The perimeter of a rectangle is 800 yards. What are the dimensions of the rectangle if the length is 50 yards more than the
width?

Answer:

1.3

Step-by-step explanation:

[tex]\frac{14100-13920}{14100} \times 100 \approx 1.3[/tex]

Using a system of equations, it is found that there are 204 boys at the school.

A system of equations is when multiple variables are related, and equations are built to find the values of each variable, according to the relations given in the problem.

For this problem, the variables are given as follows, considering the situation described:

The average of the number of boys, girls, male teachers, and female teachers is 117, hence:

(x + y + z + w)/4 = 117

x + y + z + w = 468.

The average of the number of boys, girls, and male teachers is 151, hence:

(x + y + z)/3 = 151

x + y + z = 453.

Then:

x + y + z + w = 468.

453 + w = 468

w = 15.

There are 6 fewer male teachers than there are female teachers, hence:

z = w - 6 = 15 - 6 = 9.

So:

x + y + z = 453.

x + y = 444.

The number of female teachers is 1/16 the number of girls, hence:

There are 204 boys at the school.

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Answer:

$14.67

Step-by-step explanation:

The value of the discount is,

→ (10/100) × 16.30

→ 0.1 × 16.30

→ $1.630

Then the amount he should pay is,

→ 16.30 - 1.630

→ $14.67

Hence, he must pay $14.67.

Answer:

=14.67

Step-by-step explanation:

0.10×16.30=1.63 or

16.30-1.63=14.67 or[tex]\frac{1467}{100}[/tex]

i

Answer:

9(10+5)

Step-by-step explanation:

because 10+5 is fifteen so then when you as them together you get the same expression as before

Answer:

9(10+5)

Step-by-step explanation:

because 10+5=15 and it's 9(15)

As given Paul's Bikes rents bikes for $11 plus $4 per hour and  Amanda paid $31 to rent a bike shows she rent the bike for 5hours.

As given in the question,

Let 'h' represents the number of hours

Paul's Bikes rents bikes for $11 plus $4 per hour

Amanda paid $31 to rent a bike

Required equation is:

31 = 11 + 4h

⇒4h = 20

⇒h = 5hours

Therefore, as given Paul's Bikes rents bikes for $11 plus $4 per hour and  Amanda paid $31 to rent a bike shows she rent the bike for 5hours.

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The derivative of the function y = (sin(7x))ln(x) is [tex]\frac{Sin(7x)}{x} +7*ln(x)*Cos(7x)[/tex]

Derivative of a function f(x) is defined as the rate of change of that function with respect to x at a point in its domain.

For Example , Derivative of [tex]3x^{2} =6x[/tex].

Product Rule of Differentiation

Let f(x) and g(x) be any two function. The derivative of their will be

F(x)=f(x)*g(x)

[tex]F'(x)=f(x)*g'(x)+g(x)*f'(x)[/tex]

Given y=(sin(7x))ln(x)

[tex]y'=Sin(7x)*\frac{d}{dx} ln(x)+ln(x)*\frac{d}{dx}Sin(7x)[/tex]

[tex]y'=Sin(7x)*\frac{1}{x} +ln(x)*Cos(7x)*7[/tex]

[tex]y'=\frac{Sin(7x)}{x} +7*ln(x)*Cos(x)[/tex]

Therefore , the derivative of the function y = (sin(7x))ln(x) is [tex]\frac{Sin(7x)}{x} +7*ln(x)*Cos(7x)[/tex]

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Answer: y = 8

Step-by-step explanation:

      Point-slope form is written as y - [tex]y_1[/tex] = m(x - [tex]x_1[/tex]) where m is the slope and ([tex]x_1[/tex] , [tex]y_1[/tex]) are points on the line.

      First, we need to find the slope. This can be found with change in y over change in x:

[tex]\displaystyle \frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

[tex]\displaystyle \frac{8-8}{-4--4}=\frac{0}{-4+4}=\frac{0}{0}=[/tex] undefined

      Now, we will plug this undefined slope (0) into the equation below. Anything times 0 is 0, so no matter what (x - [tex]x_1[/tex]) is, the right side of the equation will always be 0.

y - [tex]y_1[/tex] = m(x - [tex]x_1[/tex])

y - [tex]y_1[/tex] = (0)(x - [tex]x_1[/tex]) ➜ y - [tex]y_1[/tex] = 0

      Lastly, we will take the y-value of 8 and plug it into the equation and simplify.

y - [tex]y_1[/tex] = 0 ➜ y - (8) = 0 ➜ + 8 (y - 8) = (0) + 8

      y = 8

See attached for a visual explanation.

The change of 74.375 bushels is seen with around 86 bushels remaining with farmer for further sale.

We are given the total number of bushels as 160. Now, the average sale on each day is [tex]14\frac{7}{8}[/tex] bushels.

Converting this mixed fraction into fraction -

Average bushels sold everyday = ((8×14)+7)÷8

Performing multiplication and addition to find average bushels sold each day

Average bushels sold everyday = 119÷8

So, at this rate the total number of bushels sold in five days will be = (119÷8)×5

Performing multiplication and division on Right Hand Side of the equation to find the number of bushels

Total number of bushels sold in five days will be = 74.375

So, after five days of sale, the available number of bushels are 160 - 74.375

Change in number of bushels = 85.62

Rounding off to find the exact number of bushels = 86

Hence, the change of 74.375 bushels is seen with around 86 bushels remaining with farmer for further sale.

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The value of c is 25° and x is 116°.

From figure 1, we can see hat the entire angle is given to be 90°. This angle is divided into 2 parts, one is 65° and the other is c

This means that-

65 + c = 90

c = 90 - 65

c = 25

Thus, the value of c is 25°.

Now, in the 2nd figure, we can see that both the horizontal lines are parallel and a transversal is drawn between them.

Both the angles thus formed are opposite interior angles and are hence supplementary.

Therefore, (x - 20) + 84 = 180

x - 20 = 180 - 84

x - 20 = 96

x = 96 + 20

x = 116

Thus, the value of x is 116°

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When the velocity of the car is zero. Then the time will be 1 second.

The rate of change of a function with respect to the variable is called differentiation. It can be increasing or decreasing.

The position of a car is given, for positive t, by x = 9t - 3t³. x is in meters and t is in seconds.

We know that velocity is the rate of change of displacement. Then we have

v = dx / dt

v = 9 - 9t²

When the velocity of the car is zero. Then the time will be

v = 0

9 - 9t² = 0

1 - t² = 0

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

t = 1, -1

When the velocity of the car is zero. Then the time will be 1 second.

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The sum of the whole numbers from 1 to 680 is 231540.

Arithmetic sequence is a list of numbers where each number is equal to the previous number, plus a constant called the common difference.

The formula for sum of first n numbers can be expressed as;

Sₙ = (n/2)( a₁ + aₙ )

Where n is the number of terms, a₁ is the first term and aₙ is the nth term.

Given that,

The numbers are whole numbers from 1 to 680

Plug the given values into the equation above.

Sₙ = (n/2)( a₁ + aₙ )

S₆₈₀ = (680/2)( 1 + 680 )

S₆₈₀ = 340( 681 )

S₆₈₀ = 231540

Therefore, the sum of the whole numbers from 1 to 680 is 231540.

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Using algebraic expressions and equations, Carol should buy 2 t-shirts and 9 sweatshirts.

We can set up an algebraic expressions and equations to determine how many of each type of gift should Carol buy.

An algebraic expression is a number, variable, or the combination of both and operational symbols. On the other hand, an equation is the equality of two expressions separated by "=".

1. Write an equation for the total number of members.

x + y = 11   (equation 1)

where x is the number of members who will get t-shirt

y is the number of members who will get sweatshirt

2. If each t-shirt costs $5 and each sweatshirt costs $12, write an equation for the total amount spent buying the gift.

$5(x) + $12(y) = $118     (equation 2)

where x is the number of members who will get t-shirt

y is the number of members who will get sweatshirt

3. Rewrite equation 1 as an equation of y in terms of x.

x + y = 11   (equation 1)

y = 11 - x

4 . Plug in the expression for y in equation 2 and solve for x.

$5(x) + $12(y) = $118     (equation 2)

5x + 12(11 - x) = 118

5x + 132 - 12x = 118

-7x = -14

x = 2

5. Substitute the value of x in either equation 1 or 2 and solve for x.

x + y = 11   (equation 1)

2 + y = 11

y = 11 - 2

y = 9

Hence, Carol should buy 2 t-shirts and 9 sweatshirts.

Checking,

2 + 9 = 11

Each member will receive a gift.

2($5) + 9($12) =$118

Carol will be spending $118 for the gifts.

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Answer: The total number of stamps is 132.

Step-by-step explanation:

We know that Erin has 36 stamps.

Given that information, we can calculate how many stamps Julia has which is 2/3 as many stamps as Erin.

2/3 * 36 = 24

Julia has 24 stamps.

Julia also has 1/3 as many stamps as Robert.

24 = 1/3 * Robert

Robert = 72 stamps

Add the three numbers together to get your final answer

24 + 72 + 36 = 132

(x+3i)(x-3i)

A real number and an imaginary number are effectively combined to create a complex number. The complex number is written as a+ib, where a and ib are real and imaginary numbers, respectively. Additionally, I = √-1 and both a and b are real numbers.

Consequently, a complex number is a straightforward illustration of the addition of two integers, specifically a real number and an imaginary number. It consists of two parts: one that is entirely real, the other entirely fantastical.

Using complex numbers,

x²+81 = x² - (-9i)²

           = (x²- 9²i²)

           = (x+3i)(x-3i)

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Answer:

0.00000057652

Step-by-step explanation:

5.764 × 10^-7 = 0.0000005764 (move the decimal place 7 steps forward)

0.00000057652>0.0000005764 (65>64)

Therefore 0.00000057652 is greater.

Hope this helped! ^^

Applying it's properties, the limits of the functions are given as follows:

1. 9.

2. -2.

A limit is given by the value of function f(x) as x tends to a value. Algebraically, for continuous functions, we have that:

[tex]\lim_{x \rightarrow a} f(x) = f(a)[/tex].

Hence, applying the property above, for item 1, we have that:

limx→0 f(x−1)g(x) = f(0 - 1)g(0) = f(-1)g(0) = -3 x 3 = 9.

For item 2, we have that:

limx→0 f(x+4)+g(x) = limx→4 f(x) + limx→0 g(x) = 3 - 5 = -2.

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a. The conditional statement p → q is true

b. The converse q → p is False.

c. The inverse p → ~q is False

d. The contrapositive -q→ ~p is True

We are given the conditional statement;

Let p be "an animal is a puppy" and let q be "it is a dog."

a) The conditional statement p → q which is "If an animal is a puppy, then it is a dog" is true.

b) The converse statement q → p which is "If an animal is a dog, then it is a puppy" is false.

c) The inverse statement p → ~q which is "If an animal is not a puppy, then it is not a dog" is false.

d) The contrapositive statement: q → ~p which is  "If an animal is not a dog, then it is not a puppy" is true.

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Answer:

1.72m is height of man

Step-by-step explanation:

since we know tan60°=[tex]\sqrt{3}[/tex];

then here tan60°=height/base;

height =64-height of man (let be x)

base=36;

now

[tex]\sqrt{3}[/tex]=[tex]\frac{64-x}{36\\}[/tex]

x=64-36[tex]\sqrt{3}[/tex]

x=1.72 m

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Answer: Answer is 4(16 - 9[tex]\sqrt{3}[/tex])

Step-by-step explanation: Concept:

The term angle of elevation denotes the angle from the horizontal upward to an object. An observer’s line of sight would be above the horizontal.

tan θ = [tex]\frac{opposite}{adjacent}[/tex]

tan 60 =[tex]\sqrt{3}[/tex]

Given:

It is given that AB is the height of the man, the angle of elevation is 60°, the distance from the man to the tower BC is 36 m and the height of the tower is 64 m.

The height of the man AB.

In ΔADE

tan 60 = [tex]\frac{ED}{AD}[/tex]

[tex]\sqrt{3}[/tex] = [tex]\frac{ED}{36}[/tex]

36 [tex]\sqrt{3}[/tex] = ED

Now,

DC=CE-CD

CD = 64 -36  [tex]\sqrt{3}[/tex]

CD = 4(16 - 9  [tex]\sqrt{3}[/tex])

Now, given that  AB=CD

Therefore, The height of the man is 4(16 - 9[tex]\sqrt{3}[/tex])

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The probability that three of the children have sickle cell anemia and three of the children are healthy 13.2%.

Sickle cell anemia is an autosomal recessive condition, the trait is only visible in the homozygous state.

The parents are heterozygous( Aa × Aa), and the progeny (AA, Aa, Aa, and aa) have a normal probability of 3/4 and an affected probability of 1/4.

The binomial theorem can be used to calculate the probability of a normal and affected child:

Probability =  n! / x! ( n! - x!) × pˣqⁿ⁻ˣ.

Here, n is the total children 6,

Let 'x' be the normal child

Then, n! - x! is the affected child.

Let 'p' is the normal child probability (= 3/4) and

Then, 'q' is affected child probability (= 1/4).

Substituting the values in the formula;

probability = (6!/3!×3!)×(3/4)³×(1/4)³

on solving

probability = 0.1318

probability = 13.18%

probability = 13.2% (approximately)

Therefore,  the binomial theorem to determine the probability that three of the children have sickle cell anemia and three of the children are healthy is 13.2%.

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Answer:

32

Step-by-step explanation:

[tex]5\cdot \:5+7[/tex]

The total distance covered is 6,000 m.

Distance is defined as an object's total movement without regard for direction. Distance can be defined as how much ground an object had also covered regardless of its starting as well as ending point.

Now, as per the question;

The distance around track is 400 m.

14 more laps has been covered along with the initial one.

Thus the total distance will be;

Total distance  = 400 + 400×14

                         = 400 + 5,600

Total distance  = 6,000

Therefore, the total distance covered is 6,000 m.

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Answer:

Step-by-step explanation:

Y-3x=13+3x

The sample mean of the given data is 24.

To find the mean:

Therefore, the sample mean of the given data is 24.

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, <--- That is called a comma

The actual mean weight of the infants when they were 1 month old is 4.297

The residual plot doesn't show any obvious leftover pattern, confirming that a linear model is appropriate.

the equation of this line as ˆy=12x−1 with an accent on the y to indicate that the y-values computed using this equation

y = 4.88 + 0.267(1)

y = 5.147

residual = -0.85 = A - 5.147 + 5.147

residual = 4.297

the actual mean weight of the infants when they were 1 month old is 4.297

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The cardianality of the set {2, 4, 6, 8, 10, 12} is 6.

According to the given question.

We have a set {2, 4, 6, 8, 10, 12}.

Here, we have to find the cardianality of the set  {2, 4, 6, 8, 10, 12}.

As we know that, the cardinality of a set is a measure of the number of elements of the set.

From the given set {2, 4, 6, 8, 10, 12} we can say that the total number of elements in the given set is 6. So, the cardianality of the set is 6.

Hence, the cardianality of the set {2, 4, 6, 8, 10, 12} is 6.

Thus, option b is correct.

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