A 70-meter path surrounds a rectangular garden. The width of the garden is two-thirds its length. Find its area (in m2).

Answer: The solution set of the system of inequalities is the region above the dashed line (y=-2x-2) and below the solid line (y=x+4).

The range of values possible for the length of her garden is 19 ≤ length ≤ 36 .

In the question ,

it is given that ,

the length of the deer resistant fence = 110 ft

let the width of the garden be "x" ,

and let the length of the  garden be "y" .

So , the equation representing the perimeter of the rectangular garden is

2(x + y) = 110

y = 55 - x

and the equation representing the area of the rectangular garden is

xy = 684

Substituting the value of y = 55 - x in xy = 684 ,

we get ,

x*(55 - x) = 684

55x - x² = 684

x² - 55x + 684 = 0

x² - 36x - 19x + 684 = 0

x(x - 36) -19(x - 36) = 0

(x - 19)(x - 36) = 0

x = 19            OR        x = 36 .

Substituting the values of x= 19 we get

the length (y) = 55 - 19 = 36

putting the values of x = 36 , we get

the length (y) = 55 - 36 = 19 .

So , we get the range of length as   19 ≤ y ≤ 36 .

Therefore ,  The range of values possible for the length of her garden is 19 ≤ length ≤ 36 .

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The answer will be (1,3), (3,2), and (4,5), reflation along the x-axis and so on when we did the transformation.

What is are of triangle?

The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.

After reflation along the x-axis, the triangle's vertices are (1,3), (3,2), and (4,5).

Upon reflation along the y-axis, the triangle's vertices are (-1,-3), (-3,-2), and (-4,-5).

The triangle's vertices are (-3,1), (-2,3), and (-2,4) following reflation across y=x (-5,4).

Hence the transformation have done and all the points have to mentioned above.

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Answer: -$250.00

Step-by-step explanation:

[tex][(5000)(0.09)+150000(0.0040)]-1300 =-\$250[/tex]

The expected value of the policy to the insurance company is  -$ 250

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the value of probability owners of hours of worth between $120,000 to $170,000 making a claim of $ 5000 = 0.09

Let the value of probability of the house and contents being totally destroyed = 0.0040

Now , the tragedy happens and the company pays = $ 150,000

The amount the insurance company charges = $ 1300

So , the equation will be

The expected value of this policy to the insurance company =
( probability owners of hours of worth between $120,000 to $170,000 making a claim of $ 5000 x $ 5000 ) + ( the amount company pays x 0.0040) - amount the insurance company charges

So , the equation will be

The expected value of this policy to the insurance company =
( ( 0.09 x 5000 ) + ( 150000 x 0.0040 ) - 1300 )

The expected value of this policy to the insurance company =
( ( $ 450 + $ 600 - $ 1300 )

The expected value of this policy to the insurance company = - $ 250

Hence , The expected value of policy to the insurance company is -$ 250

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Answer:

Step-by-step explanation:

17

Answer:

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

Answer:

$10,307.11

Step-by-step explanation:

Compound Interest Formula

[tex]\large \text{$ \sf A=P\left(1+\frac{r}{n}\right)^{nt} $}[/tex]

where:

Given:

Substitute the given values into the formula and solve for A:

[tex]\implies \sf A=8200\left(1+\dfrac{0.058}{2}\right)^{2 \times 4}[/tex]

[tex]\implies \sf A=8200\left(1+0.029\right)^{8}[/tex]

[tex]\implies \sf A=8200\left(1.029\right)^{8}[/tex]

[tex]\implies \sf A=8200\left(1.25696445...\right)[/tex]

[tex]\implies \sf A=10307.10856...[/tex]

Therefore, the value of Sarah's investment after four years is $10,307.11 (nearest cent).

The measures are:

The opposites sides of a parallelogram are parallel. Here, PQ ‖ RT and PR ‖ QT.

The opposite sides of a parallelogram are equal. Here, PQ = RT and PR = QT

The opposite angles of a parallelogram are equal. Here, ∠P = ∠T and ∠Q = ∠R

The diagonals of a parallelogram bisect each other. Here, RE = EQ and PE = ET

Same-side interior angles supplement each other. Here, ∠PRT + ∠RTQ = 180°, ∠RTQ + ∠TQP = 180°∘, ∠TQP + ∠QPR = 180°, ∠QPR + ∠PRT = 180°

The diagonals divide the parallelogram into two congruent triangles. Here, ΔRPQ is congruent to ΔQTR, and ΔRPT is congruent to ΔQTP

Therefore,

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Answer:1/2

Step-by-step explanation:

Answer:

x = 3 3/8

Step-by-step explanation:

I believe you would have to solve it with the reverse operation. If

x - (-2 7/8) = -1/2, than x has to be -1/2 more than -2 7/8. Because they are both negative numbers, the answer will be positive.

-2 7/8 + -1/2 = 3 3/8  x = 3 3/8

3 3/8 - (-2 7/8) = -1/2

Feel free to correct me. I hope you do well.

The value of mean is 158 and the value of standard deviation is 190.99

Let m be mean

Mean= sum/ n

Mean= (1730+1689+1326+1614+1460+1867+1430) / 7

m= 11116 / 7

M= 1588

Mean= 158

Standard deviation sample formula is :

S.D=sqrt((|x-m|^2)/ n-1)

So let start find |x-m|^2

For 1st: |1730-1588|^2=20164

For 2nd: |1689-1588|^2=10201

For 3rd: |1326-1588|^2=68644

For 4th: |1614-1588|^2=676

For 5th: |1460-1588|^2=16384

For 6th: |1867-1588|^2=77841

For 7th: |1430-1588|^2=24964

Summation of |x-m|^2 = 218874

Standard deviation formula is:

S.D = sqrt((summation of |x-m|^2) / n-1)

S.D=sqrt(218874/6)

S.D=sqrt(36479)

S.D=190.99

Therefore the mean and standard deviation  is 1588 and  190.99

The complete question is : A person's metabolic rate is the rate at which the body consumes energy. Metabolic rate is important in studies of weight gain, dieting, and exercise. Here are the metabolic rates of 7 men who took part in a study of dieting. (The units are calories per 24 hours. These are the same calories used to describe the energy content of foods.) 1730 1689 1326 1614 1460 1867 1430 Calculate the mean and standard deviation of the metabolic rates, showing each step in detail.

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The regular price of the table based on the information is $177.41.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

Let the regular price be x.

Since the table is on sale for 100.80, which is 76% less than the regular price, that will be illustrated as:

x = 100.80 × (100% + 76%)

x = 100.80 × 1.76

x = 177.408

The value is $177.41.

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The value of P(8)=0.0039

What is binomial distribution?

The binomial distribution gives out either success or failure as two possible results in an experiment, is the discrete probability distribution used in probability theory and statistics.

In binomial terms, what is PMF?

Since the 17th century, researchers have focused on the binomial probability mass function, a discrete probability mass function that is particularly popular. It applies to numerous experiments with two possible results, such as the heads-or-tails coin toss or the decay-or-no decay radioactive nucleus experiment.

let x ~ Binomial(n=20, p=0.7)

Use following binomial p.m.f:

[tex]P(x)=^{n}C_{x}p^{x}(1-p)^{n-x}[/tex]

[tex]P(x=8)=^{20}C_{8}(0.7)^{8}(0.3)^{20-8}[/tex]

P(x=8)=0.0039

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The number of elements of event E n(E) is 70.

The selecting of r items out of n items is done by using Combination. The formula for combination is as follows,

[tex]C(n,r)=\frac{n!}{r!(n-r)!}[/tex]

Where n is the total number of elements and out of which r is selected and ! is factorial sign and n is greater than or equal to r.

Now, Finding the number of elements in the event E that at least two 5-dollar bills are drawn from the bag.

Here, three bills are drawn out of which at least two 5-dollar bills must be drawn, so

[tex]n(E)=C(5,2)\times C(6,1)+C(5,3)\\\\=\frac{5!}{2!(5-2)!} \times \frac{6!}{1!(6-1)!} +\frac{5!}{3!(5-3)!}\\\\=10\times6+10\\=70[/tex]

Therefore, the number of elements n(E) in event E is 70.

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Answer:

138.16 inches

Step-by-step explanation:

C=Circumference. r=radius. d=diameter

C=2πr

C=2π(d/2)  ==> a radius is half of a diameter

C=2(d/2)π

C=dπ ==> simplify

C=44π

C=44*3.14

C=138.16 inches

Answer:

Equation.

Step-by-step explanation:

The term equation state that the two expression are equal that means left hand side of the expression and right hand side of expression are equal.

Whereas if the two equation are not equal then it is known as inequality.

Thus, the given statement is correctly filled with equation.

The number of adults is 882 adults.

The number of teenagers is 252 teenagers.

The number of children is 441 children.

From the information, 1575 people visited the amusement park. 56% of the visitors were adults, 16% were teenagers, and 28% were children ages 12 and under.

The number of adults will be:

= 56% × 1575.

= 882 adults

The number of teenagers will be:

= 16% × 1575

= 252 teenager

The number of children will be:

= 28% × 1575

= 441 children

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Answer:

Number of adults

56/100×1575=882

Number of teenagers

16/100×1575=252

Number of children

28/100×1575=441

The equation of the line is 1st line f(x)= y=x+5 for -3≤x≤4, 2nd line f(x)=y=2/3x for -6≤x≤-3.

Given that,

In the picture we have a graph with 2 lines.

We have to find the equation of the lines and the limits.

The slope of the line and a point on the line can be used to create the equation of a line. Let's learn more about the line's slope and the crucial point on the line in order to better understand how the equation for a line is created.

y=mx+b

We can see the lines,

The 1st lines has -3≤x≤4

The 2nd line has -6≤x≤-3

First we find the 1st line

The points are (0,5) and (1,6)

Slope of the line is m is rise/ run

m = 6-5/1-0

m =1

Take the equation of the line

y=mx+b

5=1(0)+b

b=5

We get the first equation of the line as y=x+5.

Second we find the 2nd line

The points are (-3,-2) and (-6,-4)

Slope of the line is m is rise/ run

m = -4+2/-6+3

m =-2/-3

m=2/3

Take the equation of the line

y=mx+b

-2=2/3(-3)+b

-2=-2+b

b=0

We get the first equation of the line as y=2/3x.

Therefore, the equation of the line is 1st line f(x)= y=x+5 for -3≤x≤4, 2nd line f(x)=y=2/3x for -6≤x≤-3.

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Answer:

a) (-9)/10

Step-by-step explanation:

Given number,

→ -(9/10)

Now the equivalent number is,

→ -(9/10)

→ -9/10

→ (-9)/10

Hence, the answer is (-9)/10.

The value of -2−(−10) in a addtition expression is 8.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

Addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them.

In this case, -2 - (-10) will be:

= -2 -(-10)

= -2 + 10

= 8

The value is 8.

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Answer: 104.1

Step-by-step explanation:

If [tex]P(t)[/tex] represents the initial population in millions. [tex]t[/tex] years after 1990, then [tex]P(t)=64e^{0.027t}[/tex].

2008 is 18 years after 1990, so [tex]P(18)=64e^{0.027 \cdot 18} \approx 104.1[/tex]

The exponential growth of population in 2008 is 95.4 million

What is exponential growth factor?

The exponential growth or decay formula is given by

x ( t ) = x₀ × ( 1 + r )ⁿ

x ( t ) is the value at time t

x₀ is the initial value at time t = 0.

r is the growth rate when r>0 or decay rate when r<0, in percent

t is the time in discrete intervals and selected time units

Given data ,

Let the population of the country in 1993 be = 64 million

The exponential growth rate r = 2.7 %

So , the population of the country in 2008 is calculated by

The time t in years = 2008 - 1993

                               = 15 years

So , the equation for exponential growth rate is given by

x ( t ) = x₀ × ( 1 + r )ⁿ

And substituting the values in the equation , we get\

x ( 15 ) = 64 × ( 1 + 0.027 )¹⁵

x ( 15 ) = 64 × ( 1.027 )¹⁵

x ( 15 ) = 64 × 1.49127

x ( 15 ) = 95.4413

So , the value of x ( 15 ) = 95.4 million

Hence , The exponential growth of population in 2008 is 95.4 million

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The transformations are:

The transformations that appear here are:

Vertical dilation:

For a function f(x), a vertical dilation of scale factor k is written as:

g(x) = k*f(x)

Horizontal translation:

For a general function f(x), a horizontal translation of N units is written as:

g(x) = f(x + N).

If N is positive, the shift is to the left.If N is negative, the shift is to the right.

Vertical translation:

For a general function f(x), a vertical translation of N units is written as:

g(x) = f(x) + N.

If N is positive, the shift is upwards.If N is negative, the shift is downwards.

so:

f(x) + 5.5 is a translation of 5.5 units upwards.

5.5*f(x) is a vertical dilation of scale factor 5.5

f(x + 5.5) is a translation of 5.5 units to the left.

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Answer:

-2

Step-by-step explanation:

Look at the bottom right point. To get to the point above it only moving vertical and horizontally, you would move 2 units up (or vertically) and one unit left (or horizontally).

The slope is negative.  Imagine a person starting on the very left side of the line and he starts walking.   As he walks on the line, he is going down hill.  That tells us that the slope is negative.

The graph of the function g(x) is described as 5 units translation down.

A visual representation or diagram that represents data or values is known as a graph.

The function equations are provided as

f(x) = 1/3x+1

f(x) - 1 = 1/3x

g(x) = 1/3(6x) + 1

g(x) = (1/3x)6 + 1

In the equation g(x) = (1/3x), replace f(x) with f(x) - 1 = 1/3x.

6 + 1

Thus, we have

g(x) = (f(x) - 1)

6 + 1

g(x) = 6f(x) - 6 + 1

g(x) = 6f(x) - 5

The rule mentioned above means that:

A translation of the function f is the function g(x) (x)

As a result, the translation's unit is 5 and its direction is downward.

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Answer:

Step-by-step explanation:

You want the minimum number of pie slices and the amount of sugar in each such that the sugar in each slice is less than 22 grams when the whole pie has 187.64 grams of sugar.

The sugar in each of n slices is 1/n times the sugar in the whole pie. You want ...

  (187.64 g)/n < 22 g

Multiply by n/(22 g) to get

  n > 187.64/22

  n > 8.53

The smallest whole number that satisfies this inequality is n = 9.

The minimum number of pie slices is 9.

When the sugar in the pie is divided into 9 equal parts, each part is ...

  (187.64 g)/(9 slices) = 20.85 g/slice

Each slice of pumpkin pie will contain about 20.85 grams of sugar.

Answer:

Step-by-step explanation:

the answer is 9

Using mathematical operations, Joanna needs an additional $2.25 to meet her requirements for the zoo visit.

The additional amount that Joanna requires is calculated with mathematical operations of addition and subtraction.

First, when you add $12.25 to $15.00, the sum is $27.25. This sum is subtracted from $25 or vice versa to get a difference of $2.25, which is the additional amount required to pay for her expenses at the zoo.

Another way to work out the difference is to first subtract the entrance fee of $12.25 from Joanna's amount. The difference becomes the minuend from which the amount of the snacks (the subtrahend) is deducted to obtain the difference as -$2.25.

Thus, with mathematical operations, Joanna's required additional amount is $2.25.

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Joanna has $25 to spend at the zoo. Admission costs $12.25, and she plans to buy snacks worth $15.00.  How much more does she require to meet her needs at the zoo?

Answer:

Step-by-step explanation:

know it isnt the best but here gives

a. The ratio of the height of the building to the number of floor is 14:1

b. the unit rate is 14ft per floor and this means that each floor is 14ft high.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity. Ratios can be classified into two types. One is part to part ratio and the other is part to whole ratio. The part-to-part ratio denotes how two distinct entities or groups are related.

if h is the height of the building and n is the number of floor.

Therefore h:n= h/n

h:n = 112/8

divide through by 8

h:n= 14/1=14:1

the unit rate is therefore 14feet per floor and this means that one floor has a height of 14 feet.

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Answer: 1/60

Step-by-step explanation:

1/4 times1/4  times 1/4 eqauls 1/60

The three inequalities will be :

1) 400 + 15x > 520

2) 520 < 400 + 15x

3) 15x > 120

Given,

In the question:

Dan’s dog-walking job pays $15 per hour.

His job as a car-wash attendant pays $400 each week.

Walking dogs to earn more than $520 in a week.

To find the which three inequalities can model this situation?

Now, According to the question:

Car wash = $400 per week

Dog - walking = $15per hour

To earn more than $520 in a week .

Let the hour be = x hour

Based on the given conditions:

Hence, The three inequalities will be :

1) 400 + 15x > 520

2) 520 < 400 + 15x

3) 15x > 120.

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