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An expression is defined as a set of numbers, variables, and mathematical operations. The male cheetah's average speed for the last month is 20 mph.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

A.) Let the male cheetah's average speed for the last month be represented by x.

Given the male cheetah runs at a speed of 26 mph, that is 30% faster than his average last month.

x + 30% of x = 26 mph

1.30x = 26

x = 20 mph

Hence, the male cheetah's average speed for the last month is 20 mph.

B.) Sadie makes 1.5 liters of iced tea. She pours a liter into a pitcher to take to her neighbor. Her sister drinks the remaining iced tea. Therefore,

Iced tea Sadie's sister drink  = 1.56 liters - 1 liter = 0.56 liter

Hence, the amount of tea Sadie’s sister drinks is 0.56 liters.

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The volume of the cylinder with height 6 meters and the radius 18 meters is [tex]6,104.16 m^{3}[/tex].

The volume of a cylinder is the capacity of the cylinder which calculates the amount of material quantity it can hold.

Given that, the height of a cylinder=6 meters and the diameter of a cylinder=6×6=36 meters (A diameter that is 6 times the measure of the height)

Now, radius [tex](r)=\frac{d}{2} =18 meters[/tex]

[tex]\pi =3.14[/tex]

We know that, the volume of the cylinder[tex]=\pi r^{2} h[/tex]

[tex]=3.14\times 18^{2} \times 6 m^{3}[/tex]

[tex]=6,104.16 m^{3}[/tex]

Hence, the volume of the cylinder with height 6 meters and the radius 18 meters is [tex]6,104.16 m^{3}[/tex].

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The total number of red cars is 34, the total number of blue cars is 36, and the total number of silver cars is 70.

The ratio problems can be solved as follows:

11. The total number of red cars can be calculated as follows:

Number of red car in the first car park = (1 / (1 + 2 + 3)) * 60 = 10

Number of red car in the second car park = (3 / (2 + 3 + 5)) * 80 = 24

Total number of red cars = 10 + 24 = 34

12. The total number of blue cars can be calculated as follows:

Number of blue car in the first car park = (2 / (1 + 2 + 3)) * 60 = 20

Number of blue car in the second car park = (2 / (2 + 3 + 5)) * 80 = 16

Total number of blue cars = 20 + 16 = 36

13.  The total number of silver cars can be calculated as follows:

Number of silver car in the first car park = (3 / (1 + 2 + 3)) * 60 = 30

Number of silver car in the second car park = (5 / (2 + 3 + 5)) * 80 = 40

Total number of silver cars = 30 + 40 = 70

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Answer:

h = 17.5 m

Step-by-step explanation:

We have 2 similar right triangles as models of the situation

one has legs with George's height and shadow

the other is the height h of the tree and length of it's shadow

the corresponding sides of the 2 triangles are in proportion, that is

[tex]\frac{6.25}{h}[/tex] = [tex]\frac{10}{28}[/tex] ( cross- multiply )

10h = 175 ( divide both sides by 10 )

h = 17.5 m

english and maths teacher

Answer:

ED + EF < DF

Step-by-step explanation:

shorter side lengths added together > larger side length

however, smaller side lengths are < larger

So ED + ED < DF means that this cannot be a triangle

Answer:

ED + EF < DF

(second option listed)

Step-by-step explanation:

for a triangle, the sum of the two shorter side lengths must be greater than the larger side length

so we know that the two smaller lengths (DE and FE) would have to add up to be greater than the larger side length (DF)

because this is not the case, we know that we cannot construct a triangle

[to construct a triangle:]

smaller + smaller > bigger

DE + FE > DF; which is false/not the case

so because DE + FE < DF, we cannot form a triangle

so, ED + EF < DF explains why these three segments cannot construct a triangle

The distance traveled is 62.8 inches.

We know that the gear is rigidly attached to the center of the wheel. This means that in one complete rotation of the gear, we also have a complete rotation of the wheel.

Then the distance that the bicycle travel with a single rotation of the gear is equal to the circumference of the wheel, which is:

C = 2*pi*R

Where pi = 3.14 and R is the radius, which we know is 10inches.

Then:

C = 2*3.14*10in = 62.8in

The distance traveled is 62.8 inches.

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Answer:

14.3 km  (1 d.p.)

Step-by-step explanation:

To find the mean, divide the sum of all data values by the total number of data values.

If Mark ran a mean distance of 13.2 km in five days, we can use the mean distance for each of the 5 days in our calculation.

[tex]\begin{aligned}\implies \sf mean\:distance & = \sf \dfrac{13.2+13.2+13.2+13.2+13.2+20}{6}\\ & \sf =\dfrac{86}{6}\\\\ & = \sf 14.3\:km\:\:(1\:d.p.)\end{aligned}[/tex]

Answer:

A

Step-by-step explanation:

I think your right!

Answer:

B

Step-by-step explanation:

I think it means the roots, at which the line crosses the x-axis, in which case, the answer is B, 0 and 1.4

The equivalent expression is: .[tex]3\frac{3}{8}[/tex]

An expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division)

Given:

(- 2 1/4)/(- 2/3)

=-9/4÷ (-2/3)

= -9/4 * (-3/2)

= 27/8

= [tex]3\frac{3}{8}[/tex]

Hence, the equivalent fraction is [tex]3\frac{3}{8}[/tex].

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Answer:

The basic way to calculate the number of members is finding the area under the curve. The total members are 20

Step-by-step explanation:

The given graph shows that how many team members have a particular weight.

The first rectangle shows that 5 team members have a weight of 115kg.

The second rectangle shows that 3 team members have a weight of 115kg.

The third rectangle shows that 2 team members have a weight of 115kg.

The forth rectangle shows that 0 team members have a weight of 115kg.

The fifth rectangle shows that 3 team members have a weight of 115kg.

The sixth rectangle shows that 4 team members have a weight of 115kg.

The seventh rectangle shows that 3 team members have a weight of 115kg.

So, the total team members are = 5 + 3 + 2 + 0 + 3 + 4 + 3 = 20

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No. Because the x is raised to the 2nd power the equation is not linear.

The years in which Tina's raise was more than $0.50 an hour over the previous year are

2002

2004

2005

2006

2007

From the question, we are to determine the years in which her raise was more than $0.50 an hour over the previous year

Considering the graph

Her raise was $6.50 - $5.50 = $1.00

Her raise was $7.00 - $6.50 = $0.50

Her raise was $7.75 - $7.00 = $0.75

Her raise was $8.50 - $7.75 = $0.75

Her raise was $10.50 - $8.50 = $2.00

Her raise was $11.50 - $10.50 = $1.00

Hence, the years in which Tina's raise was more than $0.50 an hour over the previous year are

2002

2004

2005

2006

2007

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Answer:

C

Step-by-step explanation:

I guess it is the answer because the manager separates the customers into 3 ange groups and randomly selects a sample from each group

Answer:

B. Stratified random sampling

Step-by-step explanation:

Answer:

Graph A is correct.

Step-by-step explanation:

Graph A is the graph with the open circle and the arrow pointing to the right.

Answer:

according to my calculation it is 13

Step-by-step explanation:

hope I helped

In the given graph point B is a relative maximum with the coordinates (0, 2).

The given function is [tex]y=x^{4}-2x^{2} +1[/tex].

In the given graph, we need to find which point is a relative maximum.

The function's graph makes it simple to spot relative maxima. It is the pivotal point in the function's graph. Relative maxima are locations where the function's graph shifts from increasing to decreasing. A point called Relative Maximum is higher than the points to its left and to its right.

In the graph, the maximum point is (0, 2).

Therefore, in the given graph point B is a relative maximum with the coordinates (0, 2).

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Answer:

vertex: (3,1)

y-intercept = (0,-8)

x-intercept- Smaller=2 Larger=4

Domain= all real numbers, identity, infinite

Range= 1 is greater than or equal to y

axis of symmetry=3

Step-by-step explanation:

Answer:

1/2(8 + x)

Step-by-step explanation:

In this statement, it tells us to add 8 and x and then multiply that with 1/2.

If I am driving the train , the colour of the eye will be my eye colour.

The questions that do not need critical reasoning while only need logical thinking to find the answer.

It is given that the "If you are driving a train and your going over 180 mph, and you pass 20 houses, 10 stores, 3 gas stations, and 1 hospital per every ten minutes"

If I am driving the train , the colour of the eye will be my eye colour.

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There is an infinite number of length-width pairs that will result in a diagonal value of c.

Let a = the length. This is unknown.

Let b = the width. This is unknown.

Let c = the diagonal. This is a known value.

We have a right triangle with side a, side b, and hypotenuse c.

Since this is a right triangle, we will use the Pythagorean Theorem.

The Pythagorean Theorem is

[tex]c^2 = a^2 + b^2.[/tex]

Rearranging this formula gives

[tex]a^2 = c^2 - b^2[/tex]

And,[tex]a = \sqrt{(c^2 - b^2)}[/tex]

Now, if you chose a value for the width, b, then you can compute the corresponding for the length, b, since c is a known value. If you chose another value for the width, you can compute the length value corresponding to your width value.

There is an infinite number of length-width pairs that will result in a diagonal value of c.

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To eliminate the y terms and solve for x in the fewest steps, the first equation 4x - 3y = 34 should be multiplied by 2, and the second equation 3x + 2y = 17 should be multiplied by 3 before adding them.

Elimination is a process of solving a system of equations to eliminate one variable and solve for the other.

To eliminate the y terms from the equations,

first equation: 4x - 3y = 34, and

second equation: 3x + 2y = 17,

we take the L.C.M. of the coefficients of y, that is 3 and 2, which is 6, and multiply the equation by the value = (LCM of the coefficients/respective coefficient of y).

That is, for :

the first equation, we multiply the equation by (LCM of the coefficients/respective coefficient of y) = 6/3 = 2.

the second equation, we multiply by (LCM of the coefficients/respective coefficient of y) = 6/2 = 3.

Thus, to eliminate the y terms and solve for x in the fewest steps, the first equation 4x - 3y = 34 should be multiplied by 2, and the second equation 3x + 2y = 17 should be multiplied by 3 before adding them.

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Answer:

33

Step-by-step explanation:

do it in reverse

there are 3 numbers

average is 20

that means total is 20 times 3 which is

60

7+20+x=60

27+x=60

x=60-27=

33

Answer:

x = 33

Step-by-step explanation:

we find the "average" of a data set by adding all of the numbers in the data set together, and then dividing by the number of numbers/values present

for example,

the average of 2 and 20

2 + 20 = 22

(there are two numbers, so we divide by 2)

22 / 2 = 11

so, this example has an average of 11

we can apply the same logic to a variable:

we know that

[tex]\frac{20+7+x}{3}[/tex]  = 20

We can now solve for x:

[tex]\frac{20+7+x}{3}[/tex] = 20  

 · 3          ·3      {multiply both sides by 3}

20 + 7 + x = 60  {combine like terms}

27 + x = 60  {subtract 27 from both sides to isolate x}

x  = 33

{check answer:
7 + 20 + 33 = 60

60 / 3 = 20      (divided by 3 because we have 3 numbers) }

so, the value of x is 33

(x = 33)

hope this helps!!

Answer:

A = -12

B = -8

C = -4

Step-by-step explanation:

[tex]y=2x-8[/tex]

x = -2

[tex]y=2(-2)-8=-4-8=-12[/tex]

A = -12

x = 0

[tex]y = 2 (0)-8=-8[/tex]

B = -8

x = 2

[tex]y = 2 (2) -8 = 4-8 = -4[/tex]

C = -4

Hope this helps

The optimal ticket price is $ 65.The amount of tickets sold is 39000 and the amount of the extra revenue will be $ 135000.

What is the objective function?

The objective function is simply an equation that represents the goal production capability that relates to maximizing profits from manufacturing.

Current revenue;

⇒ 80 × 3000 = 240000

From the given condition the price decrease by 0.5 times. So that the ticket sold will be 300 times the cost. The inequality relationship is found as;

30000+300x  49282

x≤64

The revenue value is found as;

y = ( 80 - 0.5 x )(30000+300 x)

y=-150 x²+9000 x+2400000

The value of x is found as;

[tex]\rm x= \frac{9000}{150 \times 2 }\\\\ x=30[/tex]

Hence, the optimal ticket price is $ 65.The amount of tickets sold is 39000 and the amount of the extra revenue will be $ 135000.

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Answer:

1) 8 m^3

2) 125 + 25

3) 8

Step-by-step explanation:

1) It's a cube shape => length = width = height = 2 m

Volume = length × width × height = 2 × 2 × 2 = 8 m^3

2) 5^2 + 5^3 = 150

25 + 125 = 150

3) Now she is 8 years old (8 = 2^3)

Next year she'll be 9 years old (9 = 3^2)

By functional analysis we have the following conclusion about the function given: The domain for f(x) is all real numbers greater than or equal to 2.

Domain is the set of x-values such that the value of the function exists. By algebra we know that the domain of polynomials is the set of all real numbers, whereas the domain of radical functions is the set of x-values such that y ≥ 0. If we know that f(x) = 2 · x² + 5 · √(x - 2), then the domain is restricted by the radical component and defined by x ≥ 2.

By functional analysis we have the following conclusion about the function given: The domain for f(x) is all real numbers greater than or equal to 2.

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1≥2x and 6x≥3+8x-4 are correct representations of the inequality 6x ≥ 3 + 4(2x – 1).Option A,B and C are correct.

Inequality is a sort of equation in which the equal sign is missing. As we will see, inequality is defined as a statement regarding the relative magnitude of two claims.

The solution to the given inequality is;

6x≥3+4(2x-1)

6x≥3+8x-4

2x≤1

x≤(1/2)

The correct options are;

A)1 ≥ 2x

B)6x ≥ 3 + 8x – 4

C)A number line from negative 1.5 to 1.5 in increments of 0.5. A point is at 0.5 and a bold line starts at 0.5 and is pointing to the left.

1≥2x and 6x≥3+8x-4 are correct representations of the inequality 6x ≥ 3 + 4(2x – 1).

Hence, options A, B, and C are correct.

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Answer:

A, B, C

Step-by-step explanation: