Gareth buys two oranges. He pays with a £1 coin and gets 52p change. Work out the cost of one orange.

The equivalent expressions for the costs are 8 * (14 + c) and 112 + 8c

The given parameters are:

Number of uniform = 8

Cost of each = $14

The cost of the uniforms and the shorts is then calculated as:

Cost = Number of uniforms * (Cost of uniform + Cost of short)

This gives

Cost= 8 * (14 + c)

Expand

Cost = 112 + 8c

Hence, the equivalent expressions for the costs are 8 * (14 + c) and 112 + 8c

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Answer: b and d

Step-by-step explanation:

Since the roots are x=2 and x=6, we can write the equation as

[tex]f(x)=a(x-2)(x-6)[/tex]

Substituting in the coordinates of the vertex,

[tex]-4=a(4-2)(4-6)\\\\-4=-4a\\\\a=1[/tex]

So, the equation is [tex]f(x)=(x-2)(x-6)[/tex]

On expanding, we get [tex]f(x)=x^2 - 8x+12[/tex]

Answer:

Option A

Step-by-step explanation:

       The ratio of the side of 30-60-90 triangle is x : x√3 : 2x

 The angle opposite to 90° = 2x

            2x = 10

              x = 10÷2

               x = 5

The side opposite to 30° is x which is 5.

The side opposite to  60° is x√3 = 5√3

The ratio of sides of 30-60-90 triangle:

        5 : 5√3 : 10

Answer:

The first one is correct

Step-by-step explanation:

I got a 100 on the test, hope this helps

A scale factor is a contracting scale such that x < 1, where x is the scale factor.

For example, if the scale factor x is less than 1, then it must be decreasing in size, and thus be contracting in size.

But, if the scale factor is greater than 1, then it is expanding in size and increasing.

1) -5 is expanding. It is greater than one.

2) -1/4 is contracting. It is less than one.

3) 3.5 is expanding. It is greater than one.

4) 6/7 is contracting. It is less than one.

The number of different meals possible is 96, computed using combinations.

The combination is a method of choosing a number of articles from a larger set of articles in no particular order.

In the question, we are asked about the different dinner meals possible when a dinner meal is made up of an appetizer, a main course, a dessert, and a drink.

The choices for the appetizer are soup or salad, so the number of ways of choosing an appetizer = 2C1 = 2.

The choices for the main course are chicken, fish, steak, or lobster, so the number of ways of choosing a main course = 4C1 = 4.

The choices for the dessert are ice cream, pie, sorbet, or pastry, so the number of ways of choosing a dessert = 4C1 = 4.

The choices for the drink are coffee, tea, or milk, so the number of ways of choosing a drink = 3C1 = 3.

The total number of ways is the product of all of them.

Therefore, the total number of ways = 2*4*4*3 = 96.

The number of different meals possible is 96, computed using combinations.

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Answer:

(2, -32)

Step-by-step explanation:

1) Expand them.

y = 2(x² - 6x + 2x - 12)

y = 2(x² - 4x - 12)

y = 2x² - 8x - 24.

2) Complete the square to find the vertex.

y = 2([x² - 4x)] - 24

y = 2[(x - 2)² - 4] - 24

y = 2(x - 2)² - 8 - 24

y = 2(x - 2)² - 32

The vertex: (2, -32)

or you can use this: x = -b/2a

x = -(-8)/2(2)

x = 8/4

x = 2

Substitute the value into the original equation for y.

y = 2(2)² - 8(2) - 24

y = 2(4) - 16 - 24

y = 8 - 16 - 24

y = -32

Vertex: (2, -32)

Answer:

  (2, -32)

Step-by-step explanation:

The vertex of the graph of a quadratic equation is on the line of symmetry, halfway between the x-intercepts. It can be found by evaluating the equation at that point.

The given function is written in factored form, so the x-intercepts are easy to find. They are the values of x that make the factors zero:

  (x +2) = 0   ⇒   x = -2

  (x -6) = 0   ⇒   x = 6

The midpoint between these values of x is their average:

  x = (-2 +6)/2 = 4/2

Then the x-coordinate of the vertex, and the equation of the line of symmetry is ...

  x = 2

Using this value of x in the quadratic relation, we find the y-value at the vertex to be ...

  y = 2(2 +2)(2 -6) = 2(4)(-4)

  y = -32

The coordinates of the vertex are (x, y) = (2, -32).

Answer:

[tex]x =\dfrac{20 +\sqrt{454}}{18}, \quad \dfrac{20 -\sqrt{454}}{18}[/tex]

Step-by-step explanation:

Given functions:

  [tex]p(x)=2x-4[/tex]

  [tex]r(x)=\dfrac{6x-1}{9x+1}[/tex]

Solve for p(x) = r(x):

[tex]\begin{aligned}p(x) & = r(x)\\\implies 2x-4 & = \dfrac{6x-1}{9x+1}\\(2x-4)(9x+1)&=6x-1\\18x^2+2x-36x-4&=6x-1\\18x^2-40x-3&=0\end{aligned}[/tex]

As the found quadratic equation cannot be factored, use the Quadratic Formula to solve for x:

Quadratic Formula

[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]

Therefore:

[tex]a=18, \quad b=-40, \quad c=-3[/tex]

Substitute the values of a, b and c into the quadratic formula and solve for x:

[tex]\begin{aligned}\implies x & =\dfrac{-(-40) \pm \sqrt{(-40)^2-4(18)(-3)} }{2(18)}\\\\& =\dfrac{40 \pm \sqrt{1816}}{36}\\\\& =\dfrac{40 \pm \sqrt{4 \cdot 454}}{36}\\\\& =\dfrac{40 \pm \sqrt{4}\sqrt{454}}{36}\\\\& =\dfrac{40 \pm2\sqrt{454}}{36}\\\\& =\dfrac{20 \pm\sqrt{454}}{18}\end{aligned}[/tex]

Therefore, the solutions are:

[tex]x =\dfrac{20 +\sqrt{454}}{18}, \quad \dfrac{20 -\sqrt{454}}{18}[/tex]

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Using proportions, the scenario modeled by the equation 0.6x = 86.46 is:

D. A picnic table is on sale for 40 percent off. The original price of the picnic table is x, $144.10.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

When a product is 40% off, 100 - 40 = 60% of the original price x is paid, hence the expression for the price is:

0.6x.

In this problem, the expression is:

0.6x = 86.46

x = 86.46/0.6

x = 144.1.

Hence option D is correct.

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Using the bisection concept, it is found that the measure of angle PQR is of 130º.

A bisection divides an angle into two equal angles. In this problem, the angles are given as follows:

Hence the value of x is given as follows:

3x + 5 = 2x + 25

x = 20º.

Hence the measure of angle PQR is given as follows:

m<PQR = 3x + 5 + 2x + 25 = 5x + 30 = 5 x 20º + 30º = 130º.

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Answer:

C

Step-by-step explanation:

negative exponent flips the fraction

4^2=16

x^2 becomes x^4

y becomes y^2

The test statistic z will be equal to -0.946 and it shows that there is no significant difference in the proportion of rehires between full time and part time.

Given sample sizes of 833 and 386 and result of samples 434 and 189.

[tex]n_{1} =833, n_{2}=386[/tex]

Proportion  of full time=434/833=0.52

Proportion of part time=189/386=0.49.

Difference in proportion =0.52-0.49

[tex]H_{0}:[/tex]TTF- i∈ rho=0

[tex]H_{1}:[/tex] TTF+i∈ rho≠0.

Mean of difference=0.03

Z=(X-μ)/σ

σ=[tex]\sqrt{0.4517/447}[/tex]

=0.0317

σ=0.0317

z=(0-0.03)/0.0317

=-0.03/0.0317

=-0.317

p value will be =0.1736.

Because p value is greater than 0.01 so we will accept the null hypothesis which shows that there is no significant difference in the proportions.

Hence there is no significant difference in the proportion of rehires between full time and part time.

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Answer:

The distance is 7.3 units.

Step-by-step explanation:

Two given points: (-3, 1) and (4, -1)

[tex]\sf Distance \ between \ two \ points = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

Here given:

Applying the formula:

[tex]\sf d = \sqrt{(4 - (-3))^2 + (-1 - 1)^2}[/tex]

[tex]\sf d = \sqrt{(7)^2 + (-2)^2}[/tex]

[tex]\sf d = \sqrt{49 + 4}[/tex]

[tex]\sf d = \sqrt{53} \ \approx \ 7.28 \ \approx \ 7.3 \ (rounded)[/tex]

Answer:

7.3

Step-by-step explanation:

The distance of a line segment between two points (x1, y1) and (x2, y2) is given by the formula

[tex]d = \sqrt{(x2-x1)^2 + (y2-y1)^2}[/tex]

If we look at the graph,

the leftmost point of the line is at (-3, 1). Let's call this (x1, y1)

the rightmost point is at (4, -1). Let's call this (x2, y2)

Substituting these values into the distance formula gives us

[tex]d = \sqrt{(4-(-3)^2 + (1-(1)^2} \\ \\d = \sqrt{(7)^2 + (-2)^2} \\ \\d = \sqrt{49 + 4} \\\\d = \sqrt{(x2-x1)^2 + (y2-y1)^2}\\\\d = \sqrt{53} = 7.28[/tex]

Rounded to one decimal place, this is 7.3

The statement that is definitely true about x = 2 is Both a(x) and b(x) have the same output value at x = 2.

If we have two functions a(x) and b(x), a statement is made that a(x) = b(x) at x = a, this implies that the values of the functions a(x) and b(x) are equal at x = a.

Then the statement that is definitely true about x = 2 is Both a(x) and b(x) have the same output value at x = 2.

So, the statement that is definitely true about x = 2 is Both a(x) and b(x) have the same output value at x = 2.

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Answer: Algebraic expression

Step-by-step explanation:

Answer:

8x^2

Explanation:

First, do prime factorization of each of the coefficients:

32   ⇒   2^5

24   ⇒   2^3, 3

The greatest common factor (GCF) of the coefficients is 2^3 = 8.

Next, find the GCF of the variables:

x^2

x^2, y

The GCF of the variables is x^2.

Finally, multiply the GCF of the coefficients by the GCF of the variables to get:

8x^2

Answer: 4x^2

Step-by-step explanation: I took the test and got this answer right

Cubing of integers from 1 to 5 will have their cubes in the interval 1 to 200. There are such 5 positive numbers (1,2,3,4,5).

To calculate the variety of integers, locate and subtract the integers of the hobby after which subtract 1. As evidence of the concept, calculate the wide variety of integers that fall between five and 10 on more than a few lines. We realize there are four (6, 7, 8, 9).

All entire numbers are integers (and all herbal numbers are integers), however now not all integers are whole numbers or natural numbers. as an example, -five is an integer but not an entire variety or a natural quantity. An integer is an entire variety (not a fractional number) that can be fine, bad, or 0. Examples of integers are: -5, 1, 5, 8, 97, and 3,043. Examples of numbers that are not integers are: -1.forty three, 1 3/four, three.14, . 09, and five,643.1.

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Answer:

(4,6)

Step-by-step explanation:

To calculate the midpoint of two points, just calculate the arithmetic mean (average) of the x and y values of the two points given. For example, it is easy to see visually that the midpoint of (2, 0) and (4, 0) is (3, 0), since (3,0) falls right in the middle of the two points. However, the way to calculate this would be to take the average of 2 and 4 (3), along with the average of 0 and 0 (0). This process gives us our new point (3, 0). In case this doesn't make sense, here is the formula for the midpoint of two points - (x1,y1) and (x2,y2):

[tex]M=(\frac{x1+x2}{2},\frac{y1+y2}{2} )[/tex]

For this problem, E is (2,4) and F is (6,8). So, the midpoint would be:

[tex](\frac{2+6}{2},\frac{4+8}{2})=(\frac{8}{2},\frac{12}{2})=(4,6)[/tex]

Therefore, the midpoint is (4,6)

The probability that the company will be fined is 0.1587.

From the information given, it was assumed that μ = 500 ml and σ = 10 ml.

Also, the random sample of 5 bottles has a sample mean under 490 ml.

Here, the probability will be:

= P(x < 490)

= P[(z < (490 - 500)/10]

= P (z < -10/10)

= P(z < -1)

Looking at this under the z table, the probability will be 0.1587

The probability is 0.1587.

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Using the ASA congruence theorem, the missing statement in her proof is: A. ΔACD ≅ ΔECB.

Two triangles are congruent by the ASA congruence theorem if they have two pairs of corresponding congruent angles and a pair of included congruent sides.

In the proof given in the diagram, using the ASA congruence theorem, Rowena has been able to prove that ΔACD and ΔECB have two pairs of corresponding congruent angles and a pair of included congruent sides.

Therefore, the missing statement in her proof is: A. ΔACD ≅ ΔECB.

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Answer:

A   see picture

Step-by-step explanation:

The expression 3⁴ × 3² when rewritten in the form 3ⁿ is;  (3²)³

We want to find the expression;

3⁴ × 3²

Now, according to law of exponents, we know that;

y² × y³ = y⁽² ⁺ ³⁾

Thus, applying that exponent form to our question gives us;

3⁴ × 3² = 3⁽⁴ ⁺ ²⁾ = 3⁶

Now, we want to find the answer in the form 3ⁿ. Thus;

3⁶ = (3²)³

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Answer: 3^6 on khan academy

Step-by-step explanation: add the exponents 4 and 2 and you get the exponent 6

The slope m = -1 and the y-intercept = ( 0, 4 ).

The graph is a solid line, shaded area above the boundary line since y is greater than -x + 4.

Given that;

y ≥ -x + 4

First, we use the slope intercept form y = mx + b to determine the slope and y-intercept.

y ≥ -x + 4

y = mx + b

We can see that;

m = -1

b = 4

Hence, the slope m = -1 and the y-intercept = ( 0, 4 ).

The graph is a solid line, shaded area above the boundary line since y is greater than -x + 4.

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Answer:  36 square units

Work Shown:

area = base*height/2

area = 12*6/2

area = 72/2

area = 36

The base and height are always perpendicular to each other. The triangle formula above applies to obtuse triangles, as well as any other type of triangle. It might help to rotate the triangle so that side IJ is at the bottom rather than the top.

Answer:

B) Because of one man’s actions, whales never eat human beings.

Step-by-step explanation:

I'm pretty sure :P

Answer:

Because of one man’s actions, whales never eat human beings.

Step-by-step explanation:

The given relation is function, because the curve of y = p(x) has its exist for every x in its domain(-6, 3) and the range of the function is lies between (-1, 9).

Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in set of y. x is independent while Y is dependent variable.

As Clearly the shows in the graph the structure is decreasing, increasing and then decreasing. And implies, curve is continuous in its limits and for every x (-6,3) there is exist in range of y(-1, 9).

Thus, The given relation is function, and domain is (-6, 3) and the range of the function is lies between (-1, 9).

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Answer:

Invalid statement: There is exactly 1 yellow marble in the box

Step-by-step explanation:

The probability of finding a yellow marble is Py = 1/30, according to the sample. Then, the number of yellow marbles expected to find in the box is:

N x Py > 1 ,

where N = 250 (number of marbles in the box).

Thus, we expect to find more than one yellow marble in the box and the Invalid statement is: "There is exactly 1 yellow marble in the box".

Both the computers will take 18 minutes to do the job together.

The slower computer sends all the company's email in 45 minutes.

The faster computer completes the same job in 30 minutes.

Let's take minutes t  to complete the task together.

As they complete one job, we get the following equation:

[tex]\frac{t}{45}[/tex]+[tex]\frac{t}{30}[/tex]=1

LCM of 45 and 30 is:

45 = 3 x 3 x 5

30 = 2 x 3 x 5

LCM = 2 x 3 x 3 x 5 = 90

Now, solving for t;

⇒[tex]\frac{2t+3t}{90} = 1\\\frac{5t}{90} =1\\5t=90\\[/tex]

Dividing both sides by 5;

[tex]\frac{5t}{5}=\frac{90}{5}[/tex]

We get t = 18

Hence, it will take both the computers 18 minutes to do the job together.

A company has two large computers. The slower computer can send all the company's emails in 45 minutes. The faster computer can complete the same job in 30 minutes. If both computers are working together, how long will it take them to do the job?

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Answer:

1/5

Step-by-step explanation:

P(event) = # of favorable outcomes / # of total outcomes. Multiples of 5 are 5, 10, 15, 20, 25, 30, 35, 40 ... and there are 3 multiples of 5 within 1 to 15. So the # of favorable outcomes is 3. # of total outcomes is 15 because there are 15 equal-sized sections.

P = 3/15 = 1/5

The points where both coordinates are integers lie within the intersection of these circles, including its boundary are 8 points.

To answer the question, we need to find the equation of the circles.

The equation of a circle with center (h, k) and radius r is

(x - h)² + (y - k)² = r²

Given that the first circle has

Its equation is

(x - 0)² + (y - 0)² = 5²

x² + y² = 25  (1)

Given that the second circle has

Its equation is

(x - 8)² + (y - 0)² = 5²

x² - 16x + 64 + y² = 25  (2)

To find the point of intersection of both circles, subtracting (1) from (2), we have

x² - 16x + 64 + y² = 25  (2)

-

x² + y² = 25  (1)

-16x + 64 = 0

-16x = -64

x = -64/-16

x = 4

Substituting x = 4 into (1), we have

x² + y² = 25

4² + y² = 25

16 + y² = 25

y² = 25 - 16

y² = 9

y = ±√9

y = ±3

So, the circles intersect at (4,-3) and (4, 3).

So, all the points that lie within their points of intersection where both coordinates are integers including their points of intersection are

So, there are 8 points.

So, all the points where both coordinates are integers lie within the intersection of these circles, including its boundary are 8 points.

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Answer:

False, False, True

Step-by-step explanation:

Matrix addition or subtraction can only be performed on two matrices if they are the same dimensions.  The number of rows for both must match, and the number of columns for both must match.  If either is different, they cannot be combined with addition or subtraction.

So, the first two questions are false because the first number from each pair doesn't match (and neither does the second number from each pair, but we just need one mismatch for it to fail).

The last question is true because both of the first numbers are a 3, and both of the second numbers are a 4.