A group of students was surveyed in a middle school class. They were asked how many hours they work on math homework each week. The results from the survey were recorded.


Number of Hours Total Number of Students
0 1
1 8
2 2
3 5
4 9
5 7
6 3


Determine the probability that a student studied for exactly 1 hour. Round to the nearest hundredth.

Answer:

7 feet per second

Step-by-step explanation:

The change in elevation of the parachutist is -35 ft in 5 seconds. To find the change in elevation per second, we can divide the total change by the number of seconds.

Change in elevation per second = -35 ft / 5 seconds = -7 ft/s

So the parachutist's elevation changes by -7 ft/s each second.

It means the elevation of the parachute is decreasing by 7 feet per second.

x² + y = 55 ---1

y=6---2

subs 2 in 1

x²+ 6 = 55

x² = 55-6

x² = 49

x =√49

x = 7

The sum of the two polynomials 6s^2t^2 + 2st^2 + 4s^2t + 3st^2 is

6s^2t^2 + 2st^2 + 4s^2t + 3st^2 = (6+4)s^2t^2 + (2+3)st^2 = 10s^2t^2 + 5st^2

The polynomials are being added term by term, and the coefficient of each term is being added.

The coefficient of s^2t^2 in the sum is 10, which is the sum of the coefficients of s^2t^2 in the original polynomials (6 and 4).

The coefficient of st^2 in the sum is 5, which is the sum of the coefficients of st^2 in the original polynomials (2 and 3).

So the sum of the polynomials is 10s^2t^2 + 5st^2, this is the final result.

It's important to note that the polynomials have to be in the same order of terms (same exponent) to obtain the correct result when adding them.

Answer:

by helping some one fast

The function h(t) models the height of a ball thrown into the air, so it makes sense for the range of the function to be all non-negative values. This means that the range of the function will be all non-negative values up until the point where the ball reaches its maximum height, and then it will decrease to zero as the ball hits the ground.

To determine when the ball reaches its maximum height, we can find the vertex of the parabola. The vertex is found by taking the average of the x-coordinates of the roots of the quadratic. In this case, the roots of the quadratic are found by setting h(t) = 0 and solving for t:

-16t^2 + 48t - 36 = 0

By factoring the quadratic, we get:

(t-9)(-16t+4) = 0

So the roots of the quadratic are t = 9 and t = -0.25. The average of these two values is (9 - 0.25)/2 = 4.375. Therefore, the vertex of the parabola is at (4.375, h(4.375)).

To find the y-coordinate of the vertex, we can plug in 4.375 for t in the function h(t):

h(4.375) = -16(4.375)^2 + 48(4.375) - 36 = -16(19.140625) + 195 - 36 = -307.5 + 159 = -148.5

So the vertex of the parabola is at (4.375, -148.5). This means that the maximum height of the ball is -148.5 feet. Since the ball can't go below ground level, the range of the function h(t) is all non-negative values less than or equal to -148.5. Therefore, a reasonable range for the function is [-148.5, ∞).

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Reason: It's the coefficient to the left of the input variable.

There are various methods by which you can solve a quadratic equation such as:

In algebra, a quadratic equation is any equation that can be rearranged in standard shape wherein x represents an unknown cost, and a, b, and c represent acknowledged numbers, in which a ≠ 0. Quadratic equations are in detail related to issues about squares and quadrangles (every other name for rectangles). In reality, the word quadratic is derived from the Latin word quadratus for square.

The general shape of the quadratic equation is ax² + bx + c = 0. for instance, x² + 2x +1 is a quadratic or quadratic equation. A quadratic feature is a characteristic of the form f(x) = ax² +bx+c, in which a, b, and c are constants and a = 0. The term ax² is called the quadratic time period (therefore the call given to the feature), the term box is known as the linear term, and the time period c is known as the steady term.

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The list  below that  shows all the possible outcomes of sack lunches, and select the outcomes from that list that represent picking a ham or turkey sandwich with carrots List 2

the statement states that the school is providing one sack lunch for each student. Each lunch has either a ham, turkey, or bologna sandwich along with either carrots or celery.

List 1 mentions that there is "Ham, Carrots, celery". We know that students can only have either carrots or celery, but the list shows that the students have both. Therefore, list 2 is correct.

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Answer:

9

Step-by-step explanation:

exterior angle=x⁰

interior angle=3x⁰+20⁰

3x⁰+20⁰+x⁰=180⁰

4x=160⁰

x=40⁰

number of sides = 360⁰/exterior angle

360⁰/40⁰= 9sides

Answer: d=0.5

Step-by-step explanation: 4.8d=2.4

Divide 4.8 form both sides to isolate d.

[tex]\frac{4.8d}{4.8} =\frac{2.4}{4.8}[/tex]

Then, just do 2.4 divided by 4.8 to get d=0.5.

Answer:   [tex]\text{x}^3\text{y}[/tex]

This is the same as writing x^3y

===================================

Explanation:

When finding the GCF, we look for the smallest exponent for each variable.

The x terms of the given expressions are x^3 and x^5. The smallest exponent here is 3, so x^3 is part of the GCF.

The y terms are y^2 and y. Think of y as y^1, which shows 1 is the smallest exponent. We'll have y as part of the GCF.

-----------

We found that...

The overall GCF is x^3y which can be written as [tex]\text{x}^3\text{y}[/tex]

Side note: We ignore the coefficients since they are 1 for each monomial.

The algebraic identities are

(x + y)² = x² + y² + 2xy,

(x – y)² = x² + y² – 2xy,

x² – y² = (x + y) (x – y),

(x + a) (x + b) = x² + (a + b)x + ab,

(x + y)³ = x³ + y³ + 3xy(x + y),

(x – y)³ = x³ – y³ – 3xy(x – y),

(x + y + z)² = x² + y² + z² + 2xy + 2yz + 2zx,

x³ + y³ + z³ – 3xyz = (x + y + z) (x² + y² + z² – xy – yz – zx) .

These algebraic identities basically carry variable equations in such a way, that the Left-hand side (L.H.S) of the equation is equal to its Right-hand side(R.H.S).

What is the use of algebraic identities?

Algebraic Identities help in simplification. Algebraic Identities play a major role in solving quadratic equations and higher power equations.

The algebraic identities are also used to calculate products of numbers and other things.

Let us consider x, y and z are variables.

Algebraic Identities for Two Variables x and y :

(x + y)² = x² + y² + 2xy

(x – y)² = x² + y² – 2xy

x² – y² = (x + y) (x – y)

(x + a) (x + b) = x² + (a + b)x + ab ; a and b are two constant values

(x + y)³ = x³ + y³ + 3xy(x + y)

(x – y)³ = x³ – y³ – 3xy(x – y)

Algebraic Identities for Three Variables x, y and z :

(x + y + z)² = x² + y² + z² + 2xy + 2yz + 2zx

x³ + y³ + z³ – 3xyz = (x + y + z) (x² + y² + z² – xy – yz – zx)

So, the algebraic identities are

(x + y)² = x² + y² + 2xy,

(x – y)² = x² + y² – 2xy,

x² – y² = (x + y) (x – y),

(x + a) (x + b) = x² + (a + b)x + ab,

(x + y)³ = x³ + y³ + 3xy(x + y),

(x – y)³ = x³ – y³ – 3xy(x – y),

(x + y + z)² = x² + y² + z² + 2xy + 2yz + 2zx,

x³ + y³ + z³ – 3xyz = (x + y + z) (x² + y² + z² – xy – yz – zx) .

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The remaining amount of antibiotic in the cow's body after 6 hours will be 2,431 milligrams * [tex]0.5^5[/tex]= 305.39 milligrams.

Every hour, the cow's body will break down 50% of the initial amount of 9,724 milligrams of the antibiotic. So in the first hour, 50% * 9,724 milligrams = 4,862 milligrams will break down.

The remaining amount of antibiotic in the cow's body after the first hour will be 9,724 milligrams - 4,862 milligrams = 4,862 milligrams.

In the next hour, 50% * 4,862 milligrams = 2,431 milligrams will break down. So the remaining amount will be 4,862 milligrams - 2,431 milligrams = 2,431 milligrams.

This process will repeat for 6 hours, the remaining amount of antibiotic in the cow's body after 6 hours will be 2,431 milligrams * [tex]0.5^5[/tex]= 305.39 milligrams.

The concept used here to solve this is called the half-life, which is the amount of time required for half of the amount of a substance to decay or be used up. In this case, the antibiotic has a half-life of 1 hour, meaning that every hour, half of the initial amount of 9,724 milligrams will be broken down in the cow's body.

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To compare the unit rates, we need to find the cost per ounce for each bottle of water.

For the 16-ounce bottle, the unit rate is:

$2.40 / 16 ounces = $0.15 per ounce

For the 28-ounce bottle, the unit rate is:

$2.80 / 28 ounces = $0.10 per ounce

From the unit rate we can see that the 28 ounce bottle of water is a better deal because it cost $0.10 per ounce while the 16 ounce bottle cost $0.15 per ounce.

It's important to know that as the amount of water increases the price decreases making the 28 ounce bottle cheaper than the 16 ounce bottle.

The results for each operation are given as follows:

x-2/9=6 5/9 -> x = 61/9.

J+1/2=3 9/14 -> J = 22/7.

x-1/8=5/24 -> x = 1/3.

The first step to solve the expressions is to transform the mixed numbers to fractions, hence:

Then the solution for the first expression is of:

x = 59/9 + 2/9

x = 61/9.

The solution for the second expression is of:

J = 51/14 - 1/2

J = 51/14 - 7/14

J = 44/14.

J = 22/7.

The solution for the third expression is of:

x = 5/24 + 1/8

x = 5/24 + 3/24

x = 8/24

x = 1/3.

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Answer:

So the final solution is q < 9 and the inequality is False.

Step-by-step explanation:

To solve the given inequality, you first need to simplify the left-hand side of the inequality:

9 + 8 = 17

so the inequality becomes:

17 > 20 or 2q - 5 < 13

Since 17 is not greater than 20, this inequality is false.

Next, we need to solve the other inequality:

2q - 5 < 13

To isolate the variable on one side of the inequality, we need to add 5 to both sides:

2q < 18

Then, we divide both sides by 2:

q < 9

So the solution is q < 9

So the final solution is q < 9 and the inequality is False.

For the given set of information, the inequality 25 - 1 ≤' temperature ≤' 25 + 1

Linear inequalities in two variables are statements containing symbols such as "'<'(less than), '>' (greater than), '≤''(less than or equal to), '≥' (greater than or equal to) and two separate variables.

Linear inequalities are defined as an inequality (expressed by inequality symbols) that holds a linear function.

A linear function is any function with a straight line as its graph.

The inequality representing the situation is:

25 - 1 <= temperature <= 25 + 1

So the temperature must be greater than or equal to 24°C and less than or equal to 26°C.

The highest possible temperature is 26°C.

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The entire range of values visible on a graph, from left to right, constitutes the graph's domain. All of the graph's values, from lower to higher, are included in the range.

How do you tell the difference between domain and range on a graph?

A function's range is all of its y values, which are its outputs, and all of its x values, which are its inputs. The entire range of values visible on a graph, from left to right, constitutes the graph's domain. All of the graph's values, from lower to higher, are included in the range.

Every potential value of y is included in a function's range. A function's range can be determined using the formula y = f. (x). Only if every x value in a relation has a unique y value can it be considered a function.

The various output values are displayed on the y-axis and make up the range. Remember that the domain and range may be larger than the observable values if the graph extends beyond the area that we can view.

Without evaluating or graphing the functions, it is not possible to determine the exact ranges of g(x) and h(x). However, we can see that both functions are linear and have the same slope (2), so their ranges will be in the same direction.

Since the y-intercept of g(x) is 1 and the y-intercept of h(x) is 2, it can be inferred that the range of h(x) will be greater than the range of g(x) for all values of x in the given domain (0 < x < 5).

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The additive inverse of 7 is -7.

The additive inverse of any numeral is the opposite of that numeral. If a number is added to its additive inverse, the sum of both numbers becomes zero. In other words, the additive inverse is the number that is added to a given number to make the sum zero. That is what you add to a number to get zero is called its additive inverse.

That is, Number + Additive inverse = 0

OR

The negative of a number.

Now we are given the number

7

So, the additive inverse of 7:

⇒7 + Additive inverse = 0

⇒Additive inverse = -7

Thus the additive inverse of is 7 is -7.

--The given question is incorrect; the correct question is

"What is the additive inverse of 7?"--

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The value of x from the given figure is 12 units.

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.

From the given figure,

Consider ΔPQR and ΔPQS,

∠P=∠P (Reflex property)

PQ=PQ (Reflex property)

∠PQR=∠PSQ=90°

By AA similarity, ΔPQR ~ ΔPQS

So, PQ/PR = PS/PQ

x/45 = 25/x

x²=45×25

x=15√5 units

Therefore, the value of x from the given figure is 15√5 units.

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Answer:

I also don't know good luck girly

27500 ≥ 120x + 12600 is the inequality that can be used to determine x, the great 120-kilogram crates that can be loaded onto the shipping container.

A relation that compares two numbers or other mathematical expressions inequitably is known as an inequality in mathematics. [1] Most frequently, size comparisons are made between two numbers on the number line. Different notations can be used to represent various kinds of inequalities, including:

A is smaller than b, as shown by the symbol a < b.

When the expression a > b is used, it means that a is greater than b.

The greatest weight that can be loaded into a container = 27500kg

Shipment weight already present in the container = 12400kg

Amount of weight that can be loaded = 27500 - 12400 = 15100kg

Weight of each crates = 120 kg

Let x be the maximum number of 120 kg crates that can be loaded to the container

Weight of 'x' number of 120 kg crates = 120x

Therefore, the required inequality is as follows

27500 ≥ 120x + 12600 (since the maximum amount of weight of crates that can be put in the container should be less than or equal to the total weight of the maximum number of crates that can be loaded into the container).

