A​ student's grade on the Fundamentals of Engineering exam has a​ z-score of 0.5. Make an observation about the​ student's grade.

The expression [tex]10^{t^2+2t-3}[/tex] is equivalent to the expression [tex](10^{t+3})^{t-1[/tex]

An equation is an expression that shows the relationship between two or more numbers and variables.

Given the expression:

[tex]10^{t^2+2t-3}\\\\=10^{t^2+3t-t-3}\\\\=10^{[t(t+3)-1(t+3)]}\\\\=10^{(t-1)(t+3)}[/tex]

The expression [tex]10^{t^2+2t-3}[/tex] is equivalent to the expression [tex](10^{t+3})^{t-1[/tex]

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The bolt of length more than 7.2 cm will be destroyed.

Mean refers to the central tendency of a data set. It is calculated by taking average of the data.

It is given that

any bolts that are more than 2 standard deviations from the mean will be destroyed

Mean = 7 cm

Standard Deviation is = 0.10 cm

The length of the bolt which is not acceptable is = Mean + 2 Standard Deviation.

Length = 7 + 2 * 0.10

Length = 7.2 cm

Therefore if the bolt of length more than 7.2 cm will be destroyed.

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The number of users on new social media site increase as 21, 25, 30, 36,
The average rate of change is given by 5.

The function f (t) = 12 (1.2) ^t show how the rate of users increases in weeks.

Average of the values is the ratio of total sum of values to the number of values.

Here,  f (t) = 12 (1.2) ^t is defined in the range of (3, 6)
So the value of the function in its range is given by
1)  f (3) = 12 (1.2) ^3
          = 21
2)  f (4) = 12 (1.2) ^4
   =  25
3)   f (5) = 12 (1.2) ^5
    = 30
4)   f (6) = 12 (1.2) ^6
     = 36
Now the average rate of change = sum of all difference in values at every week / max. Difference in interval of range(3,6)

= f(6)-f(3)/6-3
= 15/3
= 5

Thus required average change of rate is 5.

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The correct statement regarding the limit, using asymptotes, is:

The function [tex]f(x) = \frac{28x - 10x^2}{4x^2 - 1}[/tex] has a horizontal asymptote at [tex]y = -\frac{5}{2}[/tex].

In this problem, we have a limit, which is associated with a horizontal asymptote. The limit is:

[tex]\lim_{x \rightarrow \infty} \frac{28x - 10x^2}{4x^2 - 1}[/tex]

x goes to infinity, hence we consider only the highest exponents.

[tex]\lim_{x \rightarrow \infty} \frac{28x - 10x^2}{4x^2 - 1} = \lim_{x \rightarrow \infty} -\frac{10x^2}{4x^2} = -\frac{10}[4} = -\frac{5}{2}[/tex]

Hence the correct statement is:

The function [tex]f(x) = \frac{28x - 10x^2}{4x^2 - 1}[/tex] has a horizontal asymptote at [tex]y = -\frac{5}{2}[/tex].

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The radius of the quadrant whose perimeter is 52cm is 14.56cm.

A quadrant is 1/4th of a circle, consisting of two radii, perpendicular to each other.

So, the perimeter of a quadrant consists of two radii and an arc, which is 1/4th the perimeter of a circle.

Therefore, the perimeter of the quadrant = 2r + (1/4)*(2πr) = 2r + (πr/2).

Now, we are given the perimeter of the quadrant = 52cm and are asked to find its radius.

We suppose the radius to be r cm.

Therefore, we can say that:

52 = 2r + (πr/2).

or, 52 = (4r + πr)/2

or, 52*2 = r(4 + π)

or, r = 104/(4 + π) = 14.56.

Therefore, the radius of the quadrant whose perimeter is 52cm is 14.56cm.

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The function which represents the annual salary for total sales of x dollars, where x is greater than $250000 is 0.025x+29750.

Given basic salary=3000 p.m. , bonus 2.5% of total sales above $250000.

We have to make a function which shows the annual salary for total sales of x dollars where x is greater than $250000.

Function is a relationship between two or more variables which have each y values corresponding to x values.

