Theorems Involving Similarity
What is the value of x? Enter as decimal.

Answer:

C. 7 - 3 = 4

Step-by-step explanation:

Given

[tex]Dataset: 3, 3, 4, 5, 6, 7, 10[/tex]

Required

The IQR

The IQR is calculated using:

[tex]IQR = Q_3 - Q_1[/tex]

Where:

[tex]Q_3 \to[/tex] Median of the upper [tex]half[/tex]

[tex]Q_1 \to[/tex] Median of the lower [tex]half[/tex]

The dataset has 7 values, so the median is: (7 + 1)/2 =8/2 = 4th position.

Split to two, we have:

[tex]Lower \to 3, 3, 4[/tex]

[tex]Median \to 5[/tex]

[tex]Upper \to 6, 7, 10[/tex]

The lower half has 3 data; So, the median is the 2nd position.

Hence:

[tex]Q_1 = 3[/tex]

The upper half has 3 data; So, the median is the 2nd position.

Hence:

[tex]Q_3 = 7[/tex]

So, the IQR is:

[tex]IQR = Q_3 - Q_1[/tex]

[tex]IQR = 7 - 3[/tex]

[tex]IQR = 4[/tex]

Answer:

7x + y =36

Step-by-step explanation:

( y- y1) = m(x - x1)

y - 8 = -7( x - 4)

y- 8 =-7x +28

y = -7x +36

7x + y =36

Answer:

n = 2.6

Step-by-step explanation:

6.5 : 5

n : 2

6.5/5 = 1.3

2 x 1.3 = 2.6

n = 2.6

i hope this helps

The expression that represents how many more cards Pat has in her collection than Quentin has in his collection is B. (p − q)(x) = 6 + 4x

An expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

Pat's collection is represented as p(x) = 34 + 16x.

Quentin's collection is represented as q(x) = 28 + 12x.

The difference will now be:

= 34 + 16x - (28 + 12x)

= 34 + 16x - 28 - 12x

= 6 + 4x

Therefore, the correct option is B.

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Answer:

=72/5

Step-by-step explanation:

Combine multiplied terms into a single fraction

Multiply all terms by the same value to eliminate fraction denominators

Cancel multiplied terms that are in the denominator

Answer:

2nd one.

Step-by-step explanation:

Answer:

12/35

Step-by-step explanation:

i don’t know the decimal but you can figure that out quickly

Answer:

the answer is 15.3. hope this helps:)

Step-by-step explanation:

Answer:

68% of the individuals in the population have an IQ between 85 and 115.  95% of the population has IQ scores between 70 and 130. 99.7% of the population has IQ scores between 55 and 145.

Step-by-step explanation:

Answer:the answer is 60

Step-by-step explanation:

The question is “what is the length” so what I think we are supposed to do is to add since the height is 4 and the area is 64 so the length has to be 6

Hope I helped

Answer:

35/72 [tex]m^2[/tex]

Step-by-step explanation:

Rectangle Formula: [tex]l*w=Area[/tex]

Switch the variables with the numbers given:

[tex]\frac{5}{9} *\frac{7}{8} =Area[/tex]

Multiply the top and bottom:

5*7 = 35

9*8 = 72

35/72 = Area

Answer:

[tex]-\frac{\sqrt{21}}{2}[/tex]

Step-by-step explanation:

ASTC (I use a sentence to memorize: All Students Take Calculus):

Q1 - All functions are positive

Q2 - Sine is positive (Cosecant is positive as well) (all others negative)

Q3 - Tangent is positive (Cotangent is positive as well) (all others negative)

Q4 - Cosine is positive (Secant is positive as well) (all others negative)

Applying ASTC:

Secant is negative, so it can't be in quadrant 1, and quadrant 4.

Quadrant 2 - Sine and Quadrant 3 - Tangent are left.

Cosecant is positive so it can't be in quadrant 3.

