What is the end behavior of the function f(x) = 5/4x²,
As x→ ∞o. f(x) → -∞
O As x-00. f(x) → ∞0
As X→ ∞o, f(x) → -∞
O As x-00, f(x) → -∞0
As x→
O As x →
∞o. f(x) → ∞0
∞0. f(x) → -∞

The following are the sets which cannot form a right triangle:

b. 27 mm, 35 mm, 46 mm

f. 12 mm, 34 mm, 37 mm

Given,

Here some set of lengths given. We have to find which set of lengths can not form a right triangle.

To check whether it is a right triangle or not we will use Pythagoras theorem. If it holds true then the set will form a right triangle and if it is not true then it will not form a right triangle.

The pythogaras theorem is c²=a²+b²,where c = hypotenuse which is the largest length of the sides, a and b are other two sides.

a. 24 mm, 32 mm, 40 mm

c = 40 mm as it is the largest side.

substitute the values:

40² = 24² + 32²

1600 = 576 + 1024

1600 = 1600

The Pythagoras theorem holds true here. So this set will form a right angled triangle

b. 27 mm, 35 mm, 46 mm

c = 46 mm as it is the largest side.

substitute the values:

46² = 27² + 35²

2116 = 729 + 1225

2116 = 1954

The Pythagoras theorem does not hold true here. So this set will not form a right angled triangle.

c.  7 mm, 24 mm, 25 mm

c = 25 mm as it is the largest side.

substitute the values:

25² = 7² + 24²

625 = 49 + 576

625 = 625

The Pythagoras theorem holds true here. So this set will form a right angled triangle

d.  6 mm, 8 mm, 10 mm

c = 10 mm as it is the largest side.

substitute the values:

10² = 6² + 8²

100 = 36 + 64

100 = 100

The Pythagoras theorem holds true here. So this set will form a right angled triangle.

e. 12 mm, 16 mm, 20 mm

c = 20 mm as it is the largest side.

substitute the values:

20² = 16² + 12²

400 = 256 + 144

400 = 400

The Pythagoras theorem holds true here. So this set will form a right angled triangle.

f. 12 mm, 34 mm, 37 mm

c = 37 mm as it is the largest side.

substitute the values:

37² = 12² + 34²

1369 = 144 + 1156

1369 = 1300

The Pythagoras theorem does not hold true here. So this set will not form a right angled triangle.

Hence we get the required answers.

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The original number was 1.85.

According to the question,

We have the following information:

Alex was thinking of a number. Alex doubles it, then adds 20 to get an answer of 22.7.

Now, in this case, let's take the original number to be x.

So, we have the following expression when something was added to the number after doubling it:

2x+20 = 22.7

Subtracting 20 from both sides of the equation:

2x = 22.7-20

2x = 2.7

Dividing by 2 on both sides of the equation:

x = 2.7/2

x = 1.85

Hence, the original number Alex was thinking of was 1.85.

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Answer: C

Step-by-step explanation:

If you look at the picture, you can see that it is decreasing from hour 3 to hour 4.

This means that from 3 < x < 4, it is decreasing.

Answerh

Step-by-step explanation:

huh

Answer:

x = 11/9 and y = 26/9 or x = 3 and y = 2

Step-by-step explanation:

x + 2y = 7 --1

2x² + 3y = 5xy - 6 --2

From 1, make x the subject.

x = 7 - 2y

Substitute x = 7 - 2y into 2.

2(7 - 2y)² + 3y = 5y(7 - 2y) - 6

Simplify and solve for y.

2(49 - 28y + 4y²) + 3y = 35y - 10y² - 6

98 - 56y + 8y² + 3y = 35y - 10y² - 6

18y² - 88y + 104 = 0

9y² - 44y + 52 = 0

Factorise.

(9y - 26)(y - 2) = 0

9y - 26 = 0 or y - 2 = 0

9y = 26 or y = 2

y = 26/9 or y = 2

Substitute values of y into x = 7 - 2y.

x = 7 - 2(26/9) or x = 7 - 2(2)

= 11/9 = 3

Thus, x = 11/9 and y = 26/9 or x = 3 and y = 2.

The sets [tex](\sqrt{7}, 4, \sqrt{23})[/tex] and[tex](\sqrt{29}, \sqrt{39}, 68)[/tex] could be used to form a right triangle.

What is right triangle?

A right triangle, also known as a right-angled triangle, an orthogonal triangle, or historically a rectangled triangle, is a triangle with one right angle, meaning that its two sides are perpendicular. Trigonometry's foundation is the relationship between the right triangle's sides and other angles.

Since for the right triangle is a, b, c are three sides of a triangle, where c is the diagonal, then

[tex]a^2 + b^2 = c^2[/tex]

Consider, the set  (3, 5, 8)

Here,  3^2 + 5^2 ≠ 8^2.

Consider, the set (8, 9, 11)

Here, 8^2 + 9^2 ≠ 11^2

Consider, the set [tex](\sqrt{7}, 4, \sqrt{23})[/tex]

Here, [tex](\sqrt{7})^2 + 4^2 = (\sqrt{23})^2[/tex]

Consider, the set [tex](\sqrt{29}, \sqrt{39}, 68)[/tex]

Here, [tex](\sqrt{29})^2 + (\sqrt{39})^2 = 68[/tex]

Hence, [tex](\sqrt{7}, 4, \sqrt{23})[/tex], [tex](\sqrt{29}, \sqrt{39}, 68)[/tex] could be used to form a right triangle.

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Answer:  square root of 7 comma 4 comma square root of 23

Step-by-step explanation: I took the test and I got it right

The minimized amount of material used to make the box is 13516 cm²

Let the side of the square base be x cm

According to the problem, the volume of the box is 13500 cm³

Therefore,

x² X height = 13500

or, height = 13500/x²

Now it is given that the top is open.

Hence, the box only has one square side.

Hence the surface area of the box will be

x² + 2x.13500/x² + 2x.13500/x²

= x² + 54000/x

Therefore, f(x) = x² + 54000/x

Now, to minimize the above problem, we equate the first derivative to 0

f'(x) = 2x - 54000/x² = 0

or, (2x³ - 54000)/x² = 0

or, 2x³ = 54000

or x³ = 27000

or, x = 30

Now, we check whether the above result is a minimal value or not.

f''(x) = 2 + 108000/x³

or, f"(30) = 2 + 108000/54000

= 4

Since f"(30) is positive, the minimized value of x is 30.

Therefore, the minimal amount of material used is

4² + 54000/4

= 16 + 13500

= 13516 cm²

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The set of 4 consecutive integers that has a sum of –270 is -69, -68, -67 and -66

The statement in the question is represented as

A set of 4 consecutive integers has a sum of –270

As a general rule of numbering;

Consecutive integers are integers that have a difference of 1

These numbers can be negative or positive

Solving further, we can represent the smallest integer with x

So, the other integers are x + 1, x + 2 and x + 3

Recall that the sum of the four integers is -270

This statement implies that

Sum = -270

So, we have

x + x + 1 + x + 2 + x + 3 = -270

Evaluate the like terms

4x + 6 = -270

Evaluate the like terms

4x = -276

Divide both sides by 4

x = -69

So, we have

x + 1 = -68

x + 2 = -67

x + 3 = -66

Hence, the integers are -69, -68, -67 and -66

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It can be inferred that there is a statistically significant result if the confidence interval excludes the value of zero effect.

Confidence Interval;

In statistics, confidence is another word for probability. For instance, if you create a confidence interval with a 95% confidence level, you can be sure that 95 times out of 100 the estimate will fall between the upper and lower values indicated by the confidence interval.

Therefore,

The confidence level is 95% if your significance level is 0.05. The hypothesis test is statistically significant if the P value is lower than your significance (alpha) level. The findings are statistically significant if the confidence interval excludes the null hypothesis value. 0

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He have 48 different possible outfits to wear at work with three one-piece jump suits, five pairs of work pants, and eight work shirts.

The basic counting principle is a method for keeping track of all the potential outcomes in a situation. According to this statement, there are n m n times m n ways to carry out both of these actions if there are n ways to perform one action and m ways to perform another action after that.

Here,

5 pants with each of 8 shirts,

=5 x 8

=40 combinations of shirts and pants.

40 shirt/pants outfits + 8 jumpsuits = 48 total outfits.

With three one-piece jumpsuits, five pairs of work pants, and eight work shirts, he has 48 different work-appropriate outfit options.

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Answer:

w = 36

Step-by-step explanation:

[tex]\frac{1}{2}[/tex] [tex]\sqrt{w}[/tex] + 1 = 4 ( subtract 1 from both sides )

[tex]\frac{1}{2}[/tex] [tex]\sqrt{w}[/tex] = 3 ( multiply both sides by 2 to clear the fraction )

[tex]\sqrt{w}[/tex] = 6 ( square both sides to clear the radical )

w = 6² = 36

The exact amount of money in his bank is $ 1.8.

acc to our question=

Given that,

There are 5 times as many pennies as dimes

Number of pennies = 5 times the number of dimes

We know that

Given that he has more than $1.60 and less than $2.00 in the bank

Therefore, 0.2d must be greater than 1.60 and less than 2.00

Thus 1.8 is greater than 1.60 and less than 2.0

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Answer:

5x+2y-16=0 (general form)

y= -5/2 x+8 (slope intercept form)

Step-by-step explanation:

y-y1/x-x1 = y2-y1/x2-x1 ( formula)

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

y+2/x-4 = 5/-2

-2 (y+2) = 5 (x-4)( cross multiply)

-2y-4 = 5x-20

-2y = 5x-20+4

-2y = 5x-16

5x+2y-16 = 0 (general form )

OR

y = -5/2 x -16/-2yyyyx

y = -5/2 x + 8

Inflection points for the given equation x^2e^{-2x} are [tex]\left(\frac{2-\sqrt{2}}{2},\:\frac{e^{-2+\sqrt{2}}\left(3-2\sqrt{2}\right)}{2}\right),\:\left(\frac{2+\sqrt{2}}{2},\:\frac{e^{-2-\sqrt{2}}\left(3+2\sqrt{2}\right)}{2}\right)[/tex]

What is inflection point and how to find an inflection point?

The point of inflection, also known as the inflection point, is when the function's concavity changes. Changing the function from concave down to concave up, or vice versa, signifies that. In other words, an inflection point is the location at which the rate of slope shift from a growing to a decreasing way, or vice versa, occurs. There is no doubt that those positions are neither local maxima nor minima. They are fixed points.

Finding the Inflection Point on a Graph?

On a curve, an inflection point is when the concavity changes, according to definition. (i.e., a shift in the sign of curvature). We are aware that the function is concave up if f " > 0, and that it is concave down if f " 0. The point of inflection on a graph is where the function switches from positive to negative, or from negative to positive, at a particular value of x = c.

f'(x) = [tex]2xe^(^-^2^x^) - 2x^2e^(^-^2^x^)[/tex]

f'(x) = [tex]-2\left(x-1\right)x\mathrm{e}^{-2x}[/tex]

Now again differentiating for inflection point :

f''(x) = [tex]-2\left(-2\left(x-1\right)x\mathrm{e}^{-2x}+x\mathrm{e}^{-2x}+\left(x-1\right)\mathrm{e}^{-2x}\right)[/tex]

f''(x) = [tex]4\left(x-1\right)x\mathrm{e}^{-2x}-2x\mathrm{e}^{-2x}-2\left(x-1\right)\mathrm{e}^{-2x}[/tex]

f''(x) = [tex]\left(4x^2-8x+2\right)\mathrm{e}^{-2x}[/tex]=0

Now we have to solve this quadratic for inflection point

[tex]2x^2-4x+1=0[/tex]

Using quadratic formula

x= -b±√(b^2 - 4ac)/2a

x=4±√(16+16)4

x=4±4√2/4

[tex]x=\dfrac{\sqrt{2}+2}{2}[/tex]

[tex]x=\dfrac{\sqrt{2}-2}{2}[/tex]

Now on putting  [tex]\dfrac{\sqrt{2}+2}{2}[/tex]  and[tex]\dfrac{\sqrt{2}-2}{2}[/tex] in f(x)

we get,

=[tex](\dfrac{\sqrt{2}+2}{2})^ 2 * e ^ (^-^ ^{\sqrt{2}+2})[/tex]

=[tex]\frac{e^{-2+\sqrt{2}}\left(3-2\sqrt{2}\right)}{2}\right)[/tex]

And   [tex](\dfrac{\sqrt{2}-2}{2})^ 2 * e ^ (^-^ ^{\sqrt{2}-2})[/tex]

=  [tex]\frac{e^{-2+\sqrt{2}}\left(3-2\sqrt{2}\right)}{2}\right)[/tex]

so, inflection points are

[tex]\left(\frac{2-\sqrt{2}}{2},\:\frac{e^{-2+\sqrt{2}}\left(3-2\sqrt{2}\right)}{2}\right),\:\left(\frac{2+\sqrt{2}}{2},\:\frac{e^{-2-\sqrt{2}}\left(3+2\sqrt{2}\right)}{2}\right)[/tex]

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The statements that use a while loop to assign a string consisting of exactly 777 asterisk to s are mentioned below:

i=0

While i<777

[Tab Key]s=s+"*"

[Tab Key]i+=1

A variable is a sign and placeholder in mathematics for any mathematical object. A variable can be a number, a vector, a matrix, a function, its argument, a set, or an element of a set.

Algebraic calculations that treat variables as if they were explicit integers solve a variety of issues in a single step. The quadratic formula, for example, solves any quadratic equation by substituting the numeric values of the equation's coefficients for the variables represented by the quadratic formula. A variable in mathematical logic is either a sign expressing an unnamed word of the theory (a meta-variable) or a basic item of the theory that is changed without reference to its theory.

Given,

A variable s is assigned to an empty string.

The statements that use a while loop to assign a string consisting of exactly 777 asterisk to s,

i=0

While i<777

[Tab Key]s=s+"*"

[Tab Key]i+=1

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[tex]\sqrt{1-cos(10x)/2}[/tex]The expression is equivalent to sin(5x)

Given that,

start root start fraction 1 minus cosine (10 x) over 2 end fraction end root which means [tex]\sqrt{1-cos(10x)/2}[/tex]

To find : The equivalent expression to the equation [tex]\sqrt{1-cos(10x)/2}[/tex] --> (1)

We know that,

From trigonometry,

Half angle formula

What is the value of 1 cos 2x? The expression 1 - cos2x is written as 1 - cos2x = 2sin2x. This makes it possible to recognize trigonometric identities. These are the phrases that enable you to discover a precise response to your query.

1−cos2x=2sin²x and

Similarly,

1−cosx=2sin²(x/2)

Then

1-cos10x = 2sin²(5x)

Substitute above expression in (1)

Then,

[tex]\sqrt{1-cos(10x)/2}[/tex] = [tex]\sqrt{2sin^2(5x)/2}[/tex]

                           = [tex]\sqrt{sin^2(5x)}[/tex]

                           = sin(5x)

Therefore, [tex]\sqrt{1-cos(10x)/2}[/tex] is equivalent to sin(5x)

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It would cost $94.24 to purchase 9.5 lbs. of walnuts.

From the question, we have

To buy 1/4 lbs. of chopped walnuts, costs $2.48

To buy 1 lbs. of chopped walnuts, costs = $2.48*4  = $9.92

To buy 9.5 lbs. of chopped walnuts, costs = $9.92 * 9.5

=$94.24

Multiplication:

In mathematics, multiplying the numbers is used to find the product of two or more numbers. We carry out one of the basic mathematical operations on a regular basis. The main application that is obvious is using multiplication tables. Mathematicians use the multiplication of two integers to express the repeated addition of one number to another. These numbers can be natural numbers, fractions, integers, whole numbers, etc. M is either added to itself 'n' times or subtracted from itself when m is multiplied by n.

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Answer: one degree of latitude is equal to 60 Minutes

Steps-  We Know that-

                                    1 min = 60 sec

                                    1 day = 24 hrs

  Additionally, The hour hand measures the clock's 360 degree arcs twice         throughout the day, i.e.

                                     2*360= 720 degree

                                     1 degree 2*360/12= 60 min

Hence proved 1 degree = 60 Minutes

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There is a 0.56 percent chance that a city resident picked at random would reside in the center or northern part of the city.

A probability is a numerical representation of the possibility or chance that a specific event will take place.

Here,

Given that, this probability distribution table displays the percentage of residents in five distinct areas of a city.

Favorable Results/Total Results is the formula for probability.

The likelihood of choosing someone from the center or northern regions is 0.44 + 0.12 = 0.56.

Consequently, there is a 0.56 percent chance that a city resident picked at random would reside in the central or northern zone.

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Using the equation of the model:

a. 150,400 or 150.4 thousand.

b. 467.5 thousand or 467,500.

An equation that models a given scenario can be used to make predictions or determine certain values of any of the variables involved.

Given the equation that models the number of college students who studied abroad each year is expressed as: y = 123.1(1.069)^x, where:

y = number of students from a country in thousands

x = number of years after 1998

a. 2001 after 1998 is 3 years. Substitute x = 3 into the equation, y = 123.1(1.069)^x:

y = 123.1(1.069)^3

y = 150.4

Number of students studying abroad in 2001 is: 150,400 or 150.4 thousand.

b. 2018 from 1998 is 20 years. Substitute x = 20 into the equation, y = 123.1(1.069)^x:

y = 123.1(1.069)^20

y = 467.5

Number of students studying abroad in 2018 is: 467.5 thousand or 467,500.

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Answer:

Step-by-step explanation:

poop

The solutions of y= x+8 and y= -2x-4 is x is -4 and y is 4

Two or more expressions with an Equal sign is called as Equation.

The given equations are

y equal to x plus eight

y= x+8...(1)

y equal to minus two x minus four

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

Subtract 2 from 1

y-y=x+8-(-2x-4)

0=x+8+2x+4

0=3x+12

3x=-12

Divide both sides by 3

x=-4

Now put x value in y

y=-4+8=4

The value of x is minus four and y is four.

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Answer:

Yes

Step-by-step explanation:

Let y = 0

3x = -6  Divide both sides by 3

x = -2

(-2,0)

Let x = 0

-y = -6  Divide both sides by -1

y = 6

(0,6)

The option that gives the tire life span that separates the upper 30% of the life spans from the lower 70%, obtained from the Z-table is 32,650 miles.

Given that  

mean = 32,000miles

standard deviation = 1,250miles

using the z - Table the answer is 0.52

which from the z-score table gives at point at a probability of 1 - 0.3 = 0.7, gives z ≈ 0.52

What is the Z-table?

The probability values of the likelihood that a z-value will be within a region of a normal distribution are provided in the Z-score table.

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The equivalent measure of 10 L when rounded to nearest 10 is 10,000 ML.

According to the question,

We have the following information:

10 Litres

Now, to find the equivalent measurement, we will convert 10 L into another unit. Let's convert litres into mililitres.

We know that 1 litre is equal to 1000 ml.

So, we have the following expression:

1 litre  = 1000 ml

10 litres = 10*1000 ml

10 l = 10,000 ml

Now, rounding it off to nearest 10, we will get:

10,000 ml  (Because the number right next to ten place value is 0. Hence, the digits are same.)

Hence, the equivalent measure of 10 L when rounded to nearest 10 is 10,000 ML.

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Answer:

(3,4)

Step-by-step explanation:

3x - 2y = 1

-3x + 4y = 7

3x - 3x = 0

-2y + 4y = 2y

1+7 = 8

2y = 8

2/2 y = 8/2

y = 4

3x -2(4) = 1

3x - 8 = 1

3x = 8 + 1

3x = 9

3/3 x = 9/3

x = 3

Answer:

See the work below.

Step-by-step explanation:

If 3x-2y=1, then

[tex]x=(\frac{1}{3})1+2y[/tex]

Substitute for x in 4y=7+3x.

[tex]4y=7+3(\frac{1}{3})(1+2y)\\4y=7+(1+2y)\\4y=7+1+2y\\4y=8+2y\\4y-2y=8+2y-2y\\2y=8\\y=4[/tex]

Substitute y=4 in 3x-2y=1

[tex]3x-2(4)=1\\3x-8=1\\3x-8+8=1+8\\3x=9\\\frac{3x}{3}=\frac{9}{3}\\x=3[/tex]

This work proves the given values are correct.

At the end of the semester, 90 members of a student organization had a picnic with 3 members who chose hamburger, milk and cake.

5 had hamburger and milk.

10 took cake and milk.

8 had cake and hamburger.

24 ate hamburger.

38 had cake.

20 drank milk.

let A,B and C are number who had hamburger, milk and cake

N(T)=    90

N(A)=    24

N(B)=    20

N(C)=    38

N(AnB)=    5

N(BnC)=    10

N(AnC)=    8

N(AnBnC) =   3

at least one =N(AUBUC)=    N(A)+N(B)+N(C )-N(AnB)-N(BnC)-N(AnC)+N(AnBnC)     =    62

a) nothing  =N(T)-N(Au B u C) =90-62=28

b) cake only =N(C)-N(A n C)-N(B n C)+N(A n B n C) =38-8-10+3=23

c) milk only =20-5-10+3 =8

d) hamburger only =24-5-8+3=14

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The percentage of free moisture on a fine aggregate is 0.5%.

Free moisture refers to the moisture which is present on the surface of the aggregate after moisture has been absorbed and can be removed by drying the sand. Free moisture or free water is determined as the difference between the mass of wet-saturated aggregate sample and the mass of saturated-surface-dry condition sample.

Based on the given information:

Stock (present) weight = Weight of wet sample = 464.3g

Oven-dry weight = Weight of dry sample = 450.6g

Total Moisture = (Weight of wet sample - Weight of dry sample)/Weight of dry sample * 100

(464.3 – 450.6)/450.6 * 100 = 0.030 *100 = 3%

Percent absorption (AC): 2.5%

Free moisture = Total moisture – Absorbed moisture

= 3 – 2.5 = 0.5%

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Answer:  The correct answer is $34.50

Step-by-step explanation:

large necklace sells for $5.10

small necklace sells for $4.90

Total = (Large*1) + (small*6)

Total = (5.10*1) + (4.90*6)

Total = 5.10 + 29.40

Total = 34.50

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Answer:

$34.50

Step-by-step explanation:

step 1

$4.90×6

=$29.40

step 2

$5.10+29.40

=$34.50

Answer:

Step-by-step explanation:

False

Answer:

False statement

Step-by-step explanation:

Currently, the inequality of the line is x < -18.75  like shown in the number line.

If you want to substitute -17 for x, you have to make sure it makes sense.

The inequality will be -17 < -18.75.

Now, is this inequality a true one? No, because -17 is not less than -18.75 making this a false statement.

You can also check with the number line in the image.

Does the line pass through -17?