According to question

Total basic salary of whole year=3000*12=$36000

We have been given total sales be x.

Sales above $250000 is x-250000

Bonus on sales=2.5%(x-250000)

Function f(x)=36000+2.5%(x-250000)

=36000+0.025x-0.025*250000

=36000+0.025x-6250

=0.025x+29750

Hence the function which shows the annual salary for total sales of x dollars is f(x)=0.025x+29750.

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Answer:

AC Factor: 420

Factors that add up to 41: 20 and 21

Rewritten equation: [tex](35x^2+21x)+(20x+12)[/tex]

Step-by-step explanation:

so a quadratic equation is generally expressed as [tex]ax^2+bx+c[/tex]. So in this polynomial 35=a and c=12. The ac product would thus be (35)(12) which is 420

The factors of the AC product include: 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20 , 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210 and 420. Since we're looking for a bigger number which is 41 you would generally want to look near the middle. and you can disregard any factors equal to or above 42. since they wouldn't add to 41. So I'll start at 30. 420/30 = 14 and 30 + 14 = 44 which is pretty close. Alright I'll try 28 instead. 420/28 = 15 and 15+28 = 43 which is also pretty close so I'll try the next factor 420/21 = 20 and 20+21 = 41! so the two factors are 20 and 21

Now using these two factors you can rewrite the equation as

[tex](35x^2+21x)+(20x+12)[/tex] which simplifies to the same quadratic equation

y=35x²+41x+12

Here

So

Now

Factors that add up to 41 are 21 and 20

Now solve

The arcs intersected by these chords are not congruent.

Given that two circles with different radii have chords AB and CD, such that AB is congruent to CD.

Let r₁ and r₂ be the radii of two different circles with centers O and O' respectively.

Assuming that the each of the ∠АОВ  and ∠CO'D is less than or equal to π.

Then, we have isosceles triangle AOB and CO'D such that,

AO = OB = r₁,

CO' = O'D = r₂,

Let us assume that r₁< r₂;

We can see that arc(AB) intersected by AB is greater than arc(CD), intersected by the chord CD;

arc(AB) > arc(CD)      .......(1)

Indeed,

arc(AB) = r₁ angle (AOB)

arc(CD) = r₂ angle (CO'D)

So, we have to prove that ;

∠AOB >∠CO'D       ......(2)

Since each angle is less than or equal to π, and so

∠AOB/2  and ∠CO'D/2 is less than or equal to π

it suffices to show that :

tan(AOB/2) >tan(CO'D/2) ......(3)

From triangle AOB :

tan(AOB/2) = AB/(2*r₁)

tan(CO'D/2) = CD/(2*r₂)

Since AB = CD and r₁ < r₂ (As obtained from the result of (3) ), therefore, arc(AB) > arc(CD).

Hence, for two circles with different radii have chords AB and CD, such that AB is congruent to CD but the arcs intersected by these chords are not congruent.

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In accordance with propositional logic, quantifier theory and definitions of simple and composite propositions, the negation of a implication has the following equivalence:

[tex]\neg (\exists \,x\, (P(x) \implies Q(x))) \iff \forall \,x (\neg \,Q(x) \,\land \,P(x))[/tex] (Correct choice: iii)

Herein we have a composite proposition, that is, the union of monary and binary operators and simple propositions. According to propositional logic and quantifier theory, the negation of an implication is equivalent to:

[tex]\neg (\exists \,x\, (P(x) \implies Q(x))) \iff \forall \,x (\neg \,Q(x) \,\land \,P(x))[/tex]

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The solution of Tx" + (4t - 2)X' + (13t - 4)X = 0, If X(0) = 0 is mathematically given as

[tex]&n \times(S)=\frac{c}{\left((s+2)^{2}+9\right)^{2}}[/tex]

Generally, the equation for is mathematically given as

[tex]&t x^{\prime \prime}+(4 t-2) x^{\prime}+(13 t-4) x=0, \quad x(0)=0\\\\&\Rightarrow \quad t x^{\prime \prime}+4 t x^{\prime}-2 x^{i}+13 t x-4 x=5\\[/tex]

By taking Laplace to transform,

[tex]&L\left\{t x^{13}\right\}+L\left\{4 t x^{\prime}\right\}-L\left\{2 x^{\prime}\right\}+L\{13 t x\}-L\{4 x\}=0\\\\\\&-25 x(s)-s^{2} x^{1}(5)-4 x(s)-45 x^{\prime}(s)-25 x(s)-13 x^{\prime}(5)-4 x(s)=0\\[/tex]

[tex]&\Rightarrow \quad-\left(5^{2}+45+13\right) x^{4}(5)-4(5+2) x(5)=0\\\\\\&\Rightarrow \quad\left(s^{2}+45+13\right) x^{1}(5)+4(5+2) x(5)=0\\\\\\&\Rightarrow\left(s^{2}+4 s+13\right) x^{\prime}(s)=-4(s+2)^{x}(s)\\\\\\&\Rightarrow \frac{x^{\prime}(s)}{x(s)}=-\frac{4(s+2)}{s^{2}+4 s+13}\\\\\[/tex]

In conclusion, By integrating both sides

The solution is

[tex]&x(s)=\frac{c}{\left(s^{2}+4 s+13\right)^{2}}\\[/tex]

[tex]&n \times(S)=\frac{c}{\left((s+2)^{2}+9\right)^{2}}[/tex]

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Answer:

A ∩ C = {0, 3, 1, 1.3, 2, 3, 4, 5, 2}

A ∩ B = {3, 1, 2, 4, 5}

Step-by-step explanation:

Given that A = {0, 3, 1, 1.3, 2, 3, 4, 5, 2}

B = the set of all Natural numbers

C= the set of all Rational numbers

So set C contains numbers that can be expressed as the ratio of two integers. Since numbers in A can be expressed as follows:

0 = 0/1,  3 = 3/1,  1 = 1/1, 1.3 = 13/10, 2 = 2/1,  4 = 4/1, 5 = 5/1

Then, A ∩ C = {0, 3, 1, 1.3, 2, 3, 4, 5, 2}.

A ∩ B = {3, 1, 2, 4, 5}, since B contains only Natural numbers = {1, 2, 3, ...}.

Answer:

Solve for x

One exterior angle (x) equals to sum of two remote interior angles 50°, 75°

x = 50° + 75

x = 125°

Solve for y

Enclosed by parallel lines, the angles equals to 180°

55° + 50° + y = 180°

105° + y = 180°

y = 180° - 105°

y = 75°

Answer:

1 2/3

Step-by-step explanation:

12 inches = 1 foot

So, 20/12 is equal to 1 8/12 foot

remeber to simplify though, so 8/12 simplified is 2/3, so the solution to the problem is 1 2/3 foot

The value of the expression is 188

Given the expression

= [tex]\frac{7 + (2 + 6)^2}{4 * \frac{1}{2}^4}[/tex]

Expand the bracket

= [tex]\frac{7 + 4 + 36}{ 4 * 1/16}[/tex]

We have

= [tex]\frac{47}{1/4}[/tex]

The denominator becomes the multiplier, we have

= 47 × 4

= 188

Thus, the value of the expression is 188

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Answer: the one on the right on the top

Step-by-step explanation:

as x increases by 1, y decreases by 2. this makes a linear function

Answer: the answer is the first option

Step-by-step explanation:

The equations for the lines tangent to and normal to the curve at the point (2, 4) are y = 4 · x - 4 and y = (-1/4) · x + 9/2, respectively.

In this question we must use the definitions of linear function, tangent and normal lines and differential calculus to determine the equations needed. The slope of the tangent line (m) is found by implicit differentiation:

2 · x + 2 · y · y' - 3 · (y + x · y') = 0

2 · x + (2 · y - 3 · x) · y' - 3 · y = 0

(2 · y - 3 · x) · y' = 3 · y - 2 · x

y' = (3 · y - 2 · x)/(2 · y - 3 · x)

By (x, y) = (2, 4)

m = (3 · 4 - 2 · 2)/(2 · 4 - 3 · 2)

m = 4

And the slope of the normal line is:

m' = -1/m = -1/4

Lastly, we obtain the intercept for each line:

Tangent line

b = 4 - 4 · 2

b = 4 - 8

b = - 4

The equation of the line tangent to the curve at the point (2, 4) is y = 4 · x - 4.

