10-9x24/8x6 (pemdas)

The unit rate of gallon to mile is calculated as: 5/6 gallon per mile.

The unit rate between two variables is simply the ratio of the quantity of one variable to the quantity of the other variable, such that the the denominator of the will be equal to exactly 1.

We are given the variables gallons and miles, where 1/4 of a gallon is to 3/10 mile.

The unit rate between these two variables would be an amount of gallons per mile.

Thus, find the unit rate by dividing 1/4 by 3/10:

1/4 ÷ 3/10

= 1/4 × 10/3

= 10/12

= 5/6

The unit rate is therefore, 5/6 gallon per mile.

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The room numbers of two adjacent classrooms are 359 and 361.

What is consecutive odd numbers?

Consecutive odd numbers are odd integers that are separated by 2 and come after one another.

Suppose the first odd number is x, then the another consecutive odd number is x + 2.

The sum of these two numbers is 720.

So,

x + (x + 2) = 720

2x + 2 = 720

2x = 718

x = 359

Therefore, the first odd number is 359 and the second add number is 361 which gives the sum 720.

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We will use simple division to solve the problem. The number of representatives attended from each country is 706.

In the given question we know that a political gathering in South America was attended by 8475 people and each 12 territories of South America were equally represented. We need to find out how many representatives attended from each country. Inorder to find the number of representatives we can divide 8475 by 12.

number of representatives= 8475/12 =706

Therefore number of representatives from each country is 706.

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Jane decides to randomly interview 10 freshmen from each of the dorms, these people are her Sample.

What is Sample?

Sampling is the process of choosing a portion of a statistical population to estimate attributes of the entire population in statistics, quality control, and survey methods. Statisticians try to get samples that are typical of the population under consideration.

A little sample or amount of someone or something that is inspected, analyzed, or otherwise investigated to learn more about the rest.

Given: Jane wants to know what percentage of freshmen at her college purchase clothing with college logos. She decides to randomly interview 10 freshmen from each of the dorms.

Therefore, by the above information, these people are her Sample.

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Answer:

Step-by-step explanation:

x

=

−

2

x

=

−

5

Explanation:

x

2

+

7

x

+

10

=

0

We could right the equation in another form using brackets.

(

x

+

2

)

(

x

+

5

)

=

0

In order to get two numbers to multiply and give 0, at least one number has to be 0.

a stands for the first bracket and b for the second.

a x b = 0

a=0 or b=0 to make this equation valid.

Therefore x= -2 or x= -5 because -2+2=0 and -5+5=0 according to both brackets.

Answer:

hii!!! z = 3, ¼

Step-by-step explanation:

Hope this helps xb

Answer:

90%

Step-by-step explanation:

To find the percent of increase in the height of the tree, we need the change of the height and the original height (40 feet)

The change of height = 76 - 40 = 36 feet

Now, we need to divide the change by the original height to find the percent of increase.

36/40 = 9/10

9/10, which is then 90%.

ANSWER

R1, R2, R3, R4, G1, G2, G3, G4. Option B.

The percentage of young adults who send fewer than 218 text messages is 99.87%.

For a normally distributed set of data, given the mean and standard deviation, the probability can be determined by solving the z-score and using the z-table.

First, solve for the z-score using the formula below.

z-score = (x – μ) / σ

where x = individual data value = 218

μ = mean = 128

σ = standard deviation = 30

z-score = (218 - 128) / 30

z-score = 90 / 30

z-score = 3

Find the probability that corresponds to the z-score in the z-table. (see attached images)

z-score = 3

probability = 0.9987

To get the percentage, multiply the probability by 100.

percentage = probability x 100

percentage = 0.9987 x 100

percentage = 99.87%

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Okay, here we have this:

Considering the provided information, we are going to write and solve the correspondinf system of equation, so we obtain the following:

According to the information given, we obtain the following system of equations, where we take x as money spent on fruit and y as money spent on green vegetables, so we have:

Now let's solve for x in the second equation:

x+x+5=30

2x+5=30

2x=30-5

2x=25

x=25/2

x=12.5

Now from the value of x that we got, then we will plug it into the first equation to get the value of y:

Then, finally we obtain that she spend $12.5 on fruits and $17.5 on green vegetables.

To solve this problem we change the structure from

1/2 + ? = 7/8

to

7/8 - 1/2 = ?

Now we need to subtract the fractions and find the difference. To do this, make the denominators (the bottom numbers on the fractions) the same.

1/2 = 4/8

then subtracts the numerator

7/8 - 4/8 = 3/8

there is your answer... 3/8

Work done in stretching spring from 36 cm to 38 cm is 0.333J.

The work needed to stretch a spring is given by the formula mentioned below:

[tex]W_{s}[/tex] = (1/2) K × [tex]x^{2}[/tex]

Here,  k is spring constant and x is the elongation.

So, x = [tex]x_{f} - x_{i}[/tex]

When spring is stretched from 40 cm to 34 cm

x = 40 - 34  = 6cm = 0.06 m

We need to know the spring constant so that we can calculate work.

3 = (1/2) K × [tex](0.06)^{2}[/tex]

K = 1666.67

Now, when spring is stretched from 36 cm to 38 cm

x = 38 - 36 = 2 cm = 0.02 m

[tex]W_{s}[/tex] = (1/2) × (1666.67) × [tex](0.02)^{2}[/tex]

[tex]W_{s}[/tex] = 0.333J

So, 0.333J work is done in stretching spring from 36 cm to 38 cm.

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The coordinates of the point C on the line AB such that AC is 2/3 the length of AB is (3,6) .

In the question ,

it is given that

the coordinates of the end points of A and B is A(-1,2) and B(5,8) .

also AC = 2/3(AB)

So , AC/AB = 2/3

and given that point C is on the line AB , hence AC+CB=AC

2+CB=3

So , CB=1

hence AC/CB = 2/1

so , the point C divides the line AB in the ration 2:1 .

and we have the coordinates of end points ,

that is x₁[tex]=[/tex] -1 , y₁=2 and x₂=5 , y₂ = 8 and the ratio m=2 and n=1 .

Substituting the above values in the section formula ,

which states that the coordinate of point C will be

((m*x₂+n*x₁)/(m+n)  ,  (m*y₂+n*y₁)/(m+n))

= ((2*5+1*(-1))/(2+1) , (2*8+1*2)/(2+1))

= ((10-1)/3 , (16+2)/3)

= (9/3 , 18/3)

= (3,6)

Therefore , The coordinates of the point C on AB such that AC is 2/3 the length of AB is (3,6) .

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The measure of Angle A and Angle B are 54° and 122° respectively.

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

In triangle ABC,

The measure of angle A = (n + 20)°

The measure of angle B = (3n - 10)°

The measure of angle C = n°

Now,

The sum of all the angles of the triangle = 180°

So, we can formulate;

(n + 20)° + (3n - 10)° + n° = 180°

Solve for n as;

n + 20 + 3n - 10 + n = 180

5n + 10 = 180

5n = 180 - 10

5n = 170

Divide by 5, we get;

n = 170/5

n = 34

Thus, The measure of angle A = (n + 20)°

                                               = 34 + 20

                                               = 54°

And, The measure of angle B = (3n - 10)°

                                             = 3 x 34 + 20

                                             = 102 + 20

                                             = 122°

Therefore,

The measure of Angle A and Angle B are 54° and 122° respectively.

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The equation of the line for the given slope 1 is y= x + 2

Equation of the line:

An equation of the line refers the algebraic form of representing the set of points, which together form a line in a coordinate system.

Given,

The point where the graphs of two equations intersect has y-coordinate 2. One equation is y = -3x + 5.

Here we need to find the other equation if its graph has a slope of 1.

We know that, the general representation of equation of line is y= ax + b

where a is the slope and b is the y intercept.

Through the given details we know that the slope of the line is 1 and why is point where two lines intersect hence, it is the intercept.

And the intercept value is 2.

Therefore, the equation of the other line is y= x + 2

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Step-by-step explanation:

12/4 = x/8

1st: cross multiply

96 = 4x

2nd: divide both sides by 4

96/4 = 4x/4

therefore x = 24

The box plot that matches the data is a box and whisker plot is shown above a number line that extends from 0 to 20 with 1-unit markings. The box extends from 4 to 8, with the median at 5. There is also a point marked at 7. The whisker on the left extends from 2 to 4. The whisker on the right extends from 8 to 12.

A box and whisker plot is a graph that is made up of two lines and a box. The two lines are known as whiskers. The end of the first whisker is the minimum value and the end of the second whisker is the maximum value.

On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile.

The data : 2, 3, 4, 4, 5, 5, 7, 8, 9, 12

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Answer:

d=y-300

Step-by-step explanation:

After combining the like terms of the given expression -4r -2r + 5 the equivalent expression is -6r +5.

As given in the question,

Given expression is equal to :

-4r -2r + 5

Now combine the like terms to get the equivalent expression we have,

Like terms of the given expression -4r -2r + 5 are -4r and -2r

( -4r -2r) +5

= -r (4+2) +5

= -6r +5

Equivalent expression of the given expression -4r -2r + 5  is -6r +5.

Therefore, after combining the like terms of the given expression -4r -2r + 5 the equivalent expression is -6r +5.

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The answer is very simple. .

6 + 2 (5 - 8 ) ² + 7

Firstly we solve what is inside the parenthesis

Then we solve the multiplications

Finally we solve the sums.

That is the solution.

The polynomial with zeros of −3, −1, and 2, and passes through the point (3,11) is:

P(x) = (11/24)*(x + 3)*(x + 1)*(x - 2)

We know that the zeros are −3, −1, and 2, so if we define the leading coefficient as A, the polynomial can be written as:

p(x) = A*(x + 3)*(x  + 1)*(x - 2)

Now we want this to pass through the point (3, 11), then we get:

p(3) = 11 = A*(3 + 3)*(3 + 1)*(3 - 2)

         11 = A*6*4*1

         11 = A*24

         11/24 = A

Then the polynomial is:

P(x) = (11/24)*(3 + 3)*(3 + 1)*(3 - 2)

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According to the factor theorem, if "a" is any real integer and "f(x)" is a polynomial of degree n larger than or equal to 1, then (x - a) is a factor of f(x) if f(a) = 0.Finding the polynomials' n roots and factoring them are two of their principal applications.

Calculate p(x(*r(x)?

I This theorem comes in very handy when we need to determine the determinant's value in "factors" form.

p(x) =5x

r(x)  = 3x  - 7

p(x)×r(x) =

=5x(3x-7)

5x²  -  7

2×15x²-1

=  30x

p(x)*r(x)  =   30x

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The function that can be used to represent the total amount that will be paid for the room is 100 + 55h.

A function simply means the expression that. an be used to show the relationship between the variables or the data given.

In this case, the interior designer charges $100 to visit a site, plus $55 to design each room.

Let the number of rooms be represented as r.

The function that represents the total amount will be:

= 100 + (55 × h)

= 100 + 55h

This illustrates the concept of functions.

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The exponential equation that represents the table is given as y = 81(3)^x.

Exponent-based equations in which the exponent or a portion of the exponent is a variable are known as exponential equations.

The standard exponential form is expressed according to the formula;

y= ab^x

Using the coordinate points (2, 9) and (3, 3) from the table, we can create simultaneous equation as shown;

9 = ab^2

3 = ab^3

Divide both equations

3/9 = ab^3/ab^2

1/3 = b^3/b^2

1/3 = b

Substitute b = 1/3 into any of the equations

3 = ab^3

3 = a(1/3)^3

3 = 1/27 a

a = 81

Determine the required equation

y = ab^x

y = 81(3)^x

This gives the required equation of the function.

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Answer: 81

Step-by-step explanation: Took the test & got it right :)

The quadratic function of h (x) in vertex form will be as h(x) = (x + 2)² − 3

A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is  ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

Given that the values of x and h (x) for the quadratic function is given by;

x = -3, -2, -1, 0, 1, 2, 3,

h (x) = -2, -3, -2, 1, 6, 13, 22

Consider the quadratic function as;

h (x) = ax² + bx + c

Now Substitute x = -3 and h (x) = -2 in quadratic function we get;

h (x) = ax² + bx + c

- 2 = a × (-3)² + b × -3 + c

- 2 = 9a - 3b + c

And, Plug x = -2 and h (x) = -3 in function we get;

h (x) = ax² + bx + c

- 3 = a × (-2)² + b × -2 + c

- 3 = 4a - 2b + c

And, plug x = -1 and h (x) = -2 in function we get;

h (x) = ax² + bx + c

- 2 = a × (-1)² + b × -1 + c

- 2 = a - b + c

After solving we get:

a = 1 , b = 4 and c = 1

Then

h (x) = ax² + bx + c

h (x) = 1 × x² + 4x + 1

h (x) = x² + 4x + 1

h (x) = x² + 4x + 4 - 4 + 1

h (x) = (x + 2)² - 3

Hence, The quadratic function of h (x) in vertex form will be as h(x) = (x + 2)² − 3

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Answer:

D y < 8

Step-by-step explanation:

the range is the interval or set of all valid y (functional result) values.

we can see the y values start at +8, and as the curve is only going down, clearly endlessly, every value smaller than 8 is valid.

8 itself is the be excluded, as there is a hollow point (a filled point would indicate "include").

and therefore we cannot say y <= 8.

we have to use y < 8.

It is known that 1 gallon is 3.78541 litres.

So it follows:

Hence the value of 3.5 gallons is 13.2489 litres.

Given the details above, the sequence of steps below shows that ABCD is a Trapezoid.

A trapezoid, also known as a trapezium, is a closed, flat object with four straight sides and one set of parallel sides. A trapezium's parallel sides are known as the bases, while its non-parallel sides are known as the legs.

Given:

The diagonals of the quadrilateral ABCD intersect at o where AO/BO = CO/DO; which also means that

AO/CO = BO/DO the proof is given as follows:

Create line OE || DC in a way that E lies on BC.

In ΔBDC, based on the Basic Proportionality Theory,

BO/OD = BE/EC ............................1

It is also given that:

AO/CO = BO/DO   ..........................2

Hence, from Equations 1 and 2,

AO/CO = BE/EC

Thus, we can state that on the basis of the Converse of the Basic Proportionality Theorem,

OE || AB

Since AB || OE || DC, it is correct to state that ABCD is a Trapezoid.

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