A fence is to be installed around a rectangular field. The field's perimeter is 208 feet. Find the dimensions of the field if the length of the
field is 4 feet more than the width, as shown in the figure to the right (use P=2L+2W)

Since Julie earns a constant rate of $12 per hour, for working 16 hours based on mathematical operations, she will earn $192.

The basic mathematical operations involve addition, subtraction, division, and multiplication.

These operations combine parts of the mathematical operations with their assigned operands and the equation symbol (=) to solve mathematical problems.

In this situation, we employ division and multiplication operations to solve the requirement.

Loren and Julie's Total Income Table

Hours    2   4   6   8   10   12  14   16   18

Dollars 18 36 54 72 90 108    ?    ?  162

Loren's Constant Rate of Pay (Hourly Rate) = $9 ($162/18)

Hours     3  6   9    12  15    18  21    24    27

Dollars 36 ? 108 144 180 216    ?  288 324

Julie's Constant Rate of Pay (Hourly Rate) = $12 ($324/27)

Total hours worked = 16

Total earnings = $192 ($12 x 16)

Thus, when Julie works 16 hours, she earns $192.

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The height of the lighthouse is 76.4 feet.

What is the angle of elevation?

The angle is formed by the line of sight and the horizontal plane for an object above the horizontal.

We can use the concept of trigonometry to solve this problem. We know that the angles of elevation and depression are formed by the line of sight of the sailor and the height of the lighthouse.

We can use the tangent function to relate these angles to the height of the lighthouse.

Tangent of angle of elevation = opposite side / adjacent side

Tangent of angle of depression = opposite side / adjacent side

Let h be the height of the lighthouse.

tan(21) = h / 200

tan(14) = h / (200 + h)

now we can use these equations to find h,

h = (200 * tan(21)) = (200 * (opposite side/adjacent side)) = (200 * (h/200))

h = 200 * tan (21)

and

h = (200* h)/(200+h) * tan(14)

we can now use these equations to find the value of h.

h = 200 * tan(21) = 200 * 0.38197 = 76.394

Therefore, the height of the lighthouse is 76.4 feet (approx).

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Answer:

Provided at image

Step-by-step explanation:

Green dot = -3.5

Red dot = -5/6

Orange dot = 2.3

Since there are 5 lines between every 1 number, you can divide 100/6 to see the distance between the lines (16.6666) and plug in the points.

Answer:

A I THINK

Step-by-step explanation:

Observing the given question, This is the problem of cryptarithmetic , Using the rules based on cryptarithmetics, The answer is 10890.

Mathematical conundrums called cryptarithmetic problems use letters from the alphabet in place of the digits. Use the trial-and-error procedure while keeping in mind the aforementioned considerations to solve cryptarithmetic problems by replacing values for the letters. Depending on whether we have a carry from A+A or not, A can now either be 2 or 3. However, since E=2, A must be 3, and there is a carry as a result.

Cryptarithm, a type of mathematical game where the object is to solve an arithmetic puzzle in which the numerical digits have been replaced with letters. Cryptarithm, a type of mathematical game where the object is to solve an arithmetic puzzle in which the numerical digits have been replaced with letters.

Applying cryptarithmetic rules,

First alphabets can't be zero and same digit can't be used for different alphabets.

we get, CBDE + ABAE = AEDCE as 9480+1410 = 10890

AEDCE = 10890.

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Considering the expression of a line, the slope of line that passes through points (-2,7) and (-3,3) is 4.

A linear equation o line can be expressed in the form y = mx + b

where

Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope m can be calculated as:

m= (y₂ - y₁)÷ (x₂ - x₁)

In this case, being (x₁, y₁)= (-2, 7) and (x₂, y₂)= (-3, 3), the slope can be calculated as:

m= (3 -7)÷ (-3 -(-2))

m= (3 -7)÷ (-3 +2)

m= (-4)÷ (-1)

m= 4

Finally, the slope is 4.

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Answer: The expression in simplified form is D. 3x³√15

To simplify the expression, we can first simplify the fractions.

2/1356 can be simplified to 12/225.

Then, we can use the distributive property to simplify the expression further.

12/225 - 3√156 = 12/225 - 18√15

The last step is to combine the terms,

12/225 - 18√15 = (-6/75) - (6√15) = -6/5 * (1/5 - √15) = -6 * (- √15/5) = 3 * √15 * 6

Therefore, the simplified form of the expression is D. 3x³√15

Step-by-step explanation:

According to the end behavior of the function h(z) = 5x³-9x²+4x+96, the graph is positive on the intervals (-∞, -8) and (-4, 3).

What is a polynomial function?

In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable.

The given polynomial function is -

h(z) = 5x³-9x²+4x+96

The end behavior of a function f(x) describes the behavior of the function as x approaches +∞, and as x approaches -∞.

Domain of function h(z) = -∞<x<∞

The end behavior of the function h(z) is -

lim x→∞, (5x³-9x²+4x+96) = ∞

as x→∞, h(z)→∞

lim x→-∞, (5x³-9x²+4x+96) = -∞

as x→-∞, h(z)→-∞

Therefore, the graph is positive on the intervals (-∞, -8) and (-4, 3).

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Step-by-step explanation:

n×2=?

The n means 1 then. 1×2 series

1 × 2 = 2

Answer:

x =5 units

Mark me as a brainiest

The value of 3.2 times 3.2 to the second power to the fourth power to all is [tex](3.2)^{12}[/tex].

The amount of times a number has been multiplied by itself is shown by its exponent.

3.2 to the second power is represented as [tex](3.2)^2[/tex].

3.2 times 3.2 to the second power, thus, is represented as:

[tex](3.2) (3.2)^2[/tex]

Since, the base is similar, the powers can be added:

[tex](3.2)^{1+2}\\\\(3.2)^3[/tex]

Now, the fourth power to all is represented as:

[tex]((3.2)^3))^4\\[/tex]

Using the rule of exponents [tex]((a^m))^n = a^{mn}[/tex] we have:

[tex](3.2)^{3*4}\\\\(3.2)^{12}[/tex]

Hence, the value of 3.2 times 3.2 to the second power to the fourth power to all is [tex](3.2)^{12}[/tex].

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The graph of the function y = ∛(x +1 ) - 2 is represented by the graph represented by option 1.

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

The expression that established the relationship between the dependent variable and independent variable is referred to as a function. In the function as the value of the independent variable varies the value of the dependent variable also varies.

The graph of the function y = ∛(x +1 ) - 2 is attached with the answer below,

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Answer:

Jayden will earn $3.21 x 18 = $<<3.21*18=57.78>>57.78 from running 18 miles.

So he will have $7.69 + $57.78 = $<<7.69+57.78=65.47>>65.47 in total.

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

See the screenshot below.

Answer:

8 quarts of white soda

Answer:

-6 , 19 , 29

Step-by-step explanation:

range = output which is required

domain = input which are given -2,3,5

simply plot the value domain one by one in given equation

The inequality equations for the rides High-Bounce, Climb-A-Thon, and Twirl-O-Coaster are 55<h<7, h<60, and h>=58 respectively.

What is an inequality?

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides.

Let the unknown height be h.

For the ride High-Bounce, the height requirement is between 55 and 72 inches tall.

This can be written in the inequality form as 55<h<72.

For the ride Climb-A-Thon, the height requirement is under 60 inches tall.

This can be written in the inequality form as h<60.

For the ride Twirl-O-Coaster, the height requirement is 58 inches minimum.

This can be written in the inequality form as h>=58.

The representations of these inequalities on number lines is given below.

Therefore, the inequalities are - 55<h<7, h<60, h>=58.

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The problems for production staff are solved as below.

Division is one of the operation in mathematics where number is divided into equal parts as that of a definite number.

1. Knit

Number produced by 1 worker in a day = 50 pairs

Annual production goal = 780,000 pairs

Daily production goal = 780,000 / 260 = 3000 pairs

Production staff needed = 3000 / 50 = 60 workers

2. Tube

Number produced by 1 worker in a day = 40 pairs

Annual production goal = 946,400 pairs

Daily production goal = 946,400 / 260 = 3640 pairs

Production staff needed = 3640 / 40 = 91 workers

3. Athletic

Number produced by 1 worker in a day = 60 pairs

Annual production goal = 1,138,800 pairs

Daily production goal = 1,138,800 / 260 = 4380 pairs

Production staff needed = 4380 / 60 = 73 workers

4. Booties

Number produced by 1 worker in a day = 24 pairs

Annual production goal = 343,200 pairs

Daily production goal = 343,200 / 260 = 1320 pairs

Production staff needed = 1320 / 24 = 55 workers

5. Children's

Number produced by 1 worker in a day = 84 pairs

Annual production goal = 518,000 pairs

Daily production goal = 518000 / 260 = 1992.3 pairs

Production staff needed = 1992.3 / 84 = 23.7 workers

Hence the production staff needed has been solved.

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The ratio of dogs to cats is 7 to 9

From the question, we have the following parameters that can be used in our computation:

You have 99 cats and 77 dogs and 10998 horses

The ratio is represented as

Ratio = Dogs : Cats

Substitute the known values in the above equation, so, we have the following representation

Dogs : Cats = 77 : 99

Divide by 11

Dogs : Cats = 7 : 9

Hence, the ratio is 7 to 9

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Answer:

A. 18

Step-by-step explanation:

............... .....k

The bearing of R from  P is 172°.

The horizontal angle between an object's direction and either north or another object is known as a bearing or azimuth in navigation. You can specify the angle value in a number of different angular units, including degrees, mils, and grad.

The angle between the magnetic north and the absolute bearing

The angle between the craft's forward motion and the relative bearing.

Given The bearing of P from Q is 040°.

The bearing of R from Q is 124°.

QR = QP.

Bearing angles are 180 degrees different than forward-bearing angles. This difficulty can be resolved by combining these relations with the standard angle sum relation for triangles.

Angle PQR will be the difference in the bearings from Q to P and Q to R:

 ∠PQR = 124° -40° = 84°

Triangle PQR is isosceles, so the base angle at P will be ...

 ∠QPR = (180° -  84°)/2 = 48°

The bearing from P to R will be 48° less than the bearing from P to Q. The bearing from P to Q is 180° more than the bearing from Q to P.

PR bearing = PQ bearing - ∠QPR

= PQ bearing - 48°

= (40° +180°) - 48° = 172°

  Hence, The bearing of R from P is 172°.

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The percent of the variation in mileage that cannot be explained by differences in the cars ages is 36.1%.

A statistical indicator of the strength of a linear relationship between two variables is the correlation coefficient. A correlation coefficient is a statistical indicator of how well changes in one variable's value predict changes in another. When two variables are positively correlated, the value either rises or falls together.

The correlation r between the age of a car x , and the cars mileage, y is 0.639. This means that 63.9 % of the variation in mileage can be explained by the differences in the cars ages, 100 – 63.9 = 36.1% of the variation cannot be explained.

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There is a percent decrease of about 43.75%

Percentages are fractions with 100 as the denominator. In other words, it is the relation between part and whole where the value of whole is always taken as 100. They are used like fractions and decimals i.e ways to describe parts of a whole.  While using percentages, the whole is considered to be made up of a hundred equal parts. The symbol % is used to show that a number is a percentage

New Process = 45 mins

Old Process = 1 hour and 20 minutes (80mins)

Increase/Decrease = Old Process - New Process

Increase/Decrease = 80 - 45

Increase/Decrease = 35

Therefore there is reduction in the manufacturing process;

% decrease = (35/80) x 100

% decrease = 43.75%

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Answer:

(5,6)

Step-by-step explanation:

x -y = -1

x - 3y = -13 ⇒ multiply through by -1 ⇒ -x + 3y = 13  Add this to the first equation

-x + 3y = 13

x   -  y = -1

       2y = 12  Divide both sides by 2

         y = 6

To find y substitute 6 for y in the equation x - y = -1

x - 6 = -1  Add 6 to both sides

x = 5

(5,6)

Answer:

You can bowl up to 4 games.

Step-by-step explanation:

2.25 + 2.50x ≤ 12.25

Let x = the number of games you bowl

2.25 + 2.50x ≤ 12.25  Subtract 2.25 from both sides

2.25 - 2.25 + 2.50x  ≤ 12.25 - 2.25

2.50x ≤ 10  Divide both sides by 2.50

[tex]\frac{2.50x}{2.50}[/tex]  ≤ [tex]\frac{10}{2.50}[/tex]

x ≤ 4

The value of ∠A is 101°.

A parallelogram is a geometric object with sides that are parallel to one another in two dimensions. It is a form of polygon with four sides (sometimes known as a quadrilateral) in which each parallel pair of sides have the same length. A parallelogram has adjacent angles that add up to 180 degrees.

Given a quadrilateral,

whose opposite sides are parallel, the figure is parallelogram,

property of a parallelogram says

ABCD is a parallelogram, where AB || CD and AD || BC.

Also, AB = CD and AD = BC

so ∠A = ∠C & ∠B = ∠D

given ∠C = 101°

so ∠A = ∠C = 101°

Hence the value of ∠A is 101°.

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The percentage of the people surveyed who were completely satisfied with the car was 55 %.

To find the percentage of people surveyed who were completely satisfied with the car, you first need to find the number of people who were survyed. This can be found by adding up all the number of people who participated in the survey :

= 1, 100 + 740 + 160

= 2, 000 people

The percentage of the people surveyed who were completely satisfied with the car is therefore:

= People completely satisfied / Number of people who participated x 100 %

= 1, 100 / 2, 000 x 100 %

= 55 %

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Answer:

----------------------------------

Solve the equation:

Answer:

[tex] \sf \: d) \: x = 7[/tex]

Step-by-step explanation:

Given equation,

→ -3 - (-8) - (-2) = x

Now the value of x will be,

→ -3 - (-8) - (-2) = x

→ x = -3 - (-8) - (-2)

→ x = -3 + 8 + 2

→ x = 5 + 2

→ [ x = 7 ]

Hence, the value of x is 7.

a) The least squares estimate of the slope (b₁) can be calculated using the formula:

b₁ = (n∑(xy) - (∑x)(∑y)) / (n∑(x^2) - (∑x)^2)

Where n is the number of observations, x and y are the explanatory and response variables, respectively.

b₁ = (5*(35+13+44+36+58) - (3+1+4+3+5)(5+3+4+6+8)) / (5*(3^2+1^2+4^2+3^2+5^2) - (3+1+4+3+5)^2) = 0.8

b) The least squares estimate of the intercept (b₀) can be calculated using the formula:

b₀ = (∑y - b₁*(∑x))/n

b₀ = (5+3+4+6+8-0.8*(3+1+4+3+5))/5 = 3.4

c) The point estimate of y when x=2 can be calculated using the equation of the line:

y = b₀ + b₁x

y = 3.4 + 0.82 = 4.8

So the point estimate of y when x=2 is 4.8

In probability and statistics, a random variable is a variable whose possible values are numerical outcomes of a random event. It is a function that maps outcomes of a random experiment to a real number. It can be discrete, meaning it can take on only a countable number of values, or it can be continuous, meaning it can take on any value within a given range. The probability distribution of a random variable describes the likelihood of different outcomes occurring. It can be used to calculate expected values, variances, and other measures of statistical dispersion.

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Answer:

12

Step-by-step explanation:

4 / 12   =  12 / 36      so answer : 12

That was just by looking.....here is mathematical way :

4/ x  = x/36       cross multiply

144 = x^2

x = 12