fraction or decimal for ease of calculation and then find the sum of all the segments.

After this, we divide the total distance by the number of segments.

The distances given are:

The total distance travelled is the sum of all these distances:

12.333... + 8.75 + 17.25 + 23.666... + 10.5 = 72.5 miles

There are 5 segments in the trip, so to find the average, we divide 72.5 miles by 5:

72.5 miles / 5 = 14.5 miles

Therefore, the average distance for all segments of this trip is 14.5 miles.

To calculate the slant height of a cone with a diameter of 15 yards and lateral area of 287.5 square yards, divide the lateral area by the product of pi and the radius of the base. The slant height is approximately 12.3 yards when rounded to the nearest tenth.

To find the slant height of a cone with a known lateral area, we use the formula for lateral surface area of a cone: L = \\(\pi\\)r\ell, where L stands for lateral area, r for radius of the base, and \ell for the slant height. Given the diameter of 15 yards, we first calculate the radius as half the diameter, which is 7.5 yards. The equation with the given lateral area (287.5 square yards) would look like this: 287.5 = \\(\pi\\) \\times 7.5 \\times \ell. Solving for \ell, we divide the lateral area by \\(\pi\\) times the radius:

\ell = 287.5 / (\\pi \\times 7.5)

To get an approximate value, we use \\(\pi\\) = 3.1416:

\ell \\approx 287.5 / (3.1416 \\times 7.5)

\ell \\approx 12.27 yards

Thus, the slant height of the cone is approximately 12.3 yards when rounded to the nearest tenth.

Final answer:

To calculate the area of the blue border of the circular rug, subtract the area of the red center from the area of the entire rug. Using the area formula for a circle, the area of the blue border is approximately 100.5 square feet when rounded to the nearest tenth.

Explanation:

To find the area of the blue border of Kelsey's circular rug, we first need to calculate the area of the entire rug and then subtract the area of the red circular center. The diameter of the entire rug is 12 feet, which means its radius is 6 feet. Similarly, the diameter of the red center is 4 feet, giving it a radius of 2 feet. We use the formula for the area of a circle, A = πr^2, where A is the area and r is the radius.

First, we calculate the area of the entire rug with a radius of 6 feet:
Atotal = π * 6^2 = π * 36 = 36π square feet.

Next, we calculate the area of the red center with a radius of 2 feet:
Acenter = π * 2^2 = π * 4 = 4π square feet.

Now, we subtract the area of the red center from the total area to find the area of the blue border:
Aborder = Atotal - Acenter = 36π - 4π = 32π square feet.

To provide an answer rounded to the nearest tenth, we approximate π to 3.14:
Aborder ≈ 32 * 3.14 ≈ 100.48 square feet, which rounds to 100.5 square feet as the area of the blue border.

A cross section obtained by cutting a right rectangular prism with a square base parallel to its base will also be a C. square, as it reflects the shape of the prism's base.

The question is asking about the shape of a cross section obtained by cutting a right rectangular prism with a square base parallel to its base. Such a cut would expose a shape on the surface of the prism that directly corresponds to the shape of the base. Since the base is given as a square, the cross section in this case would also be a square. The hypothesis of the right angle implies that the sides of the prism are perpendicular to the base, thereby maintaining the square shape upon slicing parallel to the base.

The cross section would not be a triangle (option A) or a trapezoid (option B), as these shapes do not correspond to a square base. It would not be a rectangle that is not a square (option D), because the length and width of the cross section would be the same, maintaining its square shape. Therefore, the correct answer is option C - a square.

The number that Dennis started with is 24

Solving linear equation mean calculating the unknown variable from the equation.

Let the linear equation : y = mx + c

If we draw the above equation on Cartesian Coordinates , it will be a straight line with :

m → gradient of the line

( 0 , c ) → y - intercept

Gradient of the line could also be calculated from two arbitrary points on line ( x₁ , y₁ ) and ( x₂ , y₂ ) with the formula :

[tex]\large {m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

If point ( x₁ , y₁ ) is on the line with gradient m , the equation of the line will be :

[tex]y - y_1 = m ( x - x_1 )[/tex]

Let us tackle the problem.

