Given the following piecewise function,

f(3) =
f(8) =
f(-1) =

The percentage of racers that  did not complete the marathon is 12.9 %

What is arithmetic?

Arithmetic is an elementary a part of mathematics that consists of the study of the properties of the normal operations on numbers—addition, subtraction, multiplication, division, involution, and extraction of roots

Main Body:

Total racers = 240

racers that completed race = 209

so racers that did not complete the marathon = 240 - 209

 = 31

percentage of racers that  did not complete the marathon = (31/240)*100

                                                                           = 12.9 %

Hence percentage of racers that  did not complete the marathon is 12.9%

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The converse, inverse and contrapositive statements for the given conditional statement are :

Converse: if I sleep well, then I go to be early

Inverse: if I don't go to be early, then I don't sleep well

Contrapositive: if I don't sleep well, then I don't go to be early.

A conditional statement is a part of mathematical reasoning which is a critical skill that enables students to analyze a given hypothesis without any reference to a particular context or meaning.

Given is a conditional statement, "If I go to be early, then I sleep well", we need to form its converse, inverse and contrapositive statements,

The rules for the given conditional statement are ;

Let p and q be the parts of the statement,

1) Converse statement = if p then q, converse = if q then p.

Therefore,

Converse: if I sleep well, then I go to be early.

2) Inverse statement = if p then q, inverse = if not p then not q.

Therefore,

Inverse: if I don't go to be early, then I don't sleep well.

3) Contrapositive statement = if p then q, Contrapositive = if not q then not p.

Therefore,

Contrapositive: if I don't sleep well, then I don't go to be early.

Hence, the converse, inverse and contrapositive statements for the given conditional statement are :

Converse: if I sleep well, then I go to be early

Inverse: if I don't go to be early, then I don't sleep well

Contrapositive: if I don't sleep well, then I don't go to be early.

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The expected variance of red balls chosen is 2/3 from the urn.

Six red balls and four green balls are in an urn.

Till a urn is empty, we take balls out of it one at a time without replacing them and noting their order of the colors.

The, the variance is found as-

Variance(X,Y) = E(XY) - E(X).E(Y).E(XY)

E(XY)  = 25×(6/10)(4/9)

E(X) = 5×(6/10)

E(Y) = 5×(4/10)

Thus,

Variance(X,Y) = 25(6/10)(4/9) - 25(6/10)(4/10)

Variance(X,Y) = 2/3

Thus, the variance for choosing red balls is 2/3.

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Answer: 3

Step-by-step explanation:

The lengths of the sides of the rectangular field so as to minimize the amount of fencing needed is 30 feet by 20 feet

Let x represent the length of the fence and y represent the width of the fence.

Since the area is 3750, hence:

Area = length * width = x * y

3750 = xy

y = 3750/x

A fence divide the field in half and is parallel to one of the sides of the rectangle. Hence:

Amount of fencing needed (P) = x + x + y + y  + y = 2x + 3y

Amount of fencing needed (P) = 2x + 3(3750/x) = 2x + 1800/x

To minimize the amount of fencing needed, dP/dx = 0, hence:

dP/dx = 2 - 1800/x²

2 - 1800/x² = 0

2 = 1800/x²

2x² = 1800

x² = 900

x = 30 feet

y = 600/x = 600/30 = 20 feet

Hence, the lengths of the sides of the rectangular field so as to minimize the amount of fencing needed is 30 feet by 20 feet

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Answer:

Given,

Let's assume the maximum safe height of wall = h

angle formed between ladder and ground = 70°

length of ladder = 16 ft

From the given data, it can be seen that ladder will form a right angle triangle structure with the wall

So,from the concept of trigonometry,

Sin70^o\ =\ \dfrac{\textrm{maximum safe height of wall}}{\textrm{length of ladder}}Sin70

o

=

length of ladder

maximum safe height of wall

= > Sin70^o\ =\ \dfrac{h}{16\ ft}=>Sin70

o

=

16 ft

h

= > \ h\ =\ 16\times Sin70^o=> h = 16×Sin70

o

=> h = 16 x 0.9396

=> h = 15.03 ft

So, the maximum safe height that can be reached by the ladder will be 15.03 ft.

