1
2
3
4
5
I
Statement
+
ZHKI ZGKH
HJ I GI
H
m2GKH+mZHKI = 180°
m2GKH + m2GKH = 180°
m2GKH = 90°
Reason
Given
Angles forming a linear pair sum to 180°
Definition of congruence

Answer:

  47.5%    (rounds to 48%)

Step-by-step explanation:

You want the probability that a tree has between 240 and 300 apples, given the distribution of numbers of apples is normal with mean 300 and standard deviation 30.

The given diagram shows the center 95% of numbers of apples lies between 240 and 360. The number between 240 and 300 is half that symmetical distribution, so is ...

  95%/2 = 47.5%

The probability a tree will have between 240 and 300 apples is about 47.5%.

__

Additional comment

The figure "95%" is an approximation. A closer value is 95.45%. Hence, a closer value to the probability is 47.7%.

No rounding requirement is shown. To the nearest whole percentage point, the probability would be 48%.

<95141404393>

Below are the right probabilities for each scenario;

8. P(red, then green) [tex]\frac{1}{32}[/tex]; P(yellow, then blue) = [tex]\frac{1}{16}[/tex] and P(blue both times) [tex]\frac{1}{4}[/tex]

9. The probability of choosing a boy then rolling a number that is at most 4 is [tex]\frac{5}{14}[/tex]

10. The probability that both flights will be delayed is [tex]\frac{2}{7}[/tex].

11. P(nickel, then quarter) [tex]\frac{1}{20}[/tex];  P(penny, then not a dime) [tex]\frac{1}{10}[/tex]; P(both dimes)[tex]\frac{3}{20}[/tex]; P(both nickels) [tex]\frac{1}{20}[/tex]

For the compounded probability, we can solve them the following way;

8. a) P(red, then green) = P(red) × P(green) = (2/8) × (1/8) = 1/32

b) P(yellow, then blue) = P(yellow) × P(blue) = (1/8) ×(4/8) = 1/16

c) P(blue both times) = P(blue) × P(blue) = (4/8) ×(4/8) = 1/4

9. There are 28 total students and 6 total outcomes on a standard die.

P(boy, then a number at most 4) = (15/28) × (4/6) = 5/14

10. The probability of the first flight being delayed is 6/14, and the probability of the second flight being delayed is 8/12.

P(both flights delayed) = 6/14 × 8/12 = 2/7

11. There are 25 total coins: 4 pennies, 6 nickels, 10 dimes, and 5 quarters.

a) P(nickel, then quarter)  = (6/25) × (5/24) = 1/20

b) P(penny, then not a dime)  = (4/25) × (15/24) = 1/10

c) P(both dimes) = (10/25) × (9/24) = 3/20

d) P(both nickels) = (6/25) × (5/24) = 1/20

Find more exercises on probability;

https://brainly.com/question/5637693

#SPJ1

The solution of the given equations is: (3,-1).

Here, we have,

from the given graph we get,

1st line passes through ( 0,2 ) and (2,0)

so, equation: y = -x+2 .....1

2nd line passes through ( 0,-4 ) and (4,0)

so, equation: y = x-4 .....2

now, from 1 and 2 we get,

-x + 2 = x -4

or, 2x = 6

or, x = 3

so, we have, y = -1

so, the point of intersection is (3, -1)

Hence, The solution of the given equations is: (3,-1).

To learn more on Equation 0f Straight-Line click:

brainly.com/question/11116168

#SPJ1

Answer: 18

Step-by-step explanation:

Multiply number of each item possible

3*2*3=18

The Triangle Inequality Theorem holds for these values, and only one triangle is possible with these side lengths. Lucas' claim is false.

According to the Triangle Inequality Theorem, any two triangle sides' sums must be greater than the length of the third side. In other words, the following three inequalities must hold for any three positive numbers, a, b, and c:

a+b>c

a+c>b

b+c>a

In this case, a=9, b=13, and c=15. Let's check if the Triangle Inequality Theorem holds for these values:

9+13>15 (true)

9+15>13 (true)

13+15>9 (true)

Therefore, the Triangle Inequality Theorem holds for these values, and only one triangle is possible with these side lengths.

Learn more about Triangle Inequality Theorem here : brainly.com/question/29916338

#SPJ1

If we know that <C is congruent to <E, we can say that: (a). the two triangles are similar by SAS.

from the question, we have the following parameters that can be used in our computation:

The triangles (see attachment)

Two triangles are similar when the ratio of their corresponding sides are equal and their corresponding angles are congruent.

So, we have

Ratio = BC/AC = 6/3 = 2.

Ratio = FE/DE = 4/2 = 2.

Since we know that <C is congruent to <E, we can say that the two triangles are similar by side, angle, side (SAS) criterion.

Read more on triangles here:

https://brainly.com/question/14285697

#SPJ1

Value of an exterior angle of a triangle is equal to the sum of values of two opposite interior angles of a triangle.

[tex]\qquad\displaystyle \tt \dashrightarrow \: 5x + 10 = 40 + 70[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: 5x = 110 - 10[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: 5x = 100[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: x = 100 \div 5[/tex]

[tex]\qquad\displaystyle \tt \dashrightarrow \: x = 20[/tex]

Value of x = 20°

Hey! there . Thanks for your question :)

Answer:

Step-by-step explanation:

In this question we are given with two interior angles of the triangle that are 40° and 70° , also we are given an exterior angle that is (5x + 10)°. And we are asked to find the value of angle x.

Solution :-

For finding the value of angle x , we have to use exterior angle property of triangle which states that sum of opposite interior angles of triangle is equal to the given exterior angle. So :

Step 1: Making equation :

[tex] \longmapsto \: \sf{40 {}^{°} + 70 {}^{°} = (5x + 10) {}^{°} }[/tex]

Solving :

[tex] \longmapsto \: \sf{110 {}{°} = (5x) {}^{°} +10 {}^{°} }[/tex]

Step 2: Subtracting 10 on both sides :

[tex] \longmapsto \sf{ 110 {}^{°} - 10 {}^{°} = 5x + \cancel{10 {}^{°}} - \cancel{10 {}^{°} } }[/tex]

We get ,

[tex] \longmapsto \sf{(5x ){}^{°} = 100 {}^{°} }[/tex]

Step 3: Dividing both sides by 5 :

[tex] \longmapsto \dfrac{ \cancel{5}x {}^{°} }{ \cancel{5}} = \dfrac{ \: \: \: \: \cancel{ 100} {°}^{} }{ \cancel{5} }[/tex]

On cancelling , we get :

[tex] \longmapsto \underline{\boxed{\red{\sf{ \bold{ x = 20 {}^{°} }}}}} \: \: \bigstar[/tex]

Verification :-

For verifying sum of both the interior angles is equal to given exterior angles. As we get the value of x as 20 we need to substitute it's value in place x and then L.H.S must be equal to R.H.S :

Therefore , our answer is correct .

The length of FE is equal to 35 units.

In Mathematics and Geometry, the triangle midpoint theorem states that the line segment which connects the midpoints of two (2) sides of a triangle must be parallel to the third side, and it's congruent to one-half of the third side.

By applying the triangle midpoint theorem to the triangle, we have the following:

AE = 1/2(FE)

BD ≅ FE (midpoints of AC and CE)

BD = FE = 35 units.

Read more on triangle midpoint theorem here: brainly.com/question/12234706

#SPJ1

Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The given picture with Midpoints B, D, and F, AC is 50 units, CE is 60 units, and BD is 35 units. The length of segment FE is determined to be 35 units.

In the given picture, let's label the points as A, B, C, D, E, and F. It is mentioned that points B, D, and F are midpoints.

Given information:

AC = 50

CE = 60

BD = 35

Since B, D, and F are midpoints, we know that BD is equal to half of AC and half of CE. Therefore, BD = AC/2 and BD = CE/2.

We are given that BD = 35, so we can set up the equations:

35 = AC/2    ...(Equation 1)

35 = CE/2    ...(Equation 2)

Let's solve Equation 1 for AC:

AC = 35 * 2

AC = 70

Similarly, solving Equation 2 for CE:

CE = 35 * 2

CE = 70

Now, let's consider triangle AFE. Since B and D are midpoints, we know that BD is parallel to FE, and FD is parallel to AE. Therefore, triangle AFE is similar to triangle ADC.

In similar triangles, corresponding sides are proportional. Hence, we can write the following ratios:

FE/AC = FD/AD

Substituting the known values, we get:

FE/70 = 35/AC

Cross-multiplying, we have:

FE * AC = 70 * 35

Since we know AC is 70, we can solve for FE:

FE = (70 * 35) / 70

FE = 35

Therefore, the length of FE is 35 units.

the given information, in the given picture with midpoints B, D, and F, AC is 50 units, CE is 60 units, and BD is 35 units. The length of segment FE is determined to be 35 units.

To know more about Midpoints .

https://brainly.com/question/28368644

#SPJ8

Answer:

The surface area of the hexagonal pyramid is 313.13 square inches.

Step-by-step explanation:

Hexagonal pyramid,

Surface Area = Area of hexagon base + areas of six triangles

b = 6

h = 12.2 (height of the triangle)

A = [tex]\frac{3\sqrt{3} }{2}b + 6(\frac{1}{2} bh)[/tex]

A = [tex]\frac{3\sqrt{3} }{2}b +3bh[/tex]

A = [tex]\frac{3\sqrt{3} }{2}6 +3*6*12.2\[/tex]

A = 93.53 + 219.6

A = 313.13 square inches

Answer:

It maybe 12,000/120,000

Step-by-step explanation:

12months a year

12+12=24 so,

500×24=12,000

or 120,000

Tamara should expect the sum of the two cubes to be equal to 7 around 30 times when rolling the two number cubes 180 times.

To determine how many times Tamara should expect the sum of the two number cubes to be equal to a certain value, we need to analyze the chart and calculate the probabilities.

Let's examine the chart and count the number of times each sum occurs:

Sum: 2, Occurrences: 1

Sum: 3, Occurrences: 2

Sum: 4, Occurrences: 3

Sum: 5, Occurrences: 4

Sum: 6, Occurrences: 5

Sum: 7, Occurrences: 6

Sum: 8, Occurrences: 5

Sum: 9, Occurrences: 4

Sum: 10, Occurrences: 3

Sum: 11, Occurrences: 2

Sum: 12, Occurrences: 1

Now, let's calculate the probabilities of each sum occurring.

Since there are 36 possible combinations when rolling two number cubes, the probability of each sum is the number of occurrences divided by 36:

Probability of sum 2 = 1/36

Probability of sum 3 = 2/36

Probability of sum 4 = 3/36

Probability of sum 5 = 4/36

Probability of sum 6 = 5/36

Probability of sum 7 = 6/36

Probability of sum 8 = 5/36

Probability of sum 9 = 4/36

Probability of sum 10 = 3/36

Probability of sum 11 = 2/36

Probability of sum 12 = 1/36

To find out how many times Tamara should expect a certain sum when rolling the two number cubes 180 times, we can multiply the probability of that sum by 180.

For example, to find the expected number of times the sum is 7:

Expected occurrences of sum 7 = (6/36) [tex]\times[/tex] 180 = 30

Similarly, we can calculate the expected occurrences for all other sums.

For similar question on probabilities.

https://brainly.com/question/30768613  

#SPJ8

Step-by-step explanation:

1 qt = 2 pts     multiply both sides by two

2 qt = 4 pints

Answer:

A.  19.8

B.  15.9

Step-by-step explanation:

A.  

To find the geometric mean between two numbers, you multiply them together and then take the square root of the product.

28 × 14 = 392

[tex]\sqrt{392}[/tex] = 19.799 ≈ 19.8

B.

7 x 36 = 252

[tex]\sqrt{252}[/tex] = 15.8745 ≈ 15.9

Answer:

B.  90 tickets

Step-by-step explanation:

For t tickets sold, we want the revenue equal to the cost.

25t = 450 +20t

5t = 450 . . . subtract 20t

t = 90 . . . . . divide by 5

90 tickets is the break-even point.

___

:D

Answer:

5.85

Step-by-step explanation:

The numerical value of x in the dimensions of the rectangle is 9.

A rectangle is a 2-dimensional shape with parallel opposite sides equal to each other and four angles are right angles.

Area of a rectangle is expressed as;

A = length × width

From the diagram:

Wdith of the rectangle = x - 2

Length of the rectangle = x + 5

Area = 98 ft²

Since area of a rectangle =  length × width:

98 = ( x - 2 )( x + 5 )

Simplify

( x - 2 )( x + 5 ) = 98

Apply distributive property:

x² + 3x - 10 = 98

x² + 3x - 10 - 98 = 0

x² + 3x - 108 = 0

Factor using AC method:

( x - 9 )( x + 12 ) = 0

Hence:

x - 9 = 0 or x + 12 = 0

x = 9 or x = -12

Since, we are dealing with dimensions, we take the positive value.

Hence, the value of x is 9.

Learn more about area of rectangle here: brainly.com/question/12019874

#SPJ1

Answer:

-6

Step-by-step explanation:

Because two lines that are parallel have the same slope

The graph shows the solution set for -4.4 ≥ 1.6x - 3.6 is Graph I.

To solve the inequality -4.4 ≥ 1.6x - 3.6, we can follow these steps:

Add 3.6 to both sides of the inequality to isolate the term with x:

-4.4 + 3.6 ≥ 1.6x - 3.6 + 3.6

-0.8 ≥ 1.6x

Divide both sides of the inequality by 1.6

-0.8 / 1.6 ≥ 1.6x / 1.6

-0.5 ≥ x

So, the solution to the inequality is x ≤ -0.5.

Now, from the solution the graph for the inequality start with closed dot from 0.5 and move towards the points -0.6, -0.7, -0.8, ....

Thus, the graph shows the solution set for -4.4 ≥ 1.6x - 3.6 is Graph I.

Learn more about Inequality here:

https://brainly.com/question/20383699

#SPJ1

Answer: C-Cylinder

Step-by-step explanation:

In this problem, you are rotating the rectangle on the x axis. If you rotate it along this side, the rectangle makes it a cylinder.

Para aquellos que necesitas este respuesta en español: En este problema, estás girando el rectángulo sobre el eje x. Si lo giras a lo largo de este lado, el rectángulo lo convierte en un cilindro.

I hope this helps!

Answer:

The correct answer is (C), cylinder.

Explanation:

When the rectangle is rotated around the axis shown, it will create a three-dimensional shape with two parallel bases that are connected by a curved surface. This shape is called a cylinder.

Answer:

  x = 2

Step-by-step explanation:

You want the value of x that satisfies x|x| = 4.

The absolute value function splits the domain of the equation into two parts.

For x < 0, the equation is ...

  x(-x) = 4

  x² = -4

There are no real solutions in this domain.

For x ≥ 0, the equation is ...

  x² = 4

  x = √4 = 2

The only solution is x = 2.

__

Additional comment

In the attachment, we have rewritten the equation to ...

  x|x| -4 = 0

The graphing calculator readily identifies x-intercepts, so this is a convenient way to find the solution. You will notice that for x < 0, the graph is of -x²-4, which is never zero.

<95141404393>

Answer:

Step-by-step explanation:

it is only moving 3 to the right, so shift the green dot to (3,0)

I used desmos . com for the graph

The answers are given as:

Ai. The price at Store B would be $583 / 1.21 = $481.82

ii. The price at Store A would be $1200 * 1.21 = $1452.

b. The percent increase in membership from 2020 to 2021 is 13.64%

A.

i. If the price at Store A was $583, the price at Store B would be $583 / 1.21 = $481.82 (approximately).

ii. If the price at Store B was $1200, the price at Store A would be $1200 * 1.21 = $1452.

b. The percent increase in membership from 2020 to 2021 is ((12,500 - 11,000) / 11,000) * 100 = 13.64% (approximately).

