The points (4,2) and (5,r) fall on a line with a slope of
–7. What is the value of r?

a)  it costs more money to make 100 photocopies

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

What are coordinates?

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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The measure of the hypotenuse can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides.

For the given triangle, let's call the length of the hypotenuse "h". Then, using the Pythagorean theorem:

h^2 = 2^2 + 7^2

h^2 = 4 + 49

h^2 = 53

h = √53

Rounding to the nearest tenth, h = 7.3 cm.

So, the measure of the hypotenuse of the right triangle with legs of length 2 cm and 7 cm is 7.3 cm.

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13/4 is the value of  [tex]4\frac{1}{2} -(2\frac{1}{2}-1 \frac{1}{4})[/tex]

A fraction represents a part of a whole.

The given expression is [tex]4\frac{1}{2} -(2\frac{1}{2}-1 \frac{1}{4})[/tex]

Convert each mixed fraction to improper fraction

9/2-(5/2-5/4)

9/2-(10-5/4)

9/2-5/4

LCM of 4 and 2 is 4

18-5/4

13/4

Hence, 13/4 is the value of  [tex]4\frac{1}{2} -(2\frac{1}{2}-1 \frac{1}{4})[/tex]

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The probability that it lands heads at least once is 1.0720.

Probability is the measure of the likelihood of an event occurring. In this case, we are looking at the probability of a coin landing heads at least once after three tosses.

Let's denote the event of the coin landing heads on the first toss as event A, the event of the coin landing heads on the second toss as event B, and the event of the coin landing heads on the third toss as event C.

The probability of landing heads at least once is equal to the sum of the probabilities of each individual event occurring (A, B, or C) minus the probability of all three events occurring (A and B and C).

P(A or B or C) = P(A) + P(B) + P(C) - P(A and B and C)

Since the coin is unfair and has a probability of 0.4 of landing heads, P(A) = P(B) = P(C) = 0.4.

Using the formula for the probability of multiple events happening simultaneously, we find that P(A and B and C) = P(A) * P(B) * P(C) = 0.4 * 0.4 * 0.4 = 0.064.

Plugging in all the values, we get:

P(A or B or C) = 0.4 + 0.4 + 0.4 - 0.064 = 1.136 - 0.064 = 1.072

Rounding to four decimal places, the answer is 1.0720, which means that the probability of the coin landing heads at least once after three tosses is 1.0720.

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The required value of d in the given arithmetic operation is 9/10.

What are subtraction and addition?

The two main arithmetic operations that we learn to add and subtract two or more integers or other mathematical values are addition and subtraction. To add, one must add two or more numbers or values to produce a new number. The inverse of addition is subtraction and vice versa.

For instance, 10 - 1 = 9 if 9 + 1 = 10. That demonstrates that adding 1 produces the number 10 when added to 9, but subtracting 1 from 10 produces the number 9.

Given, -1/3d + 4/5 = 1/2

[tex]\frac{-1}{3} d+\frac{4}{5} =\frac{1}{2} \\\\\frac{-1}{3} d =\frac{1}{2}-\frac{4}{5}\\\\\frac{-1}{3} d = \frac{5-8}{10}\\\\\frac{-1}{3} d = \frac{-3}{10}\\\\\frac{d}{3}=\frac{3}{10}\\\\d = \frac{9}{10}[/tex]

So, the required value of d = 9/10.

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1) Vertex -  A,B,C,O,Q,F

2) Points in the interior of ∠COB - Q,F

3) Sides of ∠2 - side OC and side OA.

What is Interior angles?

Interior angles can be generated in two methods in geometry. The first occurs within a polygon, whereas the second occurs when parallel lines are cut by a transversal. Angles are classified into many sorts based on their measurements.

1) Vertex of angles would be A,B,C,O,Q,F

2) The points in the interior of ∠COB would be, Q,F

3) The sides of ∠2 would be, side OC and side OA.

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Answer:

The correct answer is D: Head, head Tail, tail Head, tail Tail, head.

Step-by-step explanation:

When Henry tosses a coin twice, there are four possible outcomes, each with equal probability:

Head, head

Tail, tail

Head, tail

Tail, head

Answer:

x = 41

Step-by-step explanation:

Supplementary Angles rule (straight lines in total have the angle of 180):

180 - 147 = 33

Total angles in a triangle equal 180:

180 - 33 - 106 = x

x = 41

Answer:

Length = 5 cm

Width = 3 cm

Step-by-step explanation:

Part (a)

Length L = c

(i) Width W = c- 2 (width is 2 cm less than width)

(ii) Area of the rectangle = L x W
= c(c - 2) = c² - 2c

Part (b)
Area is given as 15 cm²

Therefore, c²- 2c = 15

Part (c)

The equation for area from part (b) is

c² - 2c = 15

Carry 15 to the left side by subtracting 15 from both sides:
c²- 2c - 15 = 15 - 15

c²- 2c - 15 = 0

This is a quadratic equation which can be solved easily by factoring

The factors of the constant 15 are 5 and 3
The constant is product of the factors is -15; so one of the numbers is negative

The sum of the numbers is the coefficient of c

Since this -2, the numbers are -5 and 3

Therefore the factorization of the equation

c² - 2c - 15 = (c + 3)(c - 5)

And since c² - 2c - 15 = 0 this means  (c + 3)(c - 5) = 0

So either c + 3 = 0 ==> c = -3 which can be rejected because length cannot be negative

This gives us
c - 5 = 0

Or c = 5

So length = 5 cm

Since width = c - 2

width = 5 - 2 = 3

Length = 5

Width = 3

The concept is a Dependent Variable. It's the outgrowth variable of interest that's observed to see whether it's told by a manipulated variable.

The dependent variable is the variable that's being measured or tested in a trial. One way to help identify the dependent variable is to the flashback that it depends on the independent variable.

When experimenters make changes to the independent variable, they also measure any performing changes to the dependent variable. An experimenter might also choose dependent variables grounded on the complexity of their study.

Stability is frequently a good sign of an advanced quality-dependent variable. The dependent variable belongs on the y-axis ( perpendicular line).

Question

What type of variable is the outgrowth of a study?

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The value of x from the given equation is 7.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation is ∛(4x-1)-7=-4.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

Here, ∛(4x-1)-7=-4

∛(4x-1)=3

Cubing on both side of an equation, we get

(∛(4x-1))³=3³

4x-1=27

4x=28

x=7

Therefore, the value of x is 7.

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To balance a see-saw, the product of the distance of the person's weight from the pivot and their weight must be equal on both sides.

Let's call Daniela's mass "m".

The force on Lucy's side is:

distance * weight = 3.5 meters * 50 kg = 175 kg * meters

The force on Daniela's side is:

distance * weight = d * m

Since the see-saw is balanced, the two forces must be equal:

3.5 * 50 = d * m

Solving for m, we get:

m = 175 / d

Without knowing the distance "d" that Daniela is sitting from the pivot, it is impossible to calculate her weight.

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The value of the cubic polynomial evaluated at x = 0.5 is equal to 8.

In this problem we find the case of a cubic polynomial in standard form:

y = a · x³ + b · x² + c · x + d

Where a, b, c, d are real coefficients.

The values of the coefficients must be determined on the knowledge of the leading coefficient (a = 2), the constant term (d = 5) and two values (y(- 1) = 2, f(1) = 14). First, substitute the leading coefficient and the constant term in the definition:

y = 2 · x³ + b · x² + c · x + 5

y - 2 · x³ - 5 = b · x² + c · x

Second, form the system of linear equations by using the given values:

b - c = - 1

b + c = 7

Third, solve the resulting system by numerical methods:

(b, c) = (3, 4)

Fourth, write the resulting polynomial:

y = 2 · x³ + 3 · x² + 4 · x + 5

Fifth, evaluate the polynomial at x = 0.5:

y = 2 · 0.5³ + 3 · 0.5² + 4 · 0.5 + 5

y = 8

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After rewriting the expression [tex]4 ^ {( 2x -4)}[/tex] using distributive property, [tex]4^{2x} . 4^{-4}[/tex] is the equivalent expression.

In mathematics, it is acceptable to multiply, divide, add, or negate. The construction of an expression looks like this: Amount, a mathematical operator, and an expression A mathematical expression's variables can be numbers, amounts, or functions (such as addition, subtraction, multiplication or division etc.)

Contrasting concepts and language is typical practice. Any mathematical statement that rates systems, numbers, and then an arithmetic operation between them is referred to as an expression, sometimes known as a formula. For instance, the arithmetic operator + separates the word m from the terms 4m and 5 in the balanced formula, just as it does for the variable m in the phrase 4m + 5.

given

Expressions that are equivalent do the same thing even when they have distinct appearances.

Two quadratic expressions that are analogous have the same value when we use the same value for the variable.

[tex]4 ^ {( 2x -4)}[/tex]

[tex]4^{2x} . 4^{-4}[/tex]

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Answer:

No it's not!

Pythagorean theorem

15² + 9² = it's not 20

15² + 9² = 17 so

NO

The sample consists of 4 selected sites, and the corresponding parameter is the population's minimum temperature. The lowest temperature for the sample is 170 °F .

The sampling size is the number of records which used derive estimates for a certain population. A sample size from the population was selected. The amount of subjects the observations that compose up a study is referred to as the "sample size." This number is sometimes referred to as the symbol n. Two statistical traits are influenced by the sample size: 1) The accuracy of our estimations; 2) The power of investigations to draw conclusions. The samples represent the outcomes of random tests. A specific value is selected from a set of possible values when sample a random variable. This particular value is a sample. The potential values and their possibilities are determined by the random variable's posterior distribution.

given

A parameter is a descriptive measure for a population, as opposed to a statistic, which is a descriptive measure for a sample.

170 F is a statistic because it represents the sample minimum temperature and is based on a sample of four randomly selected sites.

The corresponding parameter is changed to the minimum population temperature.

The lowest temperature for the sample is 170F. (F).

Minimum population temperature as a parameter

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The solution is Option A.

The dilation scale factor is given by the equation D = 5

Resizing an item uses a transition called Dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. Dilation transformations ensure that the shape will stay the same and that corresponding angles will be congruent

Given data ,

Let the dilation scale factor be represented as D

Now , the equation will be

The coordinates of the triangle ΔABC is given as

A ( -3 , -3 ) , B ( 3 , 3 ), C ( 0 , 3 )

And , coordinates of the triangle ΔA'B'C' is given as

A′ ( -15 , -15) , B′ ( 15 , 15 ) , C′ ( 0 , 15 )

The dilation factor is given by D = x₂ / x₁ or D = y₂ / y₁

Substituting the values in the equation , we get

D = -15 / -3 = 5

And , D = 15 / 3 = 5

Hence , the dilation factor is 5

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Answer:

g(x) = 2x + 2

g(x) = 3(x-3)

g(x) = 1/3x

g(x) = 5(x + 2)

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

g(x) = -x + 4

Vertical shift of 3 units to the right.

Step-by-step explanation:

Answer:

the area of each cookie made by Tony is approximately 63.62 square cm.

Step-by-step explanation:

The area of a cookie can be found if we know its radius. To find the radius, we can divide the circumference by 2 times pi (π).

Let's call the radius of the cookie "r".

45 cm / (2 * π) = r

Now that we have the radius, we can find the area using the formula:

π * r^2 = area

So,

π * r^2 = π * (45 / (2 * π))^2 = (45^2) / (4 * π)

Therefore, the area of each cookie made by Tony is approximately 63.62 square cm.

The area of the given shape is  90.4  cm².

The area is the entire amount of space occupied by a flat (2-D) surface or an object's shape.

On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies.

Given the shape of the boat, which contain, a rectangle and two right triangles,

total area = area of rectangle + area of triangle,

dimensions of the rectangle are,

length = 12 cm width = 5.2 cm

area of rectangle = l*b

area of rectangle = 12*5.2

area of rectangle = 62.4 cm²

area of triangle = 1/2*b*h

height = 8 cm

total base of both triangles = 3 + 4

base = 7 cm

area of triangle = 1/2*8*7

area of triangle = 28 cm²

total area =  62.4 cm² + 28 cm²

total area = 90.4  cm²

Hence the area is 90.4  cm².

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Answer:

see explanation

Step-by-step explanation:

given y varies as t , then the equation relating them is

y = kt ← k is the constant of variation

to find k use the condition y = 6 when t = 4

6 = 4k ( divide both sides by 4 )

[tex]\frac{6}{4}[/tex] = k , that is

k = [tex]\frac{3}{2}[/tex]

y = [tex]\frac{3}{2}[/tex] t ← equation of variation

(a)

when t = 6 , then

y = [tex]\frac{3}{2}[/tex] × 6 = 3 × 3 = 9

(b)

when y = 4 , then

4 = [tex]\frac{3}{2}[/tex] t ( multiply both sides by 2 to clear the fraction )

8 = 3t ( divide both sides by 3 )

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

A scatterplot of miles per gallon (MPG) against weight can reveal the relationship between the two variables. If there is a trend in the graph, it can help us understand the relationship between the two variables.

For example, if the graph shows a negative correlation, meaning that as the weight of the vehicle increases, the MPG decreases, this trend may be what is expected, as heavier vehicles typically have lower fuel efficiency. On the other hand, if the graph shows no trend or a positive trend, it would indicate that weight and MPG are not significantly related, which might not be what was expected.

It is important to keep in mind that a scatterplot can only show the relationship between two variables and cannot provide a definitive explanation of the cause-and-effect relationship between them

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Complete Question: you created a scatterplot of miles per gallon against weight; check to make sure it was included in your attachment. does the graph show any trend? if yes, is the trend what you expected? why or why not?

Answer:

32.) Yes

33.) 7

34.) No because 40 is less than 50

Step-by-step explanation:

32.)

Were trying to see is 35 is 3/4ths of 50, so we set up a ratio and solve

[tex] \frac{3}{4} = \frac{x}{50} [/tex]

Next we cross multiply

[tex]4x = 150[/tex]

Lastly divide by 4

[tex]x = 37.5[/tex]

33.) We have to convert 2/5 and 5/6 into a value over 30.

For 2/5, 5 times 6 is 30. 2 times 6 is 12, so we get 12/30 playing Chess.

6 times 5 is 30. 5 times 5 is 25. Making it 25/50 playing Sudoku

[tex] \frac{12}{30} = chess \: \frac{25}{30} = sudoku[/tex]

Since 5 don't play sudoku and 18 don't play chess.

18+5 = 23...

30-23 = 7

34.) The picture to the right shows 20 stamps.

Two sheets of stamps means 20x2 = 40, which is less than 50

The number of different rational numbers between [tex]$\dfrac{1}{1000}$[/tex] and 1000 that can be written either as a power of 2 or as a power of 3, where the exponent is a (possibly negative) integer, is 33.

To find all of the possible rational numbers, we need to find all the integer exponents for 2 and 3 that satisfy the conditions. [tex]2^0 = 1, 2^{-3} = 1/8, 2^{-2} = 1/4, 2^{-1} = 1/2, 2^1 = 2, 2^2 = 4, 2^3 = 8[/tex], and so on.

Similarly, for 3, we have [tex]3^0 = 1, 3^{-3} = 1/27, 3^{-2} = 1/9, 3^{-1} = 1/3, 3^1 = 3, 3^2 = 9, 3^3 = 27[/tex], and so on.

By combining the positive and negative exponents of 2 and 3, we get 33 different rational numbers that satisfy the conditions.

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Answer:

12

Step-by-step explanation:

2/3 of 48 is 32, 16 leftover.

1/4 of 16 is 4, 12 leftover

answer=12

The possible definitions of f(x) and g(x), considering the composition of the functions, are given as follows:

The composite function of f(x) and g(x) is given by the following rule:

(f ∘ g)(x) = f(g(x)).

It means that the output of the inside function serves as the input for the outside function.

The functions for this problem are defined as follows:

As the composition of the functions is then given as follows:

[tex]h(x) = f(g(x)) = f(8x + 6) = \sqrt{8x + 6}[/tex]

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Answer: To determine whether 2.5 is a solution to the equation 4n + 4 = 14, we can substitute 2.5 for n in the equation and see if it makes the equation true.

So, if we substitute 2.5 for n in the equation:

4(2.5) + 4 = 14

Expanding the left-side expression:

10 + 4 = 14

Simplifying further:

14 = 14

Since the equation is true, we can conclude that 2.5 is a solution to the equation 4n + 4 = 14.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Volume is whl.

= 1680 = (14)(12)(x)

= 1680 = 168x

= x = 10

The length is 10ft

Answer: 10 Feet

Step-by-step explanation:

Volume of pool = Length x Width x Depth = LxWxD  

We know  D = 12 feet   W = 14 feet  

So  Lx  14 x 12 = 1680      Solving for L = 10 feet

The volume of wheat in the silo is about 1,570 feet and it would take about 63 minutes at the given rate for the silo to empty fully.

The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.

Various forms have various volumes. We have studied the several solids and forms that are specified in three dimensions, such as cubes, cuboids, cylinders, cones, etc., in 3D geometry. We will discover how to find the volume for each of these shapes.

The silo is in the shape of cone, so use the formula of volume of a cone to find volume of wheat the tank can hold.

The formula to find volume of a cone is:

V = 1/3 · πr2h -----(1)

Substitute π ≈ 3.14, r = 10 and h = 15 in (1).

V ≈ 1/3 · 3.14 · 102 · 15

V ≈ 1/3 · 3.14 · 100 · 15

V ≈ 1,570

So, the volume of wheat in the silo is about 1,570 feet.

Silo can release wheat from its bottom at the rate of 25 cubic feet per minute.

= 1,570 / 25

= 62.8

≈ 63

Hence, it would take about 63 minutes for the silo to empty fully.

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