Antonio earns $6 an hour helping his grandmother. Write and solve an equation to find out how many hours she needs to work to earn $48.​

Answer:

There were 378 students who chose to study French their freshman year. This means that 72% of the total number of students chose to study French their freshman year. Therefore, the total number of students must be 378 / 0.72 = 527.5. This means that there were 148.5 students who chose not to take French their freshman year.

Step-by-step explanation:

The value of given expression 7 raised to the power 2 divided by 7 raised to the power 3 is 1 / 7

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

Given expression,

7 raised to the power 2 divided by 7 raised to the power 3

7 ^ 2 / 7 ^ 3

The value of a ^ m / a ^ n  = a ^ m-n

= 7 ^ (2-3)

= 7 ^ ( -1)

= 1 / 7 .

Therefore, The value of given expression 7 raised to the power 2 divided by 7 raised to the power 3 is 1 / 7

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A graph of each function is shown in the image attached below.

The number of commercials (x) is equal to 8 commercials while the number of movies (y) is equal to 4 movies.

In order to graphically solve the system of equations, we would write two (2) equations that models the situation by assigning variables to the number of commercials and number of movies respectively, and then translate the word problem into algebraic equation as follows:

Since Gianna would earn $50 every time one of her songs is played in a commercial and $100 every time one of her songs is played in a movie, an equation which models it is given by;

50x + 100y = 800

Additionally, Gianna's songs were played on twice as many commercials as movies;

x = 2y

Next, we would use an online graphing calculator to plot the above system of equations with a point of intersection at (8, 4) as shown in the image attached below.

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By using this absolute value equation, the chef can determine the range of cake diameters that meet the desired margin of error of 3 inches and make an informed decision when purchasing the cake.

The absolute value of the difference between the actual diameter of the cake and the ideal diameter of 24 inches should be less than or equal to 3 inches.

To describe the statement using an absolute value equation, let's define the variable "d" as the actual diameter of the cake.

The ideal diameter of the cake is given as 24 inches.

The margin of error is specified as 3 inches, which means the chef is willing to accept a cake with a diameter within 3 inches of the ideal size.

Considering the margin of error, we can express the acceptable range of diameters for the cake as follows:

d - 24 ≤

This inequality states that the difference between the actual diameter "d" and the ideal diameter of 24 inches should be less than or equal to 3 inches, indicating that the actual diameter should be no more than 3 inches larger or smaller than 24 inches.

However, to represent this condition using an absolute value equation, we need to remove the inequality signs.

We can rewrite the inequality above using absolute value:

|d - 24| ≤ 3

This absolute value equation states that the absolute value of the difference between the actual diameter "d" and the ideal diameter of 24 inches should be less than or equal to 3 inches.

It encompasses both possibilities of the actual diameter being within 3 inches greater or smaller than 24 inches.

By using this absolute value equation, the chef can determine the range of cake diameters that meet the desired margin of error of 3 inches and make an informed decision when purchasing the cake.

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People at the concession stand as input Cost of their order's output.

(1) The relation in question is a function.

(II) This function is not constant. (Each category of concession has a different order cost.)

Not a 1-1 function (iii). (Several persons arrived seeking the same sort of concession. So they all pay the same price for their order.)

A function describes the relationship between patrons' inputs at the concession stand and the cost of their order as an output. A function is a relationship between a set of possible inputs and outputs, where each input is associated to exactly one output.

The quantity of patrons at the concession stand serves as the input in this scenario, while the cost of their order serves as the output.

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The eiffiel tower will be 32.49 times larger than the drawing because the drawing wil be about 2.7 inches if each inch represents 400 ft since the eifell tower is about 1083 feet.

Step-by-step explanation:

\((9\pi \frac{2}{2} )\div 3\pi \\ \)

\( \frac{9\pi}{3\pi} \\ \)

\(3\pi\)

3π is the answer

we have that

The swimmer that dives down the farthest is option C because is the greater distance in absolute value from the level zero

swimmer D elevation -21 ft

First you need to figure out the games the Cubs lost. 11-7=4, so they lost 4 games.

Now you must plug in the ratio of games lost to games played. You know they lost 4 games and played 11, so the ratio would be 4:11.

I hope you find this helpful :)

Call the unknown number X.

Understand:

I am looking for an unknown number that I'll call x. From the problem:

5 times the number X minus 25= 175

Plan:

I will write an equation to reflect what we know/understand.

5x - 25 = 175

Solve:

5x - 25 = 175

5x = 200

Divide both sides by 5

x = 40

Answer:

The number is 40.

Check:

Let's go back to the original problem written on the slide and check our work.

Twenty five less than five times a number is 175.

25 less than 5*40 is 175.

25 less than 200 is 175.

200-25 =175.

So my answer is correct.

5x - 25 = 175

5*40-25 = 175

200-25 = 175

175 = 175

Again, my answer is correct.

Answer:

the correct answer is 7.78

Step-by-step explanation:

?×4-18=94

(28)×4-18=94 I'm just trying

The operation that will result in a trinomial for the given expression is subtraction operator ( - ).

A trinomial is an algebraic expression that has three terms. It is also a polynomial consisting of three terms or monomials.

The given polynomial expression;

( 4x⁵ - 8x ) ?  (3x² - 8x + 9 )

To simplify the given polynomial expression into trinomial, we will use the following operation.

The chosen operation will be such that, we will have only three terms left after simplification.

So we will choose subtraction operator "-"

( 4x⁵ - 8x ) -  (3x² - 8x + 9 )

= 4x⁵ - 8x  - 3x² + 8x - 9

simplify further; (-8x and +8x will cancel out)

= 4x⁵ - 3x² - 9

Finally, we have our desired trinomial as 4x⁵ - 3x² - 9.

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Answer:

answer is 3 1/8

Step-by-step explanation:

In the picture is what my teacher did.

Answer:5/7

Step-by-step explanation:

6/7-1/7=5/7

you cant simplify it lower

Answer:

5/7

Step-by-step explanation:

First, what is 6/7 - 1/7? Well, the answer is 5/7 by just subtracting the numerator. So Simplifying is not needed in this equation.

To solve for x in the equation 4x3 = -5x - 21, we can follow these steps:

1. Move all the terms containing x to one side of the equation, and move the constant term to the other side. We can do this by adding 5x to both sides and then adding 21 to both sides:

   4x3 + 5x = -21

2. Factor out x from the left-hand side of the equation:

   x(4x2 + 5) = -21

3. Divide both sides by (4x2 + 5):

   x = -21 / (4x2 + 5)

So the solution for x is x = -21 / (4x2 + 5). Note that this is a rational function, which means that the value of x depends on the value of the variable x. This equation has no real solutions because the denominator is always positive, and the numerator is negative.

Answer:

10$

Step-by-step explanation:

because 10$ + 10$ + 10$ equals 30$ so one is 30$

The value of y is 4√3

Similar triangles have the same corresponding angle measures and proportional side lengths. The corresponding angles of similar triangles are congruent or equal.

Also , the ratio of corresponding sides of similar triangles are equal.

There are two triangles that are similar

Therefore;

y /16 = 4/y

y² = 48

y = √48

y = √16 × √ 3

y = 4√3

Therefore, the value of y is 4√3

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Answer:

-12, -17, -204

Step-by-step explanation:

Answer:

The area is changing at the point of  \(\mathbf{61200 m^2/year}\)

Step-by-step explanation:

From the given information:

Let's recall from our previous knowledge that the formula for finding the area of a rectangle = L × w

where;

L = length and w = width of the rectangle

Suppose the Length L is twice the width w

Then L = 2w --- (1)

From The area of a rectangle

A = L  × w

A = 2w  × w

A = 2w²

Taking the above differentiating with respect to time

\(\dfrac{dA}{dt }= 4w \times \dfrac{dw}{dt} --- (2)\)

At the time t

\(\dfrac{dw}{dt}= 34 m \ per \ year ; w = 450 \ m\)

Replacing the values back into equation 2, we get:

\(\dfrac{dA}{dt }= 4 \times 450 \times 34\)

\(\mathbf{\dfrac{dA}{dt }= 61200 m^2/year}\)

The number of trials and the probability of obtaining success will be given as P(X ≤ 2) = 0.9728.

Binomial distributions consist of n independent Bernoulli trials.

Bernoulli trials are those trials which end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))

Suppose we have random variable X pertaining to a binomial distribution with parameters n and p, then it is written as

X \sim B(n,p)

The probability that out of n trials, there'd be x successes is given by

\(\rm P(X =x) = \: ^nC_xp^x(1-p)^{n-x}\)

Assume the random variable X has a binomial distribution with the given probability of obtaining success.

Then the number of trials and the probability of obtaining success will be

P(X ≤ 2), n = 4, p = 0.2

Then we get

\(\rm P(X =2) = \: ^4C_2(0.2)^2(1-0.2)^{4-2}\\\\P (X=2) = 6 \times 0.0256 \\\\P (X=2) = 0.1536\)

Then the cumulative probability will be

\(\rm P(X\leq 2) = 0.9728\)

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Answer:

33

Step-by-step explanation:

Assume that each cell on the grid represents one unit. One can use the formula, (\(A=\frac{(base)(hieght)}{2}\)) to find the area of the triangle. One can see that the base of the triangle is, (11), and the height is (6). Substitute in the given values and solve for the area,

\(A=\frac{(11)*(6)}{2}\)

\(A=\frac{66}{2}\)

\(A=33\)

The remainder is 5 + c, which means that the expression P(x) = \(5x^4 + 7x^3 - 2x^2 - 3x + c\) divided by (x + 1) results in a quotient of\(5x^3 + 2x^2 - 4x + 4\) and a remainder of 5 + c.

To divide the polynomial P(x) = \(5x^4 + 7x^3 - 2x^2 - 3x + c\) by the binomial (x + 1), we can use polynomial long division.

Let's set up the long division:

    \(5x^3 + 2x^2 - 4x + 4\)

_______________________

x + 1 | \(5x^4 + 7x^3 - 2x^2 - 3x + c\)

We start by dividing the highest degree term of the dividend (5x^4) by the divisor (x + 1), which gives us 5x^3. We then multiply this quotient by the divisor (x + 1) and subtract it from the dividend:

              \(5x^3(x + 1)\)

     _______________________

x + 1 | \(5x^4 + 7x^3 - 2x^2 - 3x + c\)

- (\(5x^3 + 5x^2)\)

This leaves us with a new polynomial:\(2x^3 - 7x^2 - 3x + c\). We repeat the process by dividing the highest degree term of this polynomial (2x^3) by the divisor (x + 1), resulting in 2x^2. We then multiply this quotient by the divisor and subtract it from the polynomial:

              \(5x^3(x + 1) + 2x^2(x + 1)\)

     _______________________

x + 1 | \(5x^4 + 7x^3 - 2x^2 - 3x + c\)

-\((5x^3 + 5x^2)\)

_______________________

\(2x^2 - 3x + c\)

We continue this process until we reach the constant term, resulting in the remainder of the division.

At this point, we have:

               \(5x^3(x + 1) + 2x^2(x + 1)\)

     _______________________

x + 1 | \(5x^4 + 7x^3 - 2x^2 - 3x + c\)

- \((5x^3 + 5x^2)\)

_______________________

\(2x^2 - 3x + c\)

-\((2x^2 + 2x)\)

_______________________

- 5x + c

- (-5x - 5)

_______________________

5 + c

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The most reasonable unit of measurement for 3) is option (C): \(m^2\), 4) is option (B): \(km^2\), 5) is \(in^2\).

3) The most reasonable unit for the measurement of the baseball field is \(m^2\) because the baseball field covers a large distance which is not accurately measured by small units  \(cm^2\) or \(mm^2\)  where it is not that big to be measured in large units like \(km^2\). So option C is the correct option.

4) The most reasonable unit for the measurement of a lake is \(km^2\) because lakes are generally very large water bodies that cover a large distance and are not accurately measured by small units like \(cm^2\) , \(mm^2\) , and \(m^2\). So option B is the correct option.

5) The most reasonable unit for the measurement of the area of a door is \(in^2\) because doors are relatively small compared to the other options and are often measured in square inches or square feet. So option B is the correct option.

Therefore the correct answers question-wise are:

3) \(m^2\)

4) \(km^2\)

5) \(in^2\)

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Answer:

26

Step-by-step explanation:

Fifteen minues negative eleven equals to twenty six. Hope this helps and good luck with your assignment.

15-(-11)=26

The value of x is 26 .

Given,

-11+blank equals 15 .

Now,

Let the number in the blank be x .

So, rewriting the equation with x,

-11 + x = 15

Now combine the like terms,

x = 11 + 15

x = 26

Thus the blank is equal to 26 .

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Answer:A 94

Step-by-step explanation:

Trust me lol

Answer:

C

Step-by-step explanation:

using the theorem of Pythagoras

x = sqrt * 10.2^2 - 9.6^2 *

using the calculator

x = 3.4 units

rounded to 1 decimal place