conditions for drawing triangles
side lengths of 6cm and 9 cm , 70° angle​

Answer:

its C. do you need an explanation? i could give one if you want

Step-by-step explanation:

Answer:

c) 0.1

P(5) = 0.1

Step-by-step explanation:

Given data

x  :              0      1      2       3       4      5

p(x):          0.2    0.1  0.3   0.1     0.2    ?

Given data is discrete distribution

if the numbers \(P(x_{i} )\)  i = 1,2,3.....  satisfies the two conditions

i) \(P(x_{i} )\geq 0\)   for all values of 'i'

ii) ∑P(x) = 1

Given data

i) \(P(x_{i} )\geq 0\)   for all values of 'i'

ii)            ∑P(x) = 1

        P(x=1) + P(x=2) +P(x=3) +P(x=4)+P(x=5) =1

⇒      0.2 + 0.1 + 0.3 +0.1 +0.2 + p(X=5) = 1

⇒     0.9 +p(5) =1

⇒             p(5) = 1 -0.9

⇒              P(5) = 0.1

A) The algebraic expression will be 12d + 7 = 91

B) He drives 7 miles per day to work.

For 11 days straight, Ms. Chung drove the same distance every day going to and coming from work.

The distance she drove on Saturday was; 0.9 miles.

The number of miles she drives per day:

84 miles/12

= 7 miles per day

Let the number of miles she travels be day = d

12d + 7 = 91 miles

12d + 7 = 91

12d = 91 - 7

12d = 84

d = 84/12

d = 7 miles per day

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Answer:

DARK Blue! 0.4!

Step-by-step explanation:

Answer:

  c = -41/16

Step-by-step explanation:

You want to solve the 2-step linear equation -7/3=2/3c-5/8.

The two steps for such an equation are ...

Step 1 - add the opposite of the constant on the side with the variable term.

  -7/3 +5/8 = 2/3c -5/8 +5/8

  -41/24 = 2/3c . . . . . . . . . . . . . simplify

Step 2 - multiply by the inverse of the coefficient of the variable.

  (-41/24)(3/2) = (2/3c)(3/2)

  -41/16 = c

Some folks like to solve equations like this by eliminating fractions as a first step. Here, that can be accomplished by multiplying the equation by 24 (the least common denominator).

  (-7/3)(24) = (2/3c)(24) -(5/8)(24) . . . multiply the equation by 24

  -56 = 16c -15 . . . . . . . simplify; fractions are gone

  -41 = 16c . . . . . . . . . step 1, add the opposite of the unwanted constant

  -41/16 = c . . . . . . . . step 2, divide by the coefficient of the variable

To prove that there are only these five regular polyhedra, we can consider Euler's polyhedron formula, which states that for any convex polyhedron, the number of vertices (V), edges (E), and faces (F) satisfy the equation V - E + F = 2.

The five regular polyhedra, also known as the Platonic solids, are the only convex polyhedra where all faces are congruent regular polygons, and the same number of polygons meet at each vertex.

The five regular polyhedra are:

1. Tetrahedron: It has four triangular faces, and three triangles meet at each vertex.

2. Cube: It has six square faces, and three squares meet at each vertex.

3. Octahedron: It has eight triangular faces, and four triangles meet at each vertex.

4. Dodecahedron: It has twelve pentagonal faces, and three pentagons meet at each vertex.

5. Icosahedron: It has twenty triangular faces, and five triangles meet at each vertex.

To prove that there are only these five regular polyhedra, we can consider Euler's polyhedron formula, which states that:

"for any convex polyhedron, the number of vertices (V), edges (E), and faces (F) satisfy the equation V - E + F = 2".

For regular polyhedra, each face has the same number of sides (n) and each vertex is the meeting point of the same number of edges (k). Therefore, we can rewrite Euler's formula for regular polyhedra as:

V - E + F = 2  

=>  kV/2 - kE/2 + F = 2  

=>  k(V/2 - E/2) + F = 2

Since each face has n sides, the total number of edges can be calculated as E = (nF)/2, as each edge is shared by two faces. Substituting this into the equation:

k(V/2 - (nF)/2) + F = 2  

=>  (kV - knF + 2F)/2 = 2  

=>  kV - knF + 2F = 4

Now, we need to consider the conditions for a valid polyhedron:

1. The number of faces (F), edges (E), and vertices (V) must be positive integers.

2. The number of sides on each face (n) and the number of edges meeting at each vertex (k) must be positive integers.

Given these conditions, we can analyze the possibilities for different values of n and k. By exploring various combinations, it can be proven that the only valid solutions satisfying the conditions are:

(n, k) pairs:

(3, 3) - Tetrahedron

(4, 3) - Cube

(3, 4) - Octahedron

(5, 3) - Dodecahedron

(3, 5) - Icosahedron

Therefore, there exist only five regular polyhedra.

