A scatter plot was made with a trend line that had an equation of y = -0.25x + 85, where y is the total number of cases of the flu and x is the total number of students who recieved the flu vaccine.

Predict how many students received a flu vaccine if a school had 65 cases of the flu.

Nora will have $ 4.05 money.

Given that, Sam has 3. 50 less than Junho and 2. 30 less than Nora. Junhao has 4. 25.

By using the unitary method

The unitary approach is a methodology for problem-solving that involves first determining the value of a single unit and then determining the necessary value by multiplying the single unit value.

The unitary method's formula is to get the value of a single unit and then multiply that value by the number of units to obtain the required value.

Junhao has $4.25

so, Sam has =$4.25-3.50

= $1.75

::NORA HAS = $ 1.75 +2.30

= $ 4.05

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No, these statements are not needed to prove that ABCD is a parallelogram.

A parallelogram is a type of four-sided geometric shape with two pairs of opposite sides that are parallel. Each side of the parallelogram is a line segment, and all four of the interior angles are equal. The opposite sides of a parallelogram are also equal in length. Parallelograms can be found in a variety of applications, including engineering, architecture, and other fields. The most common types of parallelograms are squares, rectangles, and rhombuses.

A parallelogram is defined as a four-sided shape with opposite sides that are equal in length and with opposite angles that are equal in measure.
To prove that ABCD is a parallelogram, it is necessary to show that two of its sides are parallel and that its opposite sides are equal in length.
The statements provided do not show any of these properties, and so are not needed to prove that ABCD is a parallelogram.

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Answer:

29x+20

Step-by-step explanation:

The distributive property states that for any real numbers a, b and c, the following is true:

a(b + c) = ab + ac

To use the distributive property to write an expression that is equivalent to 6 - 9x, we can factor out the -9x from the second term:

6 - 9x = 6 - 9x + 0 - 0x = 6 - 9x + (-9x) = 6 + (-9x)

Therefore, using the distributive property, we can write an expression that is equivalent to 6 - 9x as:

6 + (-9x)

Answer:

-3 ( 3x - 2 )

Step-by-step explanation:

- 9x + 6

Work done when a 100 lb rock is lifted to height of 3 ft is 9652.215 ft-lb.

What is meant by work done?

The work done on an object is equal to the force applied to it multiplied by the distance over which the force is applied. In this case, the force applied is the weight of the rock, which is equal to the force of gravity acting on it.

The weight of an object is given by the formula:

W = mg

Where m is the mass of the object (in this case, 100 lb) and g is the acceleration due to gravity (approximately 9.8 m/s^2 or 32.17405 ft/s^2).

So the weight of the rock is:

W = (100 lb)(32.17405 ft/s^2) = 3,217.405 ft-lb

The work done on the rock is equal to the force applied (its weight) multiplied by the distance it is lifted (3 ft), so the work done is:

Work = (3,217.405 ft-lb) x (3 ft) = 9652.215 ft-lb

Therefore, the work done when a 100 lb rock is lifted to a height of 3 ft is 9652.215 ft-lb.

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Answer:

slope = 1

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, - 1) and (x₂, y₂ ) = (3, 2) ← 2 ordered pairs from the table

m = [tex]\frac{2-(-1)}{3-0}[/tex] = [tex]\frac{2+1}{3}[/tex] = [tex]\frac{3}{3}[/tex] = 1

An equation for the plane consisting of all points that are equidistant from the points (1,4,4) and (-4, 1, 2) is 5x+3y+2z-6=0

Given, the points are (1, 4, 4) and (-4, 1, 2).

We have to find an equation for the plane consisting of all points that are equidistant from the given points.

Let the parametric point be (x, y, z) on the plane which is equidistant from the given points.

Using the distance formula:

[tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2+(z_{2}-z_{1} )^2 } }[/tex]

Distance between the points (x, y, z) and (1, 4, 4)

=[tex]\sqrt{(x-1)^2+(y-4)^2+(z-4)^2}[/tex]

Distance between the points (x, y, z) and (-4, 1, 2)

=[tex]\sqrt{(x-(-4)^2+(y-1)^2+(z-2)^2}\\\\ \sqrt{(x+4)^2+(y-1)^2+(z-2)^2}[/tex]

Given, [tex]\sqrt{(x-1)^2+(y-4)^2+(z-4)^2}=\sqrt{(x+4)^2+(y-1)^2+(z-2)^2}[/tex]

By using algebraic identity,

(a-b)² = a²-2ab+b²

(a+b)² = a²+2ab+b²

(x² - 2x + 1)+(y²-8y+16)+(z²-8z+16)=(x²+8x+16)(y²-2y+1)+(z²-4z+4)

x²+y²+z²-2x-8y-8z+1+16+16=x²+y²+z²+8x-2y-4z+16+1+4

By grouping,

-2x-8x-8y+2y-8z+4z+33-21

-10x-6y-4z+12=0

Dividing by -2 into both sides,

5x+3y+2z-6=0

Therefore, the equation of the plane is 5x+3y+2z-6=0

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Answer:I apologize, but I am not able to understand your question as it is written in a mix of mathematical notation and text that is not clear. Could you please rephrase your question or provide more context? I'll be happy to help you with your question.

Step-by-step explanation:

The inverse of the expression +9 is -9.

Expression in math is defined as  any mathematical statement which consists of numbers, variables and an arithmetic operation between them.

Here we have the expression +9 and we need to find the inverse for it.

As we all know that the term inverse in math is known as a function or operation which reverses the order or operation of another function or operation

Based on the definition, the given expression is written as,

=> +9

Now, the inverse of the expression is written as in the negative form such that,

=> -9

Therefore, the resulting value is -9.

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Step-by-step explanation:

since a ratio is a fraction with all calculation and comparison rules (but with a special overall meaning), we need to observe the main rule for transforming fractions : when multiplying one part of the fraction by a factor, we also need to multiply the other part by the same factor to keep the value of the fraction unchanged.

the basic ratio is here

145/52 (or written 145:52 - it has the same meaning)

290/104 is just (145×2)/(52×2)

435/156 is just (145×3)/(52×3)

to complete the table we simply have to keep following that structure :

580 = 145×4

so, 52×4 = 208

and the ratio is

580/208

725 = 145×5

52×5 = 260

and the ratio is

725/260

If 10 people share 3 brownies equally, each person will get the same amount. To find out how much each person will get, you can divide the total number of brownies by the number of people.

Unitary Method:

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

3 brownies / 10 people = 0.3 brownies per person

So, each person will get 0.3 of a brownie. Since a brownie is a solid object, it is not possible for each person to get 0.3 of a brownie, It would be best to cut the brownies into 10 equal pieces.

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From the given angles of the triangle, it was possible to find the angle x=29°.

Triangles are geometric figures with three (3) sides. They present different classifications regarding their sides or angles.

Like a classification for angles, it is possible to cite, a right triangle. A triangle is classified as a right triangle when it presents one of your angles equal to 90º.

For another side, an equilateral triangle whose classification is associated with the sides. An equilateral triangle presents the three  equal sides.

Regardless of its classification, the sum of the a triangle's angles will always be 180°.

The question gives two angles: 50° and 101°. And, it asks the value of angle x.

Therefore,

50+101+x=180

x+151=180

x=180-151

x=29°

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Answer:

B.10

Step-by-step explanation:

Because it increases by 10

To depict the curve, we will make use of the idea of slope and intercept in linear equations.

A line's slope and y-intercept are represented by the equation y = mx + c, where m represents the slope and c represents the y-intercept.

When y = 2x - 4 is put into comparison with the generic form, we get

The curve has a slope of 2 and a y-intercept of -4.

To assist us plot the graph, let's take two points along the line y = 2x – 4.

The line y = 2x - 4 passes through since its y-intercept is equal to -4. (0, -4)

In the formula y = 2x - 4, replace y with 0.

0 = 2x - 4

2x = 4

x = 2

the line therefore goes through (2, 0).

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Full Question = Which graph represents the function y = 2x - 4?

The cost of the shirt given the ticketed price is $16.66.

When the price of an item is marked down, it means that the price of the item is reduced. The item would become cheaper after the mark down. The shirt would become cheaper after it is marked down.

Price of the shirt after the mark down = (1 - fraction of mark down in price) x ticketed price

= (1 - 1/3) x $24.99

= 2/3 x $24.99

= $16.66

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Answer: To find the answer to the expression x(-2.54y+6y-3.77)+x, I followed these steps:

Distribute the x coefficient:

x(-2.54y+6y-3.77) = -2.54xy + 6xy - 3.77x

Combine like terms:

-2.54xy + 6xy - 3.77x + x = -2.54xy + 6xy - 2.77x

Simplify the expression:

-2.54xy + 6xy - 2.77x

The result is a polynomial with x and y as variables, and the coefficients -2.54, 6, -2.77.

It is a good practice to check the work by substituting the variables with some numbers to see if the output is correct.

Step-by-step explanation:

Answer:

he given expression can be simplified as:

X(-2.54y+6y-3.77)+x

= X(-2.54y + 6y) + X(-3.77) + x

= X(3.46y) - 3.77X + x

= 3.46xy - 3.77X + x

So, the simplified form of the given expression is 3.46xy - 3.77X + x.

The triangle with angles of 90 degrees, 29 degrees, and 61 degrees is a general right triangle that does not belong to any specific type of triangle and it has no specific ratios between the sides.

The triangle with angles of 90 degrees, 29 degrees, and 61 degrees is not a special type of triangle. It is a general right triangle because it has one right angle (90 degrees) and two acute angles (29 degrees and 61 degrees).

This triangle is not a 30-60-90 triangle because it does not have the specific angle measurements of 30-60-90 degrees. Similarly, it's not a 45-45-90 triangle because the angles don't match the specific angles of 45-45-90 degrees. There are no specific ratios between the sides of this triangle.

In general, right triangles are triangles that have one right angle (90 degrees), and the other two angles can take any value between 0 and 90 degrees. The sides of a right triangle have a relationship known as the Pythagorean Theorem. This theorem states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Therefore, In short, the triangle with angles of 90 degrees, 29 degrees, and 61 degrees is a general right triangle that does not belong to any specific type of triangle and it has no specific ratios between the sides.

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The corresponding point on the unit circle for the angle θ = 5pi/3  is given by: (0,5, -0.866).

What is the unit circle?

Basically, the unit circle is a circle with a radius of 1. It is used in trigonometry to help define and understand angles and their associated trigonometric values. The unit circle is centered at the origin (0, 0) of the coordinate plane, and each point on the circle is defined by its distance from the origin and its angle from the positive x-axis.

What is area of circle ?

The area of circle can be defined as the product of pi and square of radius of a given circle.

In this problem, we have that θ = 5pi/3 , hence:

cos θ = 0.5

sin θ = -0.866

Thus the point is (0,5, -0.866).

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In the expression (ax⁶)^(1/n) = 7x³ the values of a and n are

The expression (ax⁶)^(1/n) = 7x³is simplified as follows

Information from the problem

(ax⁶)^(1/n) = 7x³

to make x⁶ to be equal to x³ we use the powers

6 * y = 3

y = 1/2

hence n = 2

substituting n = 2 and solving

(ax⁶)^(1/2) = 7x³

√(a) x³ = 7x³

dividing both sides by x³

√a = 7

squaring both sides of the equation wil result to

√a = 7

(√a)² = 7²

a = 7²

a= 49

We can therefore say that a = 49 and n = 2

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the length of the sections will be 24 and 18 respectively.

Parallel lines are lines in a plane that are always the same distance apart. Parallel lines never intersect. Perpendicular lines are lines that intersect at a right (90 degrees) angle.

Given, Some pair of lines in that three lines are parallel and two of them are intersecting them.

Since, these are the the section made by two parallel lines. Thus, these given section will be Proportional to each other.

Thus,

20/15 = ( 7x - 11)/(4x - 2)

4/3 = ( 7x - 11)/(4x - 2)

16x - 8 = 21x - 33

5x = 25

x = 5

therefore, the length of the sections will be 24 and 18 respectively.

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Answer:

129,156

Step-by-step explanation:

The vertex of the graph of the quadratic function f(x )= x² located at the origin of the graph.

The function f(x)=x²  looks like a quadratic equation.

The most basic quadratic function is f(x) = x², Its shape should look familiar from Intermediate Algebra – it is called a parabola. The point (0,0) is called the vertex of the parabola.

To find the vertex of a quadratic function on a graph:

Get the equation in the form y = ax²+bx+c.

Calculate -b/2a. This is the x-coordinate of the vertex.

To find the y-coordinate of the vertex, simply plug the value of -b/2a into the equation for x and solve for y. This is the y-coordinate of the vertex.

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The solution to the inequality is x < 6

From the question, we have the following parameters that can be used in our computation:

x - 8 < -2

Add 8 to both sides of the inequality

So, we have the following representation

x - 8 + 8 < -2 + 8

Evaluate the sum in the expression

x < -2 + 8

Evaluate the other sum

x < 6

Hence, the solution is x < 6

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Answer: Expression - 10.2x
The weight carried by each hiker is 10.2 pounds.

Step-by-step explanation:

Hello! To find the answer, you have to add all of the weight together. Do 3.4 + 4.6 + 2.2 = 10.2.  You know the total combined weight that all hikers will have to carry is 10.2 pounds.  The expression will be 10.2x.  You can check this by putting a random number in for x to represent the number of hikers.  10.2 (2) = 20.4.  20.4 would be the total weight that two hikers would have to carry, so the expression is correct.  You already know the weight each hiker will have to carry, 10.2 pounds, so you can put that in for the second question.

The most likely happened in Sandy's experiment is that,

Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments.

Option D is the correct answer.

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,

Tossing a coin:

The probability of getting a head = 1/2

The probability of getting a tail = 1/2

This is the theoretical probability.

Now,

Experiment probability:

Virtual coins too have the same probability of getting a head and a tail as compared to the theoretical probability.

Thus,

Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments.

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Answer:Not Sure but it is not D at all so please don't use that!

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

c

The probability of selecting an orange marble is 0.33.

Option B is the correct answer.

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,

The number of times each marble is selected.

Green = 4

Black = 6

Orange = 5

Total number of times all marbles are selected.

= 4 + 6 + 5

= 15

Now,

The probability of selecting an orange marble.

= 5/15

= 1/3

= 0.33

Thus,

The probability of selecting an orange marble is 0.33.

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Answer:

Step-by-step explanation:

b:c= 3:6

Answer:

Step-by-step explanation:

We know that:
a : b = 1 : 2 (or a = (1/b)*b)
b : c = 3 : 4 (or b = (3/4)*c)

So, we can substitute the value of b from the second equation into the first equation to get the ratio of a : c:

a = (1/b)*b = (1/((3/4)c))((3/4)c) = (4/3)(1/c)*c = (4/3)*1 = 4/3

So, the ratio of a : c is 4 : 3.

Alternatively, we can use the cross-multiplication method to find the ratio.

a : b = 1 : 2, and b : c = 3 : 4

so a4 = b3, and b4 = c3

so a4 = c3

so a:c = 3:4

In this way also we got the ratio of a:c as 3:4

Answer:

m1 = 4, m2 = 176

Step-by-step explanation:

Using complementary angle rule you know the total angle is 180 thus:

[tex]180 - (x-18) = 8x\\198 - x = 8x\\198 = 9x\\x = 22[/tex]

m1 = (22 - 18) = 4

m2 = 8(22) = 176

The solution of the expression is 216(cd)³.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the exponential expression is (6cd⁻¹)⁻³. The expression will be simplified as below,

E = (6cd⁻¹)⁻³.

Use the property of the exponents to multiply the powers and now solve.

E= (6cd³)

E = 6³ x (cd³)

E = 216(cd³)

Therefore, the simplified value of the expression is 216(cd)³.

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