4) (20 pts) A box contains 5 apples and 6 oranges. Four children each receive a fruit from the box, one after the other, randomly chosen, without replacement. What is the probability that all four children receive the same fruit

Answer:

(Choice A) A graph of an increasing linear function in quadrant 1 with a positive y-intercept.

Step-by-step explanation:

The weight of the sumo wrestler starts at a positive value of 79.5 kilograms, and we are given that the sumo wrestler gains a linear amount of weight per month at 5.5 kilograms per month.

If we were to graph this relationship, the sumo wrestler's weight would be represented on the y-axis, and the amount of time on the x-axis.

So the initial weight would occur at (0, 79.5) which is the positive y-intercept.

And since his weight is increasing at 5.5 kilograms per month, the slope of the linear function is positive.

Hence, the graph of the linear increasing function in quadrant 1 with a positive y-intercept.

Cheers.

Answer:

To find the x-intercept, substitute in  0  for y and solve for x.

To find the y-intercept, substitute in  0 for x  and solve for y.

x-intercept(s):  

(−6,0)

y-intercept(s):  

(0,3)

So I would say -6 and 0 and 2 are in domain

Answer:

-6, 0 ,2 are in the domain

Step-by-step explanation:

The domain is what values that x can take

There are no restrictions on the values that x can take

All real numbers are in the domain

-6, 0 ,2 are in the domain

Answer:

Try to find the unit rate for bulk items that you have for these and then compare all of the prices together.

Answer:

Step-by-step explanation:

The perpendicular bisector of any chord is a diameter and therefore passes through the center of the given circle.

The triangle OMA is thus rectangle.

The locus of M is the circle of diameter OA  with center (1,0) and radius 1.

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

I answered this already a few minutes ago.

Answer:

yes you can

Step-by-step explanation:

you can write algebraic expressions and use variables for the unknown

Answer:

1365

Step-by-step explanation:

We figure out combinations using this formula:    n!

                                                                              r!(n-r)!

n=15

r=4

So n!= 15x14x13x12x11x0x9x8x7x6x5x4x3x2x1

r! = 4x3x2x1 times 15-4!, which is 11! = 11x10x9x8x7x6x5x4x3x2x1

Put this together and you have 15x14x13x12/4x3x2x1=

There are 1365 different ways to award the 4 door prizes to 4 guests from a group of 15 guests.

Combinations are the procedures used in mathematics to pick k things from n different items without replacement.

The following formula computes the combinations of k items from n:

(n, k) = n! / k!×(n-k)!

The number of ways to award the 4 door prizes to 4 guests out of a group of 15 guests is a combinatorial problem that can be calculated using the formula.

Here, n = 15 (the total number of guests) and k = 4 (the number of prizes to be awarded).

So, the number of ways to award the prizes is:

C(15, 4) = 15! / (4! (15 - 4)!)

= 15! / (4! 11!)

= 15 x 14 x 13 x 12 / (4 x 3 x 2 x 1)

= 1365.

Therefore, there are 1365 different ways to award the 4 door prizes to 4 guests from a group of 15 guests.

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Answer:

Step-by-step explanation:

The money Alonso has is $21 which he wants to use to buy eggs and Avocados. The eggs he bought costs $2.50. Therefore the money remaining after the egg is bought is $18.50 (21 - 2.50)

Each bag of avocado cost $5, therefore the number of bags that can be bought with $18.50 is:

Bags of Avocado = $18.50 / $5 = 3.7 = 3 (to the previous whole number).

