im not sure how to answer thank you

7th interval is not perfect

7th interval is not perfect

A (real) interval in mathematics is a collection of real numbers that includes all real numbers that fall within any two of the collection's numbers. For instance, the interval containing 0, 1, and all integers in between is the set of values x satisfying 0 ≤ x ≤1. The group of numbers such that 0 < x< 1 and the group of all real numbers are other examples of intervals.

the empty set, any singleton, the set of positive real numbers, the set of nonnegative real numbers, and (set of one element).

Real intervals are the simplest sets whose "length" (or "measure" or "size") is straightforward to define, making them significant in the theory of integration. The Borel measure and ultimately the Lebesgue measure can subsequently be produced by applying the concept of measure to more intricate sets of real numbers.

Interval arithmetic is a broad numerical computing method that automatically generates assured enclosures for all formulas, even in the presence of errors, approximations in mathematics, and arithmetic roundoff.

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Answer:

60 degrees and an equilateral triangle

Step-by-step explanation:

every triangle adds to 180 degrees

add 60+60=120

180-120=60 to find remaining angle

all angles are the same which makes all sides the same: equilateral

Answer:

1 =60

Step-by-step explanation:

a+b+c=180

60+60+c=180

120+c=180

-120. -120

c=60

The value of AB after solving the triangle is 10√3.

Since angle C is the right angle in triangle ABC, we know that angle A = 90 - m2C = 90 - 30 = 60. And since triangle ABC is a right triangle, we can use the Pythagorean Theorem to find the length of the hypotenuse, AB.

The Pythagorean Theorem states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. So in this case,

We know that angle A is 60, so we can use the trigonometric function sine to find the value of BC/AB. We know that

We can then square both sides of this equation to get

Since we know that BC/AB = 3/4, we can substitute this value into the equation

AB^2 = 100 + BC^2 to get

AB^2 = 100 + (BC^2) = 100 + (3/4)AB^2.

Solving this equation for AB, we get AB = 10√3

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answer:

my answer to the first one would be false

my answer to the second would be a

let's firstly convert the mixed fraction to an improper fraction, and then let's multiply both sides by the LCD of all denominators

[tex]\stackrel{mixed}{83\frac{1}{3}}\implies \cfrac{83\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{250}{3}} \\\\[-0.35em] ~\dotfill\\\\ 12x-\cfrac{2}{3}=\cfrac{250}{3}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{3\left( 12x-\cfrac{2}{3} \right)=3\left( \cfrac{250}{3} \right)}\implies 36x-2=250 \\\\\\ 36x=252\implies x=\cfrac{252}{36}\implies x=7[/tex]

Answer: 112 degrees

Explanation:

By the alternate interior angles theorem, m<CAD=40 and m<ACD=28. The quadrilateral is divided into two triangles. The sum of the angles of a triangle is equal to 180 degrees. Now that you know the measurements of two out of the three angles, you can add them up and subtract them from 180.

180-(40+29)=112

Answer:

-8.52, -8.15, 0.55, 8.25

Step-by-step explanation:

The lowest of negatives goes first, and the highest of positives goes last.

Answer:

from the least to the highest which is:

-8.52

-8.15

0.55

8.25

a) The equation that models Alice's total cost of filling up her car tank using regular unleaded gas and premium gas is 4.65r + 4.95p = 874.80.

b) Based on the above equation, if Alice purchases 87 gallons of regular unleaded gas, it means that she also purchases 95 gallons of premium gas.

An equation is a mathematical statement equating two or more mathematical expressions using the equation sign (=).

The cost per gallon of regular unleaded gas = $4.65

The cost of premium gas per gallon = $4.95

The total cost for gas = $874.80

Let gallons of regular unleaded gas = r

Let gallons of premium gas = p

4.65r + 4.95p = 874.8

If r = 87, the value of p is:

4.65(87) + 4.95p = 874.8

404.55 + 4.95p = 874.8

4.95p = 470.25

p = 95 gallons

Thus, during Alice's first leg from the East Coast to the West Coast, she purchases 87 gallons of unleaded and 95 gallons of premium gas for her car.

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The number of cups of serving that is possible in a two-liter bottle is 8.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

We know 1 liter is equal to 4 cups.

Therefore, The number of cups serves possible in a two-liter bottle is,

= (2×4) cups.

= 8 cups.

So, 8 cups of servings are possible from a two-liter bottle.

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The correct statement regarding the probabilities from the table is given as follows:

C The golf ball is 2 times as likely to be orange as it is to be pink.

A probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

The total number of balls for this problem is given as follows:

4 + 11 + 8 + 18 = 41.

Hence the probability of selecting each ball is obtained as follows:

Hence statement C is correct, as:

2 x 4/41 = 8/41.

(which is the probability of orange, obtained multiplying the probability of pink by two).

The number of pink balls is of 4.

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Answer:

The statement "The value of f(–10) = 82" is not true. To find the value of f(–10), we substitute –10 for x in the equation:

Step-by-step explanation:

The statement "The value of f(–10) = 82" is not true. To find the value of f(–10), we substitute –10 for x in the equation:

f(–10) = (–10)^2 – 5(–10) + 12 = 100 – (–50) + 12 = 162

The statement "The graph of the function is a parabola" is true. Because the equation of the function is of the form f(x) = ax^2 + bx + c, where a, b, and c are constants and a is not equal to 0, the graph of the function is a parabola.

The statement "The graph of the function opens down." is true. The coefficient of x^2 is a positive value, which means the parabola opens down.

So, the true statements are

The graph of the function is a parabola.

The graph of the function opens down.

The graph does not contain the point (20, –8)

Answer:

22

Step-by-step explanation:

I timesed 11 by 12 which is 132 and then timesed 10 with 11 which then gave me 110. I then subtracted 132 with 110 which gave me the answer 22. if we remove 11 from the 22 books we then end up with 11. then times it by 12 = 132. then if you subtract 10 of the 22 books then we end up with 12. then times it by 11 which is 132 as well.

The given algebraic equation can be written in many ways as shown.

The term "algebraic equation" refers to a formulation of the equality of two expressions using the algebraic operations of addition, subtraction, multiplication, division, raising to a power, and extraction of a root on a set of variables.

Solution:-

-5x-15+25x-30

it can be written as

-5(x+3-5x+6)

20x-45

5(4x-9)

and also

-5(9-4x)

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Find the equation that is equivalent to [tex]-5x-15+25x-30[/tex].

First, complete arithmetic operations on linear equations [tex]-5x-15+25x-30[/tex]

*Remember : how to complete arithmetic operations on linear equations, grouping terms with the same variable and then adding them up

[tex]-5x-15+25x-30 = -5x+25x-15-30=20x-45[/tex]

Then, find the common factors of [tex]20x[/tex] and [tex]-45[/tex].

Both have the same factor is [tex]-5[/tex].

Use the distributive property to find the equation that is equivalent.

[tex]20x-45=-5(\frac{20x}{-5}-\frac{45}{-5} )=-5(-4x-(-9))=-5(-4x+9)[/tex]

So, [tex]-5x-15+25x-30[/tex] equivalent to [tex]-5(-4x+9)[/tex]

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Answer: m=3

Step-by-step explanation:

The strategy to finding the slope is the use the slope formula, which Is [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]. Since we are given a point, we can directly plug them in and solve.

[tex]m=\frac{15-0}{5-0} =\frac{15}{5}=3[/tex]

The way we can use mental math is mainly because we are given the origin. We know that anything subtracted by 0 is itself. With the formula, the subtraction gives us 15 and 5. With basic division, we know that 15/5=3.

There is a relationship between the numbers of strawberries gathered and the amount of rainfall that can be found in a model (function).

A scatter plot with a trendline along which the data points are situated can be used to demonstrate the relationship between correlated variables.

Indicating a positive correlation is when the trendline slopes higher from left to right, while the opposite is true.

Part A:

The correlation coefficient of r = 0.1 is valid based on the provided scatter plot.

Part B:

The independent variable (the explanatory variable) is the cause of the dependent variable in a causal connection.

As a result, you need to identify a plausible factor that can influence the number of strawberries collected.

The week before harvest, I could picture how much it would rain.

Hence, There is a relationship between the number of strawberries gathered and the amount of rainfall that can be found in a model (function).

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The solution to the system of linear equations 3x + 2y = 14 and 5x + y = 32 is (x, y) = (6, 10).

3x + 2y = 14

5x + y = 32

Subtracting 3x from both sides of the first equation:

2y = 14 - 3x

Substituting this into the second equation:

5x + (14 - 3x) = 32

Simplifying:

8x = 18

x = 18/8

x = 2.25

This x value is substituted into the first equation.:

2y = 14 - 3(2.25)

2y = 14 - 6.75y

= 7.25

The solution is (x, y) = (2.25, 7.25)

The solution to the system of linear equations 3x + 2y = 14 and 5x + y = 32 is (x, y) = (2.25, 7.25). To solve the system, we first subtracted 3x from both sides of the first equation and then substituted this into the second equation. After simplifying, we obtained a value of x, which we then substituted into the first equation to obtain a value of y. This gave us the solution (x, y) = (2.25, 7.25).

