50 pts if you answer correctly

STATEMENT REASON
1. 1.
2. 2. 3rd Angle Theorem
4. 4.

The truth value of the ~[P v (Q v R)] >~ (S v P) is true.

Truth-value, in logic, is the degree to which a particular proposition or assertion is true (T or 1) or false (F or 0). Because the truth-value of a compound proposition is a function of, or a quantity depending upon, the truth-values of its component components, logical connectives like disjunction and negation can be conceived of as truth-functions.

Given, ~[P v (Q v R)] >~ (S v P) since P v (Q v R) is true, thus ~ [ P v ( Q v R ) ] is false, therefore the implication is true.

⇒~[T v (F v T)] >~ (F v T)

⇒[F v (F v T)]>(T v T)

⇒[F v (F v T)]>(T v T)

⇒F v T

⇒T

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The equation of the line normal to the curve y = square root(3x² + 2x) at point (2,4) is given as follows:

y - 4 = -4/7(x - 2).

The equation of the line normal to a curve follows the point-slope definition of a linear function, given as follows:

y - y' = m(x - x').

The function in this problem is defined as follows:

y = square root(3x² + 2x).

Then the derivative of the function, applying the chain rule, is given as follows:

y' = (6x + 2)/(2 x square root(3x² + 2x))

y' = (3x + 1)/square root(3x² + 2x)

At x = 2, the numeric value of the derivative is of:

y' = 7/square root(16) = 7/4.

The slope of the normal line is calculated as follows:

m x 7/4 = -1

m = -4/7.

(as the normal line is perpendicular to the tangent line, which has slope equals to the numeric value of the derivative at the point).

The coordinates of the point at (2,4), hence:

x' = 2, y' = 4.

Then the definition of the normal line is given as follows:

y - 4 = -4/7(x - 2).

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Answer: 3 sports drinks

Step-by-step explanation:

6 divde by 2= 3

36 divided by 12 =3

in other words

3x2=6

12x3=36

hope this helps

Answer:

first you need to write the given equation in a standard form

4x - 7y = 9

-7y = -4x + 9

y = 4/7x - 9/7

*parallel lines have equal gradient

m = 4/7

y - y1 = m(x - x1)

y - 3 = 4/7(x -7)

y - 3 = 4/7x - 4

y = 4/7x - 1

your equation is y = 4/7x - 1

Answer:

[tex]y = \frac{4}{7} + 5[/tex]

Step-by-step explanation:

Isolate the variable, y. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS is the order of operations, and stands for:

Parenthesis

Exponent (& Root)

Multiplication

Division

Addition

Subtraction

~

First, subtract 4x from both sides of the equation:

4x (-4x) - 7y = 9 (-4x)

-7y = -4x + 9

Next, divide -7 from both sides of the equation:

(-7y)/-7 = (-4x + 9)/-7

[tex]y = \frac{-4x}{-7} + \frac{9}{-7}[/tex]

[tex]y = \frac{4}{7}x - \frac{9}{7}[/tex]

Next, as long as your slope (4/7) is the same, you can adjust the b (-9/7 for original) to get a parallel line.

In this case, I will utilize 5

[tex]y = \frac{4}{7}x + 5[/tex]

See attached image for the result. The blue line is the adjusted parallel line, while the red line is the original line given by the question.

~

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Answer:

100 metere is 1 km

Thanks for the question

The area of the given irregular figure is 143 square inches.

What is area of irregular figure?

We divide an irregular shape into its component common shapes before calculating its area. After that, we add the areas of each shape. For instance, if a square and a triangle make up an irregular polygon, the area of the polygon is equal to the sum of their areas.

We have to divide the given irregular figure into known shapes.

That is rectangle and square.

Rectangles with sides '7 in and 10 in' and '12 in and 4 in' and the square of side 5 in.

So, the area of irregular figure is,

Area = Area of rectangle + Area of rectangle + Area of square

= (7 x 10) + (12 x 4) + 5^2

= 70 + 48 + 25

Area = 143

Hence, the area of the given irregular figure is 143 square inches.

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Answer:

Step-by-step explanation:

0 is the answer

The 95% confidence interval that estimates proportion of 8th graders that are involved in an after school activity (0.745, 0.895) , the correct option is (a) .

In the question ,

it is given that ,

simple random sample of 100 8th graders is taken ,

that means ,

n = 100 ,

also given that , 82% of them are involved with some type of after school activity.

means ; p = 0.82 .

the level of significance (α) = 100 - 95 = 5% = 0.05 .

the critical value=  [tex]Z_{\alpha /2}[/tex] = [tex]Z_{0.025}[/tex] = 1.959964   ......from the Z table .

the lower limit of the 99% confidence interval is = p - [tex]Z_{\alpha /2}[/tex]*SE

and the upper limit for the 99% confidence interval is=  p + [tex]Z_{\alpha /2}[/tex]*SE  .

the standard error is √(p(1-p)/n

= √(0.82(1 - 0.82)/100

= 0.0384

So , the lower limit is ⇒ 0.82 - 1.959964*0.0384

On simplification ,

we get ,

lower limit is = 0.7447006 ≈ 0.745 .

the upper limit is =  p + [tex]Z_{\alpha /2}[/tex]*SE  

= 0.82 + 1.959964*0.0384

On Simplification ,

we get ,

upper limit is = 0.8952994 ≈ 0.895 .

Therefore , the confidence interval is (0.745, 0.895) .

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There is enough evidence to conclude that the doctor's claim is true.

We have given that,

population mean μ = 11 pounds

sample size n = 25

sample mean x = 12 ponds

standard deviation σ = 4 pounds

so the null hypothesis is H₀ : μ = 11 pounds

and the alternative hypothesis is Hₐ : μ > 11 pounds

now we will calculate test statistics,

t = (x-μ)/(σ/√n)

 = (12 - 11)/(4/√25)

 = 1/(4/5)

t = 1.25

p-value from the z-table is 0.10565

the result is non significant at p < 0.01.

Hence the null hypothesis rejected .

Therefore there is enough evidence to conclude that the doctor's claim is true.

The level of significance is the measurement of the statistical significance. It defines whether the null hypothesis is assumed to be accepted or rejected. It is expected to identify if the result is statistically significant for the null hypothesis to be false or rejected.

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The true or false values of the statements are:

From the question, we have the graph which represents the given parameters that can be used in our computation

Analysing the graph, we have:

The graph crosses the y-axis at y = 18

This means that the y-intercept of the graph is

y-intercept  = 18

This in other words mean that:

The cost of the book is $18

So, (a) is true

Also, the graph crosses the x-axis at x = 90

This means that the x-intercept of the graph is

x-intercept  = 90

This in other word mean that:

Giselle gets $18 if she pulls all the weed (i.e. 90 weeds) in the garden

So, (b) and (d) are true

The amount paid by her grandma is calculated as

Amount = 18/90

Amount = 1/5

So, (c) is true

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The disadvantage is that the coefficients of x in the four equations can only take two values, so if one of every values ​​is m, the alternative will be -1/m.

A relationship between two terms on either side of an equal sign is depicted by a straightforward equation.

Simple equations also pursue one or a mixture of the four arithmetic computations of addition, simple arithmetic, multiplication, and division.

There are three basic forms of the system of equations: point-slope form, standard form, and slope-intercept form.

So, Shannon's error:

In a rectangle, the neighboring sides are perpendicular to one other, whereas parallel runs between the opposing sides.

The slope of line segments is equal, and the slope, of a perpendicular line to some other line with a slope, m, is -1/m , thus the slopes of the axis of symmetry should be equal, which gives:

The equation should consist of two sets of linear equations with equal slopes: B. Pair y = -x + 6 and y = -x - 5

Therefore, the slopes of the other two lines are -1/-1 = 1 and the equations of the other two lines are y = x - 4 and y = x - 5 respectively.