Normal line

b = 4 - (-1/4) · 2

b = 4 + 1/2

b = 9/2

The equation of the line normal to the curve at the point (2, 4) is y = (-1/4) · x + 9/2.

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Answer:

K=4a-1

Step-by-step explanation:

K = 4a- 1 (shifting -4a to right side from left)

Question : Draw a triangle ABC. Next, create a line through point C that is perpendicular to . Label the intersection between the perpendicular line and as point E. Take a screenshot of the triangle with CE, save it, and insert the image in the space below.

We know that having three sides, three angles, and three vertices, a triangle is a closed, two-dimensional shape. A polygon also includes a triangle.

A line is a straight, one-dimensional figure in geometry that is infinitely long in both directions and has no thickness.

The definition of a perpendicular line in geometry is a pair of lines that meet or intersect at right angles (90°). The Latin word "perpendicularis," which denotes a plumb line, is where the word "perpendicular" first appeared. Two lines, AB and CD, can be written as AB⊥CD if they are perpendicular to one another. The perpendicular nature of the lines is denoted by the symbol.

Here, we have to draw a triangle. Then we have to draw a line CE which intersects AB at point E.

Image is attached below.

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Considering that there are only two possible outcomes for each number, and a fixed number of numbers, the distribution is:

C. binomial.

We have that:

Hence the binomial distribution should be used and option B is correct.

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four less than three times that number is:3x-4

is:=

three more than two times the number: 2x+3

Problem to solve:

3x-4=2x+3

3x-2x-4=2x-2x+3

x-4=3

x-4+4=3+4

x=7

Calculated:

3(7)-4=2(7)+3

21-4=14+3

17=17

Answer:

The G.C.F of (8,24) is 8

Step-by-step explanation:

look at the attachment above ☝️

The solution of the graph can be located at the point of intersection of the two lines. The solution, approximated to the tenths place will be (0.4, 2.8)

The solution of a system of two linear equations can be calculated by determining the point of intersection.

Therefore, the solution = the coordinates of the point of intersection (x-coordinate, y-coordinate).

Given graph shows the system of equations in two lines:

The solution of the graph can be located at the point of intersection of the two lines, the x-coordinate against the y-coordinate.

The integers that the x-coordinate of the point of intersection is in between are 0 and 1.

The y-coordinates of the point of intersection lie between the integers 2 and 3.

The solution, approximated to the tenths place will be (0.4, 2.8)

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Answer:

262 passengers can have both headphones and blankets .

Step-by-step explanation:

I hope it will help you

Answer:

=======================

Use circumference formula to find the tire circumference:

Find the distance by multiplying the number of revolutions by circumference:

Convert the inches to feet, or yards, considering 12 in = 1 foot and 3 feet = 1 yard:

The volume of volume of the rectangular prism is=240cm³ while the surface area of cylinder =225.04cm²

The volume of rectangular prism

= l×w×h

= 10× 6× 4

= 240cm³

The surface area of cylinder,

= 2πrh+2πr²

= 2× 3.14× 2.8 × 10 + 2×3.14×2.8²

= 175.84 + 49.2

= 225.04cm²

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Answer:

Graph Number 2

Step-by-step explanation:

Use the horizontal line test: If you can draw a horizontal line at any point and it only intersects the line once, then it's a one-to-one function.

Answer: a

Step-by-step explanation:

[tex]z_0=-1-2i\\\\z_1=2(-1-2i)+(3-2i)=-2-4i+3-2i=1-6i[/tex]

This eliminates all the options except for a.

Answer:

Answers are below.

Step-by-step explanation:

1) 60 centimeters

2) Perimeter = 48, Area = 144

3) Circumference = 20π, Area = 100π

4) 180 feet

5) 75 meters

6) 15 yards

Hope this helps!