Therefore, angle x is in Quadrant 2 or QII

Secant is hypotenuse / adjacent

5 = hypotenuse (hypotenuse is never a negative number)

-2 = adjacent

use pythagorean theorem to solve for opposite (bc tan = opp / adj)

[tex](-2)^2+o^2=5^2;4+o^2=25;o^2=21;o=\sqrt{21}[/tex]

tanx = [tex]\frac{\sqrt{21}}{-2}=-\frac{\sqrt{21}}{2}[/tex]

Answer:

cos(37°)

Step-by-step explanation:

sin(53°) = cos(90° - 53°)

sin(53°) = cos(37°)

Answer:

a

Step-by-step explanation:

the answer is asset because asset is the best option to be choosed

Answer:

. Bisector cut a segment into 2 ≅ parts. 3. Intersect lines form vertical ∠ ... Prove: EC ≅ FB ... Prove: AD ≅ CB ... or SR ≅ ST Side ... SX + XR ≅ SY + YT.

Step-by-step explanation:

In the given triangles, as per given conditions ΔRSY≅ Δ TSX  by SAS (Side Angle Side) theorem.

" Triangle is defined as the two dimensional geometrical shape with three vertices , three sides, and three angles enclosed in it."

Theorem used

SAS theorem ( Side angle side)

In given triangles, corresponding sides and included angle of one triangle is equals to corresponding sides and included angle of another triangle , then triangles are said to be congruent.

According to the question,

Given,

In a  triangles,

SX ≅ SY              ______ [tex]( 1)[/tex]

XR ≅ YT             ______[tex]( 2 )[/tex]

Add [tex](1)[/tex] and [tex](2)[/tex] we get,

SX + XR ≅ SY + YT

⇒SR ≅ ST           ____[tex](3)[/tex]

In triangle ΔRSY and ΔTSX,

SY ≅ SX ( given)

∠RSY ≅∠TSX ( Common angle)

SR ≅ ST (from [tex](3)[/tex] )

By SAS theorem (side angle side theorem ) stated above we get,

ΔRSY≅ Δ TSX

Hence, ΔRSY≅ Δ TSX by SAS theorem as per the given condition of a triangle.

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Answer:

c: 75 minutes

Step-by-step explanation:

50/4 = 12.5

6 x 12.5 = 75

Answer:

yeah it's B

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

answer is d

Step-by-step explanation:

4+3=7

2i+I=3i

Answer:

7 bookcases

Step-by-step explanation:

Find how many bookcases the custodian can repaint by dividing 5.25 by 0.75:

5.25/0.75

= 7

So, the custodian will be able to repaint 7 bookcases

Answer:

your answer should be, B

Answer:

lol

Step-by-step explanation:

Answer:

a) p(H) = 0.15

,   p(M) = 0.55

,   p(C) = 0.30,

p(S | H) i.e. sunny and hot  = 0.67

P(c | H) i.e. cloudy and hot  = 1 - 0.67 = 0.33

P( S | M) i.e. sunny and mild = 0.36

P(c | M) i.e. cloudy and mild  = 1 - 0.36 = 0.64

P( S | C )i.e. sunny and cold  = 0.33

P( c | C)   = 1 - 0.33 = 0.67

b) ≈ 0.40

c) P ( H | S )  = 0.2513

  P( M | S )   = 0.495

  P(C | S) = 0.2475

d) P( H I c ) = 0.0825

Probability of mild and cloudy= 0.587

Probability of cold and cloudy  = 0.335

e)  No

Step-by-step explanation:

a) List All probabilities given in this problem

lets represent each condition with the first letter

Temperature : Hot ( H ) , mild ( M ) , cold ( C )

weather : Sunny ( S ) and cloudy ( c )

hence the probabilities are ;

p(H) = 0.15,   p(M) = 0.55,   p(C) = 0.30,

p(S | H) i.e. sunny and hot  = 0.67

P(c | H) i.e. cloudy and hot  = 1 - 0.67 = 0.33

P( S | M) i.e. sunny and mild = 0.36

P(c | M) i.e. cloudy and mild  = 1 - 0.36 = 0.64

P( S | C )i.e. sunny and cold  = 0.33

P( c | C) i.e. cloudy and cold  = 1 - 0.33 = 0.67

b) probability of a sunny day

P ( s ) =  P( H ) * P( S | H ) +  P( M ) * P( S | M ) + P(C) * P( S | C)

          = (0.15 * 0.67) + ( 0.55 * 0.36 ) + ( 0.30 * 0.33 )

           = 0.3975 ≈ 0.40

c) Given the weather is sunny ( application of Bayes theorem = P(A and B) / P(B) )

P ( H | S ) = ( 0.15* 0.67 ) / 0.4  

               = 0.2513

P( M | S ) = 0.55 * 0.36 / 0.3975  

               = 0.198 / 0.4

               = 0.495

P(C | S) = 0.3 * 0.33 / 0.4

            = 0.099  = 0.2475

D) Given that the weather is cloudy

P( c ) = 1 - 0.4    = 0.6

P( H I c ) = ( 0.15*0.33) / 0.6

= 0.0825

Probability of mild and cloudy = (0.55*0.64) / 0.6  = 0.587

Probability of cold and cloudy  = ( 0.30 * 0.67) / 0.6  = 0.335

e) The cloudy weather ( c ) is not Independent of the hot weather

because condition for independency ( P(c) x P( H )  = P( c and H) ) is not fulfilled.

Answer:

Median= 14

Mean= 90

Step-by-step explanation:

Median:

Put the numbers in order,

4, 7, 9, 14, 16, 19, 20 Then after that you find the number exactly in the middle. That number ends up to be 14.

Mean:

Add up all of the numbers and then round it to the nearest tenth: 90

Median= 14

Mean= 90

Answer:

C dot plot shows a sample that is most representative of the number of pets in a household.

Answer:

98 degrees

Step-by-step explanation:

first find angle G

53 + 45 + G = 180

subtract 45 and 53 from both sides

G = 82

angle g is supplementary (add up to 180) to x

x +82 = 180

subtract 82 from both sides

x = 98

Answer:

x = 98°

Step-by-step explanation:

There are 180° in a triangle, and 180° on a line.

180° - 53° - 45° = 82°

180° - 82° = 98°

Answer:

(22d-22) cm

Step-by-step explanation:

perimeter= 2×(4d-8+7d-3)

= 2× (11d-11)

(22d - 22) cm

Answer:

(22d-22)cm

Step-by-step explanation:

Perimeter = 2 x (width + Length)

= 2 x [(4d – 8) + (7d – 3)]

= 2 x (11d-11)

= (22d-22)cm

Answer:

f(100) = 160.

Step-by-step explanation:

Linear function:

The equation of a linear function has the following format:

[tex]y = mx + b[/tex]

In which m is the slope(how much f(x) changes when x changes by 1) and b is the y-intercept(value of f(x) when x = 0).

Finding the slope:

Suppose we have two points. The slope is the change in the output divided by the change in the input.

In this question, we have points (45,50) and (60,80).

Change in the output: 80 - 50 = 30

Change in the slope: 60 - 45 = 15

Slope: 30/15 = 2

So

[tex]y = 2x + b[/tex]

Point (45,50)

This means that when [tex]x = 45, y = 50[/tex]. We use this to find the value of b.

[tex]y = 2x + b[/tex]

[tex]50 = 2(45) + b[/tex]

[tex]b = -40[/tex]

So

[tex]y = 2x - 40[/tex]

With y = f(x)

What is the value of f(100)?

This is y when x = 100. So

[tex]f(100) = 2(100) - 40 = 200 - 40 = 160[/tex]

f(100) = 160.

Answer:

Step-by-step explanation: