PGR is a right-angled triangle.

Work out the size of angle PGR. Give your answer correct to 1 decimal place.

The given statement (A-B) ∩ (C-B) = A - (B ∪ C) is False , and the counter example is given below .

In the question ,

it is given that ,

(A-B) ∩ (C-B) = A - (B ∪ C)  ,

we use Boolean algebra to prove it ,

Solving LHS first ,

= (A-B) ∩ (C-B)

= A ∩ B' ∩ C ∩ B'          .....because (A - B) = A ∩ B'

= A ∩ B' ∩ C                  ..... because B' ∩ B' = B'

Solving RHS ,

we get ,

= A - (B ∪ C)

= A ∩ (B ∪ C)'            ....because (A - B) = A ∩ B'  ,

= A ∩ (B' ∩ C')            .....by DE Morgan's Law

= A ∩ B' ∩ C'

we see that , LHS ≠ RHS ,

So , the statement is False .

The counter Example is ,

Let A = { 1, 2, 3} , B = { 1, 2, 4} , C = { 2, 4, 5}

LHS is = (A - B) ∩ (C - B)

Putting the values,

LHS = { 3 } ∩ { 5 } = ∅

and  RHS = A - (B υ C)

Putting  the  values,

RHS = { 1, 2, 3} - { 1, 2, 4, 5}

= { 3 }

So , LHS ≠ RHS

Therefore , we have proved that the given statement is false using a counter example .

The given question is incomplete , the complete question is

Prove that each statement is true and find a counterexample for each statement that is false. assume all sets are subsets of universal set u .

For all sets A,B,C,

(A-B) ∩ (C-B) = A - (B ∪ C)

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The correlation coefficient that represents the strongest relationship between two variables is -0.75.

In correlation coefficients, the absolute value indicates the strength of the relationship between variables. The strength of the association increases with the absolute value's proximity to 1.

The maximum absolute value in this instance is -0.75, which denotes a significant negative correlation. The relevance of the reverse correlation value of -0.75 is demonstrated by the noteworthy unfavorable correlation between the two variables.

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50 quarts of sparking water and 25 quarts of grape juice are needed for 75 quarts of punch.

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. The numerical relationship between two values demonstrates how frequently one value contains or is contained within another.

Given that a punch recipe calls for 1(¹/₂) quart of sparkling water and 3/4 of a quart of grape juice.

The ratio of sparkling water to grape juice is,

1(¹/₂) : (3/4 quarts) = (3/2) : (3/4) =  2 : 1

The amount sparkling water in the total volume is 2 : (2+1) = 2/3 of the total volume. For a volume of 100 quarts, the sparkling water content is

2/3 · 75quarts = 50 quarts

Then the grape juice content is,

1/3 · 75 quarts = 25 quarts

Therefore, 50 quarts of sparking water and 25 quarts of grape juice are needed for 75 quarts of punch.

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Answer:

Step-by-step explanation:

Use periodic compound formula:

\(F=P\cfrac{(1+r/n)^{nt}-1}{r/n}\)

Substitute the values and calculate:

\(F=200\cfrac{(1+0.032/12)^{12*2}-1}{0.032/12} =4950.12\)     rounded

Step-by-step explanation:

Use periodic compound formula:

\( \sf \: F=P\cfrac{(1+ \frac{r}{n})^{nt}-1}{\frac{r}{n}}\)

Substitute the values and calculate:

\(\sf \: F=200\cfrac{(1+ \frac{0.032}{12})^{12 \times 2}-1}{\frac{0.032}{12}}\)

\(\sf \: F=200\cfrac{( \frac{ 12 + 0.032}{12})^{24}-1}{\frac{0.032}{12}}\)

\(\sf \: F=200\cfrac{( {11.002 }{})^{24}-1}{0.002} \)

\(\sf \: F=200 \times 24.7506\)

\(\sf \: F=4950.12rounded\)

Answer:

$27.25

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Side QP is equal to side QR so 4x-2=10, then just solve for x and you get 3

Answer:

x=3

Step-by-step explanation:

the trangal is isosoles so both sides need to equal 10 so the equation would be 4x-2=10.

frist you would add both sides by 2

4x-2=10

    +2 +2

4x=12

then you would divide both sides by 4

4x/4=12/4

so your anser should be x=3

Answer:

negative

Step-by-step explanation:

Answer:

The graph/slope is negative. The slope intercept form is : y=-2x+5

Step-by-step explanation:

Table is

x   y

0  5

2  3

4  1

The equation of the graph is given by  C = 2V +70 and it costs $670 to order 300 liters of paint.

It is given that the graph of the line passes through the points (0,70) and (40,150)

Now it is given that cost is represented by C and the volume of paint ordered is denoted by V .

Slope of the line = (150-70)/(40-0) = 2

Hence the equation will be

C -70 = 2 (V-0)

or, C = 2V +70

Now we can use this given equation to find the cost that is the dependent variable of all the paint of 300 liters.

Volume of paint that is to be bought = 300litre

Cost of paint =

C = 2×300 +70

C = 670

It costs about $670 for 300 liters of paint.

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Since, the kite is taut the vertical height of the kite from the ground is 66.82 meters

A right angle triangle has one of its angles as 90 degrees. The sides and angles can be found using trigonometric ratios.

Therefore, the string length is the hypotenuse side. The angle formed is between 54 degree to 55 degrees. Therefore,

sin 54.5 = opposite / hypotenuse

sin 54.5 = h / 80

cross multiply

h = 80 × sin 54.5

h = 80 × 0.81411551835

h = 65.1292414685

Therefore, the vertical height of the ground from the ground is as follows:

vertical height = 65. 13 + 1.69 = 66.82 meters

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Answer:

(x - 2) or (x + 5)

Step-by-step explanation:

Step 1: Write quadratic

x² + 3x - 10

Step 2: Factor

(x - 2)(x + 5)

Answer:  x2 + 3x – 10= (x+5)⋅(x−2)= -6

so x=-6

Step-by-step explanation:  "x2"   was replaced by   "x^2".

Factoring  x2+3x-10  

The first term is,  x2  its coefficient is  1 .

The middle term is,  +3x  its coefficient is  3 .

The last term, "the constant", is  -10  

Step-1 : Multiply the coefficient of the first term by the constant   1 • -10 = -10  

Step-2 : Find two factors of  -10  whose sum equals the coefficient of the middle term, which is   3 .

     -10    +    1    =    -9  

     -5    +    2    =    -3  

     -2    +    5    =    3

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -2  and  5  

                    x2 - 2x + 5x - 10

Step-4 : Add up the first 2 terms, pulling out like factors :

                   x • (x-2)

             Add up the last 2 terms, pulling out common factors :

                   5 • (x-2)

Step-5 : Add up the four terms of step 4 :

                   (x+5)  •  (x-2)

            Which is the desired factorization

so (x + 5) • (x - 2)= x=-6

Answer:

\(\frac{5^{12}}{5^{6} } = 5^{2} = 15,625\)

Hope it helps!

Step-by-step explanation:

1) highlight left top, left bottom, middle bottom and right top

2)(-3;-infty)

3)a

4) [-4;-infty)

Answer: 5/13

Step-by-step explanation: i did this IXL and got it right

Answer:

here is the answer

Step-by-step explanation:

except first every statement is right according to y intercept

the moment generating function of x, Mx(t) is:eμ(4t-3) + σ2(4t-3)2/2. Hence, the correct option is (A) eμ(4t-3) + σ2(4t-3)2/2.

Given y ∼ N(μ, σ2) and x = -3y4. We need to find the moment-generating function of x, Mx(t).

The moment generating function of x, Mx(t) is defined as: Mx(t) = E(etx) = E[et(-3y4)]Here, we have x = -3y4So, substituting the value of x, we get: Mx(t) = E[et(-3y4)] = E[e(-3t)y4]

Now, let's find the moment generating function of y, My(t)My(t) = E[ety]Since y ∼ N(μ, σ2), the moment generating function of y, My(t) is given as: My(t) = E[ety] = eμt + σ2t2/2Therefore, we can write: Mx(t) = E[e(-3t)y4] = E[e4log(e(-3t)y)] = E[e4log(e(-3t))e4logy]Since log e(-3t) = -3tMx(t) = E[e-12t.e4y]

Now, using the fact that y ∼ N(μ, σ2), we know that -3y ∼ N(-3μ, 9σ2)

Therefore, Mx(t) = E[e-12t.e4y] = E[e-12t.e4(-3y/3)]= E[e(4t-3) y]By using the moment generating function of y, My(t), we can rewrite the above equation: Mx(t) = E[e(4t-3) y] = My(4t-3)

Substituting My(t) in the above equation, we get: Mx(t) = My(4t-3) = eμ(4t-3) + σ2(4t-3)2/2.

Therefore, the moment generating function of x, Mx(t) is:eμ(4t-3) + σ2(4t-3)2/2. Hence, the correct option is (A) eμ(4t-3) + σ2(4t-3)2/2.

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Answer:

Surface area: 199.27 cm

Volume: 129.8 cm³

Step-by-step explanation:

Answer:

See explanation

Step-by-step explanation:

If A = 30 = 1/2ab = 1/2(5)(b)

60 = 5b

b = 12

a/b = 5/12

a + b = 5 + 12 = 17

Answer:

See explanation

Step-by-step explanation:

If A = 30 = 1/2ab = 1/2(5)(b)

60 = 5b

b = 12

a/b = 5/12

a + b = 5 + 12 = 17

In an orthic triangle, triangle AEF, triangle BFD, and triangle CDE are each similar to triangle ABC.

An orthic triangle is formed by constructing perpendiculars from the vertices of a given triangle to the opposite sides. In this case, we have triangle ABC, and by constructing perpendiculars from the vertices A, B, and C to the opposite sides, we obtain triangle AEF, triangle BFD, and triangle CDE.

To show that triangle AEF, triangle BFD, and triangle CDE are each similar to triangle ABC, we need to demonstrate that their corresponding angles are congruent and their corresponding sides are proportional.

Since triangle ABC and its orthic triangles share the same vertices, their corresponding angles are congruent. The perpendiculars drawn from the vertices of triangle ABC to the opposite sides create right angles, ensuring that the corresponding angles in the orthic triangles are also right angles.

Regarding the sides, the perpendiculars from the vertices of triangle ABC divide the sides into segments. By the properties of perpendicular lines, these segments form similar triangles with triangle ABC. Therefore, the corresponding sides of triangle AEF, triangle BFD, and triangle CDE are proportional to the sides of triangle ABC.

By establishing congruent angles and proportional sides, we can conclude that triangle AEF, triangle BFD, and triangle CDE are each similar to triangle ABC.

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Explanation:

The parallel lines in the diagram indicate that those corresponding angles are congruent, i.e. the same measure.

Set the expressions equal to one another. Solve for x.

9x-4 = 7x+14

9x-7x = 14+4

2x = 18

x = 18/2

x = 9

Answer:

The Answer Is: 33.846153846154

round to the digit needed

Step-by-step explanation:

Answer:

1. Slope is 3/2

2. Slope is -2/3

3. Slope is 3/2

Step-by-step explanation:

Plz mark as Brainliest!

Answer:

Step-by-step explanation:

(-8-4)/(5+3)= -12/8= -3/2

perp. 2/3

y - 4 = 2/3(x + 3)

y - 4 = 2/3x + 2

y = 2/3x + 6

y - 4 = -3/2(x + 3)

y - 8/2 = -3/2x - 9/2

y = -3/2x - 1/2

According to Weber's law, two items must differ in weight by "5 percent"of weight in order to detect a difference.

We are given that Weber's law

For weight discrimination, Weber’s law states that the JND is proportional to the weight of the stimulus.

The JND is defined as the smallest difference between two weights that can be detected by an observer.

The proportionality constant is known as Weber’s fraction and varies depending on the type of stimulus and the sensory modality involved.

For weight discrimination, Weber’s fraction is typically around 2-3%.

This means that two items must differ in weight by approximately 2-3% of their weight in order to detect a difference.

The difference of weight in percent is 5%, the correct option is A.

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Based on the percentage of men workers in the company and the number of non-men workers, the total number of workers is 313.

The second way to solve this problem is using the ratio of non-men to men workers, which is 2:3, to form and solve the equation.

The percentage is the fractional value of a variable in relation to another.

Percentages are like ratios and proportions, which show the numerical relationship between the independent and dependent variables.

The percentage of men workers = 60%

The number of non-men workers = 125

The percentage of non-men workers = 40% (1 - 60%)

If 40% of the workers are 125, the total number of workers, 100% = 313 (125/40% x 100%)

Check:

Men workers = 60% = 188

Non-men workers = 40% = 125

Total = 313

Ratio of men workers to non-men workers = 3:2 (60% : 40%)

The sum of ratios = 5

Non-men workers = 2/5x = 125

x = 125 ÷ 2/5

x = 125 x 5/2

x = 313

Thus, given the percentage of men workers as 60% and the relative number of non-men workers as 125, the total number of workers in the company is 313.

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In a​ company, ​60% of the workers are men. If 125 people work for the company who​ aren't men​, how many workers are there in​ all? Use a pencil and paper. Show two different ways that you can solve this problem.

Answer:

F

Step-by-step explanation:

rise/run is 3/2 which is the number before the x and the y intercept (the last number in the equation) is 3

Answer:

answer is yes,yes, no

Step-by-step explanation:

The area of the rectangular carpet is equivalent to 397.7 ft².

        Area = Length x Breadth

        [A] = [L] x [B]

Given is that the length of the carpet is 24.25 feet and the width is 16.4 feet.

The area of the rectangle is equivalent to -

A = L x B

A = 24.25 x 16.4

A = 397.7 ft²

Therefore, the area of the rectangular carpet is equivalent to 397.7 ft².

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The simplified expression of the expression given as (62)4 is 248

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

(62)4

Remove the bracket and rewrite the expression as a product expression

So, we have the following representation

(62)4 = 62 * 4

Evaluate the products

This gives

(62)4 = 248

The above expression cannot be further simplified

Hence, the solution is 248

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Answer:

Below

Step-by-step explanation:

Equivalent interest rate in decimal form will be   ( 1+i)^n - 1    

   where i = periodic interest in decimal = .05/4     n = periods = 4  per year  

(1+ .05/4)^4 -1 = 5.09 % equivalent interest per year

.05 / 4 = .0125    or    1.25%   16 times   ( 4 times per year x 4 years)  

Answer:

x = 8

Step-by-step explanation:

\(\frac{9x}{4y}=1\)

\(\frac{9x}{4*18} =1\)

9x = 72

x = 8

Answer:

This value is the ratio of the circumference of a circle to its diameter and is called π (Pi).

Step-by-step explanation: