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Answer: a) It costs more money to make 101 photocopies than 100 photocopies. This can be seen from the graph as the cost increases as the number of photocopies increases.

b) You cannot buy more than 500 photocopies with $40. This can be seen from the graph as the cost of making photocopies exceeds $40 when the number of photocopies is more than 500.

Step-by-step explanation:

The solution is,

a)  it costs more money to make 100 photocopies

b) you can buy more than 500 photocopies for $40

Here, we have,

we know that,

A pair of numbers that use the separations between the two reference axes to define the location of a point on a coordinate plane. usually represented by the x- and y-values, respectively, (x, y).

a) In the  graph , 100 photocopies cost $10,

For 101  photocopies, the point on the line comes below of 10 on y axis

So, it costs more money to make 100 photocopies

b)  graph arrow shows line moves on...

so, you can buy more than 500 photocopies for $40

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Answer:

17

Step-by-step explanation:

To solve this problem, we need to use the distance between two points formula. It states that the distance is [tex]\sqrt{(x_{1} - x_{2} ) ^{2} + (y_{1} - y_{2})^{2} }[/tex]. Here, [tex]x_{1} = 1, x_{2} = 9, y_{1} = 0, y_{2} = 15[/tex]. Plugging these values in gets us [tex]\sqrt{64 + 225}[/tex] which equals [tex]\sqrt{289}[/tex] = 17 .

Step-by-step explanation:

To calculate the potential energy of the ball at its highest point, we first need to find the gravitational potential energy of the ball. Gravitational potential energy is given by the equation:

PE = mgh

where m is the mass of the ball, g is the acceleration due to gravity (9.8 m/s^2 on the surface of the earth), and h is the height of the ball above the ground.

At its highest point, the height of the ball is 80 m, so the gravitational potential energy can be calculated as:

PE = m * g * h = m * 9.8 * 80

where m is the mass of the ball.

Since the ball was thrown at an angle of 30 degrees with the horizontal, its initial velocity can be broken down into horizontal and vertical components:

v0x = v0 * cos(30) = 10 * cos(30) = 10 * sqrt(3)/2 m/s

v0y = v0 * sin(30) = 10 * sin(30) = 10/2 m/s

The potential energy of the ball at its highest point can be found by adding the initial kinetic energy of the ball to its gravitational potential energy. The kinetic energy of the ball can be calculated as:

KE = 1/2 * m * v0y^2

where m is the mass of the ball and v0y is the vertical component of its initial velocity.

The total potential energy of the ball at its highest point is given by:

PE = KE + mgh = 1/2 * m * v0y^2 + m * g * h

Substituting in the given values, we find:

PE = 1/2 * m * (10/2)^2 + m * 9.8 * 80

Note: The mass of the ball (m) is not given, so the answer is given in terms of m.

Answer:

Step-by-step explanation:

PE = 1/2 * m * (10/2)^2 + m * 9.8 * 80

The amount invested in the 3% interest account is $11,342.11, and the amount invested in the 1.1% interest account is $10,000 - $11,342.11 = $-342.11.

What is the interest?

Interest is the price you pay to borrow money or the cost you charge to lend money. Interest is most often reflected as an annual percentage of the amount of a loan. This percentage is known as the interest rate on the loan.

Let's call the amount invested in the 3% interest account x. Then, the amount invested in the 1.1% interest account is $10,000 - x.

The interest earned in the 3% interest account is 0.03x, and the interest earned in the 1.1% interest account is 0.011($10,000 - x).

The total interest earned is equal to the sum of the interest earned in each account:

0.03x + 0.011($10,000 - x) = $215.04

Expanding and solving for x:

0.03x + 0.011 * $10,000 - 0.011x = $215.04

0.019x = $215.04 + 0.011 * $10,000 - 0.011 * $10,000

0.019x = $215.04

x = $215.04 / 0.019

x = $11,342.11

Hence, the amount invested in the 3% interest account is $11,342.11, and the amount invested in the 1.1% interest account is $10,000 - $11,342.11 = $-342.11.

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The area of the given parallelogram is 6.6 square units.

The region or space occupied by a parallelogram in a two-dimensional plane is referred to as the area of a parallelogram. A unique category of a quadrilateral is a parallelogram.

A quadrilateral is referred to as a parallelogram if it has two sets of parallel opposite sides. A parallelogram can be anything from a rectangle to a square to a rhombus.

The area of the partogram is calculated as:-

Area =  Base x Height

Area = 2.2 x 3

Area = 6.6 square units

Therefore, the parallelogram will have an area of 6.6 square units.

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Answer: The expression (-14) - 8 has the same value as -22.

To verify if the representation is a function for this problem, we should verify if each input is mapped to a single output. If there is an input that is mapped to more than one output, then the relation is not a function.

A relation represents a function when each input value is mapped to a single output value.

On a graph, a function is represented if the graph contains no vertical aligned points, that is, if there are no values of x at which we could trace a vertical line that would cross the graph of the function more than once.

With arrows, only one arrow can depart from each value of x, or more than one arrow departing from the same value of x but necessarily arriving at the same value of y.

The problem is incomplete, hence the general procedure to verify if a relation represents a function was presented.

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Answer:

44.44%

Step-by-step explanation:

Error percent can be found by this formula

Estimation/Actual number x 100/1

= 2/4.5 x 100/1

= 200/4.5 = 2000/45

= 400/9

= 44.44 %

Answer:

Step-y-step explanation: я хз

The volume of a sphere with radius 10 units was found to be approximately 42 cubic units.

The volume of a sphere can be calculated using the formula:

V = (4/3) * π * r^3

Where, r is the radius of the sphere. In this case, the radius is 10 units, so we can plug in the values and calculate the volume:

V = (4/3) * π * 10^3 = 4184 cubic units

So, the approximate volume of the sphere with a radius of 10 units is 4184 cubic units.

Rounding off to the nearest whole cubic unit, 4184 cubic units becomes 42 cubic units.

Volume of a sphere is the amount of space inside a sphere.

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The function is the relation between number of cars and toll collected in the toll booth. So the correct option is that the reasonable domain is a set of natural numbers.

While considering a function regarding to mathematical domain, for f(x) = 3.25x, x can be any values between -∞ to +∞. For every x value, we could calculate f(x).

But here, we are dealing with number of cars. So it can have only values as a natural number. A negative integer, fraction or decimal cannot represent x. So it will be a set of natural numbers.

So the domain here is the set of natural numbers.

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Answer:

C

Step-by-step explanation:

3607 ( "7" ones)

7391 ( "7" thousands)

1738 ( "7" hundreds)

7246 ( "7" thousands)

Answer:

Step-by-step explanation:

-2.67

Answer:

160 tourists like only one place. This can be determined by using a Venn diagram. Of the 500 tourists surveyed, 350 like Pokhara, 200 like Chitwan, and 50 like both places. That leaves 20 who like neither of the two places. To get the number of tourists that like only one place, subtract the number of tourists who like both (50) and the number of tourists who like neither (20) from the total number of tourists surveyed (500), resulting in a total of 160 tourists who like only one place.

A linear equation giving the value v of the equipment during the 5 years it will be in use is v = 955 - 191t

A linear equation models a linear relationship between two variables, where the rate of change between the two variables is constant. In this case, we can model the value of the equipment as it depreciates over time using a linear equation.

Since the value of the equipment decreases linearly over time, we can write an equation in the form:

v = a - bt

where v is the value of the equipment in year t, a is the initial value of the equipment, and b is the constant rate of depreciation.

Since the initial value of the equipment is $955, we can set a equal to 955. To find the constant rate of depreciation, we need to find the change in value over the 5 years it will be in use and divide by the number of years. Assuming after 5 years the value is 0,

constant rate of depreciation = 955/ 5

= 191

So, with a = 955 and b = $191 per year, the linear equation that models the value of the equipment over time is:

v = 955 - 191t

This equation gives the value of the equipment in year t based on the initial value and the constant rate of depreciation.

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Based on the information provided, if a block weighs w kg, then it is expected for 8 blocks to weigh 8w kg.

The weight can be defined as the mass contained in an object or body, this is often expressed using units such as grams, pounds, kilograms, or tons.

Considering w = the weight of a single block, the best expression to show the weight of 8 blocks is 8wkg. This letter can be replaced by the value of the weight if known, for example, 8 x 25 kg.

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The height of the cone is 24 centimetres.

A cone has a volume of 392π cubic centimetres and a radius of 7 centimetres. Therefore, the height of the cone can be found as follows;

Hence,

volume of a cone = 1 / 3 πr²h

where

Therefore,

volume = 392π

r = 7 cm

392π = 1 / 3 × π × 7² × h

392π = 49 / 3 πh

cross multiply

1176π = 49πh

divide both sides by 49π

h = 1176π / 49π

h = 24 cm

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Answer:

BK=AK: no

BK=DK:yes

CK=AK:yes

CK=DK:no

Step-by-step explanation:

for the first and last, it is not needed because a rectangle is a parallelogram, for example, but its diagonals are not congruent. The diagonals intersect each other at both of their midpoints, on the other hand, so therefore the second and third must be true. Does this make sense?

The probability of having no defectives in a sample of size 3 from a lot of 24 items with 5 known defectives is 0.0403 or approximately 4%.

The probability of having no defectives in a sample of size 3 from a lot of 24 items with 5 known defectives can be calculated using the binomial probability formula. The formula is given by:

P(X=k) = (n choose k) * p^k * (1-p) ^(n-k)

where:

n = sample size (3)

k = number of successful trials (0)

p = probability of success (probability of an item being non-defective)

Since there are 24 items in the lot and 5 of them are known to be defective, the probability of success (p) is equal to 19/24.

Plugging in the values, we get:

P(X=0) = (3 choose 0) * (19/24) ^0 * (5/24) ^3

= 1 * 1 * (5/24) ^3

= (5/24) ^3

= 0.0403

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Answer: [tex]\frac{1}{4}[/tex]

Step-by-step explanation:

1) Subtract Michael's voters from all the voters 56/56 - 42/56. When you have the same denominator, subtract the numerator and keep the denominator the same to get 14/56.

2) Simplify, both the numerator and denominator is divisible by 14, so divide 14/14 to get 1 as our new numerator and divide 56/14 to get 4 as our denominator leading us to our answer of 1/4

The expression for the statement is 20 - (6 + b).

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

Given statement is 20 decreased by the sum of 6 and b.

Sum means adding two or more numbers or expressions.

Sum of 6 and b means 6 + b.

Decreased means some number is subtracted.

The expression is 20 - (6 + b).

Hence the expression for the phrase is 20 - (6 + b).

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Your options for the question seems a little confusing. Probably the options for the question is given below :

By the definition of vertically opposite angle, the value of measure of ∠5 is, 100°.

An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.

Given that;

In the figure,

⇒ m ∠7 = 100°

Now, By the figure we have;

Both the angles 7 and angle 5 are vertically opposite angle.

And, We know that the vertically opposite angles are equal to each other.

Hence, We get;

⇒ m ∠7 = m ∠5

⇒ 100° = m ∠5

⇒ m ∠5 = 100°

Thus, We get;

⇒ m ∠5 = 100°

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Answer:

Step-by-step explanation:

[tex]2123.72 = 4 \times 3.14 \times {r}^{2} [/tex]

[tex]2123.72 = 12.57 {r}^{2} [/tex]

[tex] \frac{12.57 {r}^{2} }{12.57} = \frac{2123.72}{12.57} [/tex]

[tex] {r}^{2} = 168.95[/tex]

[tex]r = 13.0[/tex]

[tex] \frac{4}{3}\pi {r}^{3} [/tex]

[tex] \frac{4}{3} \times 3.14 \times {13}^{3} = 9202.77 {m}^{3} [/tex]

Step-by-step explanation:

2.5:10 = 1/4

1.4:1.8 = 7/10

0.04: 0.3 = 2/50

1/5: 4/5 = 1/5

3/4: 1/2 = 3/2

6.2:5 2/5 = 12/5

The field is full of 18 horses and 15 geese.

Let's assume that there are x horses and y geese in the field. The number of heads can be represented as x + y = 33. The number of feet can be represented as 4x + 2y = 102.

We can use substitution to solve for one variable in terms of the other. From the first equation, we can solve for y in terms of x:

y = 33 - x

Substituting this expression for y into the second equation, we get:

4x + 2(33 - x) = 102

Expanding and simplifying the expression, we get:

4x + 66 - 2x = 102

Solving for x, we get:

2x = 36

And x = 18

So there are 18 horses in the field. Substituting this value for x into the expression for y, we get:

y = 33 - x = 33 - 18 = 15

So there are 15 geese in the field. Thus, the field is full of 18 horses and 15 geese.

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One of the numbers is 21, and the other number is 2.5

What is an algebraic expression?

An algebraic expression is when we combine numbers and words to solve a mathematical problem.

Let's call one of the numbers "x". We know that x is 8 times greater than the other number, which we'll call "y". So we have:

y = x / 8

The product of x and y is 57, so:

x * y = 57

Substituting y = x / 8 into the equation above:

x * (x / 8) = 57

Expanding the right side of the equation:

[tex]x^2 / 8 = 57[/tex]

Multiplying both sides by 8:

[tex]x^2 = 8 * 57[/tex]

Solving for [tex]x^2[/tex]:

[tex]x^2 = 456[/tex]

Taking the square root of both sides:

[tex]x =\sqrt{456}[/tex]

x = 21

So, One of the numbers is 21, and the other number is 21 / 8 = 2.5.

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The value of x is 13.85.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

From the figure,

(7x + 1)° and (6x - 1)° makes a straight angle.

This means,

(7x + 1) + (6x - 1) = 180

7x + 1 + 6x - 1 = 180

13x = 180

x = 180/13

x = 13.85

Thus,

x is 13.85°

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The answer is A)The list of favorable outcomes are 1) 1-1, 1-2 ; 2) 2-1, 2-2 ; 3) 3-1, 3-2 ; 4) 4-1, 4-2 ; 5) 5-1, 5-2 ; B) There's 50% chance of probability of being odd.

A) If the sample space of tossing a coin and picking a number between 1 and 5, inclusive then there are 5 set of probabilities as an outcome:

1) 1-1, 1-2 ;

2) 2-1, 2-2 ;

3) 3-1, 3-2 ;

4) 4-1, 4-2 ;

5) 5-1, 5-2

B) And in the case of getting odd numbers as an probability outcome, there are  50% chance of it being odd.                

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Answer:

1.106209714987%

Step-by-step explanation:

Negative values detected. All input values threated as percentages (e.g. an input of 0.1 is threated as 0.1%, -10 is threated as -10%).

Angle - 51 degrees represent a counterclockwise rotation of 51 degrees.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.

If 39 degrees represents a clockwise rotation of 39 degrees.

Then we can conclude that the clockwise is taken as positive and counterclockwise is taken as negative.

Angle - 51 degrees represent a counterclockwise rotation of 51 degrees.

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