Sorry I put the wrong answer.

Part a: Height of tree;  15 feet.

Part b: distance of tree from person; 14.25 feet.

Part a: Height of the tree;

We get the following mathematical formula (equation) since the ratio of a corresponding sides of similar triangles is equal in magnitude:

22.5/8.25 = x/5.5

In which

x is the height of the tree.

Then,

22.5/8.25 = x/5.5

Further simplifying;

8.25x = 22.5 × 5.5

8.25x = 123.75

x = 123.75/8.25

x = 15 feet. (height of the tree)

Part b: distance of tree from person;

These calculations can be used to determine how far away from the tree this individual is:

Distance equals the product of a person's shadow and a tree's shadow

Distance = 22.5 - 8.25

Distance = 14.25 feet.

Thus,  distance of tree from person is 14.25 ft.

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Answer:

I would be C

Step-by-step explanation:

lookup here

Answer:

PR

Step-by-step explanation:

The longest side is opposite the largest angle.

Answer: There are two equal sides

Step-by-step explanation:

Considering P and R are both 48 degrees and the only different angle is Q that would mean there are two equal sides.

the length and breadth of the rectangle is L = 4, B =16

Let L and B stand for length and width, respectively.

a rectangle is 4 times a long as it is wide

L=4B …….(1) (1)

L1 and B1 should represent the revised length and width.

L1=(L+4)

B1=(B-1)

Area = L1 + B1 + 60.

=> (L+4)×(B-1)=60 …….(2) (2)

Using (1)-

=> (4B+4)×(B-1) =60

=> 4×(B^2–1) = 60

=> B^2–1 = 15

=> B^2 = 16

=> B = +4 or -4

B=4 inches because breadth is always positive.

L = 4 B = 16 inches.

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Answer:

3. 70 degrees

4. 110 degrees

Step-by-step explanation:

3. The angles are mirrored on both sides

4. A straight line is equal to 180 degrees so if <AED is 70 degrees then you would do 180-70 to get 110 degrees

Answer:

Answer: 3 or 2 1/2 ethier is right

Step-by-step explanation:

Using Pythagoras theorem, the numbers are from a right angled triangle

Pythagorean triples are a2+b2 = c2 where a, b and c are the three positive integers. These triples are represented as (a,b,c). Here, a is the perpendicular, b is the base and c is the hypotenuse of the right-angled triangle.

In this question, to find out if the numbers are a Pythagorean triple, we can use pythagoras theorem while assuming the longer side is the hypothenuse.

13² = 12² + 5²

169 = 144 + 25

169 = 169

The numbers are Pythagorean triple because the sum of square of the two sides is equal to the square of the hypothenuse.

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Avea received 28 stickers when brianna, and carson in the ratio 1:3:4 and  brianna received 21 stickers.

The ratio is defined as the comparison of two or more quantities of the same units, which shows how much bigger one quantity is than another.

Given,The ratio of the distribution of stickers among Avea, Brianna and Carson is 1:3:4

The number of stickers Briana received is 21

Let us consider x as the common factor of the given ratio then, The number of stickers received by the girls are

Avea = xBriana = 3x

Carson = 4x

As we know 3x = 21 x

 = 21/3

= 7

then,4x

= 4×7

= 28

The number of stickers that Avea received is 28. Hence, the answer is 28

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Answer:

Show that the ratios UV/XY and WV/ZY are equivalent, and ∠V ≅ ∠Y.

Answer: The first option

Step-by-step explanation: Once you multiply all the denominators to make them the same, the numerators (in the original order they are given in) become 63, 16, and 44.

16<44<63, which is the first option.

The maximum volume of this cylinder = 256π  cubic inches

What is volume?

In three-dimensional space, volume is the area occupied by an object within its borders. Another name for it is an object's capacity.

Let h be the height and r be the radius.

Then, h+r = 12

=> h=12-r

Volume of the cylinder (V):

V=πr²h

=> h= πr² ( 12-r )

=> h=  π ( 12r² - r³ )

Differentiate with respect to r , we get

dv/dr = 24 πr - 3πr²

Find r by taking dv/dr=0

24 πr - 3πr²  = 0

3π ( 8r - r² ) = 0

8r = r²

r=8

Again differentiating, we get

d²V/dr² = 24π - 6 π r

When r=8, 24π - 48 π  <0

So, V is maximum at r= 8 inches

And h= 12-8= 4 inches

Hence, the required volume of the cylinder = π8²*4 = 256π  cubic inches

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The pH of the cleaning compound is 2.51.

pH, quantitative measure of the acidity or basicity of aqueous or other liquid solutions.

Given that, The hydrogen ion​ concentration, ​[H​+], in a certain cleaning compound is [H+]=3.3x10^-12.

[OH-] = 1.0*10^-14/3.3*10^-12 = 0.303*10^-12

pH = -log0.303*10^-12 = 2.51

Hence, The pH of the cleaning compound is 2.51.

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What grade is that?

Step-by-step explanation:

Answer: -3/7

Step-by-step explanation:

So the fomula for slope is m=x2-x1/y2-y1

if (6,6) is our first coordinate and (3,13) is our second that means 6 is x1 and 3 is x2. 6 will be y1 and 13 will be y2. now we plug in the numbers

m=3-6/13-6

m= -3/7

The dimensions of the garden would be length = 28 meters and width = 9.5 meters.

What are quadratic equations?

A quadratic equation in math is a second-degree equation of the form ax² + bx + c = 0. Here a, and b, are the coefficients, c is the constant term, and x is the variable. Since the variable x is of the second degree, there are two roots or answers for this quadratic equation.

Let the width be = w

Let the length be = L

enclose three side ( 2w+L) = 47 meter

L = 47-2w

Area of field = w*L

Area = w(47 - 2w)

266  = 47w - 2w²

2w² - 47w + 266 = 0

Solving this, we get

w = 14 or w = 9.5

The width should be less than the length so w = 9.5
Length = 47 - 2(9.5)

            = 47 - 19

            = 28 meters.

Hence, the dimensions of the garden would be length = 28 meters and width = 9.5 meters.

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The correct option e. Statements (1) and (2) TOGETHER are NOT sufficient.

For the stated question-

1. R is less than 20: insufficient since s is unknown.

2. Because there is no date for r, statement 2 is insufficient because S is bigger than 65.

We now have two conditions when combined. s>0 and s>65, r 20 and r>0.

Using the maximum possible value of r as an example and the least possible value of s as an example, the value is greater than 1/3.

Therefore, every values for r would only decrease, while s will rise.

Therefore, simply stating that it won't be below 1/3 will do.

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The complete question is-

If r and s are positive integers, is r/s less than 1/3 ?

(1) r is less than 20.

(2) s is greater than 65.

a. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

b. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

c. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

d. EACH statement ALONE is sufficient.

e. Statements (1) and (2) TOGETHER are NOT sufficient.

The radius of the circle  with arc length of 2.4 and subtended angle at the center, 7.1 radians is 0.3

The arc of a circle is defined as the part or segment of the circumference of a circle. A straight line that could be drawn by connecting the two ends of the arc is known as a chord of a circle. If the length of an arc is exactly half of the circle, it is known as a semicircular arc.

length of arc = 2.4

if 7.1 rad is the angle subtended by the intercepts of the arc

But [tex]\pi[/tex] rad = 180°

so 7.1 rad in degree = [tex]\frac{7.1}{\pi }[/tex] x 180  which is [tex](\frac{1278}{\pi } )^{} }[/tex] degree which is [tex]\alpha[/tex]

Length of an arc = [tex]\frac{\alpha }{360} * 2\pi r[/tex]

2.4 =  [tex](\frac{1278}{\pi } )^{} }[/tex] x [tex]\frac{1}{360}[/tex] x 2 x [tex]\pi[/tex] x r

The equation reduces to

2.4 = 7.1r

r = 2.4 ÷ 7.1

r = 0.334 which is 0.3

In conclusion the radius of the circle is 0.3

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Answer:

length of base = 9 feet

Step-by-step explanation:

b= base   A= area   h= height

[tex]b=2*\frac{A}{h} = 2*\frac{29.25}{6.5} = 9[/tex]

The probability that one of the first five customers agrees to take the survey is 71%

Here we have to use binomial distribution.

What is binomial distribution?

A common probability distribution known as the binomial distribution simulates the likelihood of getting one of two outcomes given a set of parameters. It provides a summary of the number of trials when each trial has an equal chance of producing a particular result.

A binomial distribution with the following formula could be used to represent the proportion of clients who agree to participate in the survey out of 5:

X ~ Bin (n = 5, p = 0.22)

Thus the probability is computed as:

P(X >= 1) = 1 - P(X = 0) = [tex]1 - (1-0.22)^5[/tex]

= 0.71

The required probability in this case is therefore 71%.

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The FALSE condition for the given inequality 3(n−6)<2(n+12) is (D) S:{42}.

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way.

The majority of the time, size comparisons between two numbers on the number line are made.

So, we have the inequality: 3(n − 6) < 2(n + 12)

Now, verify the false inequality as follows:

(A) S:{−5}

3(n − 6) < 2(n + 12)

3(-5 − 6) < 2(-5 + 12)

3(-11) < 2(7)

-33 < 14: TRUE

(B) S:{3}

3(n − 6) < 2(n + 12)

3(3 − 6) < 2(3 + 12)

3(-3) < 2(15)

-9 < 30: TRUE

(C) S:{12}

3(n − 6) < 2(n + 12)

3(12 − 6) < 2(12 + 12)

3(6) < 2(24)

18 < 48: TRUE

(D) S:{42}

3(n − 6) < 2(n + 12)

3(42 − 6) < 2(42 + 12)

3(36) < 2(54)

108 + 108: FALSE

Therefore, the FALSE condition for the given inequality 3(n−6)<2(n+12) is (D) S:{42}.

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Correct question:

Given the inequality 3(n − 6) < 2(n + 12), determine which integer makes the inequality false.

a. S:{−5}

b. S:{3}

c. S:{12}

d. S:{42}

Answer:

= 16x - 8

Step-by-step explanation:

3(2x - 1) + 5(2x - 1)

8(2x - 1)

16x - 8

Answer:

16x - 8

Step-by-step explanation:

Given expression,

→ 3(2x - 1) + 5(2x - 1)

Simplifying the expression,

→ 3(2x - 1) + 5(2x - 1)

→ 6x - 3 + 10x - 5

→ (6x + 10x) + (-3 - 5)

→ 16x +(-8)

→ 16x - 8

Hence, solution is 16x - 8.

Both slope-intercept form and point-slope form are equally important and useful, and easy to use. The advantages and disadvantages of both forms of linear equations are shown below.

Advantages: One of the three forms we can use to express a straight line is the point-slope form, also referred to as the point-gradient form.

This form is helpful since it allows us to find the equation of the line by only knowing the slope and one point along the line.

Disadvantages: Since vertical lines have arbitrary slopes, one limitation of the point-slope form is that it cannot be used to describe the equation of a vertical line.

Standard form and slope-intercept form are two additional frequently used forms.

Slope-intercept:

Advantages: The slope of the line and the y-intercept are both clearly displayed in slope-intercept form.

The slope of the line and the single point the line passes through are both plainly displayed in point-slope form.

When working with equation systems, the standard form is more convenient. (specifically, to locate the intersection with matrices).

Disadvantages: Slope-intercept form has the same drawbacks as a point-slope form in that vertical lines cannot be represented since the slope of a vertical line is ill-defined.

Therefore, both slope-intercept form and point-slope form are equally important and useful, and easy to use. The advantages and disadvantages of both forms of linear equations are shown below.

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