1) The eighth grade class has 20% fewer students this year than they
had as seventh graders. Write an expression to show the decline in
class numbers, and then simplify the expression. Use (s) to represent
the number of seventh grade students.

Answer:

it depends on how many students?

Step-by-step explanation:

The correct statements are -

In statistics, an outlier is a data point that differs significantly from other observations. An outlier may be due to a variability in the measurement, an indication of novel data, or it may be the result of experimental error; the latter are sometimes excluded from the data set.

Given is to identify which of the following statements is most accurate with respect to outliers in this example.

The correct statements are -

Therefore, the correct statements are -

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The correct equation of the table is John's

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

John: y = -6x + 510

Jim: y = 6x + 51

From the table (see below), we have the following x and y values

x = 0, 1, 2, 3, 4

y = 510  504  498 492 486

Next, we test the equations:

John: y = -6x + 510

Substitute the known values in the above equation, so, we have the following representation

y = -6(0) + 510 = 510

y = -6(1) + 510 = 504

y = -6(2) + 510 = 498

y = -6(3) + 510 = 492

y = -6(4) + 510 = 486

Jim: y = 6x + 51

y = 6(0) + 51 = 51

y = 6(1) + 51 = 57

y = 6(2) + 51 = 63

y = 6(3) + 51 = 69

y = 6(4) + 51 = 75

The above shows that John's y values corresponds to the table of values added at the end of the equation.

Jim would be correct if the table of values is:

x = 0, 1, 2, 3, 4

y = 51  57  63 69 75

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Complete question

Given the table of values

x    y

0   510

1    504

2   498

3   492

4   486

John says that the function representing the table is y = -6x + 510

Jim says that the function representing the table is y = 6x + 51

Who’s is correct?

Answer:

Step-by-step explanation:

175

With Scale factor=4, the area of bigger square is 2304 and perimeter is 192 and for smaller square area=144 unit and perimeter=48.

What is the definition of scaling factor?

The Scale Factor is used to scale shapes of different sizes. Geometry teaches us about different geometrical shapes in two and three dimensions. The scale factor is a statistic that is used to compare statistics that appear comparable but have distinct scales or metrics. Consider two circles with the same shape but different radii.

The scale factor indicates how much bigger or smaller a figure is in comparison to the original figure. You may create an extended or reduced version of any original form by using a scale factor.

Now,

side of smaller square=12

area=12²=144

perimeter=12*4=48

For bigger square, as scaling factor=4

then side=12*4=48

area=48²=2304

perimeter=4*48=192

Hence,

            the area of bigger square is 2304 and perimeter is 192 and for smaller square area=144 unit and perimeter=48.

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The value of the expression 3 (x - y) is 12

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

x - y = 4

Multiply both sides of the equation by 3

So, we have the following representation

3 * (x - y) = 4 * 3

Evaluate the products

This gives

3 (x - y) = 12

Hence, the soluton of 3 (x - y) is 12

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0.06 can be expressed as literally 0.06%

Oh okay I see now, as a fraction you would multiply by 100, so it would be 6 / 100

Answer: 6%

Step-by-step explanation:

if you multiply 0.06 by 100 it gets you 6%

Answer:

90  berries

Step-by-step explanation:

Answer:

Step-by-step explanation:

If 20% of the test is made up of 10 open-ended questions, we can set up a proportion to find the total number of questions on the test.

Let x be the total number of questions on the test.

We can write the proportion as:

open-ended questions/total questions = 20%/100%

or

10/x = 20/100

To solve for x, we can cross-multiply to get:

10 * 100 = 20 * x

1000 = 20x

x = 50

Therefore, there are 50 total questions on the test.

Answer:

it dude

Step-by-step explanation:

use internet

Distance reading at the start of journey = 12468

Distance reading at the end of the journey = 12845

Distance traveled in the journey = 12845 - 12468 = 377 miles

Cost of petrol per mile = 13p

Cost of petrol for the journey = 13 × 377 = 4901p

Since one pound is one hundred pence, 4901p in pounds will be 4901/100 = 49.01 pounds

Cost of petrol used in the journey is 49.01 pounds

The value of A n (B U C) = {q, s, w, y} for the given sets.

A set is a clearly defined group of things in mathematics. We may define several operations on sets and look at their attributes, unlike numbers. An operation in set theory is a task that involves combining different sets in order to create a new set with unique attributes.

The set containing all elements shared by sets A and B is the intersection of the two sets.

The given sets are:

U= {q,r,s,t,u,v,w,x,y,z}, A={q,s,u,w,y}, B={q,s,y,z}, and C= {v,w,x,y,z}

The value of (B U C) depicts all the terms in B and C:

(B U C) = {q, s, y, z, v, w, x}

The value of A n (B U C) depicts all the common terms in set A and B U C:

A n (B U C) = {q, s, w, y}

Hence, the value of A n (B U C) = {q, s, w, y} for the given sets.

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There are 16 sweets that are fizzy and orange and the fraction is 4/15

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

Fizzy = 2/5

Orange = 4/6 of Fizzy

So, we have

Orange = 2/5 * 4/6

Orange = 4/15

Using (a) as a guide, we have

Fizzy and orange​ = 4/15 * 60

Fizzy and orange​ = 16

Hence, the fizzy and orange​ is 16

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Answer:

------------------------------

As per question we have:

Find the required segment length using segment addition rule:

Answer: Sherry wants to buy at least 2 movies and at least 8 songs, and her gift card has a value of $25. To represent this information as a system of inequalities, we can use the following:

Let x be the number of movies Sherry buys, and y be the number of songs she buys.

The cost of buying x movies is 5.99x dollars, and the cost of buying y songs is 0.99y dollars. Since Sherry's gift card is worth $25, we have the inequality:

5.99x + 0.99y ≤ 25

In addition, Sherry wants to buy at least 2 movies, which means x must be greater than or equal to 2. She also wants to buy at least 8 songs, which means y must be greater than or equal to 8. This gives us the inequalities:

x ≥ 2

y ≥ 8

Therefore, the system of inequalities that represents the number of movies and songs that Sherry can download is:

x ≥ 2

y ≥ 8

5.99x + 0.99y ≤ 25

The answer is (A).

Step-by-step explanation:

As we discovered in chapter, there is a 1/12 chance of getting a 3.

By reducing the number of successful effects by the total amount of possible outcomes, probability—the chance that a will occur—is determined. A coin toss serves as the most fundamental example. There are just two results when users flip a coin: either it shows up heads or tails.

There are 12 potential results in total because the die has 12 sides.

(1) Since there is only one side of the die with a 3 on it and all sides are equally probable, the chance of rolling the die and having the 3 face on top is 1/12.

(2) The likelihood that the die will fall on top with a 3 or a 7 is calculated as the product of the odds of rolling a 3 and a 7 minus the likelihood of simultaneously rolling a 3 and a 7. (which is zero, since the die has only one side).

As we discovered in chapter, there is a 1/12 chance of getting a 3. (1). Given that the dice only has a 7 on one side, the likelihood of getting a 7 is also 1/12. The likelihood of tossing the dice and having the 3 or 7 face up is therefore:

1/12 + 1/12 - 0 = 1/6

(3) Since the die doesn't have a face marked "15," there is no chance that tossing the die will result in a 15 face landing on top.

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Answer:

-$32

Step-by-step explanation:

Credited = Positive Change

Debited = Negative Change

48-80 = -32

-$32

Answer:

y = (-1/5)x + b

Step-by-step explanation:

The given line is y = 5x. To find a line perpendicular to it, we need to use the fact that the slopes of perpendicular lines are negative reciprocals of each other.

The slope of the given line y = 5x is 5, so the slope of the line perpendicular to it is -1/5.

Let (x1, y1) be any point on the line L. Then the point-slope form of the equation of L is:

y - y1 = m(x - x1)

where m is the slope of the line, which in this case is -1/5.

So the equation of line L in point-slope form is:

y - y1 = (-1/5)(x - x1)

To find the equation of line L in slope-intercept form, we need to solve the point-slope equation for y. First, we can simplify the equation to:

y = (-1/5)x + (1/5)x1 + y1

This equation can be rearranged to the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept. In this case:

m = -1/5

b = (1/5)x1 + y1

Therefore, the equation of line L in slope-intercept form is:

y = (-1/5)x + b, where b = (1/5)x1 + y1.

Answer:

A.35°, 114°, 31°.

B.61°,119°,153°,27° and 92°

A. alternates angles are equal;

35°=35°

Vertically opposites angles are equal;

114°=114°

Sum of interior angles of a triangle is 180;

114+35+x=180

x=180-(114+35)

x=31

Picture B.

Corresponding angles are equal;

61°=61°

Sum of angles on a straight line is 180°

61+x=180

x=180-61

x=119°

Corresponding angles are equal;

153°=153°

Sum of angle on straight line is 180;

153+x=180

x=180-153

x=27

Sum of interior angle of a triangle is 180;

27+61+X=180

x=180-(27+61)

x=92

The $500,000 and $350,000 invested by Mario and Luigi, and the $3 million profit from the business in the first year indicates;

a) The amount Luigi made a day is about $3,384.4

b) The amount Luigi made per hour is about $141

Profit is the revenue, less costs, expenses and tax.

The amount Mario invests = $500,000

Amount Luigi invests = $350,000

The ratio in which the profit was split after their first year = Within the same ratio of their initial investments

The amount of profit made by the business = $3 million

The ratio of their initial investment = 500,000 : 350,000 = 10 : 7

Therefore, the ratio in which the profit is split = 10 : 7

The amount Luigi received in a year = (7/(10 + 7)) × 3 = 1235294 2/17

The time unit conversion from year to day is presented as follows;

Number of days in a year = 365 days

The amount Luigi received peer day = (1235294 2/17)/365 = 3384 456/1241

3384 456/1241 ≈ 3384.4

b) The number of hours in a day = 24 hours

Amount Luigi received per hour = (3384 456/1241)/24 = 141 19/1241

141 19/1241 ≈ 141

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The correct conclusions about the triangle reflections are -

        {y} - axis.

        {x} - axis.

Reflections of graphs involve reflecting a graph over a specific line.

Given is a triangle along with their reflections.

We can conclude the following points regarding the reflected triangles -

        {y} - axis.

        {x} - axis.

Therefore, the correct conclusions about the triangle reflections are -

        {y} - axis.

        {x} - axis.

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The solution to the ordinary differential equation y' - y = 3 · t is the equation [tex]y(t) = C\cdot e^{t} + A\cdot t + B[/tex], where C, A and B are real numbers.

Differential equations are equations that involves functions and its derivatives. In this case we have an example of a first order linear non-homogeneous ordinary differential equation, whose standard form is introduced below:

y' - y = 3 · t

Given the linearity of the differential equation, the solution of the differential equation is the sum of the homogeneous component and the particular component. First, we must determine the homogeneous component:

y' - y = 0

y' = y

dy / dt = y

dy / y = dt

∫ dy / y = ∫ dt

ln y = t + C

[tex]y = C \cdot e^{t}[/tex], where C is the integration constant.

Second, find the particular component:

f(t) =3 · t → yP(t) = A · t + B, where A, B are real coefficients.

Third, write the complete solution:

[tex]y(t) = C\cdot e^{t} + A\cdot t + B[/tex]

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The value of sin -1(square root 2/2) is π/4 or 45 degrees.

Inverse sine, also known as arcsine, is a trigonometric function that is the inverse of the sine function. It is denoted as sin^-1(x), where x is a number between -1 and 1.

The inverse sine function is used to find the angle in a right triangle that has a given sine value. In other words, if we know the ratio of the length of the side opposite an angle to the length of the hypotenuse in a right triangle, we can use the inverse sine function to find the measure of that angle.

The inverse sine function returns an angle in radians, which can be converted to degrees if needed. It has a domain of -1 ≤ x ≤ 1 and a range of -π/2 ≤ sin^-1(x) ≤ π/2.

Like other inverse trigonometric functions, the inverse sine function is a multivalued function. This means that for a given value of x, there can be multiple angles that satisfy sinθ = x. To address this, the principal value of the inverse sine function is defined as the angle between -π/2 and π/2 that satisfies sinθ = x.

The inverse sine function has many applications in mathematics, physics, engineering, and other fields. It is used in the calculation of angles in a variety of contexts, such as in the design of structures and in the analysis of wave phenomena. It is also used in calculus and other advanced mathematics courses to solve integrals and differential equations.

To see why, we can use the definition of the inverse sine function, which gives us the angle whose sine is equal to the input value. In this case, we have:

sin -1(square root 2/2) = θ

where sin(θ) = square root 2/2.

We know that the sine of 45 degrees (or π/4 radians) is also equal to square root 2/2. Therefore, we have:

sin(45 degrees) = square root 2/2

Taking the inverse sine of both sides gives us:

sin -1(square root 2/2) = 45 degrees = π/4

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The height of the balloon is 1.3 miles above the ground.

Height is the measure of vertical distance, either how "tall" something or someone is, or how "high" the point is. For example, a person's height is typically measured using a stadiometer and is recorded in centimeters or feet and inches. The height of a mountain is usually measured in meters or feet. In aviation, height is measured from the surface of the earth, either above ground level (AGL) or above mean sea level (AMSL).

The answer to this question can be found by using the trigonometric formula of Tangent. To calculate the height of the balloon, we must find the length of the hypotenuse in the triangle formed by the two towns and the balloonist.

Using the formula for tangent, we can calculate the length of the hypotenuse. The formula is:

tan (angle) = opposite side/adjacent side

In this case, the opposite sides are the two towns, and the adjacent side is the height of the balloon.

For the first town, the formula is:

tan 36° = 1.6/x

Solving for x, we can calculate the length of the hypotenuse for the first town to be 2.8 miles.

For the second town, the formula is:

tan 32° = 1.6/x

Solving for x, we can calculate the length of the hypotenuse for the second town to be 2.9 miles.

Since the hypotenuse is the total distance between the two towns and the balloonist, the height of the balloon can be calculated by subtracting the total length of the two towns (1.6 miles) from the hypotenuse of the second town (2.9 miles).

The height of the balloon is 1.3 miles above the ground.

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Answer:

What is height?

Height:

When a rectangle is drawn with horizontal and vertical sides, the word height makes it clear which dimension is meant; height labels how high (how tall) the rectangle is. That makes it easy to indicate the other dimension—how wide the rectangle is from side to side—by using the word width. And if the side-to-side measurement is greater than the height, calling it the length of the rectangle is also acceptable, as it creates no confusion.

The answer to this question can be found by using the trigonometric formula of Tangent. To calculate the height of the balloon, we must find the length of the hypotenuse in the triangle formed by the two towns and the balloonist.

Using the formula for tangent, we can calculate the length of the hypotenuse. The formula is:

tan (angle) = opposite side/adjacent side

In this case, the opposite sides are the two towns, and the adjacent side is the height of the balloon.

For the first town, the formula is:

tan 36° = 1.6/x

Solving for x, we can calculate the length of the hypotenuse for the first town to be 2.8 miles.

For the second town, the formula is:

tan 32° = 1.6/x

Solving for x, we can calculate the length of the hypotenuse for the second town to be 2.9 miles.

Since the hypotenuse is the total distance between the two towns and the balloonist, the height of the balloon can be calculated by subtracting the total length of the two towns (1.6 miles) from the hypotenuse of the second town (2.9 miles).

The height of the balloon is 1.3 miles above the ground.

Answer:

60

Step-by-step explanation:

a tringle always adds ups to 180 add them then subtract.

On dividing 153 by 4, we get the value as 38[tex]\frac{1}{4}[/tex].

An algebraic expression is a combination of terms both constants and variables. For example -

2x + 3y + z

3x + y

Given is to find the equivalent value for the division as -

"153 ÷ 4"

On dividing 153 by 4, we can write the result as follows -

{x} = 153/4

{x} = 38.25

{x} = 38[tex]\frac{1}{4}[/tex]

Therefore, On dividing 153 by 4, we get the value as 38[tex]\frac{1}{4}[/tex].

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{Question in english -

What is the remainder when 153 is divided by 4?}

Answer:

Step-by-step explanation:

(a) To find the minimum possible mass of the four barrels, we want to arrange them in a way that minimizes the total mass. One way to do this is to put the two lightest barrels together and the two heaviest barrels together. This way, the total mass is minimized because the lighter barrels balance out the heavier ones.

So, the minimum possible mass of the four barrels is:

2(30 kg) + 2(30 kg) = 120 kg

(b) To find the maximum possible mass of the four barrels, we want to arrange them in a way that maximizes the total mass. One way to do this is to put the heaviest barrel with the lightest barrel and the other two barrels together. This way, the total mass is maximized because the heaviest and lightest barrels are paired together, making the total mass greater than if they were all paired together.

So, the maximum possible mass of the four barrels is:

30 kg + 90 kg + 30 kg + 30 kg = 180 kg

The key features of this rational function include the following:

Domain: (-∞, 2) ∪ (2, ∞)

Range: (-∞, 1) ∪ (1, ∞)

Y-intercept: 1.

X-intercept: 2.

Vertical asymptote: x = -2.

Horizontal asymptote​: y = -1.

In Mathematics, a rational function simply refers to a type of function  which is expressed as a fraction. This ultimately implies that, a rational function is composed of two (2) main parts and these include the following:

Additionally, the vertical extent of any graph of a rational function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

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For the given percenatge of total cost, the total value of Gabe's health care coverage for the year is $9,984.

What is percentage?

Percentage is a way of expressing a fraction or a part of a whole as a portion out of 100. It is represented by the symbol "%".

We can start by using the information given to determine the total cost of the health care coverage. Let's call this cost "C". Since Gabe contributes 15% of this cost and pays $28.80 per week, we can write:

0.15C = 28.80

To solve for C, we can divide both sides by 0.15:

C = 28.80 / 0.15

= 192

So the total cost of the health care coverage is $192 per week. To find the total value of Gabe's health care coverage for the year, we need to multiply this weekly cost by the number of weeks in a year.

Assuming there are 52 weeks in a year, we have:

Total value of Gabe's health care coverage = 192 x 52

= 9984

Therefore, the total value of Gabe's health care coverage for the year is $9,984.

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Answer:

Step-by-step explanation:

First 3 + 4 is 7. Then for the red paint ( 3 ) , this is written.

= [tex]\frac{3}{7}[/tex] * 1400

Then calculated.

= [tex]\frac{3}{7}[/tex] * [tex]\frac{1400}{1}[/tex] = [tex]\frac{4200}{7}[/tex] = 600 ml for the red paint.

Then its easy to find the blue paint, either the long way ( above ) or...

= 1400 ml - 600 ml = 800 ml for blue paint.

Have a wonderful day! :-)