Therefore, the disadvantage is that the coefficients of x in the four equations can only take two values, so if one of every values ​​is m, the alternative will be -1/m.

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The total distance traveled by the object after 30.0 seconds is 450 meters.

For the stated function;

As, the total distance is modelled by the quadratic equation-

Let the quadratic equation be-

d = at² + bt + c

For (10, 50)

d = a(10)² + (10)b + c  ....eq 1

For (20, 200)

d = a(20)² + (200)b + c  ....eq 2

For (0, 0)

d = a(0)² + (0)b + c  ....eq 3

Solving eq 1, 2 and 3

a = 1/2 ; b = 0 and c =0

Thus, equation for the distance travelled by the object is-

d = 1/2 t²

For t = 30. sec

d = 1/2 (30)²

d = 450 m

Thus, the total distance traveled by the object after 30.0 seconds is 450 meters.

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Answer:

$13 overpayment

Step-by-step explanation:

We can find the amount Trevor should pay each month by dividing the $26,555 by 36 months:

               ($26,555/(36 months)) = $737.64 per month

Since Trevor decide to round up to the nearest dollar, he will pay $738 each month.  That's an overpayment of $0.361 each month.

After 36 months of overpaying by $0.361 each month, Trevor will have overpaid:

  ($0.36/month)*(36 months) = $13 overpayment

Answer:

There are 8! (8 factorial) ways for 8 people to be seated in an 8-passenger van. This is because there are 8 choices for the first person to sit, 7 choices for the second person, 6 choices for the third person, and so on, until there is only 1 choice for the last person. Therefore, the total number of ways for the 8 people to be seated is 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 8!, which is equal to 40,320.

Answer:

1/3 * [tex]4\pi[/tex] * h = 207, h = 155.25[tex]\pi[/tex]

Step-by-step explanation:

Since we know the area of the base is [tex]4\pi[/tex], that means the volume of the cone is:

1/3 * [tex]4\pi[/tex] * h

If we substitue, we get:

1/3 * [tex]4\pi[/tex] * h = 207

(This is the answer! If you want to solve, go below)

Now, we just solve

[tex]4\pi\\[/tex] * h = 621

h = 621/[tex]4\pi\\[/tex]

h = 155.25[tex]\pi[/tex]

Answer:

box plot becauase wire width is numerical :)

Step-by-step explanation:

Answer:

Answer Option C: SSA test

The division of 6x⁴ + 11x³ + 13x² - 3x + 27 by 3x + 4 will have a quotient of 2x³ + x² +3x -5 and a remainder of 47 using the remainder theorem.

The remainder theorem states that if a polynomial say f(x) is divided by x - a, then the remainder is f(a).

We shall divide the 6x⁴ + 11x³ + 13x² - 3x + 27 by 3x + 4 as follows;

x⁴ divided by 3x equals 2x³

3x + 4 multiplied by 2x³ equals 6x⁴ + 8x³

subtract 6x⁴ + 8x³ from 6x⁴ + 11x³ + 13x² - 3x + 27 will give us 3x³ + 13x² - 3x + 27

3x³ divided by 3x equals x²

3x + 4 multiplied by x² equals 3x³ + 4x²

subtract 3x³ + 4x² from 3x³ + 13x² - 3x + 27 will give us 9x² - 3x + 27

9x² divided by 3x equals 3x

3x + 4 multiplied by 3x equals 9x² + 12x

subtract 9x² + 12x from 9x² - 3x + 27 will give us -15x + 27

-15x divided by 3x equals -5

3x + 4 multiplied by -5 equals -15x - 20

subtract -15x - 20 from -15x + 27 will result to a remainder of 47

using the remainder theorem, x = -4/3 from the the divisor 3x + 4

thus:

f(-4/3) = 6(-4/3)⁴ + 11(-4/3)³ + 13(-4/3)² - 3(-4/3) + 27 {putting the value -4/3 for x}

f(-4/3) = (1536/81) - (704/27) + (208/9) + (12/3) + 27

f(-4/3) = (1536 - 2112 + 1872 + 324 + 2157)/81 {simplification by taking the LCM of the denominators}

f(-4/3) = (5919 - 2112)/81

f(-4/3) = 3807/81

f(-4/3) = 47

Therefore, the quotient of after the division of 6x⁴ + 11x³ + 13x² - 3x + 27 by 3x + 4 is 2x³ + x² +3x -5 and there is the remainder of 47 using the remainder theorem.

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Answer:

246.5

Step-by-step explanation:

86275÷35

= 246.5

approximately 247

At a = √25/π^2 - 0.04 revolutions will the circular helix r = acosti + asintj + 0.2tk make in a distance of 10 units measured along the z-axis.

In the given question, we have to find how many revolutions will the circular helix r = acosti + asintj + 0.2tk make in a distance of 10 units measured along the z-axis.

r = acosti + asintj + 0.2tk, length = 10 unit

So |r| = [tex]\int^{2\pi}_{0}\sqrt{(dx/dt)^2+(dy/dt)^2+(dz/dt)^2}dt[/tex]

From the given equation,

x = acost, y = asint, z = 0.2t

dx/dt = -asint, dy/dt = acost, dz/dt = 0.2

10 = [tex]\int^{2\pi}_{0}\sqrt{(-a\sin t)^2+(a\cos t)^2+(0.2)^2}dt[/tex]

10 = [tex]\int^{2\pi}_{0}\sqrt{a^2\sin^2 t+a^2\cos^2t+0.04}dt[/tex]

As we know that sin^2x+cos^2x = 1. So

10 = [tex]\int^{2\pi}_{0}\sqrt{a^2+0.04}dt[/tex]

10 = [tex]\sqrt{a^2+0.04}\int^{2\pi}_{0}dt[/tex]

10 = [tex]\sqrt{a^2+0.04}\cdot[t]^{2\pi}_{0}[/tex]

10 = √(a^2+0.04)∙[2π-0]

2π√(a^2+0.04) = 10

Divide by 2π on both side, we get

√(a^2+0.04) = 5/π

Taking square on both side, we get

a^2+0.04 = 25/π^2

Subtract 0.04 on both side, we get

a^2 = 25/π^2 - 0.04

taking square root on both side, we get

a = √25/π^2 - 0.04

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The right question is:

How many revolutions will the circular helix

r = acosti + asintj + 0.2tk

make in a distance of 10 units measured along the z-axis?

Answer: 1 decameter

Step-by-step explanation:

Answer:

1 decameter

Step-by-step explanation:

1 decameter is 10 meters or 1000 centimeters

In step 1, y was made the subject of the second equation to get:

y=5x-4

To proceed, the next step is to substitute the expression into the other equation, not the equation we solved for y.

8x+2y=-12

8x+2(5x-4)=-12

8x+10x-8=-12

18x=-12+8

18x=-4

x=-[tex]\frac{4}{18}[/tex]

x=[tex]\frac-{2}{9}[/tex]

answer=  the value of x is -2/9

Answer:

50 degrees

Step-by-step explanation:

100 - 60 degrees

therorem

The number of seconds to reach Jane will be 2.25 seconds. Then the correct option is B.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The curve of the ball's path is given below.

d = -16t² + 32t + 9

The number of seconds to reach Jane is given as,

0 = -16t² + 32t + 9

16t² - 32t - 9 = 0

16t² - 36t + 4t - 9 = 0

4t(4t - 9) + 1(4t - 9) = 0

(4t - 9)(4t + 1) = 0

t = 9/4, -1/4

t = 2.25, -0.25

The number of seconds to reach Jane will be 2.25 seconds. Then the correct option is B.

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We utilize a two factors, independent measurements ANOVA, where, factor has 2 level and a factor likewise has 2 levels.

A factor in mathematics is an integer that evenly divides another number by itself, leaving no residue.

Factors and multiples are a part of our daily life. For example, they are employed in arranging objects in a box, handling money, recognizing patterns in numbers, solving ratios, and working with expanding

A number totally divides the provided number without leaving any residual is said to be the factor of that number.

The components of a number might be positive or negative. For example, let us find the factors of 8. Since 8 is divisible by 1, 2, 4, and 8, we may list the positive factors of 8 as, 1, 2, 4, and 8. Apart from this, 8 has negative elements as well, which might be stated as, -1, -2, -4,

According to our question-

Degrees of freedom for the F-test of the two way ANOVA

In this case, we utilize an ANOVA with two independent variables and two factors, each with two levels.

So, here,

= 2 for the number of layers of A

= B's level count is 2,

Moreover, n = sample size in each treatment condition is equal to 10.

So we have,

= df of the main effect A = ( - 1) = 2 - 1 = 1

= df of the main effect A = ( - 1) = 2 - 1 = 1

= df of interaction effect (A x B) = ( - 1)( - 1) ( - 1)

= (2-1)(2-1) (2-1)

= 1

And = df of within variation (i.e. error variation) =

= 2 x 2 x (10 - 1) (10 - 1)

= 36

Consequently, the df value for the F-ratio measuring factors-primary A's impact is

= () ()

= (1, 36) (1, 36)

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Answer: below

Step-by-step explanation:

A. x=20+2n n= number of months

y=10(1+0.15)^n

B.

x 20,22,24,26,28,30....40

y 12.5,13.225,15.2,....40.5

C. The solution is 11 months because at 10 months even though the number of animals surpass the number of homes, you cannot have half a animal.

D.

The exponential function that represents the employee’s salary, S, after t years since the employee began working with the company is given as follows:

S(t) = 35400(1.08)^t.

An increasing exponential function is modeled according to the rule presented as follows:

A(t) = A(0)(1 + r)^t.

The parameters are given as follows:

An employee receives a salary increase of 8% at the end of each full year working with a company, hence the growth rate is given as follows:

r = 0.08.

The employee receives an initial salary of $35,400, hence the initial value is given as follows:

A(0) = 35400.

Thus the exponential function for this problem is defined as follows:

S(t) = 35400(1.08)^t.

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The ratio of p : q in its simplest form is 5 : 1

The unknown numbers are p and q

(p - 5) / (q - 5) = 9/1

(p + 20) / (q + 20) = 7/3

From equation (1)

cross product

1(p - 5) = 9(q - 5)

p - 5 = 9q - 45

p = 9q - 45 + 5

p = 9q - 40

From equation (2)

3(p + 20) = 7(q + 20)

3p + 60 = 7q + 140

Substitute p = 9q - 40 into 3p + 60 = 7q + 140

3p + 60 = 7q + 140

3(9q - 40) + 60 = 7q + 140

27q - 120 + 60 = 7q + 140

27q - 60 = 7q + 140

27q - 7q = 140 + 60

20q = 200

divide both sides by 20

q = 200/20

q = 10

Substitute q = 10 into p = 9q - 40

p = 9q - 40

p = 9(10) - 40

p = 90 - 40

p = 50

In conclusion, the ratio of p to q = 50 : 10

= 50/10

= 5/1

= 5:1

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Answer:

Hi

Step-by-step explanation:

I am just reply to see if i really understand that problem

Let's assume s the present age of the son, and f the present age of the father.

The age of the son After 10 years is equal to the age of the father before 20 years:

s+10=f+10-20

f=3s

=> s+10=f-10

=> s+10=3s-10

=> 2s=20

=> s=10 and  f=30