5.1
Mdm Ong had a basket of pears.
When she met Jason, she gave him 10 pears.
When she met Ben, she gave him of the remaining pears in the basket.
2
If Mdm Ong was left with 5 pears in the basket, how many pears did she have
at first?​

Answer:

  the first player wins

Step-by-step explanation:

The first player can always win if they adopt this strategy:

  1. make the first move in the center of the board

  2. make every subsequent move in the position that is the image of the 2nd player's move, reflected across the center.

Hence if the 2nd player can make a move, so can the first.

Answer:

b. 495

Step-by-step explanation:

Given

15, 21, 27, 33, 39, ...., 75

Number of terms = 11

Required

Evaluate

To evaluate means to add up all term of the series above;

The first step is to determine if the series is arithmetic or exponential;

If its arithmetic, then the difference between successive terms must be equal;

In other words;

21 - 15 = 27 - 21 = 33 - 27 = 39 - 33 = 6

Since the result of the above expression gives 6, then it is an arithmetic series;

The sum of n terms of an arithmetic series is calculated as this

[tex]S_n = \frac{n}{2}(a + T_n)[/tex]

Where n = 11

a = First term = 15

T_n = Last term = 75

The formula becomes

[tex]S_{11} = \frac{11}{2}(15 + 75)[/tex]

[tex]S_{11} = \frac{11}{2}(90)[/tex]

[tex]S_{11} = \frac{11 * 90}{2}[/tex]

[tex]S_{11} = \frac{990}{2}[/tex]

[tex]S_{11} = 495[/tex]

Hence, the series when evaluated is 495

Answer:

x = 4

Step-by-step explanation:

By the Alternate Exterior Angles Theorem, we know that the 2 given angles are equal to each other:

22x + 2 = 90

22x = 88

x = 4

Answer:

x = 4

Step-by-step explanation:

When lines are parallel, alternate exterior angles are congruent.  That means that the bottom left angle is 90 degrees.  Thus, 22x + 2 = 90.  Basic math then proves that x = 4.

Answer:

(-5,0)

Step-by-step explanation:

Answer:

(-5,0)

Hope this help!

Answer:

1487

Step-by-step explanation:

The inequality is 0.04m + 10 ≥ 69.48. We use ≥ and not > because it says "least", indicating that we need to use the ≥ sign. Solving for m we get:

0.04m + 10 ≥ 69.48

0.04m ≥ 59.48

m ≥ 1487

The smallest integer that satisfies this inequality is 1487 minutes.

Answer:

The answer is option A.

Step-by-step explanation:

Surface area of a sphere is 4πr²

where r is the radius

radius = diameter / 2

radius = 16/2 = 8cm

Surface area of the sphere is

4π (8)²

= 4(64)π

= 256π

= 804.2cm²

Hope this helps you.

Answer:

C.

Step-by-step explanation:

Answer:

D. The coefficient of the x^2-term must be positive.

Step-by-step explanation:

A. The coefficient of the x2-term can't be zero.

B. There can be no term whose degree is higher than 2.

C. One side of the equation must be zero.

D. The coefficient of the x2-term must be positive.

Quadratic equation is given as:

y=ax^2+bx+c

To use the quadratic formula,we have

ax^2+by+c=0

Coefficient of x^2 can not be equal to 0, that is a can not be equal to 0

There can be no term whose degree is higher than 2. The highest degree in a quadratic equation is 2

One side of the equation must be 0, that is ax^2+by+c=0

Coefficient of x^2 must be positive. The coefficient of x^2 can either be positive or negative. That is, it can either be a or -a

Answer:

5+10/6+12

Step-by-step explanation:

5+10 is 15

6+12 is 18

so that would be 15/8 which is equal to 15/18

That is the best answer but this question doesn't really make sense.

Hope this helps!

