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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 probability that the spinner will land on grey and then purple is 1/18.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

Number of grey regions = 1

Number of purple regions = 2

Total number of regions = 6

Now,

The probability that the spinner will land on grey.

= Number of grey regions / Total number of regions

= 1 / 6

The probability that the spinner will land on purple.

= Number of purple regions / Total number of regions

= 2 / 6

The probability that the spinner will land on grey and then purple.

= 1/6 x 2/6

= 1/6 x 1/3

= 1/18

Thus,

The probability that the spinner will land on grey and then purple is 1/18.

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The smallest number among the given options is 0.07.

To determine the smallest number, we compare the given options. Among the numbers 0.5, 0.17, 0.07, 1.7, and 0.071, the smallest number is 0.07. This can be determined by examining the decimal places. The number 0.07 has the fewest decimal places and is the smallest value.

When comparing decimal numbers, the digits after the decimal point are crucial.

In this case, we observe that 0.07 has the smallest digit in the hundredths place, while the other numbers have larger digits in that place. Therefore, 0.07 is the smallest number among the given options.

It is important to note that the order of magnitude (the number before the decimal point) does not affect the comparison when determining the smallest number among decimal values.

In summary, by comparing the decimal places, we find that 0.07 is the smallest number among the given options.

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Answer:

3^3

Step-by-step explanation:

Exponents

9^3 can be rewritten as

3^2 ^3

Using exponent rules a^b^c = a^ (b*c)

3^2^3 = 3^6

3^6 / 3^3

We know that a^b / a^c = a^(b-c)

3^6 / 3^3  = 3^(6-3) = 3^3

Answer:

2nd answer is correct

Step-by-step explanation:

We know that,

[tex] \rightarrow \sf {x}^{a} \times {x}^{b} = {x}^{a + b} \\ \rightarrow \sf \frac{{x}^{a} }{ {x}^{b} } = {x}^{a - b} \\ \rightarrow \sf( {x}^{a} )^{b} = {x}^{ab} [/tex]

Accordingly, let us solve it now.

[tex] \sf \frac{ {9}^{3} }{ {3}^{3} } \\ \\ \sf \frac{ {3}^{2 \times 3} }{ {3}^{3} } \\ \\ \sf\frac{ {3}^{6} }{ {3}^{3} } \\ \\ \sf {3}^{6 - 3} \\ \sf {3}^{3} [/tex]

[tex]a(t+z)=45z+67\implies at+az=45z+67\implies az=45z+67-at \\\\\\ az-45z=67-at\implies \stackrel{common~factoring}{z(a-45)}=67-at\implies z=\cfrac{67-at}{a-45}[/tex]

The number of laps around the lake that Latrell jogs is 5 1/4 laps.

A fraction simply means a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

From the information he jogs 7 miles and each lap is 4/3 miles. The number of laps will be:

= Total laps / Number of miles

= 7 ÷ 4/3

= 7 × 3/4

= 21 / 4.

= 5 1/4 laps.

He jogs 5 1/4 laps.

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Answer:

Step-by-step explanation:

the equation of the cone is given already

r=6 inches

h=7 inches

Substitute in the equation =84pi=263.89

for the sphere substitute the radius r= 6 inches in the equation, and then divide by 2. This is because the spherical shale in top of the cone is half a sphere, as it can be clearly seen.

So It’s 288pi= 904.78 /2 =452.39

add the volume of cone and volume of sphere

The final answer is 716.28 inches^3

The constant of proportionality of the graph shows how many centimeters a bamboo plant can grow and the number that the plant has been growing is 5.

We know that the constant of proportionality is nothing but the slope of the line.

The slope of the line is given by;

Slope = Change in y-coordinate / change in x-coordinate

We are given:

The numbers below are what the dots are plotted-

10, 50

20, 100

30, 150

40, 200

50, 250

Take any two points.

Let us choose (20, 100) and (30, 150).

Put the values in the slope formula;

Slope = (150 - 100) / (30 - 20) = 50 / 10 = 5

So, the slope of the line is 5.

Thus, the constant of proportionality of the graph shows how many centimeters a bamboo plant can grow and the number that the plant has been growing is 5.

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The quantity of violas Kiara collected is 76

From the question, we are to determine the quantity of violas Kiara collected.

From the given information,

"Kiara and Lee are collecting violas in a ratio of 2:5"

First, we will determine the sum of ratios

Sum of ratios = 2 + 5 = 7

Also, from the given information

The total number of violas they collected is 266

Thus,

The quantity of violas Kiara collected will be

2/7 × 266

= 2 × 38

= 76

Hence, the quantity she collected is 76

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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!

Answer:

18243.906

Step-by-step explanation:

Find how much water is used in 1 hour and then multiply that by 3

24325.208/4

6081.302

6081.302x3

18243.906

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:

[tex]x^{3}[/tex]-3[tex]x^{2}[/tex]-3x+9          

Step-by-step explanation:

(x-3)([tex]x^{2}[/tex]-3) = 0

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

There is Watusi's speed is 6miles per hour (mph), Ubangi's speed is 3 mph, and Pigmy's speed is 21 mph.

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

Let x represent Watusi's speed,

y represent Ubangi's speed,

And z represents Pigmy's speed.

According to the given information, we can write the system of equations as

x + y + z = 30  .....(i)

z + 2x/3 = 22 - y  .....(ii)

4x + 3y - z = 12  .....(iii)

The above system of equations gives the values of x, y, and z when solving

x = 6, y = 3, z = 21

This means Watusi's speed is 6miles per hour (mph), Ubangi's speed is 3 mph, and Pigmy's speed is 21 mph.

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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 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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The 30 feet by 14 feet by 8 feet, filled in 3.5 hours by two pipes in which one pipe is 1 more than twice the other, indicates;

1. The rational equation from which the time the smaller pipe takes to fill the pool is; [tex]t = \dfrac{3360}{x} =\dfrac{3360}{959-2\cdot x }[/tex]

2. The solution of the equation is t ≈ 10.51 hours

3. The time it takes to fill the pool using only the small pipe is about 10.51 hours

Rational equation are equations that have rational polynomial expressions.

The dimensions of the pool are;

Length = 30 feet

Width = 14 feet

Depth = 8 feet

1. Let x represent the flow rate of the slower pipe

The flow rate of the faster pipe = 2·x + 1

Time it will take both pies to fill the pool = 3.5 hours

The volume of the pool, V = 30 × 14 × 8 = 3360

The volume of the pool is 3360 cubic feet

The rate equation is therefore;

[tex]\dfrac{x}{3360} +\dfrac{2\cdot x+1}{3360} =\dfrac{1}{3.5}[/tex]

[tex]\dfrac{x}{3360} =\dfrac{1}{3.5} - \dfrac{2\cdot x+1}{3360}[/tex]

From the rate equation above, the time it takes the smaller pipe to fill the pool is; t = 3360/x therefore;

[tex]t = \dfrac{3360}{x} =\dfrac{3360}{959-2\cdot x }[/tex]

2. Solving for x from the volume of water in the pool, V, therefore;

The volume of water that fills the pool, V, is found from the equation;

V = 3.5 × (2·x + 1 + x) = 10.5·x + 3.5

V = 10.5·x + 3.5

Therefore;

3360 = 10.5·x + 3.5

[tex]x = \dfrac{3360-3.5}{10.5} =319.\overline 6[/tex]

t = 3360/319.[tex]\overline 6[/tex] ≈ 10.51

The time it takes to fill the pool using only the smaller pipe is approximately 10.51 hours

Aliter;

[tex]\dfrac{3\cdot x}{3360} =\dfrac{1}{3.5}-\dfrac{1}{3360}[/tex]

[tex]t = \dfrac{3360}{x} =\dfrac{3}{\left(\dfrac{1}{3.5}-\dfrac{1}{3360}\right)} \approx 10.51[/tex]

3. The interpretation of the solution is that it takes about 10.51 hours for the smaller pipe working alone to fill the pool

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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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The specifications of the furniture as an absolute value inequality is |x - 18| ≤ 0.1      .

In the question ,

it is given that ,

the specification of the furniture , is 17.9 ≤ w ≤ 18.1 ,

where w is the width of the desk drawer in inches .

we need to write the given inequality in absolute inequality form ,

we know that the a-b < x < a+b , then the absolute inequality is |x-a|<b ,

On comparing the given inequality with a-b < x < a+b ,

we get

a - b = 17.9 and

a + b = 18.1

adding both the equations , we get

2a = 36

a = 36/2

a = 18

Substituting a = 18 in a + b = 18.1 , we get

18 + b = 18.1

b = 18.1 - 18

b = 0.1

The required inequality is |x-a| ≤ b .

|x - 18| ≤ 0.1

Therefore , The specifications of the furniture as an absolute value inequality is |x - 18| ≤ 0.1   .

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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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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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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.

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

Answer: 1840 pounds

Step-by-step explanation:4x4=16

460 x 4 = 1840

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?

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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The value of P0.05 < 0.19658. We do not reject the null hypothesis. There is not sufficient evidence that the mean age is less than 26 years.

According to the question we will set up Hypothesis

Null,  H0: U=26

Alternate, H1: U<26

Test Statistic

Population Mean(U)=26

Sample X(Mean)=24.4

Standard Deviation(S.D)=9.2

Number (n)=25

we use Test Statistic (t) = x-U/(s.d/√(n))

to =24.4-26/(9.2/√(25))

to =-0.87

| to | =0.87

Critical Value

The Value of |t α| with n-1 = 24 d.f is 1.711

We got |to| =0.87  & | t α | =1.711

According to this, we have to make a decision

Hence Value of  |to | < | t α |

P-Value: Left Tail -Ha : ( P < -0.8696 ) = 0.19658

Hence Value of P0.05 < 0.19658

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