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Answer:

5%

Step-by-step explanation:

Answer:

3 is 20% of 15$

Step-by-step explanation:

Answer: The commutative property states that the numbers on which we operate can be moved or swapped from their position without making any difference to the answer. The property holds for Addition and Multiplication, but not for subtraction and division.

Step-by-step explanation:

Hope this is right!!!!

Answer:

D. 12

Step-by-step explanation:

93/3 = 31

155/5 = 31

248/8 = 31

In every case, you see that the number of pages is 31 times the number of hours.

For 372 pages, the number of hours is 372/31 = 12

Check: 372/12 = 31

Answer: D. 12

Answer:

x = -2

Step-by-step explanation:

The line passing through the points (-2, -10) and (-2, -5) is a vertical line because both points have the same x-coordinate (-2).

Therefore, the equation of the line is simple:

x = -2

This means that for any value of y, the corresponding value of x is always -2. Visually, this line looks like a straight vertical line passing through the point (-2, -10) and (-2, -5) on the coordinate plane.

Answer:

Step-by-step explanation:

Answer:

you forgot the pic

Step-by-step explanation:

For the fractions, the calculation of 3/5 of 2/3 of 3/4 of 560 is equal to 168.

To calculate 3/5 of 2/3 of 3/4 of 560, break it down step by step:

Step 1: Calculate 3/4 of 560:

3/4 × 560 = (3 × 560) / 4 = 1680 / 4 = 420

Step 2: Calculate 2/3 of the result from Step 1:

2/3 × 420 = (2 × 420) / 3 = 840 / 3 = 280

Step 3: Calculate 3/5 of the result from Step 2:

3/5 × 280 = (3 × 280) / 5 = 840 / 5 = 168

Therefore, 3/5 of 2/3 of 3/4 of 560 is equal to 168.

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Answer:

The cost for each pound of jelly beans and each pound of almonds is $1.25 and $2.25  respectively.

Step-by-step explanation:

Let the cost for each pound of jelly beans and each pound of almonds be x and y respectively.

ATQ,

For 5 pounds of jelly beans and 3 pounds of almonds, the total cost is $13.

5x+3y = 13 ...(1)

For 2 pounds of jelly beans and 6 pounds of almonds, the total cost is $16.

2x+6y = 16

x + 3y = 8 ....(2)

Subtract equation (2) from (1)

5x+3y-(x + 3y)= 13-8

4x = 5

x = 5/4

x = $1.25

Put the value of x in equation (2) as follows :

1.25 + 3y = 8

3y = 8-1.25

y =$2.25

Hence, the cost for each pound of jelly beans and each pound of almonds is $1.25 and $2.25  respectively.

The solution to the linear system is c = -6 and d = 3.

To solve the linear system using the elimination strategy, we can eliminate one variable by adding or subtracting the equations. Let's solve the first linear system:

(1) 12c + 28d = 12

(2) -20c + 16d = 168

To eliminate one variable, we can multiply equation (1) by 5 and equation (2) by 3, which will result in opposite coefficients for 'c'. This will allow us to eliminate 'c' when adding the equations together:

(1) 60c + 140d = 60

(2) -60c + 48d = 504

Now, we can add the equations:

(60c + 140d) + (-60c + 48d) = 60 + 504

188d = 564

d = 564/188

d = 3

Substituting the value of 'd' back into equation (1):

12c + 28(3) = 12

12c + 84 = 12

12c = 12 - 84

12c = -72

c = -72/12

c = -6

The solution to the linear system is c = -6 and d = 3.

Now let's analyze the second linear system:

(1) 7x - 3y = 43

(2) 7x - 3y = 13

By comparing the two equations, we can see that they have the same coefficients for both 'x' and 'y', and the constant terms on the right side are different. This means the lines represented by the equations are parallel and will never intersect.

The linear system has no solution.

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Answer:

-2x + 6 > 10

Step-by-step explanation:

Let the unknown number be x

the product of x and -2 is -2x

6 more than -2x is written as

-2x + 6

if the result of the above is greater than 10, then

-2x + 6 > 10

Number of seats in each row is 51 given that a rectangular auditorium seats 2244 people and number of seats in each row exceeds the number of rows by 7. This can be obtained by assuming the value of number of seats in each row, forming quadratic equation and using quadratic formula to find root.

Here in the question it is given that,

We have to find the number of seats in each row.

Let us assume that the number of seats in each row be x.

From the given statement, number of seats in each row exceeds the number of rows by 7, we can write that,

Number of seats in one row = Number of rows + 7

x = Number of rows + 7

⇒ Number of rows = x - 7

Total number of seats in the auditorium can be written as,

⇒ (Number of seats in one row)(Number of rows) = Total number of seats

(x)(x - 7) = 2244

x² - 7x = 2244

⇒ x² - 7x - 2244 = 0

By using quadratic formula we can find the root,

x = (-b ± √b² - 4ac)/2a

here in the question, a = 1, b = -7, c = -2244

√b² - 4ac = √(-7)² - 4(1)(-2244)

√b² - 4ac = √49 + 8976

√b² - 4ac = √9025

√b² - 4ac = 95

x = (-b ± √b² - 4ac)/2a

x = (7 ± 95)/2

x = 102/2 or x = -88/2

⇒ x  = 51 or x = -44

Hence number of seats in each row is 51 given that a rectangular auditorium seats 2244 people and number of seats in each row exceeds the number of rows by 7.

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Answer:

False. The center of a semisimple Lie algebra is usually not trivial.

Step-by-step explanation:

The center of a semisimple Lie algebra is the set of elements of the Lie algebra that commute with all other elements in the algebra. In most cases, the center of a semisimple Lie algebra is not trivial, meaning it contains at least one non-zero element. For example, the center of the simple Lie algebra sl(2,C) contains the two-dimensional Lie algebra spanned by the scalar matrices I and -I. The center of the Lie algebra so(5,C) is spanned by the five-dimensional Lie algebra spanned by the matrices diag(1,1,1,-1,-1). These examples demonstrate that the center of a semisimple Lie algebra is usually not trivial.

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Answer:

? = 77°

Step-by-step explanation:

the 3 angles in a triangle sum to 180° , that is

? + 35° + 68° = 180°

? + 103° = 180° ( subtract 103° from both sides )

? = 77°

Answer:77

Step-by-step explanation:

180-103=77

Answer:

a) reject the null hypothesis p1 – p2 = 0

Step-by-step explanation:

This is a hypothesis test for the difference between proportions.

The claim is that the East Coast warehouse proportion of orders delivered in 24 hours is significantly higher than the West Coast warehouse proportion.

Then, the null and alternative hypothesis are:

\(H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2> 0\)

The significance level is 0.05.

The sample 1 (East Coast), of size n1=200 has a proportion of p1=0.95.

\(p_1=X_1/n_1=190/200=0.95\)

The sample 2 (West coast), of size n2=400 has a proportion of p2=0.89.

\(p_2=X_2/n_2=356/400=0.89\)

The difference between proportions is (p1-p2)=0.06.

\(p_d=p_1-p_2=0.95-0.89=0.06\)

The pooled proportion, needed to calculate the standard error, is:

\(p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{190+356}{200+400}=\dfrac{546}{600}=0.91\)

The estimated standard error of the difference between means is computed using the formula:

\(s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.91*0.09}{200}+\dfrac{0.91*0.09}{400}}\\\\\\s_{p1-p2}=\sqrt{0.00041+0.000205}=\sqrt{0.000614}=0.025\)

Then, we can calculate the z-statistic as:

\(z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{0.06-0}{0.025}=\dfrac{0.06}{0.025}=2.4209\)

This test is a right-tailed test, so the P-value for this test is calculated as (using a z-table):

\(\text{P-value}=P(z>2.4209)=0.0079\)

As the P-value (0.0079) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the East Coast warehouse proportion of orders delivered in 24 hours is significantly higher than the West Coast warehouse proportion.

Answer:

x = 42

Step-by-step explanation:

2(x-8) = 68

(2)(x) + (2)(-8) = 68

2x + (-16) = 68

2x - 16 = 68

2x - 16 + 16 = 68 + 16

2x = 84

2x / 2 = 84 / 2

x = 42

Answer:

x=42

Step-by-step explanation:

2(x-8) = 68

2x - 16 = 68

    +16    +16

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

2x = 84

x = 42

hope this helps! :D

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Considering the given stem-and-leaf plot, we have that:

5. The batting average represented by the notation 0.31|2 is of 0.312.

6. The recorded batting averages between 0.28 and 0.29 were of: 0.283, 0.283 and 0.285.

The stem-and-leaf plot lists all the measures in a data-set, with the first number as the key, for example, in this problem:

0.26|1 = 0.261.

Hence the batting average represented by the notation 0.31|2 is of 0.312.

Between 0.28 and 0.29, we have these following batting averages.

The recorded batting averages between 0.28 and 0.29 were of: 0.283, 0.283 and 0.285.

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Answer:

Step-by-step explanation:

ΔFGH ~ΔMNO ( given )

FG / GH = MN / NO. ( by Basic Proportionality Theorm )

so, therefore

6 / 9 = x / 15

x = 6×15 / 9

x = 90 / 9

x = 10

Answer:  -1, -32/40, 14/35

Answer:

(9, 4).

Step-by-step explanation:

To find the corresponding point of the function f(x)+5 when (9,-1) is on the graph of f(x), we simply add 5 to the y-coordinate of the point.

If (9,-1) is on the graph of f(x), then the corresponding point on the graph of f(x)+5 would be (9, -1+5), which simplifies to (9, 4).

Therefore, the corresponding point of the function f(x)+5 is (9, 4).

Answer:

Step-by-step explanation:

Let the point X be represented as (x1, y1) and the point Y be (x2, y2). The distance between the two points is expressed as;

D² = (x2-x1)² - (x2-y2)²

Take the square root of both sides;

√D² = √(x2-x1)² - (x2-y2)²

D = √(x2-x1)² - (x2-y2)²

Also the distance between X and Y can be represented as D = |X-Y|

Answer:

49*0.53=25.97 :)

(edited) ;)

Step-by-step explanation:

53 percent of 49 is approximately equal to 25.97.  the correct answer is option B) 25.97.

To find 53 percent of 49, we can calculate it by multiplying 49 by 0.53 (which is equivalent to 53 divided by 100).

49 * 0.53 = 25.97

Therefore, 53 percent of 49 is approximately equal to 25.97.

So, the correct answer is option B) 25.97.

Options A) 2.597, C) 259.7, and D) 2,597 are not correct since they either incorrectly place the decimal point or exaggerate the value by orders of magnitude. The accurate value is 25.97.

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Given,

The weight of candies normally distributed ;

Mean  weight of candies = 0.8543 g

Standard deviation, σ = 0.0519 g

Sample of candy came from a packet of 469 candies

Net weight of the packet = 400.3 g

Average weight of the candies in the packet;

\(x_{avg} =\) ∑xi/n = 400.3/469 = 0.8535

The population standard deviation (sigma=0.0519 g) is the standard deviation for a confectionery that was chosen at random (sample size n=1).

z = (X - μ) / (σ/√n) = (0.8536 - 0.8535) / (0.0519/√1) = 0.0001/0.0519 = 0.002

P(X > 0.8536) = P(z > 0.002) = 0.4992

A randomly chosen candy has a probability P=0.4992 of weighing at least 0.8536 g.

z = (X - μ) / (σ/√n) = (0.8543 - 0.8535) / (0.0519/√441) = 0.0008/0.0024 = 0.3288

P(X > 0.8543) = P(z > 0.3288) = 0.37115

A sample of 441 candies chosen at random has a probability P=0.3712 of having an average weight of at least 0.8543 g.

z = (X - μ) / (σ/√n) = (0.8556 - 0.8535) / (0.0519/√469) = 0.0021/0.0024 = 0.89

P(X > 0.8556) = P(z > 0.89) = 0.18673

Given that the likelihood is P=0.187, the brand's claim that it delivers the amount promised to customers on the label needs to be reevaluated.

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Answer d=t*v

Step-by-step explanation: the distance is the time spent times 60 miles per hour.