3. (a) A survey on the choice of vocation for 40 students revealed that 18 liked catering, 20 liked dressmaking and 15 liked hairdressing. 2 chose catering only, 8 chose dressmaking only and 1 chose hairdressing only, 4 chose all 3 vocation. Illustrate this information on a Venn diagram. b) How many students chose dressmaking and catering only? 9)) Find the number of students who did not choose any of the 3 vocations. ​

The dimensions of the rectangle are, length = 5 inch and width = 6 inch.

What is rectangle?

A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. It can alternatively be explained in terms of an equiangular quadrilateral—a term that refers to a quadrilateral whose angles are all equal—or a parallelogram with a right angle. A square is an irregular shape with four equal sides.

Let, the length of a rectangle is  7 inches less than twice the width, w, of the rectangle.

Suppose,

width = w = x, then,

length = l = 2x - 7

Since the area of the rectangle is 30 square inches.

We know that.

Area of rectangle = length x width

                       30 = (2x - 7) x (x)

                       30 = 2x^2 - 7x

    2x^2 - 7x - 30 = 0

2x^2 - 12x + 5x - 30 = 0

2x(x - 6) + 5(x - 6) = 0

     (2x + 5)(x - 6) = 0

⇒ 2x + 5 = 0,     x - 6 = 0

⇒ x = -5/2,           x = 6

Since length is not negative.

Therefore, w = 6.

So, l = 2(6) - 7 = 12 - 7 = 5

Hence, the length is 5 inches and the width is 6 inches.

complete question

The length of a rectangle i 7 inche le than twice the width, w, of the rectangle. Find the dimenion if the area i 30 quare meter

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Answer: 7%

Step-by-step explanation:

Take 6848 divided by 6400, then times 100 = 107%

Then take 107% - 100% = 7%

The sales tax percentage is 7%

Answer:

The area of the compound shape is 5√10 cm²

Step-by-step explanation:

In the given shape, there is a rectangle and a right angle triangle.

i.e.,

Compund shape = Rectangle + Triangle

So,

Area of Compound Shape = Area of Rectangle + Area of Right Angle Triangle

Formula;

A = 2√5 × 2√2 cm

A = 4√10 cm²

Formula;

A = ½ × √2 × 2√5 cm

A = 1 × √2 × √5 cm

A = √10 cm²

Now,

Area of Compound Shape = Area of Rectangle + Area of Right Angle Triangle

A = 4√10 cm² + √10 cm²

A = 5√10 cm²

Thus, The area of the compound shape is 5√10 cm²

The required probability of the randomly selected steel rod with the average length greater than 206.1cm whose mean is 205.8cm and standard deviation is 0.5cm is equal to 0.0024012.

As given in the question,

Mean of the normally distributed steel rod ' μ '= 205.8cm

Standard deviation of the normally distributed steed rod 'σ ' = 0.5cm

Number of steel rod bundled together 'n' = 22

Randomly selected steel rods bundle the average length is greater than

'[tex]\bar {X}[/tex]' = 206.1cm

Required probability is given by :

P( [tex]\bar {X}[/tex] > 206.1 )

= P [([tex]\bar {X}[/tex] - μ )/ (σ/√n) > ( 206.1 - 205.8)/ (0.5/√22) ]

= P ( Z > (0.3/ 0.1064))

= P ( Z > 2.8195)

= P ( Z > 2.820)

= 0.0024012

Therefore, the probability of the randomly selected steel rod with the average length greater than 206.1cm is equal to 0.0024012.

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The equation to find the distance between the lions and giraffes is

x² = 121 + 256.

Option D is the correct answer.

Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We have,

Hypotenuse = Distance between lion and giraffes = x

Distance between lions and monkeys = 11 feet

Distance between monkeys and giraffes = 16 feet

Applying the Pythagorean theorem.

x² = 11² + 16²

x² = 121 + 256

x² = 377

x = √(377)

x = 19.42

Thus,

The distance between lions and giraffes is 19.42 feet.

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Answer:B and D

Step-by-step explanation:

Answer:

The smaller integer is greater than 1

Step-by-step explanation:

The integers are x and x+1

[tex]x + x + 1 < 3x \\ 2x + 1 < 3x \\ 2x - 2x + 1< 3x - 2x \\ 1< x [/tex]

1.5 litres of water are released from the faucet per minute.

It is given to us that -

There is a one quart jar

Water from the kitchen faucet fills the 1-quart jar in 10 seconds.

We need to ascertain the faucet's flow rate in gallons per minute.

We know that -

1 quart = 0.25 gallon ---- (1)

We also know that -

1 minute = 60 seconds

=> 60 seconds = 1 minute

=> 10 seconds = 10/60 = 0.16 minutes ----- (2)

Now, the flow rate can be calculated as -

Flow rate = Amount of water filled/Time taken ----- (3)

Substituting the values from equation (1) and (2) in equation (3), we have -

Flow rate = Amount of water filled/Time taken

=> Flow rate = 1 quart water/10 seconds

=> Flow rate = 0.25 gallons/0.16 minutes

=> Flow rate = 1.5 gallons per minute

Therefore, the flow rate of water from the faucet is 1.5 gallons per minute.

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Answer:

Because when you divide 100 by 4 and 50 by 2, you will get the same value

William ran for 48 minutes since Eliot ran for 8 miles in 40 fewer minutes than William. They were running at the same speed.

Eliot and William both went running and ran for 8 miles and 12 miles respectively. Eliot finished his 8 mile run in 40 fewer minutes than William. This means that if the two of them were running at the same speed, it would take William 40 minutes longer than Eliot to finish his 12 mile run. To calculate how long William ran for, we can add 40 minutes to the time it took Eliot to run 8 miles. Since Eliot ran 8 miles in 40 fewer minutes than William, this means that Eliot ran 8 miles in the amount of time that William ran 12 miles. The total time William ran for is therefore 8 miles plus 40 minutes, which is 48 minutes.

Eliot: 8 miles ÷ 40 minutes fewer

= 0.2 miles/minute

William: 12 miles ÷ (0.2 miles/minute x 40 minutes)

= 48 minutes

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Answer:

Divide 5 to both side.

Step-by-step explanation:

Original Equation:

[tex]5(x-3)=5[/tex]

2nd Equation:

[tex](x-3)=1[/tex]

Single Steps:

Divide 5 to both side on Original Equation to get 2nd Equation.

The amount of money each waiter get in tip is 44 dollars.

In this question we have been given at the yum yum cafe the waiters combine their tips and divide the total by the number of waiters.

Today's tip total is 132 and three waiters are working.

We need to find the amount of money each waiter get in tip.

Let x dollers be the amount each waiter get in tip.

Total tip amount = 132

number of waiters = 3

By unitary method,

x = 132/3

x = 44 dollars

Therefore, each waiter get 44 dollars in tip.

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Answer:

Step-by-step explanation:

good luck lol

The worth of an anticipated revenue stream as of the valuation date is known as present value, sometimes known as present discounted value.

The total of future investment returns discounted at a given level of expected return is used to determine the present value (PV), which is the value of money in today's dollars that you expect to get from future income. This idea is used for bond pricing and stock valuation.

Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.

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Answer:

aproximantly 131.1701yen

Step-by-step explanation:

Answer:

15430 Japanese yen

Step-by-step explanation:

To find out how many Japanese yen you receive for 100 British pounds, we need to find the exchange rate between British pounds and Japanese yen in the table. From the table, we can see that the exchange rate between British pounds and Japanese yen is 154.43. Therefore, if you exchange 100 British pounds, you will receive 100 * 154.43 = 15430 Japanese yen.

Since the diagonal of the suitcase is 30 inches and the length of the bat is 29 inches means the bat can fit into the case diagonally.

The dimension of a suitcase is-

length = 24 in.

width = 18 in.

The length of the bat = 29 in.

Clearly, the bat cannot fit vertically or horizontally in the suitcase.

Now to see if it fits diagonally in the suitcase, we apply the Pythagoras theorem to determine the diagonal of the suitcase or say the hypotenuse of the rectangular suitcase.

Thus, by Pythagoras' theorem,

[tex](hyp)^2 = opp^2 + adj^2[/tex]

[tex](hyp)= \sqrt{opp^2 + adj^2}[/tex]

[tex](hyp)= \sqrt{18^2 + 24^2}[/tex]

[tex](hyp)= \sqrt{324+ 576}[/tex]

[tex](hyp)= \sqrt{900}[/tex]

 hyp  = 30 in.

Hence, the diagonal of the suitcase > the length of the bat.

Since the diagonal of the suitcase is 30 inches and the length of the bat is 29 inches means the bat can fit into the case diagonally.

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Answer:

13.85$

Step-by-step explanation:

105$-8$=97$

97$/7$=13.85$

Answer: About $13.86

Step-by-step explanation: To find how much the cost of the forks is, we need to subtract the value of the lunch box from the total cost, because we don't need to find the value of the lunch box. So:

105 - 8 = 97

So, now since he bought 7 forks, we need to divide 7 by 97. So:

97 / 7 = 13.857142857142858

So, we need to round to the nearest cent. So, the 7 is greater than 5, so we round up. So, we have $13.86 each. So, check, we do:

13.86(7) + 8

97.02 + 8

= 105.02

This is the closest he can buy for each fork is ABOUT $13.86. I hope this helps ;)

The total cost of the siding material is given as follows:

B. $292.50.

To obtain the cost of material, the first step is obtaining the area that will be covered, which is given as follows:

The rectangular area of 8 feet by 24 feet will be covered, with these following exceptions:

The triangular area with base 24 feet and height 6 feet will also be covered.

Then the total area to be covered is given as follows:

Area = 8 x 24 - (2 x 6 x 4) - (3 x 7) + 0.5 x 24 x 6

Area = 195 ft².

The total cost is of $1.5 per ft², hence it is calculated as follows:

Total cost = 195 x 1.5 = $292.50.

Meaning that option B is correct.

The problem is given by the image shown at the end of the answer.

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Answer: True. Renting is a great option for many people because it offers flexibility and affordability. Renting allows individuals to live in a desired location without the financial burden and commitment of owning a home. It also provides flexibility, as renters can easily move to a different location if their needs or circumstances change. Additionally, renting can be a more affordable option compared to owning a home, as it typically involves lower upfront costs and maintenance expenses. For these reasons, renting is a viable and attractive option for many people.

Step-by-step explanation:

Answer:

The coordinates of a point are a pair of numbers that define its exact location on a two-dimensional plane. Recall that the coordinate plane has two axes at right angles to each other, called the x and y-axis. The coordinates of a given point represent how far along each axis the point is located.

Both Frida and Sam are right.

In geometry, a quadrilateral is a type of close-shaped polygon that has four sides, four angles, and four vertices. In Latin, 'Quadri' means four, and 'latus' means side.

A parallelogram is a geometrical shape having both pairs of opposite sides parallel and equal.

Squares are a type of quadrilateral having two sets of parallel sides. Parallelograms may be called quadrilaterals which have two sets of parallel sides. As squares are quadrilaterals having two sets of parallel sides, all squares may be called parallelograms. As all rectangles are having two pairs of parallel sides and all angles of a rectangle are equal, it might be called parallelograms.

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The complete question is:

Frida sorted polygons so Group 1 only squared. Group 2 was only

rectangles, not squares. Frida said all the figures are parallelograms. Sam said they are all quadrilaterals. Who is right? Why?

If the larger triangle has a perimeter of 62 feet, its area will be 120 square feet.