This means that the maximum number of bags of Avocado that can be bought is 3 bags. It can be represented by the inequality:

Bags ≤ 3  

Answer:

2.50 + 5B ≤ 21;

Step-by-step explanation:

Cost of eggs = $2.50

Cost of avocado = $5 (bag of 3)

Total budgeted amount = $21

Bags of avocado = B

Therefore :

(Cost of eggs + cost of avocado) ≤ total budgeted amount

($2.50 + $5(B)) ≤ 21

2.50 + 5B ≤ 21

5B ≤ 21 - 2.50

5B ≤ 18.50

B ≤ 18.50 / 5

B ≤ 3.7

Therefore the maximum number of bags can purchase is 3(whole number without exceeding $21)

Answer:

385

Step-by-step explanation:

Answer:

≈ 3.6

Step-by-step explanation:

Calculate the distance d using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = (P(5, 1) and (x₂, y₂ ) = Q(3, 4)

d = [tex]\sqrt{(3-5)^2+(4-1)^2}[/tex]

   = [tex]\sqrt{(-2)^2+3^2}[/tex]

   = [tex]\sqrt{4+9}[/tex]

    = [tex]\sqrt{13}[/tex] ≈ 3.6 ( to the nearest tenth )

Answer:

3.6

Step-by-step explanation:

Look above bru

Answer:

Point has co-ordinates, (0, 5)

Step-by-step explanation:

If they cut y-axis, then x = 0

[tex]2y - x = 10 \\ 2y - 0 = 10 \\ 2y = 10 \\ y = 5[/tex]

Answer:

  A. rectangle

  B. any of triangle, quadrilateral, pentagon, hexagon

Step-by-step explanation:

A. A plane perpendicular to the base will intersect 2 adjacent or 2 opposite lateral faces, as well as the two bases. Each plane intersected will result in an edge of the cross sectional figure. The figure will have two pairs of parallel edges, so is a rectangle.

__

B. If the intersecting plane is not constrained to be perpendicular to the base(s), it can intersect 3, 4, 5, or all 6 faces of the prism. Hence, the shape of the cross section can be any of ...

Answer:

A computer parts company wants to make a rectangular memory board that has a perimeter of 28 centimeters and a diagonal length of 10 centimeters. Find the dimensions of the board. Consider the length to be the longer side.: Call the two sides L & W: the perimeter 2L + 2W = 28 Simplify, divide by 2 L + W = 14 L = (14-W); use this form for substitution

Step-by-step explanation:

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

Explanation:

x = width

y = length

both x and y are positive real numbers, and the units of which are in cm.

The perimeter of any rectangle is found by saying

P = 2*(length+width)

P = 2*(x+y)

Plugging in P = 14 leads us to

P = 2*(x+y)

14 = 2*(x+y)

14/2 = x+y

7 = x+y

Solve for one of the variables. Let's say we solve for y. That should get us y = 7-x which we'll use a bit later.

--------------

Notice how the diagonal forms two identical right triangles. The legs of which are x and y as defined earlier. The hypotenuse is 5, which is the diagonal length.

Use the pythagorean theorem to help solve for x

a^2 + b^2 = c^2

x^2 + y^2 = 5^2

x^2 + (7-x)^2 = 25 ... plug in y = 7-x

x^2 + 49 - 14x + x^2 = 25 ... use FOIL rule

2x^2-14x+49 = 25

2x^2-14x+49-25 = 0

2x^2-14x+24 = 0

2(x^2-7x+12) = 0

x^2-7x+12 = 0

(x-3)(x-4) = 0

x-3 = 0 or x-4 = 0

x = 3 or x = 4

If x = 3, then y = 7-x = 7-3 = 4

If x = 4, then y = 7-x = 7-4 = 3

We have this symmetry going on. If x is one of 3 or 4, then y is the other of those values. Because x = 3 and y = 4, or vice versa, this means we have a 3-4-5 right triangle (well to be fair we have two identical copies of such a triangle to form the rectangle).

Therefore, the dimensions of the rectangular board is 3 cm by 4 cm. The order doesn't matter so you could easily say "4 cm by 3 cm" to mean the same thing.

--------------

Check:

P = perimeter

P = 2*(length+width)

P = 2*(x+y)

P = 2*(3+4)

P = 2*7

P = 14

That helps confirm the answer.

Answer:

fourth option

Step-by-step explanation:

∠ FTC = ∠ MTL ( vertical angles )

Since FC and ML are parallel, then

∠ FCT = ∠ TML (corresponding angles )

Thus

Δ TCF ~ Δ TML by the AA postulate

Answer:

[tex]\large \boxed{\mathrm{similar, \ AA \ similarity}, \ \Delta TML}[/tex]

Step-by-step explanation:

The two triangles are similar.

We can prove by angle-angle similarity, in [tex]\mathrm{AA}[/tex] similarity, there are two pairs of congruent corresponding angles in two triangles, this proves the two triangles are similar.

[tex]\angle U[/tex] and [tex]\angle M[/tex] are a pair of congruent corresponding angles.

[tex]\angle V[/tex] and [tex]\angle L[/tex] are a pair of congruent corresponding angles.

Therefore,

[tex]\Delta TUV \sim \Delta TML[/tex]

Answer:

A - L = O

Step-by-step explanation:

A = L + O

Subtract L from each side

A-L = L + O - L

A - L = O

The way that the given formula A = L + O can be rewritten to solve for O is; O = A - L

We are given the formula to find A as;

A = L + O

Now, to make O the subject of the formula, let us use subtraction property of equality to subtract L from both sides to get;

A - L = L + O - L

O = A - L

Thus, the way the formula can be rewritten to solve for O is;

O = A - L

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Answer:

See below.

Step-by-step explanation:

To find roots of an equation, we use this formula:

[tex]z^{\frac{1}{n}}=r^{\frac{1}{n}}(cos(\frac{\theta}{n}+\frac{2k\pi}{n} )+\mathfrak{i}(sin(\frac{\theta}{n}+\frac{2k\pi}{n})),[/tex] where k = 0, 1, 2, 3... (n = root; equal to n - 1; dependent on the amount of roots needed - 0 is included).

In this case, n = 4.

Therefore, we adjust the polar equation we are given and modify it to be solved for the roots.

Part 2: Solving for root #1

To solve for root #1, make k = 0 and substitute all values into the equation. On the second step, convert the measure in degrees to the measure in radians by multiplying the degrees measurement by [tex]\frac{\pi}{180}[/tex] and simplify.

[tex]z^{\frac{1}{4}}=16^{\frac{1}{4}}(cos(\frac{200}{4}+\frac{2(0)\pi}{4}))+\mathfrak{i}(sin(\frac{200}{4}+\frac{2(0)\pi}{4}))[/tex]

[tex]z^{\frac{1}{4}}=2(cos(\frac{5\pi}{18}+\frac{\pi}{4}))+\mathfrak{i}(sin(\frac{5\pi}{18}+\frac{\pi}{4}))[/tex]

[tex]z^{\frac{1}{4}} = 2(sin(\frac{5\pi}{18}+\frac{\pi}{4}))+\mathfrak{i}(sin(\frac{5\pi}{18}+\frac{\pi}{4}))[/tex]

Root #1:

[tex]\large\boxed{z^\frac{1}{4}=2(cos(\frac{19\pi}{36}))+\mathfrack{i}(sin(\frac{19\pi}{38}))}[/tex]

Part 3: Solving for root #2

To solve for root #2, follow the same simplifying steps above but change k  to k = 1.

[tex]z^{\frac{1}{4}}=16^{\frac{1}{4}}(cos(\frac{200}{4}+\frac{2(1)\pi}{4}))+\mathfrak{i}(sin(\frac{200}{4}+\frac{2(1)\pi}{4}))[/tex]

[tex]z^{\frac{1}{4}}=2(cos(\frac{5\pi}{18}+\frac{2\pi}{4}))+\mathfrak{i}(sin(\frac{5\pi}{18}+\frac{2\pi}{4}))\\[/tex]

[tex]z^{\frac{1}{4}}=2(cos(\frac{5\pi}{18}+\frac{\pi}{2}))+\mathfrak{i}(sin(\frac{5\pi}{18}+\frac{\pi}{2}))\\[/tex]

Root #2:

[tex]\large\boxed{z^{\frac{1}{4}}=2(cos(\frac{7\pi}{9}))+\mathfrak{i}(sin(\frac{7\pi}{9}))}[/tex]

Part 4: Solving for root #3

To solve for root #3, follow the same simplifying steps above but change k to k = 2.

[tex]z^{\frac{1}{4}}=16^{\frac{1}{4}}(cos(\frac{200}{4}+\frac{2(2)\pi}{4}))+\mathfrak{i}(sin(\frac{200}{4}+\frac{2(2)\pi}{4}))[/tex]

[tex]z^{\frac{1}{4}}=2(cos(\frac{5\pi}{18}+\frac{4\pi}{4}))+\mathfrak{i}(sin(\frac{5\pi}{18}+\frac{4\pi}{4}))\\[/tex]

[tex]z^{\frac{1}{4}}=2(cos(\frac{5\pi}{18}+\pi))+\mathfrak{i}(sin(\frac{5\pi}{18}+\pi))\\[/tex]

Root #3:

[tex]\large\boxed{z^{\frac{1}{4}}=2(cos(\frac{23\pi}{18}))+\mathfrak{i}(sin(\frac{23\pi}{18}))}[/tex]

Part 4: Solving for root #4

To solve for root #4, follow the same simplifying steps above but change k to k = 3.

[tex]z^{\frac{1}{4}}=16^{\frac{1}{4}}(cos(\frac{200}{4}+\frac{2(3)\pi}{4}))+\mathfrak{i}(sin(\frac{200}{4}+\frac{2(3)\pi}{4}))[/tex]

[tex]z^{\frac{1}{4}}=2(cos(\frac{5\pi}{18}+\frac{6\pi}{4}))+\mathfrak{i}(sin(\frac{5\pi}{18}+\frac{6\pi}{4}))\\[/tex]

[tex]z^{\frac{1}{4}}=2(cos(\frac{5\pi}{18}+\frac{3\pi}{2}))+\mathfrak{i}(sin(\frac{5\pi}{18}+\frac{3\pi}{2}))\\[/tex]

Root #4:

[tex]\large\boxed{z^{\frac{1}{4}}=2(cos(\frac{16\pi}{9}))+\mathfrak{i}(sin(\frac{16\pi}{19}))}[/tex]

The fourth roots of 16(cos 200° + i(sin 200°) are listed above.

Answer:

-7.

Step-by-step explanation:

g(x) = x^2 - 6x - 7

g(2) = 2^2 - 6(2) - 7

= 4 - 12 - 7

= -8 - 7

= -15

f(x) = x + 8

f(-15) = (-15) + 8

= 8 - 15

= -7

Hope this helps!

Rounding to the nearest ten:

28 → 30

188 → 190

250 → 250

101 → 100

122 → 120

Hi,

Answer:

Tachycardia is a fast heart rate

Answer:

if he needs to walk, we can see that between the street and his house he must walk 4 times a distance of 0.5km, so this is a total of 4¨*0.5km = 2km.

Now he has a jet-pack, he can ignore the buildings and just travel in the shorter path, so we can draw a triangle rectangle, in such a way that the hypotenuse of this triangle is the distance between the home and the school.

One of the cathetus is the vertical distance, in this case, is 1km, and the other one is the horizontal distance, also 1km.

So the actual distance is given by the Pythagorean's theorem:

A^2 + B^2 = H^2

Where A and B are the cathetus, and H is the hypotenuse, then:

H^2 = 1km^2 + 1km^2

H = (√2)km = 1.41km.

Now, in the case that he has a jet-pack, he can actually go to the school using this hypotenuse line as his path, so in this case the distance and the displacement would be the same.

Distance: "how much ground an object has covered"

Displacement: "Difference between the final position and the initial position"

When he walks, the distance is 2km, but the displacement is 1.41km

When he uses the jet-pack, both the distance and the displacement are 1.41km

Answer and Step-by-step explanation:

The first thing is we can see in the image, when he walks, that between the house and his school he has to walk four times a distance of 0.5 km.  The result of this is a total of 4¨*0.5 km = 2 km.  The second thing is that he must walk 2 kilometers.  On the other hand, if he has a jetpack, he can simply take the shorter path by ignoring all the buildings.  This idea is where we can draw a triangular rectangle on the map in a way so that the hypotenuse of the triangle is the distance between the school and the home.  As for the Catheti, it is a vertical distance which in this case is two blocks of 0.5 km.  The result is that these catheti have a length of 2*0.5 km = 1 km.  The other is the distance of the horizontal line, which is 1 km.  The absolute distance of this path is given by Pythagorean's theorem, which is A^2 + B^2 = H^2.  Here, A and B are the cathetus, and H is the hypotenuse, then, H^2 = 1 km^2 + 1 km^2.  As well, H = (√2)km = 1.41 km.  Currently, in the situation where he has a jetpack, he can literally fly to the school utilizing this hypotenuse line for the path he would need to follow.  For this specific situation, the displacement, and the distance would be the exact same.  The reason for this is that the definitions of displacement and distance are displacement is the difference between the final position and the initial position and distance is how much area an item has covered.  Also, when he walks, the distance is 2 km and the displacement is 1.41 km.  Also, when he utilizes the jet pack, the distance is equal to the displacement.  Both of these are 1.41 km.

Answer:

y=2

Step-by-step explanation:

A horizontal line has a slope of zero so the x term is zero

y = mx+b

y = b

y must equal a constant

The answer to this equation is 472.

Answer:

472

Step-by-step explanation:

First we make both numbers into wholes by moving the decimal point one place behind.Then divide normally.

8024 ÷ 17 = 472

I hope this helps :)

Answer:

wdym R6

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

6*2

Answer:

Graph is image, and equation is from the work result below:

Step-by-step explanation:

Take two points find the slope and y-intercept:

Slope = -2

Y-intercept = (0,16)

Equation =

y  =  − 2 x  +  16

check work for one point (to make sure equation works):

(2,12)

y = -2x + 16

12 = -2(2) + 16

12 = -4 + 16

12 = 12

The equation is correct: y  =  − 2 x  +  16

Image below are the points given:

Answer:

Since the triangle is a right angled triangle, one of the angles is 90°. In the right angled triangle, the acute angles are in the ratio 4:5. Let the measures of the acute angles of the triangle in degrees be 4k and 5k, where k is a constant.

Step-by-step explanation:

hope it helps.

Answer:

40and50

Step-by-step explanation:

let the acute angles be 4x and 5x then,

4x+5x+90=180 [sum of all angles of a right angled triangle]

or,9x=180-90

or,x=90/9

x=10

4x=4×10=40

5x=5×10=50

Answer:

Step-by-step explanation:

The question has an error. Volume is expressed in cubic units. You probably mean cm³ .

Volume = 8 cm³

Length of each edge = ∛8 = 2 cm

Answer:

2cm

Step-by-step explanation:

Volume of cube=a^3 cubic units

8=a^3

a=cuberoot of 8

which is 2

Answer:

israel spends 2.8 more (units) than peru.

Step-by-step explanation:

11.1 - 8.3 = 2.8, so israel spends 2.8 (units), more on social media.

You are giving the angle and opposite leg.

Using the law of sines:

Sin(angle) = opposite leg / hypotenuse

Sin(30) = 2/ hypotenuse

Hypotenuse = 2/sin(30)

Hypotenuse = 4 meters

The maximum length of the seesaw is : (C). 4 meters

Maximum length can be defined as the total distance between two point in consideration.

Maximum length can also be said to be the total sum of all the length along a distance.

In the case above, the hypotenuse side is the maximum length.

In conclusion, The maximum length of the seesaw is : 4 meters

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Answer:

-39

Step-by-step explanation: