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math question

The simplified form of the expression is, [tex]\frac{3}{5}x + y[/tex].

What is simplified form of the expression?

Expressions are rewritten in a compact and unlike terms-free manner when they are simplified. Expressions are simplified by combining like phrases, resolving any provided brackets, and only leaving unlike terms that cannot be further reduced in the final simplified expression.

Consider, the given expression

[tex]\frac{3}{10}x + \frac{1}{6} y+\frac{3}{10}x + \frac{5}{6} y[/tex]

Here, there are two like terms of variable x and two like terms of variable y.

So, we combine the like terms.

[tex]\frac{3}{10}x + \frac{3}{10}x + \frac{1}{6}y + \frac{5}{6}y\\\\\frac{3+3}{10}x+\frac{1+5}{6}y\\ \frac{6}{10}x + \frac{6}{6}y\\ \frac{3}{5}x + y[/tex]

Hence, the simplified form of the expression is, [tex]\frac{3}{5}x + y[/tex].

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Answer:

infinite solutions

Step-by-step explanation:

both sides are identical

The cost per pint =4

Pints do you get per dollar = 1/4

Pints can you afford for $20.00 = 5

8 pints of raspberries cost = 32

Unit rates are defined as rates that are expressed as a number of one, such as 3 feet per second or 4 miles per hour.

According to the given statement: For $12, you can pick three pints of raspberries at a farm.

then, according to the unit rate definition,

cost per unit = 12/3 = 4

Unit rate per dollar =3/12

= 1/4

= 0.25 pint

0.25 pints of raspberries get per dollar.

Pints afford for $20

= 20/4 =5

8 pints of raspberries cost

= 4 x 8

= 32

Therefore

The cost per pint =4

Pints do you get per dollar = 1/4

pints can you afford for $20.00 = 5

8 pints of raspberries cost = 32

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It is necessary to collimate the light source before using the prisim to  disperse the light so that the light rays entering the prisim are parallel.

What is collimate?

Collimator is a tool for converting a point source's divergent radiation into a parallel beam. To perform specific measurements in spectroscopy, geometrical optics, and physical optics, the light must be collimated.

An optical collimator is made up of a tube with a convex lens at one end and a variable aperture at the other end that is located in the lens' focal plane. To examine the image without parallax, radiation entering the aperture exits the collimator as a parallel beam.

Therefore collimation is needed for the light rays entering the prism to be parallel.

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The correct property is used to prove the two expressions are equivalent is;

''Commutative property''

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Lara writes the expression 1.5x + 2.75y + 3.

And, Maria writes the expression 3 + 1.5x + 2.75y.

Now,

Since, The commutative property states that;

a + b = b + a

So, Clearly, Here the commutative property used to prove the two expressions are equivalent, as;

⇒ 1.5x + 2.75y + 3 = 3 + 1.5x + 2.75y.

Thu, The correct property is used to prove the two expressions are equivalent is;

''Commutative property''

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Answer:

Domain: [-3,3)

Range: [-4,5]

Step-by-step explanation:

Domain is all the x's on the graph (or if you have an equation, all the x's allowed to be used in the equation)

Here the graph exists from -3 to 3, but not including 3. The square brackets means "including" and regular parenthesis means "not including".

The range is all the y-values on the graph (or if you have an equation, its all the y-values that can be produced by the equation) This graph goes from -4 to 5, I wrote it to include -4 and 5. If you think that curve is floating over the -4 and purposefully and absolutely missing it then the range should be (-4,5] But it looks like it touches -4 in the image.

The required Mean for movies A and C is $655, Mean for movies B, and C is $645, and Mean for movies C, and D is $515.

The top-grossing movies last year were Movie A with $700 million, Movie B with $ 680 million, Movie C with $ 610 million, and Movie D with $ 420 million.

Mean of A, C = (700 + 610)/2 = 1310/2 = 655

Mean of B, C = (680 + 610)/2 = 1290 = 645

Mean of C, D = (610 + 420)/2 = 1030 = 515

Thus, the required Mean for movies A and C is $655, Mean for movies B, and C is $645, and Mean for movies C, and D is $515.

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Two triangles may be similar sometimes (known as similar triangles) and two squares and two rectangles are always similar.

According to the question,

We have the following information:

Two triangles, two squares and two rectangles

We know that when we say two figures are similar then it means that angles of the given two figures are congruent or their corresponding sides are equal.

Now, in a triangle, it is not sure which angle or side will be there.

So, they can not always be similar but can be similar in some cases.

In a rectangle and square, four angles are right angles.

So, they are always similar.

Hence, two triangles may be similar sometimes and two squares and two rectangles are always similar.

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Answer: Sir would you mind telling me what chart your using

Step-by-step explanation:

The probability illustrates that the percentage of students at the college have a gpa between 2.5 and 3.5 is 68%.

From the information, at the college gpas are normally distributed with a meanof 3 and a standard deviation of 0.5.

The requirement to solve the probability between z-values is to know that the probability between the z-values is the difference between the probability of the greatest z-value and the lowest z-value.

This will be illustrated as:

P(2.5 < x < 3.5)

Looking at the distribution table, the value is 68%.

Therefore, the percentage is 68%.

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Answer:

You get a negative answer

Step-by-step explanation:

that is literally it! you get a negative answer. hope this helps

The correct option to this question is option A , this can be solved using triangle inequality theorem.

What is triangle Inequality Theorem?

In a triangle, the longest side is located across from the largest angle, while the shortest side is located across from the smallest angle is Triangle inequity. Any triangle in which the total of any two sides is greater than the length of the third side is said to have a triangle.

Main Body:

The theorem says that longest side will have the largest angle opposite to it, and vice versa.

Hence option A is correct answer which means the largest angle is opposite to longest side.

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Answer: -2

Step-by-step explanation:

First distribute the negative sign to the negative four then find the absolute value of 6

-(-4)-|-6| = 4-6

then subtract 4 from 6 and you get -2.

Answer:

[tex] \frac{3}{5} - \frac{3}{10} \\ = \frac{3 \times 2}{5 \times 2} - \frac{3 \times 1}{10 \times 1} \\ = \frac{6}{10} - \frac{3}{10} \\ = \frac{6 - 3}{10} \\ = \frac{3}{10} [/tex]

The zero of the function shown in this table is -2, which means that the presented function has an x-intercept.

The x-intercept is defined as an intercept that is located at the x-axis of the plane, which is the location or coordinates from where the line crosses.

The table is given in the question,

As per the given table, the value of x is -2 then the value of y = 0. This represents the x-intercept of the function. The zero of the function represented in this table is -2 which means x-intercept in the given function.

Thus, the zero of the function shown in this table is -2, which means that the presented function has an x-intercept.

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The unit rate of change (slope) from 1996 to 2016 is -.025

What is Ratio?

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all. Any two different points on a line can be used to calculate the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula. A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, m = y/x, where m is the slope, can be used to express the change in the y coordinate with regard to the change in the x coordinate.

Take notice that tan = y/x.

The given problem is about the decrease of two variables, which represent years and represent video rental.

The ratio here refers to the slope of the linear decreasing behavior, where pairs are (1996,9) and (2016, 4).

The formula for the slope is

[tex]&m=\frac{y_2-y_1}{x_2-x_1}[/tex]

So, In the given question, we have:

10 video rental locations in 1996;

So,  Assuming a constant decrease in the number of stores:

The slope or the unit rate of change from 1996 to 2016 is:

[tex]\begin{aligned}&m=\frac{y_2-y_1}{x_2-x_1}=\frac{4-9}{2016-1996}=\frac{-5}{20}=-\frac{1}{4} \\&m=-0.25\end{aligned}[/tex]

So, The Value of the Slope is -0.25

This means that the linear relation decreases, with a constant ratio of 0.25, that is, video rental decreases one per 4-years periods.

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This can be solved using proportions. Aiden needs to make 3 trips to walk 9 kilometers.

What is a proportion?

Two numerical sequences, generally experimental data, are said to be proportional or directly proportional if their corresponding elements have a constant ratio, which is known as the coefficient of proportionality or proportionality constant. Two sequences are inversely proportionate if the product of their respective elements is constant, also known as the coefficient of proportionality. This notion is frequently extended to related changing numbers, which are typically referred to as variables. For instance, if an item moves at a constant speed, the distance traveled is exactly proportional to the time spent traveling, with the speed serving as the proportionality constant.

For 2 trips, Aiden walks 6 kilometers

So, for 9 kilometers to walk he need 'x' trips (let)

Then they are in proportion, i.e.,

2/6 = x/9

or, x = (2/6)9

or, x = 3

Hence, Aiden needs 3 trips to walk a total of 9 kilometers.

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The answer to this composite function is 205.

What is a composite function?

Function composition is an operation that takes two functions, f and g, and creates a function, h, that is equal to g and f, such that h(x) = g.

Main Body:

f(x)= 3x-1 , g(x)= 4[tex]x^{2} \\[/tex]+9

now we have to insert the value of f(x) in place of x in g(x)

So (g o f) = [tex]4(3x-1)^{2}+9\\[/tex]

 Value of (g o f)(-2)= [tex]4(3(-2)-1)^{2} +9[/tex]

                              =4(-7)²+9

                              = 205

Hence the value of (g o f) (-2)= 205.

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The number of Frophy needs is 15.

What is ratio?

A ratio is a comparison of two or more numbers that indicates their sizes in relation to each other. A ratio compares two quantities by division, with the dividend or number being divided termed the antecedent and the divisor or number that is dividing termed the consequent.

Given,

There are 10 rews to 3 frophy.

The ratio for one rew  = 3/10 frophy

The value for 50 rew = 3(50)/10

= 15

There are 15 frophy for 50 rews.

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Answer:

The pencils at store A cost more.

Step-by-step explanation:

First find the price of one pencil at store A

y=0.55(1)=

y=0.55

One pencil at store A costs 0.55

Now find the price of one pencil at store B

3.06/6=

0.51

One pencil at store B costs 0.51

0.55>0.51 so The pencils at store A cost more.

Hope this helps!

After 100 days there will be 33750 bees in the bee hive .

in the question ,

it is given that

number of bees in the bee hive when discovered = 20 bees

number of bees after 5 days = 29 bees

also given that the population of the bees increases exponentially ,

the exponential growth is denoted by the function ,

A = A₀(eᵃˣ)

where A is the population after x days ,

A₀ is the initial population , x is the days and a is the constant of proportionality .

Substituting the values in the exponential growth formula ,

we get

29 = 20 ([tex]e^{a\times5}[/tex])

29/20 = [tex]e^{a\times5}[/tex]

taking ln both the side

ln(29/20) = ln( [tex]e^{a\times5}[/tex])

5a = ln(29/20)

a = 0.07431

to find the population after 100 days , we substitute x = 100,

we get

A = 20*  [tex]e^{0.07431\times100}[/tex]

A = 33749.88

A ≈ 33750

Therefore, the number of bees in the bee hive after 100 days is 33750 .

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Every hour, the medicine concentration decays by a factor of 0.09.

An exponential function simply refers to a mathematical function whose values are generated by a constant that is raised to the power of the argument. Mathematically, an exponential function can be modeled or represented by using this equation:

f(x) = abˣ

Where:

At the initial time (t), the medicine concentration is given by this exponential function:

C(t) = 61 × (0.96)^t

Note: One (1) hour is equal to sixty (60) minutes.

After an hour, the medicine concentration is given by this exponential function:

C(t + 60) = 61 × (0.96)^{t + 60}

Therefore, the rate of change every hour in the medicine concentration would be calculated as follows:

Decay factor = [C(t + 60)/C(t)]

Decay factor = [61 × (0.96)^{t + 60}]/61 × (0.96)^t

Decay factor = (0.96)^t

Decay factor = (0.96)^60

Decay factor = 0.0864 ≈ 0.09.

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Answer:

0.91

Step-by-step explanation:

1 - .09 = 0.91

The three digit number where hundreds and ones digit are same is 424 .

In the question,

it is given that

the number is a 3 digit number ,

let the 3 digit number be " xyz "

given that the ones digit and hundreds digit are same ,

which means x = z , so the number becomes " xyx " ,

given that sum of ones and hundreds digit is 8 ,

which means x + x =8

2x = 8

x = 4

and tens digit is 2 less than ones digit , that is

y = x - 2

y = 4 - 2

y = 2

the number is xyx = 424

Therefore , the three digit number is 424 .

The given question is incomplete , the complete question is

I am a 3 digit number that is even my hundreds and ones digits are the same and have a sum of 8. My tens digit is 2 less than my ones digit. What number am i ?

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Answer:

405.50

Step-by-step explanation:

hope it helped :)

Answer:

Step-by-step explanation:

405.5

The program that gives the number of multiples of 4 is given as follows:

int main(){

int value;

int multiples = 0.

printf("Enter the value\n");

scanf("%d\n", & value);

do{

if(value % 4 == 0){

multiples = multiples + 1;

printf("%d is a multiple of 4.\n", value);

}

else{

printf("%d is not a multiple of 4.\n", value);

}

printf("Enter the value\n");

scanf("%d\n", & value);

}while(value >= 0);

printf("The total number of integers entered which are multiple of 4 is %d\n", multiple);

return 0;

}

A number is a multiple of 4 if the remainder of the division of the number by four is of zero.

The command that checks if the remainder is of zero, using the C programming language, is:

if(value % 4 == 0)

If the conditional is true, then the multiple variable, storing the number of multiples of four, is incremented.

The command that reads the value is of:

printf("Enter the value\n");

scanf("%d\n", &value);

The variable value is previously declared.

The do-while loop continues until a negative number is read.

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Answer:

$5 per used book, $15 per new book

Step-by-step explanation:

Let u = cost of one used book and

n = cost of one new book.

12u + 4n = 120-------->3u + n = 30

14u + 2n = 100-------->7u + n = 50

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

4u = 20

u = 5, n = 15

So one used book costs $5, and one new book costs $15.

Answer: 0.001

Step-by-step explanation:

The solutions are as follows:

a)Opposite of |-12| =  Opposite of 12

b)Absolute value of -6 >  Opposite of |-10|

c)Absolute value of 51 <  Absolute value of -87

d)Opposite of -92 >  Absolute value of 51

a) Opposite of |-12| = -12

   Opposite of 12 = -12

   So, Opposite of |-12| = Opposite of 12

b) Absolute value of -6 = 6

   Opposite of |-10| = -10

   So, Absolute value of -6 > Opposite of |-10|

c) Absolute value of 51 = 51

   Absolute value of -87 = 87

   So, Absolute value of 51 <  Absolute value of -87

d) Opposite of -92 = 92

    Absolute value of 51 = 51

    So, Opposite of -92 >  Absolute value of 51

Therefore, the solutions are as follows:

a)Opposite of |-12| =  Opposite of 12

b)Absolute value of -6 >  Opposite of |-10|

c)Absolute value of 51 <  Absolute value of -87

d)Opposite of -92 >  Absolute value of 51

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