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Gcse Foundation.

We have P(A ∩ B) is 2/5  and P(A ∪ B) is 5/5.
Lincoln and West Pine high schools offer both hockey and golf.

P(A ∩ B) is the probability that a randomly chosen high school has both a hockey team and a golf team. The probability that a school picked at random offers both hockey and golf is 2/5 (Lincoln and West Pine are the only schools that offer both out of 5 total schools.)

East Valley, Lincoln, West Pine, Adams and North River high schools offer hockey or golf or both.

P(A ∪ B) is the probability that a randomly chosen high school has either a hockey team or a golf team or both. The probability that a school picked at random offers either hockey or golf or both is 5/5 (All 5 high schools in the district offer at least one of the sports.)

Therefore, the correct answers of the problem statement are P(A ∩ B) is 2/5  and P(A ∪ B) is 5/5.

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Answer:

x = -2 to x = 1

Step-by-step explanation:

A function is constant when the y value does not change (i.e. the graph is a horizontal line). This is true between x = -2 and x = 1.

Answer:The Funcation is Constact from x=-5 to x=8

Step-by-step explanation:

Answer:

height 14 cm

Step-by-step explanation:

The volume of the cuboid whose dimensions are  l = 22 cm, b = 14 cm, h = 14 cm is 4312 cu. cm.

What is the Volume of Cuboid?

Volume of cuboid is the total space occupied by the cuboid in a three-dimensional space. A cuboid is a three-dimensional structure having six rectangular faces. These six faces of the cuboid exist as a pair of three parallel faces.

Here, length of cuboid = 22 cm

Breadth of cuboid = 14 cm

Height of cuboid = 14 cm

Volume of Cuboid = Length X Breadth X Height

                                = 22 X 14 X 14 cu. cm.

                                = 4312 cu. cm.

Thus, the volume of the cuboid whose dimensions are  l = 22 cm, b = 14 cm, h = 14 cm is 4312 cu. cm.

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Answer:

The first one 3^7 *1/3-4

Step-by-step explanation:

Answer: 3

Step-by-step explanation:

Answer:

What is the value of A?

–4

–3

3     <<< CORRECT

4

Step-by-step explanation:

Edge 2022

Answer:

Yes

Step-by-step explanation:

[tex] - ( - 3)[/tex]

[tex] - 1 \div - 3[/tex]

[tex]3[/tex]

Answer:

[tex] \approx \: 7.33 \: {cm}^{2} [/tex]

Step-by-step explanation:

Area of the blue shaded region

[tex] = \frac{ \theta}{360 \degree} \times \pi r_1^2 - \frac{ \theta}{360 \degree} \times \pi r_2^2 \\ \\ = \frac{ \pi\theta}{360 \degree} ( r_1^2 - r_2^2) \\ \\ ( r_1 = 4 \: cm, \: \: r_2 = 3\: cm, \: \: \theta = 120 \degree) \\ \\ = \frac{ 3.14 \times 120 \degree}{360 \degree} ( 4^2 - 3^2) \\ \\ = \frac{ 3.14 }{3} \times 7 \\ \\ = \frac{21.98}{3} \\ \\ = 7.32666667 \\ \\ \approx \: 7.33 \: {cm}^{2} [/tex]

An example of x-intercept is (3,0).

Here x=3 is the x-intercept in this line.

By looking at the equation, we may determine the y-intercept when the equation is expressed in the slope-intercept form (y=mx+b). The y-intercept is the value of b. This is due to the fact that the y-intercept occurs when the x value is 0. Y = B when x = 0, since mx = 0 at this point.

We set y = 0 and solve the equation for x to determine the x-intercept. This is due to the fact that the line crosses the x-axis at y=0. If an equation is not in the form y = mx + b, we can still solve for the intercepts by substituting 0 where necessary and then solving for the final variable.

The formula for the x-intercept is y = 0: The x-intercept(s) can be determined by factoring or by employing the quadratic formula because ax2 + bx + c=0.

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Albert has made mistake in double number line in step 3 and 4.

The best time to utilize a double number line diagram is when the quantities have various units. The existence of several, maybe indefinitely numerous pairs of numbers in the same ratio, including those with rational number elements, can be illustrated using double number line diagrams. Unit rates (R) appear in the pair, just like in tables (R, 1).

Numerous equivalent ratios can be discovered using a double number line diagram. For instance, "Mix 5 cups of cranberry juice with 2 cups of soda water," is how a recipe for fizzy juice is written. Cranberry juice and soda water are combined in a 5:2 ratio. Equivalent ratios are produced by multiplying each constituents by the same number.

Albert has made mistake in step 3 and step 4,

Firstly he has written wrong units for the respective number line,

If ratio of 2 parts of blue and 5 parts of red is used(2:5)

The equivalent ratio will be 10:25

We get the desired output by multiplying (2:5) by 5.

The Correct units will be 5 instead of 20

And the number corresponding to 25 will be 10.

The correct double number line is drawn below.

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Answer:

3 and 3/20

Step-by-step explanation:

Answer:

7/25= 14/50 3/10= 15/50 common denominator: 50 so, 7/25 < 3/10

Hello there!

Answer:

[tex]36 - 25x^{2}y^{2}[/tex]

Step-by-step explanation:

We can use the special formula:

[tex](a - b)(a + b) = a^{2} - b^{2}[/tex]

If a = 6 and b = 5xy then:

[tex](6 - 5xy)(6 + 5xy) = 6^{2} - (5xy)^{2} = 36 - 25x^{2}y^{2}[/tex]

This is the final answer

But if we don't know this formula, we can solve it other way:

[tex](6 - 5xy)(6 + 5xy) = 6^{2} + 5xy * 6 - 5xy * 6 - (5xy)^{2} = \\\\= 6^{2} - (5xy)^{2} = 36 - 25x^{2}y^{2}[/tex]

Answer:

58 gold tiles

Step-by-step explanation:

Let silver = s ; purple = p ; gold = g

Number of silver Tiles = 79

44 more silver tiles than purple tiles

Purple tiles = silver tiles - 44

Purple tiles = 79 - 44 = 35

23 more gold tiles than purple tiles:

Number of gold tiles = purples Tiles + 23

Number of gold tiles = 35 + 23 = 58 tiles

If you double the amount of fluid ounces, the amount of cups also double

There is proportional relationship between the number of fluid ounces and the number of cups. So, the number of cups would change by the same factor as the number of fluid ounces.

The donation is proportional to the dinner bill

The donation for a dinner bill of $50 is $9

If there are 8 fluid ounces in one cup

8 : 1 = 16 : x

8/1 = 16/x

8 × x = 16 × 1

8x = 16

x = 16/8

x = 2

The difference between weight = 1

The difference between cost = $0.68 - $0.47

= $0.21

$0.89 - $0.68

= $0.21

$1.10 - $0.89

= $0.21

Cost of mailing 6-ounce letter

1 : 0.47 = 6 : x

1/0.47 = 6/x

1 × x = 6 × 0.47

x = $2.82

The donation for a dinner bill $50 is

Dinner bill : donation

25 : 4.50 = 50 : x

25/4.50 = 50/x

25 × x = 50 × 4.50

25x = 225

x = 225/25

x =$ 9

Therefore, there is a proportional relationship between two quantities if there is an equal change in the values of both quantities.

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Answer:

C)   [tex]\overline {AD}[/tex] ≅ [tex]\overline {AC}[/tex],  [tex]\overline {BD}[/tex] ≅ [tex]\overline {CD}[/tex], [tex]\overline {AD}[/tex] ≅ [tex]\overline {AD}[/tex]

Step-by-step explanation:

From the given diagram, we have;

Segment [tex]\overline {AB}[/tex] in triangle ΔABD is congruent to segment [tex]\overline {AC}[/tex] in triangle ΔACD

Segment [tex]\overline {AD}[/tex] is congruent to segment [tex]\overline {AD}[/tex]  by reflexive property

For ΔABD to be congruent to ΔACD, by the Side-Side-Side, SSS, congruency postulate, all the sides of ΔABD should be congruent to the corresponding side of ΔACD, the required added statement is therefore;

Segment [tex]\overline {BD}[/tex] is congruent to segment [tex]\overline {CD}[/tex]

The correct option is therefore option C;

[tex]\overline {AD}[/tex] ≅ [tex]\overline {AD}[/tex], [tex]\overline {BD}[/tex] ≅ [tex]\overline {CD}[/tex], [tex]\overline {AD}[/tex] ≅ [tex]\overline {AC}[/tex]

Answer:

c

Step-by-step explanation:

Answer:

chick fil a

Step-by-step explanation:

because chick fil a is always right

Answer:

[tex]f = m \times a = 3 \times 6 = 18 \: n[/tex]

Answer:

144 cm

Step-by-step explanation:

Bottom: 4x11 = 44

Side 3x4x1/2 = 6

Other side = 6 (same)

Slant = 3, 4 and the hypotenuse is 5 (pythagroem triple )

5x11 = 55

Back: 3x11= 33

44+6+6+55+33= 144

The solution of the equation is x = -1 and y = -3.

And the intersection point is (-1, -3).

One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation.

And simultaneous equation is the system of equation.

Given system of equations:

y = x-2      ...... equation 1

y = −3x−6  ...... equation 2

To solve the system of equations:

Substitute the value of y from the equation 1 to equation 2,

we get,

x - 2 = -3x - 6

x + 3x = -6 + 2

4x = -4

x = -1

Then y = -1 -2 = -3.

By graphically:

1). Draw the linear equation on the graph.

2). And the intersection point of the lines is a solution of the equation.

3). The solution is x = -1 and y = -3.

The complete graph is given in the attached image.

Therefore, the solution is x = -1 and y = -3.

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Answer:

1. y = -2x - 4

2. y = 3x + 2

3. Horizontal

The vector equivalent to the directed line segment from the point (x1, y1) to the point (x2, y2) is the vector <x2-x1, y2-y1>.

The vector of a directed line segment is the difference between the two endpoints of the line segment. In this case, the endpoints are the points (x1, y1) and (x2, y2). Therefore, the vector of the directed line segment is equal to the vector <x2-x1, y2-y1>.

The vector equivalent of a directed line segment from the point (x1, y1) to the point (x2, y2) is the vector with initial point (x1, y1) and terminal point (x2, y2). This vector is equal to the vector form <x2-x1, y2-y1>, which describes the displacement from the initial point to the terminal point. This vector can also be written in component form, meaning the magnitude of the vector in the x-direction is x2-x1, and the magnitude of the vector in the y-direction is y2-y1.

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Answer:

a)  25

b) the square root of 36 should be done

Step-by-step explanation:

x² - 10x = 11

take half of 10 and square it

x² - 10x + 25 = 11 + 25

(x-5)² = 36

x-5 = [tex]\sqrt{36}[/tex]

x - 5 = 6  and  x - 5 = -6

x = 11  and  x = -1

Answer:

45

Step-by-step explanation:

its going to be the same as the other corner then on the top you have to times by 2 cause it double the size of the bottom

The number √2 is called an irrational number because the value of √2 = 1.41421356... and the the value is non terminating and non repeating .

What are Irrational Numbers ?

The Numbers whose vales are Non Repeating and Non Terminating are called as Irrational Numbers ,

also the numbers that cannot be expressed on the form of [tex]\frac{p}{q}[/tex] are called as Irrational Numbers .

the number is given as √2 ;

we know that the values of √2 is = 1.41421356... ,

we see that the the value is non terminating and the numbers after decimal point are non repeating ,

Therefore  , the number √2 is an irrational number .

The given question is incomplete , the complete question is

Why the number √2 is called a Irrational Number ?

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Answer:

it is C.

Step-by-step explanation:

it is C.

The transformation is 6 units left and 2 units down and reflection about x = -2 thus option (C) is correct.

Transformation is rearranging a graph by a given rule it could be either increment of coordinate or decrement or reflection.

Reflection is a mirror image of a graph about any axis.

If we reflect any graph about y = x then the coordinate will interchange it that (x,y) → (y,x).

As the given XYZ.

Take coordinate of  Y(4,3)

Now, take it back 6 units and 2 units down as,

R(4 - 6,3 - 2) = R(-2,1)

Now, reflect the entire image about x = -2 gives the same image as OQR.

Hence "The transformation is 6 units left and 2 units down and reflection about x = -2"

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The values of k are 3 and −1.

Note: The equation taken here is 4x^2 −2(k+1)x+(k+1)=0

Given: Equation 4X^2−2(k+1)x+(k+1)=0 has real and equal roots i.e., its discriminant is zero.

⇒b2−4ac=0

[An expression that can be produced from the square of a binomial equation is a perfect square trinomial. A perfect square trinomial is a formula that has the elements ax^2 + bx + c and satisfies the condition b^2 = 4ac. The roots of the quadratic equation ax2 + bx + c = 0 are real and equivalent if the discriminant is equal to zero (b2 - 4ac = 0), a, b, and c are real values, and a0.]

For given equation, a=4,  b=2(k+1),c=(k+1)

(2(k+1))^2 −4.4(k+1)=0

⇒(2k+2)^2−16(k+1)=0

⇒4k2+8k+4−16k−16=0

⇒4k2−8k−12=0

⇒4(k2−2k−3)=0

⇒k2−2k−3=0

⇒k2−3k+k−3=0

⇒k(k−3)+1(k−3)=0

⇒(k−3)(k+1)=0

⇒k−3=0   and   k+1=0

⇒k=3   and  k=−1

So, the values of k are 3 and −1.

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270 mins - 10 laps

xmins -5 laps

(cross multiply)

270*5=10x

10x=1350

x= 1350/10

x=135 mins

With a mass of 50 kg, Becky used 588 watts power to sprint up a 3.0 m high set of stairs in 2. 5 seconds. She is able to run up a 4.5 m high flight of stairs in 3.75 s.

Work (in joules) equals your weight (in newtons) x the height of the stairs (in meters.) The power you now possess is equal to the sum of your labor times the duration of that labor, or: Work (measured in joules) divided by time equals power, measured in watts (in seconds.)

Given that mass of Becky is 50 Kg

gravity of earth is 9.8 m/s²

height of stairs is 3.0 m

time taken to run up in stairs is 2.5 s

Power = work done/ time taken

P = (50*9.8*3.0)/2.5

P = 1470/2.5

P = 588 watt

Becky is able to run up a 3.0 m high flight of stairs in 2.5 s

She is able to run up a 4.5 m high flight of stairs in t =  (2.5 * 4.5)/3

t = 11.25/3

t = 3.75 s

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