Also side note: 5/6 is not proportional to 15/16. 5 * 3=15, but 6*3 does not equal to 16! Please check the question and make sure you typed the right thing! Thanks!

actually 5/6 and 15/16 are not in proportion

since 6*15 is not equal to 16*5

Answer:

[tex]p(0) + p(1) = 2[/tex]

Step-by-step explanation:

=> [tex]p(x) = x^3-x^2+1[/tex]

Putting x = 0 in p(x)

=> [tex]p(0) = (0)^3-(0)^2+1[/tex]

=> [tex]p(0) = 0-0+1[/tex]

=> [tex]p(0) = 1[/tex]

Putting x = 1 in p(x)

=> [tex]p(1) = (1)^3-(1)^2+1[/tex]

=> [tex]p(1) = 1-1+1[/tex]

=> [tex]p(1) = 1[/tex]

So,

=> [tex]p(0)+p(1) = 1+ 1[/tex]

=> [tex]p(0) + p(1) = 2[/tex]

Answer:

12x-15

Step-by-step explanation:

In my expression, I multiplied 12(how much money she makes per hour) by x(the number of hours she worked)  then subtracted 15, which was the fine she had to pay.

Answer:

12x-15

Step-by-step explanation:

I took the test

Answer:

15.  c

16.  b

i hope you figure out later in life how to solve.

Answer:

A, D

Step-by-step explanation:

When you are writing an indirect proof, the first step is to temporarily assume that the opposite of what is given is true.

Because of this, that would mean that you would have to temporarily assume x>6, because the first step is to assume the wrong thing, making the answer A.

Same thing for number 16. It is giving you that n is an odd number, so you can temporarily say that n^2 is an even, since an odd times an odd it always going to equal an even, making the answer D.

Answer:

A. 24/7

What are sine, cosine, and tangent?

SOH - CAH - TOA

sine = opposite/hypotenuse

cosine = adjacent/hypotenuse

tangent = opposite/adjacent (that is not hypotenuse)

Step-by-step explanation:

tanX = ZY/XY = 48/14 = 24/7

Answer:

24/25

Step-by-step explanation:                    opposite side

The tangent of the angle X is tan X = ------------------------ = 48/50 = 24/25

                                                                adjacent side

Answer:

D.(1,-1)

Step-by-step explanation:

A positive plus a negative would be a negative but the negative number is less than the positive then you'll have to subtract them both

Answer:

D. 1, -1

Step-by-step explanation:

Trust me g

Answer:

5√2 Inches

Step-by-step explanation:

By definition of a square, all it's sides are the same measurement (typically signified by the variable s on all sides).

In a triangle (as with a intersection from one corner to the other (diagonal), It would create a right triangle. Remember, the two leg sides are the same measurement (typically placed as 1). There is one triangle side measurement rule:

1 , 1 , √2

Plug in the corresponding numbers to the corresponding units. the 5 inches is a side (not the hypotenuse), so it belongs in the 1:

1 x 5 = 5

1 x 5 = 5

√2 x 5 = 5√2

The measurement of it's diagonal (hypotenuse) is 5√2.

~

Answer:

5[tex]\sqrt{2}[/tex].

Step-by-step explanation:

The angles of a square are right angles. If you draw a diagonal, you'll see that it forms a right triangle. Since the sides of a square are congruent, the right triangle will be a 45-45-90 right triangle. The hypotenuse of a 45-45-90 right triangle is [tex]\sqrt{2}[/tex] times the length (5) .

The measure of the hypotenuse is  5[tex]\sqrt{2}[/tex].

The hypotenuse = diagonal.

The diagonal is  5[tex]\sqrt{2}[/tex].

Answer:

- The coordinates of C is (3,2)

-  The coordinates of D is (11/5,14/5)

Step-by-step explanation:

Given

A(1,4) and B(6,-1)

Required

a. Point C divide AB in ratio 2:3

b. Point D divide AC in ratio 3:2

When endpoints are divided into ratios, the formula to calculate the coordinates is;

[tex](x,y) = (\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n})[/tex]

Solving for (a): Point C divide AB in ratio 2:3

The ratio;

[tex]m : n = 2 : 3[/tex]

For Point A;

[tex]A(x_1,y_1) = (1,4)[/tex]

For Point B;

[tex]B(x_2,y_2) = (6,-1)[/tex]

Substitute m,n,x1,x2,y1,y2 in the ratio formula given above;

[tex]C(x,y) = (\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n})[/tex]

[tex]C(x,y) = (\frac{2 * 6 + 3 * 1}{3+2},\frac{2 *-1 + 3 * 4}{3+2})[/tex]

[tex]C(x,y) = (\frac{12 + 3 }{5},\frac{-2 + 12}5})[/tex]

[tex]C(x,y) = (\frac{15 }{5},\frac{10}5})[/tex]

[tex]C(x,y) = (3,2)[/tex]

The coordinates of C is (3,2)

Solving for (b): Point D divide AC in ratio 3:2

Using the same steps as (a) above;

The ratio;

[tex]m : n = 3:2[/tex]

For Point A;

[tex]A(x_1,y_1) = (1,4)[/tex]

For Point C;

[tex]C(x_2,y_2) = (3,2)[/tex]

Substitute m,n,x1,x2,y1,y2 in the folowing ratio formula;

[tex]D(x,y) = (\frac{mx_2 + nx_1}{m+n},\frac{my_2 + ny_1}{m+n})[/tex]

[tex]C(x,y) = (\frac{3 * 3 + 2 * 1}{2+3},\frac{3 *2 + 2 * 4}{2+3})[/tex]

[tex]D(x,y) = (\frac{9 + 2}{5},\frac{6 + 8}{5})[/tex]

[tex]D(x,y) = (\frac{11}{5},\frac{14}{5})[/tex]

The coordinates of D is (11/5,14/5)

Answer:

3,2 and 2.2,2.8

Step-by-step explanation:

got a 100 on plato

Answer:

50

Step-by-step explanation:

I have set up an equation, where 'x' is the larger number:

x + (x - 12) = 88

Solve for 'x':

x + (x - 12) = 88  

x + x - 12 = 88

2x - 12 = 88

2x -12 + 12 = 88 + 12

2x =  100

2x/2 = 100/2

x = 50

The larger number should be 50.

Answer:50

Step-by-step explanation:

Answer:

n = 8.15

Step-by-step explanation:

3/8 is 4 & 3/5 % of what number?

Rewrite this as:    3/8 is (4  3/5)% of what number?

Convert 4 3/5% into a decimal:  0.046

Then write out and solve the equation 3/8 = 0.046n, where n is the unknown number.

Dividing both sides by 0.046, we get n = 8.15

Answer:

The expected value of the points earned on a single roll in this game is [tex]\dfrac{1}{6} = 0.1667[/tex] .

Step-by-step explanation:

We are given that consider a game in which players roll a number cube to determine the number of points earned. If a player rolls a prime number, that many points will be added to the player’s total. Any other roll will be deducted from the player’s total.

Assuming that the numbered cube is a dice with numbers (1, 2, 3, 4, 5, and 6).

Here, the prime numbers are = 1, 2, 3 and 5

Numbers which are not prime = 4 and 6

This means that if the dice got the number 1, 2, 3 or 5, then that many points will be added to the player’s total and if the dice got the number 4 or 6, then that many points will get deducted from the player’s total.

Here, we have to make a probability distribution to find the expected value of the points earned on a single roll in this game.

Note that the probability of getting any of the specific number on the dice is   [tex]\dfrac{1}{6}[/tex] .

      Numbers on the dice (X)                       P(X)

                      +1                                                 [tex]\frac{1}{6}[/tex]

                      +2                                                [tex]\frac{1}{6}[/tex]

                      +3                                                [tex]\frac{1}{6}[/tex]

                      -4                                                 [tex]\frac{1}{6}[/tex]

                      +5                                                [tex]\frac{1}{6}[/tex]

                      -6                                                 [tex]\frac{1}{6}[/tex]

Here (+) sign represent the addition in the player's total and (-) sign represents the deduction in the player's total.

Now, the expected value of X, E(X)  =  [tex]\sum X \times P(X)[/tex]

   =  [tex](+1) \times \frac{1}{6} +(+2) \times \frac{1}{6} +(+3) \times \frac{1}{6} +(-4) \times \frac{1}{6} +(+5) \times \frac{1}{6} +(-6) \times \frac{1}{6}[/tex]

   =  [tex]\frac{1}{6} + \frac{2}{6} + \frac{3}{6} - \frac{4}{6} + \frac{5}{6} - \frac{6}{6}[/tex]

   =  [tex]\frac{1+2+3-4+5-6}{6}[/tex]

   =  [tex]\frac{11-10}{6}= \frac{1}{6}[/tex]

Hence, the expected value of the points earned on a single roll in this game is  [tex]\frac{1}{6} = 0.1667[/tex] .

Answer:

2 1/3 hours or 2 hours 20 minutes.

51.4 mph to 1 decimal place.

Step-by-step explanation:

Time = distance  speed

First 50 miles time taken = 50 / 60  = 5/6 hours

Second 50 miles  -  time  =  50/40 = 5/4 hours.

Final 20 miles - time taken =  20 / 80 = 1/4 hours.

Total time taken = 5/6 + 5/4 + 1/4

= 5/6 + 6/4

= 10/12 + 18/12

= 28/12

=  7/3 or 2 1/3 hours or 2 hours 20 minutes.

Average speed = total distance / total time

=  120 / 7/3

= 120 * 3/7

=  51.4 mph to 1 decimal place.

Answer:

This is just comparing what is bigger, I don't see what's so hard about it.

Step-by-step explanation:

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Answer: Bill has 12 cards

Alan and Calvin both have 19 cards each.'

Step-by-step explanation:

Let x= Number of cards Bill has.

Then Alan has cards = [tex]2\dfrac{1}{2}x-11=\dfrac{5}{2}x-11[/tex]

Calvin has cards = [tex]1\dfrac{1}{2}x+1=\dfrac{3}{2}x+1[/tex]

Since Alan and Calvin has equal number of cards.

Then, [tex]\dfrac{5}{2}x-11=\dfrac{3}{2}x+1[/tex]

[tex]\Rightarrow\ \dfrac{5}{2}x-\dfrac{3}{2}x=1+11\\\\\Rightarrow\ \dfrac{5-3}{2}x=12\\\\\Rightarrow\ \dfrac{2}{2}x=12\\\\\Rightarrow\ x=12[/tex]

So, Bill has 12 cards

Then, Alan has cards = [tex]\dfrac{5}{2}(12)-11=30-11=19[/tex]

Calvin has cards = [tex]\dfrac{3}{2}(12)+1=18+1=19[/tex]

So, Alan and Calvin both have 19 cards each.

Answer:

y = 2/5x - 2

Step-by-step explanation:

Step 1: Subtract 2x on both sides

-5y = 10 - 2x

Step 2: Divide everything by -5

y = -2 + 2/5x

Step 3: Rearrange

y = 2/5x - 2

Answer:

200 cans are worth $5

Step-by-step explanation:

0.05 : 2

x : 200

2x = 0.05*200

2x = 10

x = 5

Answer:

AA:BB:CC = 5:12:30

Step-by-step explanation:

Let

AA=Amazing Apple

BB=Brilliant Banana

CC=Crazy Coconut

then

Given

AA:CC = 1:6 = 5:30

BB:CC = 2:5 = 12:30

Therefore

AA:BB:CC = 5:12:30

Since there is no common factor among 5,12 and 30, this represents the simplest form.

Answer:

5g = 75

Step-by-step explanation:

1/2x^2 - 2x +1

Step-by-step explanation:

it cannot be negative x as the parabola has a minimum value, the coordinates of turning point is (-1,2)

as it is -1 there has to be a negative sign in equation

so the right one is 2nd one

Answer:

Step-by-step explanation:

the graph is clearly that of a parabola that opens up and has its vertex at (2, -1).  The coefficient of x^2 must be + because the parabola opens up.  

Using the point-slope formula y - k = a(x - h)^2, and letting 2 replace h and -1 replace k, we get:

y + 1 = a(x - 2)^2  or  y = a(x - 2)^2 - 1

Answer:

acute

Step-by-step explanation:

Answer:

hope it will help u .....