We know that the perimeter of the smaller triangle is 31 feet, which means that the sum of the lengths of its three sides is 31 feet. We also know that the area of the smaller triangle is 40 square feet. We can set up the following equation to calculate the length of each side of the smaller triangle:

Side 1 + Side 2 + Side 3 = 31

We can then use the formula for the area of a triangle, A = bh/2, to calculate the length of the base and height of the smaller triangle. Since we know the area is 40 square feet, we can set up the following equation:

40 = (b)(h)/2

We can then solve this equation for b and h. We know that b + h = 31, so we can set up the following equation and solve for h:

h = 31 - b

Now that we know b and h for the smaller triangle, we can use the same formula to calculate the area of the larger triangle. Since we know that the perimeter of the larger triangle is 62 feet, we can set up the following equation to calculate the length of each side of the larger triangle:

Side 1 + Side 2 + Side 3 = 62

We can then use the following formula to calculate the area of the larger triangle:

A = (b)(h)/2

We know that b + h = 62, so we can set up the following equation and solve for h:

h = 62 - b

Now that we know b and h for the larger triangle, we can plug those values into the area formula and calculate the area of the larger triangle. The area of the larger triangle is 120 square feet. Therefore, if the larger triangle has a perimeter of 62 feet, its area will be 120 square feet.

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Using the property of geometry and using a parallelogram , We can prove that the opposite sides of parallelograms are congruent.

What is a parallelogram?

In Euclidean geometry, a parallelogram is a simple quadrilateral having two sets of parallel sides. The opposite sides and the opposite angles of a parallelogram are of equal length. A parallelogram is a special kind of quadrilateral with both pairs of its opposite sides parallel and equal.

What are the 4 types of parallelograms?

There are 4 types of parallelograms with 3 special types.

They are:

parallelograms

squares

rectangles

rhombuses.

According to the given question:

Let ABCD be a parallelogram where AB and CD are in opposition to each other, while BC and AD are.

According to the definition of a parallelogram, section BC is parallel to segment AD since ABCD is a parallelogram.

The definition of a parallelogram is that segment AB is parallel to segment DC.

Segments BC and AD are transverse to line AC. As demonstrated below, this transversal generates alternate interior angles that are equal.

In the same way, segment AB and segment DC are transversals for line AC. This transversal generates equal alternate interior angles.

Segment AC is also divided into segments by its reflexive property.

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Answer:

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Given is the graph of an absolute value function.

It has no domain restrictions, so x can be any real number.

There is a restriction on its range, it has a minimum at y = 0 and the rest of the values are positive real numbers.

It is correctly described in option d).

Using the concept of percentages the total earning of Cara can be found to be $4200.

Percentage is a number expressed as a fraction of 100. The % sign means to divide the number by 100.

Cara's earning = commission + basic salary

basic salary = $1800 (this is constant)

commission = 6% of $40000

= (6/100)*40000

= $2400

Cara's earning = 1800 + 2400

Hence, her earning is $4200

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Check the picture below.

The value of material's resistance at 100 v voltage and at 2 A current is 50 Ω.

As per the data given in the question the value of Voltage is 100 v, Current is 2 A

Ohm’s law states that the current through a conductor between two points is directly proportional to the voltage across the two points.

This law is one of the most basic laws of electricity.

Ohm’s Law Formula:

Voltage = Current× Resistance

V = I × R

V = Voltage, I = Current and R = Resistance.

Using Ohm's Law we have to determine the value of R.

R is Resistance and has units of ohms, with symbol Ω.

V = I × R

At Voltage = 100 v, Current = 2 A

100 = 2 × R

R = [tex]\frac{100}{2}[/tex]

R = 50 Ω

Therefore the value of Resistance of material, R = 50 Ω

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FIGURE EX 31.38 is a current-versus-potential-difference graph for a material. What is the material's resistance?

Diagram attaches at the end of solution.

Using the concept of percentage, the percentage of dolphins that knew the difference is 26%

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.

The number of dolphins that knew the difference between strike and ball is given as 4 out of 15.

This can be represented in a fraction as 4 / 15

The percentage that knew the difference = (4 / 15) * 100

The percentage that knew the difference will be 0.26 * 100 = 26 %

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