Let :

The number that Dennis started with is X

If he adds 0.5 to that number and then multiplies the new result by 4 , then:

[tex]( X + 0.5 ) \times 4[/tex]

If he then subtracts 2 and divides the number by 2 , then:

[tex]\frac{[ ( X + 0.5 ) \times 4 ] - 2}{2}[/tex]

If his final answer is 48 , then :

[tex]\frac{[ ( X + 0.5 ) \times 4 ] - 2}{2} = 48[/tex]

[tex][ ( X + 0.5 ) \times 4 ] - 2 = 48 \times 2[/tex]

[tex]( X + 0.5 ) \times 4 = 48 \times 2 + 2[/tex]

[tex]( X + 0.5 ) \times 4 = 96 + 2[/tex]

[tex]( X + 0.5 ) \times 4 = 98[/tex]

[tex]( X + 0.5 ) = \frac{98}{4}[/tex]

[tex]( X + 0.5 ) = \frac{49}{2}[/tex]

[tex]X = \frac{49}{2} - \frac{1}{2}[/tex]

[tex]X = \frac{48}{2}[/tex]

[tex]\large {\boxed {X = 24} }[/tex]

Grade: High School

Subject: Mathematics

Chapter: Linear Equations

Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point

Final answer:

A relation where each domain value is mapped to a single, unique range value is considered a function. The relation in question is indeed a function because each domain value corresponds to only one range value, and its correctness is supported by the distinct pairs of the domain and range. The correct answer is option (B)

Explanation:

To determine whether a given relation is a function, we check if each element of the domain maps to exactly one element of the range. The relation in question is composed of the following ordered pairs: (-3, -2), (-1, 0), (1, 0), (5, -2). The domain (which consists of the first elements of the ordered pairs) includes -3, -1, 1, and 5, and the range (the second elements) includes -2, 0.

A crucial aspect of a function is that each domain value is paired with a unique range value. Here, we see that no domain value is repeated; hence, none of them map to more than one range value. This satisfies the criterion for a function. However, it is not a problem that a range value, like -2, appears more than once in the relation as long as it corresponds to different domain values.

Based on this, the correct answer would be "B. yes- only one range value exists for each domain value" because each domain value is associated with one and only one range value, which is the definition of a function.

Answer:

the answer is 2:7

Step-by-step explanation:

just because

Answer:

The amount is $275.3

Step-by-step explanation:

We can use amount formula

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

where

A is the amount

P is money invested

r is interest rate

n is number of periods

t is time in years

we are given

P=200

r=4%=0.04

t=8

n=12

so, we can plug these values

[tex]A=200(1+\frac{0.04}{12})^{12\times 8}[/tex]

we can simplify it

and we get

[tex]A=275.3[/tex]

So,

The amount is $275.3

Part A: The expression [tex]4\cdot d[/tex] represents the number of strawberries Heather needs for the desserts.

Here, the variable "d" represents the number of desserts Heather will make.

Part B:  Heather has 24 ounces of strawberries, she can make 6 desserts.

Mathematically, an expression is a combination of numbers, variables, operations, and functions that are composed together according to specific rules to represent a computation or relationship of mathematics. It can be thought of as a mathematical phrase or formula.

Part A: Let's represent the number of desserts Heather will make with the variable "d".

The expression that represents the number of strawberries Heather needs for the desserts can be written as:

[tex]4 \times d[/tex].

Here, the variable "d" represents the number of desserts Heather will make.

Part B: If Heather has 24 ounces of strawberries, we can set up an equation to determine the number of desserts she can make.

[tex]4 \times d[/tex] = 24 ounces.

To solve for "d," we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by 4 ounces/dessert:

d (desserts) = [tex]\frac{24}{4 }[/tex]

Simplifying the right side of the equation:

d (desserts) = 6 desserts.

Therefore, Heather can make 6 desserts with 24 ounces of strawberries.

Therefore, [tex]4 \times d[/tex] represents the number of strawberries, where variable "d" is the number of desserts and Heather can make 6 desserts with 24 ounces of strawberries.

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