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The slope of the line through (-9,6) and (-6,-9) is -5

Now, According to the question:

Let's know:

What is slope and example?

Whenever the equation of a line is written in the form y = mx + b, it is called the slope-intercept form of the equation. The m is the slope of the line. And b is the b in the point that is the y-intercept (0, b). For example, for the equation y = 3x – 7, the slope is 3, and the y-intercept is (0, −7).

The formula for the slope of a line when two points (coordinate pairs)

[tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are given is :

[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex] ,  where m denotes the slope of the line.

Applying this formula, we get:

[tex]m = \frac{-9-6}{-6-(-9)}[/tex]

[tex]m = \frac{-15}{-6+9}[/tex]

m = [tex]\frac{-15}{3}[/tex]

m = -5

Hence, The slope of the line through (-9,6) and (-6,-9) is -5.

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The complete question is this:

What is the slope of the line through (-9,6) and (-6,-9) ?

The Solving we get the difference of the given polynomials [tex](5x^{3} + 4x^{2} ) - (6x^{2} - 2x - 9)[/tex] as [tex]5x^{3} - 2x^{2} + 2x + 9[/tex]   .

What is a Polynomial ?

The polynomial is defined as the expression that is composed of variables, constants and exponents, which are combined by using mathematical operations such as addition, subtraction, multiplication and division .

Based on number of terms present in polynomial , they can be classified as  monomial, binomial, and trinomial .

For Example : [tex]3x^{2} +4x[/tex]  .

The polynomial is given as : [tex](5x^{3} + 4x^{2} ) - (6x^{2} - 2x - 9)[/tex] ;

On simplifying the above given polynomial ,

we get ,

= [tex]5x^{3} + 4x^{2} - 6x^{2} + 2x + 9[/tex]

On subtracting the like terms together  in above equation ,

we get ;

= [tex]5x^{3} - 2x^{2} + 2x + 9[/tex]

Therefore , the difference of the polynomials is (d)  [tex]5x^{3} - 2x^{2} + 2x + 9[/tex] .

The given question is incomplete , the complete question is

What is the difference of the polynomials?

[tex](5x^{3} + 4x^{2} ) - (6x^{2} - 2x - 9)[/tex]

A. –x³ + 6x² + 9

B. –x³ + 2x² – 9

C. 5x³ – 2x² – 2x – 9

D. 5x³ – 2x² + 2x + 9

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The initial amount of the investment is $800, the investment grows at the rate of 10% each year, and the value of the investment after 12 years is $1760.

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

The coordinates from the graph.

(0, 800), (1, 880), (2, 968)

x-coordinate is the number of years and the y-coordinate denotes the Value.

Now,

The initial amount of the investment is when x = 0.

= 800

Now,

Rate of change of the value each year.

=(880 - 800) / (1 - 0)

= $80

Rate of percentage.

= 80/800 x 100

= 10%

Now,

The value of the investment after 12 years.

= 800 + 12 x 80

= 800 + 960

= $1760

Thus,

The initial amount of the investment is $800.

The investment grows at the rate of 10% each year.

The value of the investment after 12 years is $1760.

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We know that a 90-degree clockwise rotation is the same as a 270-degree counterclockwise rotation, which means that the coordinates of each point in the original triangle BAC will be flipped across the x-axis, and then rotate 270 degrees.

We also know that a dilation at a scale factor of 2 means that the coordinates of each point are multiplied by 2.

Based on these transformations, the statement that is true is <C=<Z

In triangle BAC, point C has the same coordinates as point Z in triangle XYZ.

This because, the original point C is transformed by rotating 90 degrees counterclockwise and scaling by a factor of 2, This result in point C moving to the position of point Z.

The rest of the statements are not true based on this rotation and dilation because the coordinates of points A, B, and Y will be different from the original triangle BAC.

The cordinate of point B is -2.

To find the coordinate of point B, we need to determine its distance from point A and then add that distance to the coordinate of point A. We are given that point B lies on a number line between points A and C, and that the distance between A and B is 1/3 of the distance between A and C.

First, we'll find the distance between points A and C. We know that the coordinate of A is -9 and the coordinate of C is 12. To find the distance between these two points, we simply subtract the coordinate of A from the coordinate of C. So, 12 - (-9) = 21. This tells us that the distance between points A and C is 21 units.

Next, we'll use this information to find the distance between points A and B. We know that this distance is 1/3 of the distance between A and C, so we'll multiply 21 (the distance between A and C) by 1/3. 21 * 1/3 = 7. This tells us that the distance between points A and B is 7 units.

Finally, we'll add this distance to the coordinate of point A to find the coordinate of point B. Since A is at -9, B is at -9 + 7 = -2. Therefore, the coordinate of B is -2.

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Therefore, one mole of any substance is equal to its molar mass in grams.

Mass per mole is a definition of molar mass. In other terms, molar mass is the total mass of all the atoms in a material that makes up a mole. It is measured in gram-per-mole units.

A chemical element is uniquely defined by its atoms, which are tiny pieces of substance. An atom is made up of a core nucleus and one or more negatively charged electrons that orbit it. The positively charged, comparatively hefty protons and neutrons that make up the nucleus may be present.

The molar mass of a substance is the mass of one mole of that substance and is usually expressed in grams per mole (g/mol).

For example, the molar mass of carbon is 12.01 g/mol, so one mole of carbon weighs 12.01 grams.

Therefore, one mole of any substance equals its molar mass in grams.

It is essential to mention that the molar mass is the weight of one mole of a substance and is determined by the atomic or molecular weight of the substance.

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The total number of laps Sarah should run today is given by the equation A = 16 laps

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of laps be represented as A

Now , the equation will be

The total distance ran by Sarah yesterday = 3,682 m

The distance of one lap = 263 m

So , the number of laps ran by Sarah yesterday = total distance ran by Sarah yesterday / distance of one lap

Substituting the values in the equation , we get

The number of laps ran by Sarah yesterday = 3682 / 263

The number of laps ran by Sarah yesterday = 14 laps

Now ,

The distance Sarah wants to run today = 4,222 m

So , the number of laps Sarah should run today A = distance Sarah wants to run today / distance of one lap

Substituting the values in the equation , we get

The number of laps Sarah should run today A = 4,222 / 263

The number of laps Sarah should run today A = 16.05 laps

The number of laps Sarah should run today A = 16 laps

Therefore , the value of A is 16 laps

Hence , the number of laps is 16 laps

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The function rule to represent the total amount earned with Option A and earned with Option B are f(x) = 100 + 10x and f(x) = (1/100) * 2^x.

What is the function rule?

The function rule is the relationship between the input or domain and the output or range. A relation is a function if and only if there exists one value in the range for every domain value.

For Option A, the total amount earned can be represented by the function:

f(x) = 100 + 10x

where x is the number of days in February (x = 28 for a standard non-leap year)

For Option B, the total amount earned can be represented by the function:

f(x) = (1/100) * 2^x

where x is the number of days in February (x = 28 for a standard non-leap year)

the above function will be in cents, to get dollar values divide it by 100.

hence, the function rule to represent the total amount earned with Option A and earned with Option B are f(x) = 100 + 10x and f(x) = (1/100) * 2^x.

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By using scale factor formula we can evaluate the measure of side EF.

When a triangle is dilated by scale factors.The base and height change by the scale factor s while the area changes by a factor of s^2. While the scale distances between points dilations do not change angles.Dilation is used to make the objects larger or smaller.

The scale factor can be calculated when the new dimensions and the original dimensions are given. The basic formula to find the scale factor of a figure is Scale factor = Dimension of the new shape ÷ Dimension of the original shape.

From the question ΔE'F'G' is the image formed by the dilation of preimage ΔEFG.

Therefore,

2/3  =[tex]E_{1}[/tex][tex]F_{1}[/tex]/EF

EF=3/2[tex]E_{1}[/tex][tex]F_{1}[/tex]

By substituting any value of F'G' given in the equation we can evaluate the measure of side FG.

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So,  a 72-month loan with a 2 annual simple interest rate is the loan choice that would need her to repay the least amount of money.

An interest rate informs you of how much borrowing will cost you and how much saving will pay off. Therefore, the interest rate is the amount you pay for borrowing money and is expressed as a percentage of the entire loan amount if you are a borrower.

According to the information provided, a 72-month loan with a 2 annual simple interest rate is the loan choice that would require her to repay the least amount of money. This is because the amount she would have to pay will be the least compared to other loan options.

[tex]Loan = 72 months (2per cent of $6,000)\\Loan = 120 for 72 months\\Loan =$8,640\\[/tex]

a 72-month loan with a 2 yearly simple interest rate.

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