you are instructed to subtract four points from each score, square the resulting value, and find the sum of the squared numbers. how would this set of instructions be expressed in summation notation?

Answer:

y = 100 - 10x

Step-by-step explanation:

Let y₀ be the original water level before any marbles were removed

Let y = water level after x marbles are removed.

Let d be the water level drop for every marble removed

Then we have the general equation:

y = y₀ - x.d  

We have to find d and y₀

So we get one equation for the water level after removal of 2 marbles

80 = y₀ - 2d     [1]

After 4 more marbles were removed, the water level drops to 40ml. That means for 4 marbles removed, the water level drops from 80 to 40. So drop in water level for 4 marbles = 80-40 = 40ml

For each marble then, water level drop = 40/4 = 10ml. This is the value of d

Plug this value of d into [1] to get the original water level y₀

80 = y₀ - 2( 10)

80 = y₀ - 20

100 = y₀

or,

y₀ = 100

So original water level is 100ml and the equation for water level after x marbles are removed is

y = 100 - 10x

Answer:

8x^2-14xy+3y^2 (I think)

Step-by-step explanation:

You probably don't need it now but like here

14t-5t is another way to write the expression ​t⋅(14−5)

A number system is defined as a system of writing to express numbers.

The given expression is t(14-5)

An expression is combination of variables, numbers and operators.

t times of fourteen minus five

Here t is the variable

We need to find other way to write this expression

t(14-5)

Apply distributive property

14t-5t

9t

Hence, 14t-5t is another way to write the expression ​t⋅(14−5)

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Answer: The possible outcomes are — 1, 2, 3, 4, 5, and 6. The probability of getting any of the outcomes is 1/6

Step-by-step explanation:

Answer:

-2.875

Step-by-step explanation:

-12x-9-20x-4=79

-32x-13=79

-32x=92

92/-32= -2.875

Answer:

Step-by-step explanation:

Answer:

A), C)

Step-by-step explanation:

Let's round all numbers below to the nearest 10.

A) 34,590

B) 34,650

C) 34,590

D) 34,600

E) 35,010

Answer:

below

Step-by-step explanation:

density  *   volume = mass

7.92 g / cm^3    *   60 cm^3 = 475.2 g

Answer: last one should be it

Step-by-step explanation:

Answer:

3rd one is correct.

Step-by-step explanation:

There are 360 different skirt-blouse-shoe outfits can she wear.

What is outfits?

A group of clothes that have been specifically chosen or designed to be worn together is known as an outfit. The term "outfit" can also refer to a business, an association, or a team of people who collaborate frequently. It can be used as a verb to mean "provide with the necessary gear."

A dress is different from a blouse and a skirt!  So I'll rephrase this as how many ways can she dress, to wear one blouse, one skirt and one pair of matching shoes.

You just multiply the number of blouses, the number of skirts, and the number of pairs of shoes;

= 5*9*8 = 360

Hence, there are 360 different skirt-blouse-shoe outfits can she wear.

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Answer: i think either 256/6561 or -256/6561

Step-by-step explanation:

The constant of proportionality is 1/3, and the equation is y = (1/3)x represents the relationship.

The value of the proportionality constant is determined by the type of proportion between the two specified values.

Proportional relationships are written in the form y = kx

where k is the constant of proportionality.

As per the given table, the constant of proportionality will be

k = (1 - 2/3)/(3-2)

k = (1/3)/1

k = 1/3

So, the equation is y = (1/3)x.

Thus, the constant of proportionality is 1/3, and the equation is y = (1/3)x represents the relationship.

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The area of the Rhombus ABCD is 1.2 square meter.

What is Rhombus?

A quadrilateral with four equal-length sides is known as a Rhombus in plane Euclidean geometry. Another name for this shape is an equilateral quadrilateral because all of its sides are equal in length.

Let ABCD be the given Rhombus of Perimeter = 52 cm.

Since all the sides are equal to each other.

Therefore, each side of Rhombus measures = 13 cm

So,

AD = CD = 13 cm and AC = 24 cm.

Area of the triangle ACD = √[ s (s - a) (s - c) (s - d) ] ….. Heron’s Formula.

where s = semi-perimeter,

a, c, and d are side measures.

s = (1/2) [ 13 + 13 + 24 ] = 25

Area (A) = √[ 25 (25 – 13) (25 – 13) (25 - 24) ] = 60

Hence Area of the entire Rhombus = 2 * 60 = 120 cm²

Convert 120 cm^2 into meter square

⇒ 120 cm^2 = 1.2 m^2

Hence, the area of the Rhombus ABCD is 1.2 square meter.

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The given statement that Diagonal WY bisects angles ZWX and ZYX has been proven below to be true.

Bisection of an angle is simply defined as dividing an angle into two equal parts.

We are given that Diagonal WY bisects angles ZWX and ZYX.

Now, from the image attached, we can see that side XY is congruent to side ZY and so; XY ≅ ZY.

Similarly, XW is congruent to ZW and as such; XW ≅ ZW

Since XY is congruent to ZY and XW is congruent to ZW, then the statement that  diagonal WY bisects angles ZWX and ZYX is true

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Given that there are six blue marbles in the bag out of a total of 16, there is a 3/8 chance that the marble selected will be blue.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Here,

Total number of marbles in bag,

=3+6+5+2

=16 marbles

Number of blue marbles=6

Probability of selecting blue marbles,

=6/16

=3/8

The probability that the marble chosen is blue will be 3/8 as the bag contains 6 blue marbles when total number of marbles is 16.

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Zane's velocity climbing the volcano is given as follows:

B. 5/7 meters per second.

The linear function in the context of this problem is defined as follows:

y = 5/7x - 25.

Hence the coefficients of the linear function are given as follows:

The meaning of each of these coefficients is given as follows:

Thus the correct option of Zane's velocity climbing the volcano is of option B.

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The equation which is equivalent to 60% of 25 is x = 0.6 * 25

1. Equivalent equations: Equivalent equations are algebraic equations that are having identical roots or solutions. By adding or subtracting the same number or expression to both side of an equation we get an equivalent equation. Also by multiplying or dividing both sides of an equation by the same non zero number we get equivalent equation.

2. How to find equivalent equation : Steps to find weather the equations are equivalent are:

An equation is used to show the relationship between variables, numbers.

Let x represent the value of 60% of 25. Hence:

x = 60% of 25

x = 0.6 * 25

Hence the equation which is equivalent to 60% of 25 is x = 0.6 * 25

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The number of ft that Luke climbed, given the elevation he started from, and the summit, is 5, 050 ft

The number of feet that Luke climbed, can be found by the formula:

Number of feet climbed = Summit of K2 - Luke's starting elevation

Summit of K 2 = 28, 251 ft

Luke's starting elevations = 23, 201 ft

Elevation climbed by Luke was therefore:

= 28, 251 - 23, 201

= 5, 050 ft

In conclusion, the total elevation that Luke climbed from his starting point to the summit of K2 is 5, 050 ft.

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Answer:

[tex]\huge\boxed{\sf s = 320}[/tex]

Step-by-step explanation:

Given that,

[tex]s \propto t^2[/tex]

Converting proportionality into equality and adding a constant.

s = kt² ----------------(1)

Given that, s = 80 when t = 4

Put in Eq. (1)

80 = k(4)²

80 = k(16)

Divide 16 to both sides

80/16 = k

5 = k

Now,

Put t = 8 in Eq. (1)

s = (5)(8)²

s = (5)(64)

[tex]\rule[225]{225}{2}[/tex]

Paul earns more interest than Monica does.

Simple interest can be defined as a form of interest in which the percent rate is applied on the same principal for a given period of time.

Given that,

Money deposited by Monica is $200 at simple interest of 3.7%.

Money deposited by Paul is $300 at simple interest of 2.9%.

The expression to calculate simple interest is given as,

(P × r × t)/100

Substitute the corresponding values to obtain the simple interest for both cases as follows,

Interest gained by Monica is (200 × 3.7 × 1)/100 = $7.4.

Interest gained by Paul is (300 × 2.9 × 1)/100 = $8.7.

Hence, monica is not correct as the interest earned by Paul is greater than that of monica.

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The graph of the proportional relationship d = 4t is given by:

Graph B.

The general model of a proportional relationship is given as follows:

y = kx.

Meaning that it's graph is that of a linear function, in which:

The relation between velocity, distance and time is given as follows:

v = d/t.

Then the equation for the distance as a function of time is given as follows:

d = vt.

Meaning that the slope is the velocity.

Trey walks 12 miles in 3 hours, hence the slope of the graph is of:

v = 12/3 = 4 miles per hour.

Among the options given by the image shown at the end of the answer, the correct option is:

Graph B.

As it goes through point (4,16).

The options are given by the image shown at the end of the answer.

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Answer:

37+82+x=180

119+x=180

x=180-119

x=61

Differentiation reverses the parity of a function, means if f(x), is an even function, then its derivative f'( x ) is odd which is true i.e f(x) is even function implies f'(x) is odd and if f(x) is odd function implies f'(x) is even .

First, let's we start with the definition of even and odd functions.

f is even if and only if f(x) = f(-x) --(1)

f is odd iff f(x) = -f(-x) ---(2)

If f is even and differentiating equation (1) we get,

f'(x) = f'(-x)× (-1) = -f'(-x).

f'(x) = - f'(-x).

Since, f'(x) is some function, then let

g(x) = f'(x) So, we see g(x) = -g(-x) which shows that the derivative of an even function is an odd function.

If f is odd then: f(x) = -f(-x)

differentiating above function with respect to x we get ,

f'(x) = -f'(-x)× (-1 ) = f'(-x).

Let g(x) = f'(x), then g(x) = g(-x) which shows that the derivative of an odd function is an even function.

Hence, Differentiation reverses the parity is hold.

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Answer: -9/2

Let's solve this equation step-by-step.

−8+2(3+8)=−4(g+1)

Step 1: Simplify both sides of the equation.

−8+2(3+8)=−4(g+1)

−8+2(3+8)=(−4)(g)+(−4)(1) (Distribute)

−8+22=−4g+−4

(−8+22)=−4g−4 (Combine Like Terms)

14=−4g−4

Step 2: Flip the equation.

−4g−4=14

Step 3: Add 4 to both sides.

−4g−4+4=14+4

−4g=18

Step 4: Divide both sides by -4.

−4g/−4 = 18/−4

g = −9/2

Answer:

394.527

Step-by-step explanation:

Divide the total number of beads by the number he needs to make each necklace and you will have your answer.

4 square units will be the area of the largest rectangle.

Given,

First, let's build a rectangle ABCD, where A is the point at the bottom right corner and B,C, and D are the points designated in accordance with A.

Now,

Let A = (p, 0)

B = (-p, 0)

C = (-p, 3 - p²)

D = (p, 3 - p²)

Then the area of rectangle is given as: BA×AD

= 2p × 3 - p²

A = 6p - 2p³

Taking the derivative with respect to p, we have

A' = 6 - 6p²

Now,

A' =0

⇒ 6 - 6p² = 0

⇒ 6p² = 6

⇒ p² = 1

Since, we have to find the greater area, therefore we will take p = 1.

Now, substituting the value of p in (A), we have

Greater area = A= 6 - 2 x 1 = 4 square units

Therefore,

The  area of the largest rectangle should be 4 square units.

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Question is incomplete. Completed question is given below;

What is the area of the largest rectangle with lower base on the x-axis and upper vertices on the curve y = 3 − x2?

The physics student predicted that a force of 377.28N would be needed to stretch the spring by 15 cm using the regression model.

The relevant points from the regression model are

B. He predicted something that was outside the range of forces seen.

C. He predicted something that was outside the range of stretched distances that were observed.

D. His data contained outliers or significant points.

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A real-valued function defined on an interval with the property that its epigraph—the collection of points on or above the function's graph—is a convex set—is said to be convex. The challenge of minimizing convex functions over convex sets is the subject of the optimization discipline known as convex minimization.

A mathematical model whose needs are expressed by linear connections can be optimized using a technique known as linear programming. A particular type of mathematical programming is linear programming. When a linear function is subjected to various constraints, it is maximized or minimized using the mathematical modeling technique known as linear programming. In business planning, industrial engineering, and—to a lesser extent—the social and physical sciences, this method has proven helpful for directing quantitative decisions.

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Answer:

$63.90

Step-by-step explanation:

cost = $639

markup = 10%

cost * markup = $63.90

a)The linear equation is C=25n + 2500 to produce n 3000 toys, b) The total cost to produce 3000 toys is $77,500, c) With $32500, a total of 1200 toys can be produced in Pinwheel Industries.

An equation is a mathematical statement with an equal symbol (=) between the algebraic expression. Equations with a degree of one are called linear equations. It is the straight line's equation. Whenever values are substituted for the unknown values in linear equations, the solutions produce values that make the equation true. Since there is only one variable, there is only one solution. For instance, the equation x + 2 = 0 has just one solution, which is x = -2. In the case of the two-variable linear equation, however, the solutions are determined as the Cartesian coordinates of a point on the Euclidean plane.

The three different types of linear equations are: 1) Standard Form

2) The slope intercept form

3)Point Slope Form

How to solve?

A) Linear equation y=mx+b,

C (total cost) = y and n (number of toys) =x.

C=25n + 2500

B) Put n=1750

C= 25(3000) + 2500

C= $77,500

C)

32500= 25n +2500

30000=25n

n = 1200

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