The perimeter of a rectangular field is 344m . If the width of the field is 75m, what is its length?

Answer:

<4 is congruent to angle <6

Step-by-step explanation:

Assuming the lines are parallel

<2 , <4 , <6 , <8 are all equal

Congruent means they are equal.

There are 3 angles that are the same as angle 6, they are 2, 4, 8

The answer would be B. angle 4

Power and chain rule (where the power rule kicks in because [tex]\sqrt x=x^{1/2}[/tex]):

[tex]\left(\sqrt{\dfrac{\cos(2x)}{1+\sin(2x)}}\right)'=\dfrac1{2\sqrt{\frac{\cos(2x)}{1+\sin(2x)}}}\left(\dfrac{\cos(2x)}{1+\sin(2x)}\right)'[/tex]

Simplify the leading term as

[tex]\dfrac1{2\sqrt{\frac{\cos(2x)}{1+\sin(2x)}}}=\dfrac{\sqrt{1+\sin(2x)}}{2\sqrt{\cos(2x)}}[/tex]

Quotient rule:

[tex]\left(\dfrac{\cos(2x)}{1+\sin(2x)}\right)'=\dfrac{(1+\sin(2x))(\cos(2x))'-\cos(2x)(1+\sin(2x))'}{(1+\sin(2x))^2}[/tex]

Chain rule:

[tex](\cos(2x))'=-\sin(2x)(2x)'=-2\sin(2x)[/tex]

[tex](1+\sin(2x))'=\cos(2x)(2x)'=2\cos(2x)[/tex]

Put everything together and simplify:

[tex]\dfrac{\sqrt{1+\sin(2x)}}{2\sqrt{\cos(2x)}}\dfrac{(1+\sin(2x))(-2\sin(2x))-\cos(2x)(2\cos(2x))}{(1+\sin(2x))^2}[/tex]

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

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

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

[tex]=-\dfrac{\sqrt{1+\sin(2x)}}{\sqrt{\cos(2x)}}\dfrac1{1+\sin(2x)}[/tex]

[tex]=-\dfrac1{\sqrt{\cos(2x)}}\dfrac1{\sqrt{1+\sin(2x)}}[/tex]

[tex]=\boxed{-\dfrac1{\sqrt{\cos(2x)(1+\sin(2x))}}}[/tex]

Answer:

The probability of rolling a 3 is 1/6 because there's only one 3 out of the 6 options that are on a standard die.

The probability of rolling an odd number is 3/6 or 1/2 because 3 out of the 6 numbers on a standard die (1, 3, 5) are odd.

The probability of rolling a six or odd number is 4/6 or 2/3 because out of the 6 numbers on a standard die, there's one 6 and 3 odd numbers and 1 + 3 = 4.

Answer:

Step-by-step explanation:

3(2)^2 + 4(1)^2

3(4) + 4

12+4= 16

Answer:

[tex]\huge\boxed{16}[/tex]

Step-by-step explanation:

[tex]3x^2+4y^2\ \text{for}\ x=2;\ y=1.\\\\\text{Substitute:}\\\\3(2)^2+4(1)^2=3(4)+4(1)=12+4=16\\\\\text{Used PEMDAS}[/tex]

Answer:

23) x ≥ -140.

24) k > -9.

25) v ≥ 9.

26) m > 16.

Step-by-step explanation:

23) -14 ≤ [tex]\frac{x}{10}[/tex]

[tex]\frac{x}{10}[/tex] ≥ -14

x ≥ -140

Since it is a ≥ sign, you will put a shaded circle at -140, and the line will stretch infinitely to the right of the circle.

24) -20 < k - 11

k - 11 > -20

k > -9

Since it is a > sign, you will put a non-shaded circle at -9, and the line will stretch infinitely to the right of the circle.

25) -6v ≤ 54

6v ≥ 54

v ≥ 9

Since it is a ≥ sign, you will put a shaded circle at 9, and the line will stretch infinitely to the right of the circle.

26) 8 < [tex]\frac{m}{2}[/tex]

[tex]\frac{m}{2}[/tex] > 8

m > 16

Since it is a > sign, you will put a non-shaded circle at 16, and the line will stretch infinitely to the right of the circle.

Answer:

1584$

Step-by-step explanation:

Original price is 1800$ (100%)

Discount percent: 12%

=> The price after discount is 100 - 12 = 88% of original price

=> The price after discount is 1800 x 88% = 1800 x 88/100 = 1584$

Answer:

13200

Step-by-step explanation:

12% - 1800

100% - x

X = (1800x100)/12 = 15000 - original price

15000-1800 = original price - discount = 13200 price after discount

Answer:

  28, 30, 32

Step-by-step explanation:

Their average will be 90/3 = 30. That is the middle integer.

The three integers are 28, 30, 32.

_____

Comment on the working

It often works well to use the average value when working consecutive integer problems. The average of an odd number of consecutive integers is the middle one. The average of an even number of consecutive integers is halfway between the middle two.

Answer:

1.35

Step-by-step explanation:

next cube above 540 is 729

to get to 729: 729 / 540 = 1.35

n = 1.35

Answer:

4 2/3 :)

Step-by-step explanation:

The total paint in the bucket in the simplified mixed fraction is [tex]6\frac{2}{3}[/tex] pints.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given, A housepainter mixed [tex]3\frac{1}{2}[/tex] pints of blue paint in a bucket with [tex]1\frac{1}{6}[/tex] pints of white paint.

So, The total paint in the bucket is the sum of the pints of both paints which

is, = [tex](3\frac{1}{2} + 1\frac{1}{6})[/tex] pints.

[tex]= (\frac{7}{2} + \frac{7}{6})[/tex] pints.

[tex]= \frac{21 + 7}{6}[/tex] pints.

[tex]= \frac{28}{6}[/tex] pints.

[tex]= 6\frac{2}{3}[/tex] pints.

learn more about fractions here :

https://brainly.com/question/10354322

#SPJ2

Answer:

well if you want my answer even though it could not be right so dont get mad at me if i am wrong but i think that it is all mostly based on how far they are from each other the further it is the more it will roll the closer it is the less it it will roll

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

rolling it shows its circumference and the other pennine has the ame circumference

This question is not complete. This is because it lacks the appropriate diagram containing necessary information to solve this question.

Please find attached the appropriate diagram to solve for this question

Complete Question :

The surface area of a given cone is 1,885.7143 square inches. What is the slant height?

Answer:

25 inches

Step-by-step explanation:

In the diagram, we are given the following information

Height of the cone = 20 inches

Radius of the cone = 15 inches.

The formula for the slant height of a cone represented by l =

l² = r² + h²

l = √(r² + h²)

l = √(15² + 20²)

l = √(225 + 400)

l = √625

l = 25 inches

Therefore, the slant height of this cone = 25 inches

Answer:

The integers are the numbers such that:

- The distance between consecutive integers is always of 1 unit and the integer numbers only have zeros after the decimal point, such that the set is: Z = {..., 0, 1, 2, 3, 4, ......}

74) No digits after the decimal point, so this is an integer.

3.49) we have digits after the decimal point, so this is not an integer.

4/7) 4 is smaller than 7, so 4/7 is smaller than one and larger than zero,

one and zero are consecutive integer numbers, so 4/7 can not be an integer number.

You also can solve the division and find that the quotient has digits after the decimal point.

148.29) This number has digits after the decimal point, so this is not an integer number.

8/1) here we have 8 divided by one, we know that:

8/1 = 8

8 has no digits after the decimal point, so this is an integer.

Answer:

4x + 8y ≥ 50

Step-by-step explanation:

Lorenzo must score at least 50 points to earn a B. He cannot score any less, therefore you use the greater than or equal to sign (≥).

Answer:

4x+8y>=50 is the required inequality.

Step-by-step explanation:

Here,

4 marks (multiple choice) and 8 marks (word problem) are the marks of each questions in the exam.

also x and y represents the number of correct and wrong answer respectively.

according to the question the person must have The points equal to or more than 50 points so, the inequality must be 4x+8y>=50.

so, theanswer is 4x+8y>=50.

hope it helps...

Answer:

[tex] E(X) =\int_{4}^7 \frac{1}{3} x[/tex]

[tex] E(X) = \frac{1}{6} (7^2 -4^2) = 5.5[/tex]

Now we can find the second moment with this formula:

[tex] E(X^2) =\int_{4}^7 \frac{1}{3} x^2[/tex]

[tex] E(X^2) = \frac{1}{9} (7^3 -4^3) = 31[/tex]

And the variance for this case would be:

[tex] Var(X)= E(X^2) -[E(X)]^2 = 31 -(5.5)^2 = 0.75[/tex]

And the standard deviation is:

[tex] Sd(X)= \sqrt{0.75}= 0.866[/tex]

Step-by-step explanation:

For this case we have the following probability density function

[tex] f(x)= \frac{1}{3}, 4 \leq x \leq 7[/tex]

And for this case we can find the expected value with this formula:

[tex] E(X) =\int_{4}^7 \frac{1}{3} x[/tex]

[tex] E(X) = \frac{1}{6} (7^2 -4^2) = 5.5[/tex]

Now we can find the second moment with this formula:

[tex] E(X^2) =\int_{4}^7 \frac{1}{3} x^2[/tex]

[tex] E(X^2) = \frac{1}{9} (7^3 -4^3) = 31[/tex]

And the variance for this case would be:

[tex] Var(X)= E(X^2) -[E(X)]^2 = 31 -(5.5)^2 = 0.75[/tex]

And the standard deviation is:

[tex] Sd(X)= \sqrt{0.75}= 0.866[/tex]

Answer:

3

Step-by-step explanation:

3

Answer

Step-by-step explanation:

Answer:

See the argument below

Step-by-step explanation:

I will give the argument in symbolic form, using rules of inference.

First, let's conclude c.

(1)⇒a  by simplification of conjunction

a⇒¬(¬a) by double negation

¬(¬a)∧(2)⇒¬(¬c) by Modus tollens

¬(¬c)⇒c by double negation

Now, the premise (5) is equivalent to ¬d∧¬h which is one of De Morgan's laws. From simplification, we conclude ¬h. We also concluded c before, then by adjunction, we conclude c∧¬h.

An alternative approach to De Morgan's law is the following:

By contradiction proof, assume h is true.

h⇒d∨h by addition

(5)∧(d∨h)⇒¬(d∨h)∧(d∨h), a contradiction. Hence we conclude ¬h.  

Answer:

"B. about half the days in march had average temperatures either below 60 or above 73 degrees"

Step-by-step explanation:

To answer this question, note that a box plot is usually divided into quartiles, each representing approximately 25% each.

In the box plot above,

*about 25% (Q1) represents days with temperature of 60° and below. This is about ¼ of the days in March.

*About 25% (Q2) represents days with temperature between 61° and 68°. That's about ¼ of the days in March

*About 25% (Q3) represents days with temperature between 70° and 73°. That's about ¼ of the days in March

*About 25% (Q4) represents days with temperature between 74° and 82°. That's about ¼ of the days in March

*Coldest day in March has a temperature of 54°

*Hottest day in March is 82°

From the options given, the only statement that is true is "B. about half the days in march had average temperatures either below 60 or above 73 degrees"

¼ of the Days in March has temperatures below 60° (Q1), while ¼ of the days in March has temperatures above 73° (Q4). Therefore, ¼+¼ = ½ of the days in March having average temperatures either below 60 or above 73 degrees.

Answer:

b

Step-by-step explanation:

About half of the days in March had average temperatures either below 60 or above 73 degrees.

Answer:b

Step-by-step explanation:

Answer:

3.27 hours

Step-by-step explanation:

Calculate the difference in speed and distance between the trains.

The relative speed:

101 - 90 = 11 mph

Difference in distance:

42 - 6 = 36 miles

[tex]time=\frac{distance}{speed}[/tex]

[tex]t=\frac{36}{11}[/tex]

[tex]t = 3.27[/tex]

Answer:

D

Step-by-step explanation:

The graph above is your graph.

As x increase, y decreases

As x decrease, y increases.

However, there is a small portion of the graph where both x and y were positive.

But I'm guessing it should be D.

Answer:

D

Step-by-step explanation:

[tex]f(x)=-x^3+2x^2-x+3[/tex]

As the highest power is 3, it is odd, as [tex]x[/tex] approaches to [tex]-\infty[/tex] [tex]y[/tex] approaches to [tex]\infty[/tex]

First, we have [tex]x \rightarrow-\infty[/tex], [tex]y \rightarrow \infty[/tex]

Plotting the graph, you can easily conclude the answer to the question.

And as [tex]x \rightarrow \infty[/tex], [tex]y \rightarrow -\infty[/tex]

Answer: 6 / √26

Step-by-step explanation:

Given that f(x, y, z) = xe^y + ye^z + ze^x

so first we compute the gradient vector at (0, 0, 0)

Δf ( x, y, z ) = [ e^y + ze^x,  xe^y + e^z,  ye^z + e^x ]

Δf ( 0, 0, 0 ) = [ e⁰ + 0(e)⁰, 0(e)⁰ + e⁰, 0(e)⁰ + e⁰ ] = [ 1+0 , 0+1, 0+1 ] = [ 1, 1, 1 ]

Now we were also given that  V = < 4, 3, -1 >

so ║v║ = √ ( 4² + 3² + (-1)² )

║v║ = √ ( 16 + 9 + 1 )

║v║ = √ 26

It must be noted that "v"  is not a unit vector but since ║v║ = √ 26, the unit vector in the direction of "V" is ⊆ = ( V / ║v║)

so

⊆ =  ( V / ║v║) = [ 4/√26, 3/√26, -1/√26 ]

therefore by equation   D⊆f ( x, y, z ) = Δf ( x, y, z ) × ⊆

D⊆f ( x, y, z ) = Δf ( 0, 0, 0 ) × ⊆ = [ 1, 1, 1 ] × [ 4/√26, 3/√26, -1/√26 ]

= ( 1×4 + 1×3 -1×1 ) / √26

= (4 + 3 - 1) / √26

= 6 / √26

Answer:

  t + m ≤ 11

Step-by-step explanation:

The total weight will be the sum of the weights of the bags present. The weight of t bags of topsoil will be 30t; the weight of m bags of mulch will be 30m. We want the total weight to be at most 330. (Weight numbers are in pounds.)

  30t +30m ≤ 330

We can remove a factor of 30 to simplify this to ...

  t + m ≤ 11

_____

You may be expected to use the un-simplified form of the inequality.

You did not give any options but i will try to answer.

y < -lxl basically means that the value of y is less than the absolute value of x time - 1.

So if x = 2, then y is any number less than -2.

And if x is -3. then y is any number less than -3.

Happy to help!

Answer:

A) 0.99413

B) 0.00022

Step-by-step explanation:

A) First of all let's find the total grading time from 6:50 P.M to 11:00 P.M.:

Total grading time; X = 11:00 - 6:50 = 4hours 10minutes = 250 minutes

Now since we are given an expected value of 5 minutes, the mean grading time for the whole population would be:

μ = n*μ_s ample = 42 × 5 = 210 minutes

While the standard deviation for the population would be:

σ = √nσ_sample = √(42 × 6) = 15.8745 minutes

To find the z-score, we will use the formula;

z = (x - μ)/σ

Thus;

z = (250 - 210)/15.8745

z = 2.52

From the z-distribution table attached, we have;

P(Z < 2.52) ≈ 0.99413

B) solving this is almost the same as in A above, the only difference is an additional 10 minutes to the time.

Thus, total time is now 250 + 10 = 260 minutes

Similar to the z-formula in A above, we have;

z = (260 - 210)/15.8745

z = 3.15

P(Z > 3.15) = 0.00022

Question:

Vector A has x and y components of −8.80 cm  and 18.0 cm , respectively; vector B has x and  y components of 12.2 cm and −6.80 cm , respectively.  If A − B +3 C = 0, what are the components of C?

Answer:

x = ___ cm

y = ___ cm

Answer:

x = 7.0cm

y = -8.27cm

Step-by-step explanation:

For a vector F, with x and y components of a and b respectively, its unit vector representation is as follows;

F = ai + bj              [Where i and j are unit vectors in the x and y directions respectively]

Using this analogy, let's represent vectors A and B from the question in their unit vector notation.

A has an x-component of -8.80cm and y-component of 18.0cm

B has an x-component of 12.2cm and y-component of -6.80cm,

In unit vector notation, these become;

A = -8.80i + 18.0j

B = 12.2 i + (-6.80)j = 12.2i - 6.80j

Also, there is a third vector C. Let the x and y components of C be a and b respectively. Therefore,

C = ai + bj

Now,

A - B + 3C = 0                [substitute the vectors]

=> [-8.80i + 18.0j] - [12.2 i -6.80j] + [3(ai + bj)] =  0        [open brackets]

=> -8.80i + 18.0j - 12.2 i + 6.80j + 3(ai + bj) =  0

=> -8.80i + 18.0j - 12.2 i + 6.80j + 3ai + 3bj =  0

=> -8.80i + 18.0j - 12.2 i + 6.80j + 3ai + 3bj =  0  [collect like terms and solve]

=> -8.80i  - 12.2 i  + 3ai + 6.80j + 18.0j + 3bj =  0

=> -21.0 i  + 3ai + 24.8j + 3bj =  0       [re-arrange]

=> 3ai + 3bj = 21.0i - 24.8j

Comparing both sides shows that;

3a = 21.0  -------------(i)

3b = -24.8    -----------(ii)

From equation (i)

3a = 21.0

a = 21.0 / 3 = 7.0

From equation (ii)

3b = -24.8

b = -24.8 / 3

b = -8.27

Therefore, the x-component and y-component of vector B which are a and b, are 7.0cm and -8.27cm respectively.

Answer:

-1.031 m/s or  [tex]\frac{-\sqrt{17} }{4}[/tex]

Step-by-step explanation:

We take the length of the rope from the dock to the bow of the boat as y.

We take x be the horizontal  distance from the dock to the boat.

We know that the rate of change of the rope length is [tex]\frac{dy}{dt}[/tex] = -1 m/s

We need to find the rate of change of the horizontal  distance from the dock to the boat =  [tex]\frac{dx}{dt}[/tex] = ?

for x = 4

Applying Pythagorean Theorem we have

[tex]1^{2} +x^{2} =y^{2}[/tex]    .... equ 1

solving, where x = 4, we have

[tex]1^{2} +4^{2} =y^{2}[/tex]

[tex]y^{2} = 17[/tex]

[tex]y = \sqrt{17}[/tex]

Differentiating equ 1 implicitly with respect to t, we have

[tex]2x\frac{dx}{dt} = 2y\frac{dy}{dt}[/tex]

substituting values of

x = 4

y = [tex]\sqrt{17}[/tex]

[tex]\frac{dy}{dt}[/tex] = -1

into the equation, we get

[tex]2(4)\frac{dx}{dt} = 2(\sqrt{17} )(-1)[/tex]

[tex]\frac{dx}{dt} = \frac{-\sqrt{17} }{4}[/tex] = -1.031 m/s

Answer:

3 feet

Step-by-step explanation:

To find x, we can write the following equation:

x + 4 + x = 10

2x + 4 = 10

2x = 6

x = 3 feet

Answer: 0.0548

Step-by-step explanation:

Given, A research study investigated differences between male and female students. Based on the study results, we can assume the population mean and standard deviation for the GPA of male students are µ = 3.5 and σ = 0.05.

Let [tex]\overline{X}[/tex] represents the sample mean GPA for each student.

Then, the probability that the random sample of 100 male students has a mean GPA greater than 3.42:

[tex]P(\overline{X}>3.42)=P(\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}>\dfrac{3.42-3.5}{\dfrac{0.5}{\sqrt{100}}})\\\\=P(Z>\dfrac{-0.08}{\dfrac{0.5}{10}})\ \ \ [Z=\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}]\\\\=P(Z>1.6)\\\\=1-P(Z<1.6)\\\\=1-0.9452=0.0548[/tex]

hence, the required probability is 0.0548.

Answer: [tex]S=0.087p[/tex] .

Step-by-step explanation:

Equation for direct proportion:

y=kx

, where x= independent variable ,

y=dependent variable.

k= proportionality constant

Here, State sales tax S  is directly proportional to retail price p.

Also, dependent variable= S,  independent variable =p

Required equation: S= kp

Put S= 12.32 and x= 142

[tex]S=12.32=k(142)\\\\\Rightarrow\ k=\dfrac{12.32}{142}\approx0.087[/tex]

Hence, the required equation is [tex]S=0.087p[/tex] .

Answer:

$10 to rent shoes for 9 people

Step-by-step explanation:

Total amount of the party = $140

A bowling lane = $50

$140 - $50 = $90

$90 divided by 9 = 10

$10 to rent shoes for 9 people