Simplity (34)-1

1/34
1/3-4
-34
33

Answer:

5

Step-by-step explanation:

Multiples of 1: 1, 2, 3, 4, 5, 6, 7, ...

Multiples of 5: 5, 10, 15, 20, 25, ...

The smallest number that appears in both lists is 5, and that is the least common multiple.

The actual area of the park in square miles is 21600 miles².

A map of a rectangular park has a length of 4 inches and a width of 6 inches. It uses a scale of 1 inch for every 30 miles.

* Lets explain how to solve the problem

- A drawing that shows a real object with accurate sizes reduced or

 enlarged by a certain amount called the scale

- Drawing scale is a ratio between the drawing length and the

 actual length

- To find the actual dimensions from the drawing dimensions use the

scale drawing

* Lets solve the problem

- A map of a rectangular park has a length of 4 inches and a width

 of 6 inches

∴ The drawing dimensions are:

# length = 4 inches

# width = 6 inches

- The scale of the map is 1 inch for every 30 miles

∴ The scale drawing is 1 : 30

- To find the actual area find the actual dimensions

∵ The scale drawing is 1 : 30

∵ The length = 4 inches and the width = 6 inches

- By using cross multiplication

∴  1        :        30

  4       :  actual length

  6       :  actual width

∴ Actual length = (4 × 30)/1 = 120

∴ Actual length = 120 miles

∴ Actual width = (6 × 30)/1 = 180

∴ Actual Width = 180 miles

∴ The actual dimensions are 120 miles and 180 miles

∵ The area of any rectangle = length × width

∴ The actual area = 120 × 180 = 21600

∴ The actual area 21600 miles²

Hence the answer is the actual area of the park in square miles is 21600 miles².

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The solutions to the rectangles located on the coordinate plane questions in the first page are;

1. Jordan ran a total distance of 6 miles

2. The fourth vertex is located at (5.5, -3.5)

3. The area of the pool is 48 square yards

The area of a figure is the region covered by the closed boundary of the shape or figure.

1. The coordinates of the points expressed as decimals are;

H(-0.75, 0.5), B(1, 0.5), L(1, -0.25), (0.5, -0.25), C(0.5, -0.75), S(-0.75, -0.75)

The distances between the points Jordan visited are;

HB = 1 - (-0.75) = 1.75

BL = |-0.25 - 0.5| = 0.75

LP = |0.5 - 1| = 0.5

PC = |-0.75 - (-0.25)| = 0.5

SC = |-0.75 - 0.5| = 1.25

SH = 0.5 - (-0.75) = 1.25

The total distance Jordan ran = 1.75 + 0.75 + 0.5 + 0.5 + 1.25 + 1.25 = 6

The total distance Jordan ran is 6 miles

2. The shape of the piece of material = A rectangle

The vertices of the rectangle are; (-1.2, -3.5), (-1.2, 4.4) and (5.5, 4.4)

The above vertices indicates that the sides of the rectangle are parallel to the x and y-axis as each two of the three points share a common coordinate

(-1.2, -3.5) and (-1.2, 4.4) represent a vertical side

(-1.2, 4.4) and (5.5, 4.4) represent a horizontal side

Therefore, based on plotting the points on the coordinate plane using MS Excel, we have;

(-1.2, -3.5) and (5.5 ,-3.5) will represent the other horizontal side

(5.5, 4.4) and (5.5, -3.5) represents the other vertical side

The coordinates of the fourth vertex is (5.5, -3.5)

3. The vertices of the pool are;

A(-5, 7), B(1, 7), C(1, -1), and D(-5, -1)

The length of the sides of the pool are;

AB = 1 - (-5) = 6

BC = 7 - (-1) = 8

CD = 1 - (-5) = 6

AD = 7 - (-1) = 8

The length of the rectangular pool = 8 yards

The width = 6 yards

The area of a rectangle = Length × Width

Area of the pool = 8 yard × 6 yards = 48 square yards

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If x = -7 and y = 3, the value of the expression (x+y/x-y)²  is​  4/25  .

In the question ,

it is given that ,

the algebraic expression is given as  (x+y/x-y)² ,

we need to find the value of the given expression when the value of x = -7 and y = 3 .

Substituting the values of x = -7 and y = 3 in the expression ,

we get

= (x+y/x-y)²

= ((-7+3)/(-7-3))²

= (-4/(-10))²

= 16/100      

cancelling out the common factor 4 , from the numerator and denominator .

= 4/25

Therefore  , the value of the given expression at x = -7 and y = 3 is 4/25  .

The given question is incomplete , the complete question is

Calculate the value of the expression (x+y/x-y)²​ at x = -7 and y = 3 ?

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By using the concept of depreciation, it is obtained that

New population  after 9 years = 24012

What is Depreciation?

Depreciation is the decrease in the value of a population or any asset over a period of time at a certain rate.

The concept of depreciation has been used here

Original population = 28800

Rate of decrease of population = 2%

Time = 9 years

New population  after 9 years = [tex]28800(1 - \frac{2}{100})^9[/tex]

                                                  = [tex]28800({1 - \frac{1}{50})^9\\[/tex]

                                                  = [tex]28800(\frac{49}{50})^9[/tex]

                                                  = 24011.94

                                                  = 24012

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The equation that passes through the point (7, -2) and (11, 5) is y = 4/7x - 9

Equation of the line:

The standard form of the equation of the line is written as

y = mx + b

here

x and y represents the coordinates of the equation

m refers the slope of the equation

b refers the y intercept of the equation

Given,

Here we have the points (7, -2) and (11, 5).

Now we have to find the equation that passes through this points.

If you want to find the equation of the line, we have to find the slope and the intercept of the line.

The slope of the line is calculated by using the given point (7, -2) and (11, 5),

=> m = (11 - 7) / ( 5 - (-2))

=> m = 4/7

Now, we have to use the slope and the point (11, 5) to find the value of y intercept of the equation,

=> 5 = (4/7) (11) + b

=> 35 = 44 + b

=> b = -9

Therefore, the equation that passes through the points is y = 4/7x - 9

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Answer:

22 + h = 53

Step-by-step explanation:

I don't know if I am correct

Answer:

The answer is 31, H=31

Step-by-step explanation:

53-22=31 :)

The equation for the function described, using the translations, is given as follows:

f(x) = 2^(x - 4) + 5.

There are four cases for the translation of a parent function, and they can be represented as follows:

In the context of this problem, the parent function is defined as follows:

f(x) = 2^x

The definitions for each translation are given as follows:

Hence the translated function is defined as follows:

f(x) = 2^(x - 4) + 5.

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Step-by-step explanation:

The square mural in Olivia's classroom has dimensions x by x.

Then she paints a mural of dimensions: x+5 (the length) by x-2 (the width).

Thus the second mural (the hallway mural) has the shape of a rectangle with dimensions (x+5) by (x-2), so the area of the second mural is

(x+5)(x-2).

each side of the classroom mural is 7 feet means that x = 7 ft,

thus the area of the hallway mural is :

(x+5)(x-2)=(7+5)(7-2)=12*5=60 (square feet)

So the answer is 60 square feet.

Answer:

a) gradient

b) Line A and Line C

Step-by-step explanation:

Parallel lines are lines that have the same slope - they never intersect! Another name for slope is gradient.

Of all the lines in the image, only Line A and Line C will never intersect! They are parallel!

1a) The number of whole servings Susan can make from 4.25 pounds of flour if one serving uses ²/₃ is 6.

1b) The quantity of flour Susan has after making 6 servings is ¹/₄ pounds.

2) Garrison can drink ⁷/₈ gallons of lemonade each of the next six days.

3) The student council sold 122 bags of chips.

4) If a container can hold 3¹/₃ ounces of peanuts, 5 containers will hold 16²/₃ ounces.

5) The number of people at the football game (400) last night who were not wearing orange and black is 240.

6) The number of long sleeves in Jordan's outfits is 45.

The numbers and values can be determined using suitable mathematical operations.

The basic mathematical operations used include division, subtraction, and multiplication.

1) The total quantity of flour available = 4.25 pounds

The amount of flour required per serving = ²/₃ pounds

The number of servings from 4.25 pounds = 6³/₈ servings (4.25 ÷ ²/₃)

= 6 servings.

Quantity of flour left = ¹/₄ pounds [4 - 6(²/₃)]

2) The number of lemonades available = 5.5 gallons

The quantity Garrison took on Monday = ¹/₄ gallons (0.25)

The remaining number of gallons = 5.25 gallons (5.5 - 0.25)

The gallons for the remaining 6 days = ⁷/₈ gallons (5¹/₄ ÷ 6)

3) The total amount realized from sales = $73.20

The unit price per bag of chips = $0.60

The units sold = 122 ($73.20 ÷ $0.60)

4) The ounces of peanuts per container = 3¹/₃

The number of containers = 5

The ounces of peanuts for 5 containers = 16²/₃ ounces (3¹/₃ x 5)

5) The total number of people at the game = 400

The proportion of people wearing orange and black = ²/₅

The proportion of people not wearing orange and black = ³/₅ (1 - ²/₅)

The number of people not wearing orange and black = 240 (400 x ³/₅)

6) The total number of outfits in Jordan's closet = 200

The proportion of shirts = ³/₄

The proportion of long sleeve shirts = ³/₁₀

The number of long sleeve shirts = 45 (200 x ³/₄ x ³/₁₀)

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Answer:

2

Step-by-step explanation:

the rate of change is the coefficient of x

Based on the information given in the figure, you will agree with Andrew because ∆AEG ≅ ∆AFG by the AAS congruence postulate.

Two triangles that have a pair of congruent included sides that is non-included and two pairs of corresponding angles are proven to be congruent to each other by the AAS congruence postulate.

In the figure shown above, the following information are ascertained:

Thus, the above information shows that triangle AEG has two angles and one non-included side that are congruent to two corresponding angles and one non-included side in triangle AFG.

Therefore, you will agree with Andrea for stating that ∆AEG ≅ ∆AFG by the AAS congruence postulate.

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Answer:

Step-by-step explanation:We can find the sum of interior angles of any polygon using the following formula: where nis the number of sides of the polygon. For example, we use $latex n = 5$ for a pentagon. This formula works regardless of whether the polygon is regular or irregular.

At 95% of confidence interval estimate of the population is

(478.332, 471.668)

Given that,

Population standard deviation is assumed to be 50 hours.

Random sample of 30 light bulb

and, sample mean of 475 hours.

Sample size n =30,

x = 475 and σ = 50

At 95% confidence interval for μ is,

                           x ± zₙ₎₂ σ /n          -------------------- (1)

We already know that the table value of z = 1.96

At 95% confidence interval,

putting the values in equation (1),

                        x ± zₙ₎₂ σ /n

                = 475 ± 1.96 × 50/30

Taking the positive sign, we get,

                 = 475 + 1.96 × 1.7

                 = 475 + 3.332

                 = 478.332

Now,

Taking the negative value, we get,

                   = 475 - 1.96 × 1.7

                   = 475 - 3.332

                   = 471.668

Therefore, At 95% of confidence interval estimate of the population is

(478.332, 471.668)

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[tex]=\sqrt{2} *\sqrt{2} *\sqrt{2} *\sqrt{2} \\=(\sqrt{2} *\sqrt{2})(\sqrt{2} *\sqrt{2})\\=2*2\\=4[/tex]

The answer is 4

The value of [tex](\sqrt2)^4[/tex] is 4.

The number of times a number has been multiplied by itself is referred to as its exponent. The rules of multiplying exponents are of different types. The given equation can be calculated using the Power of a Power rule.

According to this rule, when a base has an exponent, and that entire term has an exponent, the exponents are multiplied together. This is written as

[tex](a^x)^y=a^{xy}[/tex]

Here, both exponents are multiplied together.

Therefore, using the above rule the given square root with an exponent can be written as,

[tex]\begin{aligned}\left(\sqrt2\right)^4&=\left(2^{\frac{1}{2}\right)^4\\&=2^{\frac{1}{2}\times4}\\&=2^2\\&=4\end{aligned}[/tex]

The value is 4.

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Answer:

y = -2x-13

1) plot the coordinate you have on a graph (starting at (0,0) move to the left until you hit -8 and then up until you are at +3)

2) Since your slope is negative the line will be higher on the left and lower on the right, so starting at the point you have plotted move down 2 units and to the right one unit.

3) Do this until you intersect with the y-axis (at -13), this is your value for 'b'

4) Plug your values for 'b' and 'm' into the slope-intercept equation

The equilateral triangle shown has three sides and three angles that are all the same. This should be the equilateral triangle theorem, however the answer selections do not cover it.

An equilateral triangle is a triangle with three equal-length sides in geometry. An equilateral triangle's sides are congruent, which indicates that all sides are the same length. All of the inner angles are also identical (60 degrees). An equilateral triangle is a triangle with all of its sides equal in length. Because the three sides are equal, the three angles opposing the equal sides are also equal in size. As a result, it is also known as an equiangular triangle, with each angle measuring 60 degrees.

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Step-by-step explanation:

below -2°

that means

-2 - 5 = -7° C

Answer:

-7 degrees

Step-by-step explanation:

Answer:

[tex]15\sqrt{5}[/tex]

Step-by-step explanation:

simplify [tex]\sqrt{20}[/tex] and [tex]3\sqrt{50}[/tex]

 [tex]\sqrt{20}[/tex] simplifies into [tex]\sqrt{5}[/tex]

 so [tex]\sqrt{20}[/tex] =  [tex]\sqrt{4} \sqrt{5}[/tex]

we can simplify [tex]\sqrt{4[/tex] into a whole number

[tex]\sqrt{4[/tex] =2

          =   2[tex]\sqrt{5}[/tex]

   [tex]\sqrt{50[/tex] simplifies into [tex]\sqrt{2[/tex]

   so [tex]\sqrt{50[/tex] =3( [tex]\sqrt{25} \sqrt{2}[/tex])

we can simplify [tex]\sqrt{25}[/tex] into a whole number

[tex]\sqrt{25[/tex] = 5

= 15[tex]\sqrt{2[/tex]

then we add these simplified roots back into the question

2[tex]\sqrt{5}[/tex] + [tex]5\sqrt{2[/tex] -[tex]2\sqrt{5[/tex]

we simplify again as [tex]2\sqrt{5[/tex] cancels out

to get a final answer of:
[tex]15\sqrt{5}[/tex]

If the agency has 3 cities, 1 month, and 3 airlines to choose from. then there are 9 different vacation packages they can offer.

What is the multiplication rule in permutation and combination?

1. Using the multiplication principle, we can count the number of ways to complete a sequence of tasks by multiplying the number of ways to complete each task together.

2. A permutation is a particular arrangement of objects.

Peaceful Travel Agency offers vacation packages.

If the agency has 3 cities, 1 month, and 3 airlines to choose from.

then by using the multiplication rule,

      The number of different packages = 3 × 1 × 3

                                                                 = 9 packages

Hence, If the agency has 3 cities, 1 month, and 3 airlines to choose from. then there are 9 different vacation packages they can offer.

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Answer:

105/8 = 13 1/8 = 13.125

Step-by-step explanation:

The first step is to turn the (-5 5/8) into a mixed number. The mixed number you should be getting is - 45/8. The second step is to convert the (-2 1/3) into a mixed number as well, your second mixed number should be -7/3. Next multiply the two fractions, - 45/8 x (-7/3) = 315/24.

We can simplify 315/24 by dividing by 3, so you'll divide 315 divided by 3 and 24 divided by 3 and you should get ... 105/8. So 105/ 8 is equal to

13 1/8. If you need this fraction in decimal form it is 13.125.

Interest will the charity have received after 3 years is £60

Jenny opens a "Charity Bank Account". Any interest gained goes to a local charity.

It pays 2% per annum simple interest.

She puts £1500 into the account.

interest will the charity have received after 3 years

Interest = PRT/100

Interest = 1500 x 2 x 3/100

Interest = 60

Therefore,  interest will the charity have received after 3 years is £60

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Answer: 1840 pounds

Step-by-step explanation:4x4=16

460 x 4 = 1840

a. The angle fact that Mohammed can use to find angle g is alternate angles

b) The angle fact that he then use to find angle h is alternate interior angles.

When two parallel lines are cut by a transversal, the resulting alternate interior angles or alternate exterior angles are congruent, according to the alternate angle theorem. To demonstrate: If a transversal cuts two parallel lines, the alternate interior angles are equal.

When two parallel lines are intersected by a transversal, the angles formed inside them are equal to their alternate pairs. These are known as alternate interior angles.

In this case, it should be noted that the angles will be 137° based on the illustration.

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Answer:

  y = -x -1

Step-by-step explanation:

You want an equation of the line parallel to y=-x+8 through point (3, -4).

The parallel line will have the same slope as the given line. That slope is the coefficient of x: -1.

The point-slope form of the equation of a line with slope m through point (h, k) is ...

  y -k = m(x -h)

You have m=-1, (h, k) = (3, -4), so the desired line has equation ...

  y -(-4) = -1(x -3)

  y +4 = -x +3 . . . . . . point-slope form

Add -4 to get this to slope-intercept form.

  y = -x -1 . . . . . . . . . slope-intercept form

The relation is shown in the graph is not a function. Two points have different y-values for the same x-value of 2.

What is a relation?

A relation in mathematics describes the connection between two sets of values for ordered pairs. The set of items in the first set are referred to as domain, and they are connected to the set of elements in the second set, referred to as range.

What is a function?

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable).

A relation becomes a function if there is an unique output for each input.

The given ordered pairs are (0, 0), (2, 0), (2, 2), and (3, 4).

First element of each ordered pair is the input and second element is output.

The inputs are 0, 2, 2,3. The outputs are 0, 0, 2, 4 .

For the input 2, there are 2 outputs 0 and 2.

The given relation is not a function.

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The number of angles that are formed by the intersection of the diagonals is 4.

A square is a four-equal-sided figure with diagonals cut perpendicular to each other, with a total of four angles formed by diagonals.

It is a geometrical figure with four sides, each of which must be equal, and an angle of 90 degrees between two adjacent sides.

Square area = Side²

The square's perimeter = 4 sides

Every square contains two diagonals. The intersection angle of both diagonals is 90 degrees. The number of diagonal angles equals four.

Therefore, the correct option is 4.

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Complete question

How many angles are formed by the intersection of the diagonals in a square?

The stratified random sampling is a sampling method that may allow for more accurate inferences to be made about a population.

It is the true statement.

Given,

In the question:

Stratified random sampling is a sampling method that may allow for more accurate inferences to be made about a population.

To check the above statement is true or false.

Now, According to the question:

Let's know about

Stratified random sampling is a method of sampling that involves the division of a population into smaller subgroups known as strata. In stratified random sampling, or stratification, the strata are formed based on members' shared attributes or characteristics, such as income or educational attainment.

In stratified random sampling, the strata are formed based on member's shared characteristics (e.g. female or male, occupation, education) or attribute (e.g. black or white).

Hence, The stratified random sampling is a sampling method that may allow for more accurate inferences to be made about a population.

It is the true statement.

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