Rafael ate one-fourth of a pizza and Rocco ate one-third of it. What fraction of the pizza did they eat?

They ate

Answer:

10

solution

100-98 =2

96-94 = 2

92-90 = 2

8-6 = 2

4-2 =2

2+2+2+2+2=10✓

2 supplementary angles when added together need to equal 180 degrees.

Add:

3x-23 + 2x-12 = 180

Simplify:

5x -35 = 180

Add 35 to both sides:

5x = 215

Divide both sides by 5:

X = 43

Now replace x with 43 in the equation for angle b:

2(43) -12 = 86-12 = 74 degrees

Angle B = 74 degrees

Answer:

Step-by-step explanation:

20 milligrams

Answer:

no

22.25 minutes

Step-by-step explanation:

First determine how long it will take her to read the entire book

20 pages          47 pages

--------------  = ----------------

35 minutes         x minutes

Using cross products

20x = 35*47

20x=1645

Divide by 20

20x/20 = 1645/20

x =82.25 minutes

This is more than 1 hour ( 1 hour = 60 minutes)

82.25 minutes - 60 minutes = 22.25 minutes

She will need 22.25 more minutes

Answer:

1.16 m (approximately)

Step-by-step explanation:

Let x be the width of the path.

Total area  = (5+2x)(3+2x) = 39

Expand and simplify

4x²+ 16x+15-39 = 0

4x² + 16x - 24 = 0

Simplify

x² + 4x -6 = 0

Rational factoring does not work, so use quadratic formula

x = +/- sqrt(10) -2

= 1.16 or -5.16 (reject)

= 1.16 m (approximately)

Step-by-step explanation:

Pupils are right-handed: 30:10x9=27

Answer:

[tex]y=-8x+14[/tex]

Step-by-step explanation:

Hi there!

What we need to know:

1) Determine the midpoint of the line segment

Midpoint: [tex](\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )[/tex] where the coordinates of the endpoints are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]

Plug in the endpoints (-24, -54) and (40, -46)

[tex](\frac{-24+40}{2} ,\frac{-54+(-46)}{2} )\\(\frac{-24+40}{2} ,\frac{-54-46}{2} )\\(\frac{16}{2} ,\frac{-100}{2} )\\(8 ,-50)[/tex]

Therefore, the midpoint of line AB is (8,-50).

2) Determine the slope of the line segment

This will help us find the equation of the perpendicular bisector.

slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] where two given points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]

Plug in the endpoints (-24, -54) and (40, -46)

[tex]= \frac{-46-(-54)}{40-(-24)}\\= \frac{-46+54}{40+24}\\= \frac{8}{64}\\= \frac{1}{8}[/tex]

Therefore, the slope of line AB is [tex]\frac{1}{8}[/tex].

3) Determine the slope of the perpendicular bisector

Because perpendicular lines always have slopes that are negative reciprocals, the slope of the perpendicular bisector is -8 (the negative reciprocal of 1/8). Plug this slope into [tex]y=mx+b[/tex]:

[tex]y=-8x+b[/tex]

4) Determine the y-intercept (b) of the perpendicular bisector

[tex]y=-8x+b[/tex]

Recall that we found the midpoint of line AB, (8,-50). The perpendicular bisector passes through this point. Plug (8,-50) into [tex]y=-8x+b[/tex] and solve for b:

[tex]-50=-8(8)+b\\-50=-64+b[/tex]

Add 64 to both sides to isolate b

[tex]-50+64=-64+b+64\\14=b[/tex]

Therefore, the y-intercept of the line is 14. Plug this back into [tex]y=-8x+b[/tex]:

[tex]y=-8x+14[/tex]

I hope this helps!

Answer:

its number 2 and if its a mutable answers writ 3 also

The probabilities are: (i) P(A) = 1/6

(ii) P(B) = 38/55

(iii) P(A ∩ B) = 1/110

(iv) P(A|B) ≈ 0.00152

To calculate the probabilities, let's first find the total number of ways to choose 3 balls out of the 12 balls.

Total number of ways to choose 3 balls out of 12 = 12C3 = (12 * 11 * 10) / (3 * 2 * 1) = 220

(i) P(A): Probability that all three balls selected are red.

Number of ways to choose 3 red balls out of 7 red balls = 7C3 = (7 * 6 * 5) / (3 * 2 * 1) = 35

P(A) = Number of favorable outcomes / Total number of outcomes = 35 / 220 = 1/6

(ii) P(B): Probability that the sum of the numbers on the three balls is equal to 6.

The possible combinations that sum up to 6 are: (2, 2, 2), (2, 2, 1), and (1, 1, 3).

Number of ways to choose 3 balls such that their sum is 6:

- For (2, 2, 2), we have 1 choice for each color, so 1 * 1 * 1 = 1 way.

- For (2, 2, 1), we have 1 choice for each color, so 1 * 1 * 1 = 1 way.

- For (1, 1, 3), we have 6 choices for the first red ball (all are labeled '1'), 5 choices for the second red ball (since one '1' is already taken), and 5 choices for the green ball labeled '3', so 6 * 5 * 5 = 150 ways.

Total number of ways to choose 3 balls with sum 6 = 1 + 1 + 150 = 152

P(B) = Number of favorable outcomes / Total number of outcomes = 152 / 220 = 38/55

(iii) P(A ∩ B): Probability that all three balls selected are red and the sum of their numbers is equal to 6.

From the above calculations, we know that there are 1 way to choose (2, 2, 2) and 1 way to choose (2, 2, 1) such that all three balls are red and the sum is 6.

P(A ∩ B) = Number of favorable outcomes / Total number of outcomes = 2 / 220 = 1/110

(iv) P(A|B): Probability that all three balls selected are red, given that the sum of their numbers is equal to 6.

P(A|B) = P(A ∩ B) / P(B) = (1/110) / (38/55) = (1/110) * (55/38) ≈ 0.00152 (rounded to five decimal places).

To know more about probabilities:

https://brainly.com/question/29381779

#SPJ2

Answer:

Follows are the solution to the given points:

Step-by-step explanation:

For point a:

When Player A selects Top, Player B selects Left or Right.

Player B selects Right when player A selects Bottom

Thus, player B's best statement is correct.

When player B selects the left, then game A selects the top

When player B selects the right, player A selects the top

Hence, Player A's right response is Top.

For point b:

The main strategy inside the game is Player A, which would be Top. Since he won't choose Below except under situations since the payment to Bottom is below his payoff for Top irrespective of player B.

For point c:

Player A will purely pick Top & Player B right and player A also will pick Top and player B is right. Game A will's pattern. In this case, neither player has the motive to move away. There are two Nash balances since player B is paid the same amount, irrespective of what he's playing any strategy, as player A is always at the top.

For point d:

Consider if player B plays left with "q" probability and right with "1-q" probability. We're done

[tex]2q + 2(1-q) = 3q+4(1-q) \\\\2(1-q) - 4(1-q) = 3q - 2q \\\\-2(1 - q) = q \\\\-2 + 2q = q \\\\2q-q= 2 \\\\q= 2\\[/tex]

It is not possible since q is a chance that really can exceed 1. Hence, for this game, there is no mixed strategy nash balancing.

Answer:

J and K are supplementary

Step-by-step explanation:

Given

The attached image

Required

The true statement

From the attached image, it is hard to determine the values of angles I and L as there are no enough information to determine their values.

However, J and K can be worked easily.

From the image

[tex]J = 65^o[/tex] --- vertically opposite angles

And:

[tex]K + 65^o = 180^o[/tex] ---- angle on a straight line

Substitute: [tex]J = 65^o[/tex]

[tex]K + J = 180^o[/tex]

When two angles add up to 180, the angles are supplementary.

Hence, (c) is correct

Answer:

y = -3x + 7

Step-by-step explanation:

If the line is parallel, it will have the same slope. So, this line will have a slope of -3.

Plug in the slope and given point into y = mx + b, and solve for b:

y = mx + b

4 = -3(1) + b

4 = -3 + b

7 = b

Plug in the slope and y intercept into y = mx + b

y = mx + b

y = -3x + 7

So, the equation is y = -3x + 7

A quadratic function's graph being wide or narrow is determined or depended on a-term:

[tex] \large{y = a {x}^{2} + bx + c}[/tex]

If |a| has a lot of value, for example a = 2 or a = 100. The graph will get narrower if increasing the value of |a|. On the other hand, If |a| has small value, for example a = 1/2 or a = 1/10000. The graph would be wide.

Also it does not matter if a-term is negative or not since a-term being positive or negative determines if a parabola is upward or downward. Only |a| determines how narrow/wide the graph is.

From the question, it is clear that the parabola y = 2x^2 is the narrowest graph since it has the highest |a| value out of all choices.

Answer

Answer:

10145

Step-by-step explanation:

5 times 950 equals 4750

and 6.5 times 830 equals 5395

add first and second value

4750 + 5395 equals 10145

there is no arguing

Answer:

10145 km

Step-by-step explanation:

Time x speed = Distance

5 x 950 = 4750

6.5 x 830 = 5395

add together = 10145

Answer:

a) 64 b) 12

Step-by-step explanation:

32 + 32 = 64

2*3 = 6

6*2 = 12

Answer:

a) 64 b) 12

Step-by-step explanation:

The answer for a is simple the answer is 64 just multipy 32 with 2 and the second one first you have to solve he answer iin the bracket then the answer you get from the bracket you will have to multiply with the number outside the bracket which is 2 and the answer you get will be 12.

Answer:

80

Step-by-step explanation:

more in math means add

if you multiply three by 26 is 78 + 2 would be 80  

PSA im not great in math

Answer:

Option (A)

Step-by-step explanation:

Sasha has an amount of $400 and saves $20 per week.

If we graph the savings of Sasha, her savings per week will be defined by the slope of the line = $20 per week

Similarly, from the graph attached,

Slope of the line given in the graph = Per week savings of Natalia

Slope of line passing through (0, 190) and (2, 210) will be,

Slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

          = [tex]\frac{210-190}{2-0}[/tex]

          = 10

Therefore, per week savings of Natalia = $10

Difference in savings of Sasha and Natalia = 20 - 10 = $10 per week

Here, Sasha shows the greater rate of change by $10 per week

Therefore, Option (A) will be the answer.

Answer:

-2,0 0,-8 , 2,0 hope that helps

Answer:

a) 0.0304 = 3.04% probability a randomly chosen apple exceeds 100 g in weight.

b) The weight that 80% of the apples exceed is of 78.28g.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Weights of apples are normally distributed with a mean of 85 grams and a standard deviation of 8 grams.

This means that [tex]\mu = 85, \sigma = 8[/tex]

a. Find the probability a randomly chosen apple exceeds 100 g in weight.

This is 1 subtracted by the p-value of Z when X = 100. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{100 - 85}{8}[/tex]

[tex]Z = 1.875[/tex]

[tex]Z = 1.875[/tex] has a p-value of 0.9697

1 - 0.9696 = 0.0304

0.0304 = 3.04% probability a randomly chosen apple exceeds 100 g in weight.

b. What weight do 80% of the apples exceed?

This is the 100 - 80 = 20th percentile, which is X when Z has a p-value of 0.2, so X when Z = -0.84.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-0.84 = \frac{X- 85}{8}[/tex]

[tex]X - 85 = -0.84*8[/tex]

[tex]X = 78.28[/tex]

The weight that 80% of the apples exceed is of 78.28g.

Answer:

49.13

Step-by-step explanation:

1/2×6×8=24 3.14×4²/2=23.15

24+23.15=49.13

Step-by-step explanation:

3p + 7q = 55

7p + 7q = 91

(-)

-4p=-36

p=9

q=4

Answer:

p = 9 and q = 4

Step-by-step explanation:

3p + 7q = 55 -- (1)

7p + 7q = 91 -- (2)

(2) - (1) : 4p = 36

               p = 9 -- (3)

Substituting (3) into (1),

27 + 7q = 55

7q = 28

q = 4 -- (4)

Therefore, p = 9 and q = 4

If this helps you, please mark brainliest!

Have a nice day!

Solution :

Given parametric equation for :

[tex]$x=1+2 \sqrt t$[/tex]

[tex]$y=t^3-t$[/tex]

[tex]z=t^3+t[/tex]

The point is (3, 0, 2)

The vector equation is equal to :

[tex]$r(t) = \left<1+2 \sqrt t, t^3 -t, t^3+t \right>$[/tex]

Solving for r'(t) by differentiating each of the components of r(t) w.r.t. to t,

[tex]$r'(t)= \left< \frac{1}{\sqrt t}, \ 3t^2-1, \ 3t^2+1 \right>$[/tex]

The parameter value corresponding to (3, 0, 2) is t = 1. Putting in t=1 into r'(t) to solve for r'(t), we get

[tex]$r'(1) = \left< \frac{1}{\sqrt 1}, \ 3(1)^2-1, \ 3(1)^2+1 \right>$[/tex]

We know that parametric equation for  line through the point [tex]$(x_0, y_0, z_0)$[/tex]  and parallel to the direction vector <a, b, c > are

[tex]$x=x_0+at$[/tex]

[tex]$y=y_0+bt$[/tex]

[tex]z=z_0+ct[/tex]

Now substituting the  [tex]$(x_0, y_0, z_0)$[/tex]   = (3, 0, 2) and  <a, b, c > into x, y and z, respectively to solve for the parametric equation of the tangent line to the curve, we get:

[tex]$x=3+(1)t$[/tex]

x  = 3 + t

y = (0) + (2)t

y = 2t

z = (2) + (4)t

z = 2 + 4t

Answer:

x = 18

Step-by-step explanation:

8 x 18 - 3 = 141

Answer:

(1, 7)

Step-by-step explanation:

The number is n.

7 more than 3 times his

number is at least 10 and at most 28.

Thus;

10 ≤ 3n + 7 ≤ 28

Let's solve individually;

10 ≤ 3n + 7

10 - 7 ≤ 3n

n ≥ 3/3

n ≥ 1

Also,

3n + 7 ≤ 28

3n ≤ 28 - 7

3n ≤ 21

n ≤ 21/3

n ≤ 7

Thus, since n cannot be more than 7 or less than 1, it means in interval Notation, the answer is;

(1, 7)

Answer:

12.94 units

Step-by-step explanation:

Perimeter of ∆ABC = AB + BC + AC

✔️Distance between A(1, 1) and B(3, 5):

[tex] AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]

Where,

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

[tex] B(3, 5) = (x_2, y_2) [/tex]

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

[tex] AB = \sqrt{(2)^2 + (4)^2} [/tex]

[tex] AB = \sqrt{4 + 16} [/tex]

[tex] AB = \sqrt{20} [/tex]

AB = 4.47 units

✔️Distance between B(3, 5) and C(5, 1)

[tex] BC = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} [/tex]

Where,

[tex] B(3, 5) = (x_1, y_1) [/tex]

[tex] C(5, 1) = (x_2, y_2) [/tex]

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

[tex] BC = \sqrt{(2)^2 + (-4)^2} [/tex]

[tex] BC = \sqrt{4 + 16} [/tex]

[tex] BC = \sqrt{20} [/tex]

BC = 4.47 units

✔️Distance between A(1, 1) and C(5, 1):

AC = |1 - 5| = 4 units

✅Perimeter of ∆ABC = 4.47 + 4.47 + 4 = 12.94 units

Answer:

If I'm correct I think 4 is the polygon

Answer:

1) 37

2) 23

3) 4

4) 58

5) 67

6) 7

7) x = 14

  BC = 27

  CD = 61

  BD = 88

Step-by-step explanation:

1) Add them

2) Subtract them

3) Add them and set equal to 36

6x + 1 + x + 7 = 36

4) Add them and set equal to 9x - 39

47 + 3x + 10 = 9x - 39

Substitute x into 3x + 10 to find EF

5) Add them and set equal to 6x - 35

19 + 4x - 20 = 6x - 35

Substitute x into 6x - 35 to find UW

6) Add them and set equal to 7x-27

3x - 5 + x - 1 = 7x - 27

7) Add them. Solve for x and substitute.

4x - 29 + 5x - 9 = 7x - 10

Answer:

a. 74.86%

b. 50%

c. 50%

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Normally distributed with a mean of 49 pounds, and a standard deviation of 6 pounds.

This means that [tex]\mu = 49, \sigma = 6[/tex]

a. Find the percentage of dogs of this breed that weigh less than 53 pounds.

The proportion is the p-value of Z when X = 53. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{53 - 49}{6}[/tex]

[tex]Z = 0.67[/tex]

[tex]Z = 0.67[/tex] has a p-value of 0.7486.

0.7486*100% = 74.86%, which is percentage of dogs of this breed that weigh less than 53 pounds.

b. Find the percentage of dogs of this breed that weigh less than 49 pounds.

p-value of Z when X = 49, so:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{49 - 49}{6}[/tex]

[tex]Z = 0[/tex]

[tex]Z = 0[/tex] has a p-value of 0.5

0.5 = 50% of dogs of this breed that weigh less than 49 pounds.

c. Find the percentage of dogs of this breed that weigh more than 49 pounds.

1 subtracted by the p-value of Z when X = 49, so:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{49 - 49}{6}[/tex]

[tex]Z = 0[/tex]

[tex]Z = 0[/tex] has a p-value of 0.5.

1 - 0.5 = 0.5 = 50% of dogs of this breed that weigh more than 49 pounds.