Read more about percent increase here:

https://brainly.com/question/11360390

#SPJ1

Answer:

A. mBC = 71

B. mAB = 142

C. AD = 30

D. BD = 30

E. YD = 16

F. DC = 18

Step-by-step explanation:

A. mBC = mAC = 71

B. mAB = mBC + mAC = 71 + 71 = 142

C. AD = AB/2 = 60/2 = 30

D. BD = AD = 30

E. YA^2 = YD^2 + AD^2

YD^2 = YA^2 - AD^2 = 34^2 - 30^2 = 1156 - 900 = 256

YD = √256 = 16

F. DC + YD = YC

DC = YC - YD = 34 - 16 = 18

Answer: the question doesn't give that much information but you would have 7/4 or 1.75 green counters.

Step-by-step explanation: 7/4 as a decimal is 1.75

The area of the slice of pizza is 25.1 inches squared.

The circular pizza has a diameter of 16 inches. Each slice of pizza have a angle of 45 degrees.

Therefore, the area of the slice of pizza can be calculated as follows:

area of the slice of pizza = ∅ / 360 × πr²

where

Therefore,

r = 16  /2

r = 8 inches

area of the slice of pizza = 45 / 360 × 3.14 × 8²

area of the slice of pizza = 45 / 360 × 3.14 × 64

area of the slice of pizza = 9043.2 / 360

area of the slice of pizza = 25.12 inches²

area of the slice of pizza = 25.1 inches²

learn more on area here: https://brainly.com/question/28282127

#SPJ1

The area of the required shaded portion is 123 ft²

Given is figure having some shaded portion we need to find the area of the same,

So, the shaded portion is two right isosceles triangles with equal side measuring 14 ft and 7 ft,

So, to find the same, we will calculate the area of the triangles and add them,

Area of a triangle = 1/2 x base x height

Area of the shaded portion = 1/2 x 7 x 7 + 1/2 x 14 x 14

= 122.5 ft²

≈ 123 ft²

Hence the area of the required shaded portion is 123 ft²

Learn more about area click;

https://brainly.com/question/30307509

#SPJ1

Answer:

When an exponent of the power is an even number and the base is a negative number, the value is always positive.

Autumn's bank registry will be :

Transaction Amount Balance

Paycheck $1275.00 $1275.00

Rent $400.00 $875.00

Utilities $75.00 $800.00

Cell Phone $80.00 $720.00

Subway Pass $120.00 $600.00

Groceries $200.00 $400.00

Work Clothes $100.00 $300.00

Entertainment $100.00 $200.00

Savings $200.00 $0.00

As you can see, Autumn has $0.00 left over at the end of the month. This means that she is spending more money than she is earning. In order to create a budget that works for her, Autumn will need to find ways to cut back on her expenses. Some possible areas where she could cut back include:

Autumn could look for a cheaper apartment or move in with more roommates. Autumn could turn off lights and appliances when she's not using them and seal up any cracks or holes in her apartment to keep the heat in during the winter and the cool air in during the summer.

By cutting back on her expenses, Autumn can create a budget that works for her and save money for the future.

Learn more about transactions on

https://brainly.com/question/1016861

#SPJ1

The value of the expression [tex]n^2 - 11n + 10[/tex] is equivalent to (n - 1)(n - 10).

To find the value of the expression [tex]n^2 - 11n + 10[/tex], we can follow these steps:

Start with the given expression: [tex]n^2 - 11n + 10.[/tex]

Look for any like terms that can be combined. In this case, there are no like terms.

Since there are no like terms, we can simplify further by factoring the expression. We need to find two numbers that multiply to give 10 (the constant term) and add up to -11 (the coefficient of the middle term, which is -11n).

The numbers that satisfy these conditions are -1 and -10, because

(-1) × (-10) = 10 and (-1) + (-10) = -11.

Now we can rewrite the expression using these numbers:

[tex]n^2 - 11n + 10 = (n - 1)(n - 10).[/tex]

So the factored form of the expression is (n - 1)(n - 10).

Therefore, the value of the expression [tex]n^2 - 11n + 10[/tex] is equivalent to (n - 1)(n - 10).

for such more question on equivalent

https://brainly.com/question/9657981

#SPJ8