Use the following diagram for questions 1-3.
1. Find x.
2. Find y
3. Find z

Betsie should buy the 250 envelopes from the shop Letter2go.

As, 250 envelopes will cost £31.9 in Shop Letter2go whereas will cost £33.17 in Shop Value World.

Given, that Betsie is going to buy 250 envelopes.

the cost of envelopes in two shops:

Value World:

Pack of 10 envelopes for £1.99

Buy 2 packs get 1 pack free

Letters2go:

Pack of 25 envelopes for £3.19

Now, if we see the cost of envelopes in shop 1 i.e. Value World

Cost of Pack of 10 envelopes = £1.99

Also, 1 pack is free for 2 packs

1 pack = £1.99

2 packs = 2×£1.99 = £3.98

Also, with 2 packs Betsie get 1 pack free

so, Betsie gets 3 packs for £3.98.

1 pack = 10 envelopes

3 packs = 30 envelopes.

Hence, In shop Value World:

30 envelopes = £3.98

1 envelope = £3.98/30

250 envelopes = (3.98/30)×250

So, 250 envelopes will cost £33.17 in Shop Value World.

And in shop Letter2go:

25 envelopes = £3.19

1 envelope = £3.19/25

250 envelopes = (3.19/25)×250

So, 250 envelopes will cost £31.9 in Shop Letter2go.

Hence, 250 envelopes will cost £33.17 in Shop Value World and £31.9 in Shop Letter2go.

So, Betsie should buy the 250 envelopes from the shop Letter2go.

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a) The average life of the lot is 1078.33 hrs, b) the total life is 107833.33 hours, c) a proportion of 1/2 bulbs have a life exceeding 1000 hrs while d) an estimation of 50 bulbs have a life exceeding 1000 hours.

It is given that the number of bulbs in a given lot is 100.

The number of bulbs in the sample selected is 6

The life of the sample bulbs was

no.         life (hours)

1                      950

2                     1210

3                     1070

4                      840

5                     1420

6                      980

a)

The average life of the bulbs can be calculated by

the sum of the lives of the sample/ no. of samples

= (950 + 1210 + 1070 + 840 + 1420 + 980) / 6

= 1078.3333 hrs

b) The total lives of the bulbs in the lot will be

average life X no. of bulbs

= 1078.3333 X 100

= 107833.33 hrs

c)

We can gain the proportion of the bulbs that have a life exceeding 1000 hrs by the given sample

The bulbs

2, 3, and 5 have lives exceeding 1000 hrs.

Hence, out of 6 bulbs, 3 have lives exceeding 1000 hrs.

Therefore the proportion

= 3/6

= 1/2

d)

The number of bulbs in the lot with a life exceeding 1000 will be

proportion X no. of bulbs

= 1/2 X 100

= 50 bulbs

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Answer:

x<6

Step-by-step explanation:

2x/3<4

2x<12

x<6

Answer:

x < 6

Step-by-step explanation:

[tex]\frac{2x}{3}[/tex] < 4 ( multiply both sides by 3 to clear the fraction )

2x < 12 ( divide both sides by 2 )

x < 6

Answer: x=18

Step-by-step explanation:

It just does ok

Answer:

if the root is 10 then the function is ²✓5

Answer:

Step-by-step explanation      a=0.32

The required simplified value of x in the given expression is 8.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
2.8x + 10 + 5.7x = 70+x

Simplifying,
8.5x + 10 = 70 + x
8.5x - x = 70 - 10
7.5x  = 60
x = 60 / 7.5
x = 8

Thus, the required simplified value of x in the given expression is 8.

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Answer:

as shown in underline ^^

Step-by-step explanation:

Fill in the missing words:

When a solid mixes with a liquid and becomes part of the liquid it dissolves.

A solid that dissolves in a liquid is soluble.

A solid that does not dissolve in a liquid is insoluble.

The rate of the plane in still air is a = 1170 km/hr, and the rate of the wind is w = 210 km/hr.

The distance covered in a unit of time is known as speed.

Given that, the airplane travels 7680 km in 8 hours flying against the wind, and 12420 km in 9 hours.

Therefore, the rate of the airplane against the wind is:

7680/8

= 960 km / hr

The rate of the airplane with the wind is:

12420/9

=1380 km / hr

Let the rate of the airplane in still air be a and the rate of the wind be w.

The net rate while flying against the air is:

a - w = 960       (1)

The net rate while flying with the wind is:

a + w = 1380      (2)

Add equations (1) and (2):

2a = 2340

a = 1170 km/hr

Substitute a = 1170 into equation (1):

1170 - w = 960

1170 - 960 = w

210 = w

Hence, the rate of the plane in still air is a = 1170 km/hr, and the rate of the wind is w = 210 km/hr.

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There are 2 common factors of 9 and 24, that are 1 and 3. Therefore, the greatest common factor of 9 and 24 is 3.

In mathematics, the greatest common divisor of two or more nonzero integers is the largest positive integer that divides each integer

. The greatest common divisor (GCF) of a set of numbers is the greatest factor of division of all numbers.

GCF by listing factor method :-

Factors of 9: 1, 3, 9

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

There are 2 common factors of 9 and 24, that are 1 and 3. Therefore, the greatest common factor of 9 and 24 is 3.

other two methods are attached below .

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The table (D) values would produce the same graph as shown.

Mathematical structures known as graphs are used to describe pairwise relationships between things. Graph theory is the study of these mathematical structures. Vertices (also known as nodes or points) and edges are what make up a graph in this sense (also called links or lines). It is possible to distinguish between directed and undirected graphs, where edges connect two vertices asymmetrically and symmetrically, respectively. One of the primary topics in discrete mathematics is graphs.

From the graph, find the intercepts,

At x = 0, the value of y is -1.

At, y = 0, the value of x is 4

So, from the given options, we can see that the values are given in table (D).

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The correct answer to this question is d. the value of the 6 in 364 is 10 times the value of the 6 in 346.

The place value of the 6 in 346 is six because it is in the place of ones, whereas the place value of the sixth in 364 is 60 because it is in the place of tens. As a result, the value of 60 is ten times that of the value of 6.

The value of each digit in a number is known as place value. Every digit in a number has a distinct value depending on where it is located. The value of a digit depends on its position in the number, which can result in a number having two similar digits with different values.

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Answer:

y=1/4x+3

Step-by-step explanation:

To write an equation, let's infer we need to write it in slope-intercept form. We need the y-intercept. We can plug 1/4 and (-4,2) into y=mx+b, to solve for b. We have:

2=1/4*-4+b

2=-1+b

3=b

Since we have the slope, 1/4, we can create our equation:

y=1/4x+3

Solve for b in (y=mx+b):

b=y-mx

b=2-(1/4)(-4)

b=2+1

b=3

So the equation is y= (1/4)x + 3

Answer:

25.5 feet because of some

Step-by-step explanation:

.,........

Answer:

Step-by-step explanation:

The total amount of water Karla drank before and after the tennis practice is 5 cups and 9 fluid ounces.

The correct answer option is option C.

Convert fluid ounces to cups:

1 fluid ounces = 0.125 cups

15 fluid ounces = 1.875 cups

Total volume of water Kayla drank = Volume of water Karla drank before tennis practice + Volume of water Karla drank after tennis practice

= 1.875 cups + 4 cups

= 5.875 cups

Approximately,

5 cups and 9 fluid ounces

Therefore, the total volume of water Karla drank is approximately 5 cups and 9 fluid ounce

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Answer:

answer. {-2187x}/{625}

A floor that is 3 3/4 yards wide and 5 1/2 yards long requires 20 5/8 square yards of hardwood flooring area.

length = 5 1/2 yd, breadth = 3 3/4 yd.

Make fractions out of both measurements first.

3 3/4 = 3 + 3/4

= 12/4 + 3/4

= 15/4

5 1/2 = 5 + ½

= 10/2 + ½

= 11/2

Area = (15 * 11)/(4 * 2) yd2

Area = 165/8 yd2

They essentially believed that 165/8 = 20 leftover 5 area = 20 5/8 yd2.

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The expression similar to  [tex]\sqrt[3]{56\cdot x^7\cdot y^5 }[/tex] obtained by using the laws of indices is option A.

A. [tex]2\cdot x^2 \cdot y\sqrt[3]{7\cdot x \cdot y^2}[/tex]

According to some of the laws of indices, we have;

[tex]\dfrac{1}{x^n} =x^{-n}[/tex]

[tex]x^m \cdot x^n = x^{m+n}[/tex]

[tex]\sqrt[m]{x^n} =x^{\frac{n}{m} }[/tex]

The expression can be presented as follows; [tex]\sqrt[3]{56\cdot x^7\cdot y^5 }[/tex]

Simplifying the above expression gives;

[tex]\sqrt[3]{56\cdot x^7\cdot y^5 } = \sqrt[3]{8 \times 7\cdot x^6 \times x \cdot y^3 \times y^2 }[/tex]

[tex]\sqrt[3]{8 \times 7\cdot x^6 \times x \cdot y^3 \times y^2 } = \sqrt[3]{2^3 \times 7\cdot x^6 \times x \cdot y^3 \times y^2 }[/tex]

Collecting terms with an index of a multiple of 3 gives;

[tex]\sqrt[3]{2^3 \times 7\cdot x^6 \times x \cdot y^3 \times y^2 } = \sqrt[3]{2^3\cdot x^6 \cdot y^3 \times 7\cdot x \times y^2 }[/tex]

[tex]\sqrt[3]{2^3\cdot x^6 \cdot y^3 \times 7\cdot x \times y^2 } = 2\cdot x^2 \cdot y \times \sqrt[3]{ 7\cdot x \cdot y^2 }[/tex]

The expression that is equivalent to  [tex]\sqrt[3]{56\cdot x^7\cdot y^5 }[/tex]is option A.

A. [tex]2\cdot x^2 \cdot y \times \sqrt[3]{ 7\cdot x \cdot y^2 }[/tex]

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For the given geometric mean of a required number and nine times the required number is 30 then the required number is equal to 10.

As given in the question,

Geometric mean GM = 30

Let us assume the first number is x

and second number i.e. 9 times of the first number is 9x

By the formula GM = [tex]\sqrt{x.y}[/tex]

Now putting the value

30 = [tex]\sqrt{x.9x}[/tex]

30 = [tex]\sqrt{9x^{2} }[/tex]

30 = 3x (∴ square root of 9 is 3 and sq root of x² is x)

10 = x  (by dividing both the side by 3)

Therefore, for the given geometric mean of a required number and nine times the required number is 30 then the required number is equal to 10.

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Answer:zh  0 89 1 87.6

Step-by-step explanation: 0 89 1 87.6

The equation of the parabola that similar to f(x) = [tex]7x^2[/tex] but the vertex is (3, 5) in the standard form is y = [tex]7(x-3)^2[/tex] + 5

The equation of the parabola

f(x) = [tex]7x^2[/tex]

The standard vertex form of a parabola is

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

The coordinates of the vertex of a parabola = (3, 5)

Where (h, k)  is the coordinates

From the given function of the parabola f(x) =  [tex]7x^2[/tex]

The value of a = 7

Substitute the values in the vertex form of a parabola

y = [tex]7(x-3)^2[/tex] + 5

Hence, the equation of the parabola that is similar to f(x) = [tex]7x^2[/tex] but the vertex is (3, 5) in the standard form is y = [tex]7(x-3)^2[/tex] + 5

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The area of the rectangle is increasing at the rate of 156 [tex]cm^{2}[/tex]/s .

Let the length (cm) be l , width (cm) be w , area be A ([tex]cm^{2}[/tex]) and time (s) be t .

Given : dl / dt = 6 cm/s and dw / dt = 8 cm/s

Area of rectangle = l * w

Differentiating wrt. t ,

dA / dt = ( l ) ( dw / dt ) + ( dl / dt ) ( w )

Therefore , dA / dt = 8l + 6w

Hence , when l = 12 cm and w = 10 cm

dA / dt = ( 8 * 12 ) + ( 6 * 10 )

dA / dt = 156 [tex]cm^{2}[/tex]/s .

The area of the rectangle is increasing at the rate of 156 [tex]cm^{2}[/tex]/s .

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Answer: See the image below for the table and graph

==========================================================

Explanation:

We replace x with the values mentioned. Do so one at a time to compute the corresponding y value.

For instance, if x = -2, then...

[tex]\text{y} = 2\text{x}^2\\\\\text{y} = 2(-2)^2\\\\\text{y} = 2(4)\\\\\text{y} = 8\\\\[/tex]

If x = -2, then y = 8. This produces the point (-2,8) which is on the parabola.

We'll write "8" without quotes into the box next to x = -2, as shown in the table diagram below.

Repeat for x values x = -1 through x = 2.

Once we determine those point coordinates, we then plot said points to form the parabola shown below. The more points, the better accurate picture you'll have of the curve. I used GeoGebra to make the graph and table. Desmos is another good option which I recommend.

Step-by-step explanation:

so, we have

6x² + 8xy + 8y²

and

5x² + 3xy + 16y²

we can combine only terms of the same kind (defined by the type and exponent of the used variables).

this is like adding fruit.

e.g. when we have a mixture of 3 apples, 4 oranges and 5 plums, and we add a mixture of 6 apples, 2 oranges and 3 plums - what do we get ?

we get a new mixture of

3+6 = 9 apples

4+2 = 6 oranges

5+3 = 8 plums

and exactly the same thing happens with mixing terms when adding them up.

so, we get

6+5 = 11x²

8+3 = 11xy

8+16 = 24y²

so, the result is

11x² + 11xy + 24y²

it is really that simple.

The selling price of the the purse in a department store is cents.

For the given question-

A purse in such a department store costs $12.50 at wholesale.

The purse will be 140% more expensive at the store.

Then,

140% of 12.50 = 140 x 12.50 / 100

140% of 12.50 = 17.5

Selling price  = percent increase + cost price

Selling price  = 17.5 + 12.5

Selling price  = $30.0

Selling price  = 3000 cents

Thus, the selling price of the the purse in a department store is cents.

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Answer:

5 hours

Step-by-step explanation:

$65 - $15 = $50

$50/$10 = 5

As corresponding angles ∠5 and ∠8 are equal. Hence line x is parallel to line z by converse of corresponding angles theorem.

What does converse of corresponding angles theorem states?

If two lines and a transversal form corresponding angles that are congruent, then the lines are parallel.

How can we show two lines are parallel to each other?

We can show lines are parallel by finding a pair of corresponding angles that are congruent.

Proving if two lines are parallel then third line is parallel too.

According to the given data:

       Therefore, ∠5 ≅ ∠7 (i.e. corresponding angles)

       ∠5 = ∠7

       ∠6 ≅ ∠8 (Corresponding angles are equal)

        ∴ Measure of angles is also equal ⇒ ∠6 = ∠8

       ∠5 = ∠8 (transitive property of equality of angles which says if

                               ∠a = ∠b and ∠b = ∠c then ∠a = ∠c)

       ∠5 ≅ ∠8 (If measure of angles is same then they are congruent)

Therefore, line x || line z

(Converse of the Corresponding Angles Theorem).

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The solution of the inequality 2b + 5 ≤ 30 is b ≤ 12.5

Inequalities refers to some type of equations where the relationship between the left hand side and the right hand side of an equation is expressed in terms of symbols other than equal to

The symbols include

In the problem given the symbol used is less than or equal to and the equation is solved by

2b + 5 ≤ 30

2b + 5 - 5 ≤ 30 - 5

2b ≤ 25

dividing through by 2

2b / 2 ≤ 30 / 2

b ≤ 12.5

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Answer:

[tex]\frac{4+\sqrt{11} }{5}[/tex]

Step-by-step explanation:

to rationalise the denominator, multiply the numerator and denominator by the conjugate of the denominator.

the conjugate of 4 - [tex]\sqrt{11}[/tex] is 4 + [tex]\sqrt{11}[/tex] , then

[tex]\frac{1(4+\sqrt{11}) }{(4-\sqrt{11})(4+\sqrt{11}) }[/tex] ← expand denominator using FOIL

= [tex]\frac{4+\sqrt{11} }{16-11}[/tex]

= [tex]\frac{4+\sqrt{11} }{5}[/tex]

The length of the shorter leg is 9 mm.

The length of the longer leg is 12 mm.

The length of the hypotenuse is 15 mm.

Pythagoras theory applies to every right triangle. If

Step-by-step explanation:

Known

Asked

Answer

[tex]a^2 + b^2 = c^2[/tex]

[tex]a^2 + (a+3)^2 = (a+6)^2[/tex]

[tex]a^2 + a^2 + (2 \times a \times 3) + 3^2 = a^2 + (2 \times a \times 6) + 6^2[/tex]

[tex]2a^2 + 6a + 9 = a^2 + 12a + 36[/tex]

[tex]2a^2 - a^2 + 6a - 12a + 9 - 36 = 0[/tex]

[tex]a^2 - 6a - 27 = 0[/tex]

[tex]a^2 - 9a + 3a - 27 = 0[/tex]

[tex]a \times (a - 9) + 3 \times (a - 9) = 0[/tex]

(a-9) (a+3)=0

a-9=0  or  a+3= 0

a=9     or  a=-3 (impossible)

Shorter leg

a=9 mm

Longer leg

b = a+3

b = 9+3

b = 12 mm

Hypotenuse

c = a+6

c = 9+6

c = 15 mm