Thus, 27500 ≥ 120x + 12600 is the inequality that can be used to determine  x, the great 120-kilogram crates that can be loaded onto the shipping container.

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The degree of the polynomial 2x² 5x² 7 is 4.

The biggest sum of all the exponents for all of variables in a term is the polynomial's degree. Any polynomial's degree is determined solely by its variables; coefficients are to be disregarded. The highest exponential power in a polynomial equation is called the polynomial's degree.

When x is the variable with the highest power n in an nth degree polynomial function with real coefficients, where n can take whole number values.

One of the key ideas in mathematics is the degree of polynomials, which establishes the maximum number of possible solutions and the frequency with which a function will cross the x-axis on a graph.

A polynomial with many variables is of a certain degree: Find the term with the highest degree by averaging the exponents of all the variables in each phrase. That will be regarded as the polynomial's degree.

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Improper fraction is greater than 1, their product is also greater than 1.

Now, According to the question:

A fraction is called a proper fraction if its numerator is less than its denominator. The value of a proper fraction is always less than 1. Whereas, in an improper fraction, the numerator is equal to or greater than the denominator. Its value is always one or greater than one. Consider 1/3 and 3/2. Their product is 1/3 × 3/2 = 3/6 = 1/2

Therefore, according to the definition, the product of a proper and improper fraction is less than the improper fraction.

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The equation system contains: No Solution.

A mathematical statement proving the equality of two mathematical expressions is what is meant by the term equation.

When two or more components of a situation must be taken into account in order to comprehend or describe the entire situation, this is known as an equation.

The equation in a new order:60x + 2y = 50

y+80x = 50​

On both sides of the equation, lessen the most prevalent factor:

80x + y =25

80x + y = 50

Remove the two equations:

80x + y - (80x + y) = 25-50

Take the parentheses out.

80x + y - 80x - y = 25 - 50

One variable is canceled: 0 = 25 - 50

Make a difference or total calculation: 0 = -25

The equation system contains: No Solution.

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The value of P(F or G) using the general addition rule be 8/12.

Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A number between 0 and 1 represents the likelihood of an event, with 0 generally denoting impossibility and 1 denoting certainty.

Probability is a synonym for potential. It is a field of mathematics that examines how random events happen. From zero to one, the value is stated. To forecast the likelihood of events, probability has been introduced in mathematics.

We have that

F∪G = {5, 6, 7, 8, 9, 10, 11, 12}

P(FG) = 0.667

P(F or G) = 5/12 + 4/12 - (1/12)

P(F or G) = 5/12 + 1/4

From the question we are told

S = {3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14},

F = [5, 6, 7, 8, 9]

G = {9, 10, 11, 12}

Generally

The P(F or G) by counting the number of outcomes in F or G exists

[tex]$F \& G=\{5,6,7,8,9,10,11,12\}$$[/tex]

P(F or G) using the general addition rule

[tex]$& P(F G)=\frac{N_f}{N_g} \\[/tex]

substitute the values in the above equation, we get

[tex]$& P(F G)=\frac{8}{12} \\[/tex]

simplifying the equation, we get

P(F G) = 0.667

Using addition Rue to attain P(F or G) we get

P(F or G) = PF + PG - P(F + G)

substitute the values in the above equation, we get

[tex]$& P(\text { For } G)=5 / 12+4 / 12-(1 / 12) \\[/tex]

simplifying the equation, we get

[tex]$ P({For} G)=5 / 12+1 / 4 \\[/tex]

[tex]$& P(\text { For } G)=\frac{8}{12}[/tex]

Therefore, the value of P(F or G) using the general addition rule be 8/12.

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Answer:

42 feet

Step-by-step explanation:

p = 2l + 2w

232 - 2(74) =

232 - 148 = 84

84/2 = 42

Check

232 = 2(42) + 2( 74)

232 = 84 + 148

232 = 232

25 equal pieces of lenth 7 inch is possible and 5 inch remains after the cutting string.

An inequality is a statement that compares the value of one expression to another, using one of the symbols: <, >, ≤, ≥, ≠. It shows a relationship between two expressions that are not equal. It can be represented in a graph as a boundary line, with a specific region representing the solution set of the inequality.

Convert value of  foot to inches:

we know that 1 foot = 12 inches

15 feet ⇒  15 feet × 12 inches/ft = 180 inches

now the let the number of peice be x

so 7*x<=180

=> x<=180/7

=> x<=25.71

solving the inequality we get

so there is 25 equal pieces of string of length 7 is possible.

remaining piece = 180 - 25*7

=> 180 - 175

=> 5

so 5 inch remains after  cutting the string

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