Estimate the average by first rounding to the nearest 100:

120, 230, 455, 175

Line C has a slope of -1. LINE D has a slope of -2.

To Compare the slopes of the lines.

Let us consider the following problem:

In the xy-plane, the point (-1,-2) is on the line j, and the point (-2,-1) is on the line k. Each of the lines has a Negative slope.

We should compare slopes of both the lines to each other, because we may have such kind of two lines

y=x+1 and y=x−1

so we see that their slopes are equal, but we may have also

y=2∗x or slope 2

and

y=1/2∗x or slope 1/2,

Hence, the answer is i think that there is not enough information to compare slopes of the lines.

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By simplifying a system of equations we will see that the correct option is the second one:

(2a - 7) + a  = 41

Let's define the variables:

We have the statements:

"Taylor's sister is 7 years less than twice Taylor's age"

s = 2*a - 7

"The sum of Taylor's age and her sister's age is 41"

s + a = 41

So we have a system of equations:

s = 2a - 7

s + a = 41

Replacing the first equation in the second one we get:

(2a - 7) + a  = 41

So the correct option is the second one, that is the equation that represents this relationship.

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The correct option regarding the number of bags filled by Nina, using proportions, is given as follows:

Between 20 and 30 bags.

A proportion is a fraction of an amount, and this fraction is combined with the unit rates of the problem and basic arithmetic operations, especially multiplication and division, to find the desired amounts in the context of the problem.

In this problem, a proportion is applied to find the number of bags filled by Nina, which is given by the division presented as follows:

Number of bags = Number of treats / Treats per bag.

The values of these parameters are given as follows:

Hence the numeric value of the expression is:

Number of bags = 78/3 = 26.

Which is a number between 20 and 30.

The problem states that Nina had 78 treats, and each bag has 3 treats, then it asks the correct option regarding the number of bags.

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Answer:

102.375

Step-by-step explanation:

hope it helps :)

multiply 6.5 x 2.25, get 14.625

multiply 14.625 x 7, answer is 102.375

The coordinates to which the portable irrigation system should be sent to water the area are:

(495.75, 672).

The portable irrigation system should be sent right to the middle of the dry area given by the rectangle at the end of the answer.

Hence the coordinates are given as follows:

Hence the x-coordinate of the point to which the system should be sent is:

x = (56 + 144 + 888 + 895)/4 = 495.75.

(the mean is given by the sum of the observations divided by the number of observations).

The y-coordinate of the point to which the system should be sent is:

y = (289 + 332 + 1012 + 1055)/4 = 672.

The area is given by the image at the end of the answer.

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4. Definition of complementary

5. Substitution

6. Subtraction property

7. Definition of Congruence

What are corresponding angles?

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If you are running a fuel economy study. the unit rate for miles per gallon for each​ car is 22.8 miles and 23.04 miles and the fastest car is Red car.

Units rate = Distance /Time

Blue car

Unit rate = 28 1/2 miles ÷ 1 1/4 gallons of gasoline

Unit rate = 28.5miles ÷ 1.25 gallons of gasoline

Unit rate = 22.8 miles

Red car

Unit rate = 28 4/5 miles ÷  4/5 gallons of gasoline

Unit rate = 28.8miles ÷ 0.8 gallons of gasoline

Unit rate = 23.04 miles (Fastest)

Therefore the unit rate for each​ car is 22.8 miles and 23.04 miles and the fastest car is Red car.

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Answer:

y=-3/4x + 11/4

Step-by-step explanation:

First thing is to minus 3x from 3x and 12.
You will get 4y=-3x+12.
Divide all the sides by 4.
You will get y=-3/4+3.
Now input 1(x), and 2(y) into the slope-intercept form equation.
2=-3/4(1)+b
2=-3/4+b
+3/4 +3/4
2 3/4=b
You can simplify it into 11/4
So, the equation will be y=-3/4x + 11/4
I hope I got this right.

The value [tex]x=66[/tex] and [tex]2x=132[/tex] that make line m parallel to line n.

Therefore,

∠132°=∠2x°

[tex]\frac{132}{2} =66[/tex]

hence, x=66°

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The inequality to express the information when Oleg is training for a triathlon is 2x + 2y ≤ 30

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal.

Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

In this case, Oleg jogged for 2 hours at x miles per hour and then he bicycled for 2 hours at y miles per hour.

The inequality will be:

2(x) + 2(y) ≤ 30

2x + 2y ≤ 30

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Complete question

Oleg is training for a triathlon. One day he jogged for 2 hours at x miles per hour . Then he bicycled for 2 hours at y miles per hour. Finally. He swam a distance. The total number of miles did not exceed 30. Express this as an inequality

1,858.40

2300-36%=1472

1472-70%=441.60

2300-441.6=1,858.40

The function f(x) in standard form as described in the task content is; 3x³ + 21x² - 23x + 5.

It follows from the task content that the function, f(x) which is as described is to be determined.

Since the polynomial remainder theorem postulates that;

Polynomial = (quotient × divisor) + remainder.

According to the given task content;

The quotient is; 3x² - 3x + 1.

The divisor is; (x + 8) and the remainder is; -3.

Therefore, the required polynomial is;

f(x) = (3x² - 3x + 1)(x + 8) + (-3)

= 3x³ + 24x² -3x² -24x + x + 8 - 3

= 3x³ + 21x² - 23x + 5.

Therefore, the required function, f(x) is; 3x³ + 21x² - 23x + 5.

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The coordinates of the image of point W after a rotation of 180° counterclockwise are W'(-2,-5).

The technique of altering an existing graph or graphed equation to create a different version of the following graph is known as graph transformation.

The coordinates of the given point W are W(2,5).

The coordinate rule for a 180°counterclockwise rotation is:

(x,y)→(-x,-y)

Substitute (x,y) = (2,5) into the above coordinate rule:

(2,5) → (-2,-5)

Hence, the coordinates of the image of point W after a rotation of 180° counterclockwise are W'(-2,-5).

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Answer:

3

Step-by-step explanation:

19.861>19.851

look at hundreds column

The required extra calcium that women receive is 336 g during pregnancy.

Given that,
It is recommended that a pregnant woman should increase her calcium intake by 1.2 g per day. A normal pregnancy last 40 weeks.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

Here,
According to the question,
Amount of calcium intake,
= 1.2 × 40 × 7
= 336g

Thus, the required extra calcium that women receive is 336 g during pregnancy.

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Answer:

[tex]y = \frac{1}{4} x\\[/tex] [tex]- 5[/tex]

Step-by-step explanation:

Take a look at the attachment...

Hope this helps! :)

Differentiation of function [tex]y=e^{4x^{4} } (2x^{3} -1)[/tex] is [tex]\frac{dy}{dx} =6x^{2}e^{4x^{4} } +e^{4x^{4} } (2x^{3}-1)(16x^{3} )[/tex]

A differential equation is an equation that contains one or more functions with its derivatives.

Given,

[tex]y=e^{4x^{4} } (2x^{3} -1)[/tex]

We need to apply product rule of differentiation

dy/dx=xy'+yx'

In the given equation

x=[tex]e^{4x^{4} }[/tex]

y=[tex](2x^{3} -1)[/tex]

[tex]\frac{dy}{dx} =e^{4x^{4} } .6x^{2} +(2x^{3}-1)e^{4x^{4} } (16x^{3} )[/tex]

[tex]\frac{dy}{dx} =6x^{2}e^{4x^{4} } +e^{4x^{4} } (2x^{3}-1)(16x^{3} )[/tex]

Hence, differentiation of function [tex]y=e^{4x^{4} } (2x^{3} -1)[/tex] is [tex]\frac{dy}{dx} =6x^{2}e^{4x^{4} } +e^{4x^{4} } (2x^{3}-1)(16x^{3} )[/tex]

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The probability for success is not the same for each trial, then the option D cannot be modelled using a geometric distribution.

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

One of the assumptions to consider before the use of a geometric distribution can be valid is that, the probability of success must be the same for each outcome.

In the option D, selection is done without replacement, meaning that, the number total possible outcome will decrease as we make each selection and will also depend on how the colours are being chosen.

Hence, the probability of success will differ for each outcome, thus the option D is correct.

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The polynomial function of least degree with leading coefficient 1 and having zero at the given points is, [tex]f(x) = x^3-3x^2+\sqrt{5}x^2 +2x-\sqrt{5} x[/tex].

What is polynomial?

A polynomial is an expression in mathematics that solely uses the operations of addition, subtraction, multiplication, and powers of positive-integer variables. It consists of indeterminates and coefficients. The polynomial x^2 + 4x + 7 is an illustration of one with a single indeterminate x.

From the given polynomial, the least degree polynomials are,

f(x) = x^3 -5x^2 + 3x - x

[tex]f(x) = x^3-3x^2+\sqrt{5}x^2 +2x-\sqrt{5} x[/tex]

These polynomial having leading coefficient 1.

Now to check x = 0, 1, (2 [tex]-\sqrt{5}[/tex]) are zeros of which polynomial.

Consider, the first polynomial

f(x) = x^3 -5x^2 + 3x - x

plug x = 0

f(0) = 0 - 5(0) + 3(0) - 0

f(0) = 0

plug x = 1

f(1) = 1^3 - 5(1)^2 +3(1) - 1

f(1) = 1 - 5 + 3 - 1

f(1) = -2

f(1) ≠ 0

Therefore, 1 is not the zero of this polynomial.

Now consider, the next polynomial

[tex]f(x) = x^3-3x^2+\sqrt{5}x^2 +2x-\sqrt{5} x[/tex]

Plug x = 0

f(0) = 0

f(1) = 0

[tex]f(2-\sqrt{5} )=0[/tex]

Therefore, the polynomial [tex]f(x) = x^3-3x^2+\sqrt{5}x^2 +2x-\sqrt{5} x[/tex] having given zeros.

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Answer:

[tex]f(x)=x^3-3x^2+\sqrt{5}x^2+2x-\sqrt{5}x[/tex]

Step-by-step explanation:

Given information:

Factor Theorem

If f(x) is a polynomial, and f(c) = 0, then (x – c)  is a factor of f(x).

Therefore, the function in factored form is:

[tex]\implies f(x)=1 \cdot x(x-1)(x-(2-\sqrt{5}))[/tex]

[tex]\implies f(x)=x(x-1)(x-2+\sqrt{5})[/tex]

Expand the factored function:

[tex]\implies f(x)=x(x^2-2x+\sqrt{5}x-x+2-\sqrt{5})[/tex]

[tex]\implies f(x)=x(x^2-3x+\sqrt{5}x+2-\sqrt{5})[/tex]

[tex]\implies f(x)=x^3-3x^2+\sqrt{5}x^2+2x-\sqrt{5}x[/tex]

The given sets written in interval notation are

C = (4, ∞), and  = (-∞, 9]

From the question, we are to write the given sets using the interval notation

The given sets are

C = {v | v > 4}

D = {v | v ≤ 9}

For set C,

C = {v | v > 4}

The elements of the sets are 5, 6, 7, 8, 9, ...

This can be written in interval notation as (4, ∞)

For set D,

D = {v | v ≤ 9}

The elements of the sets are 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, ...

This can be written in interval notation as (-∞, 9]

Hence, the interval notation form of the sets are

C = (4, ∞)

and

D = (-∞, 9]

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A) The monthly deposit is $503.77

B) Interest per month ≈0.42

what is compound interest?

Interest that is added to a loan or deposit sum is known as compound interest. In our daily lives, it is the notion that is employed the most frequently. Compound interest is calculated for a sum using the principal and interest accrued over time. Compound interest and simple interest differ primarily in this way.

Let A be the amount in future.

Monthly deposit= [tex]P= \frac{A \times \frac{r}{n}} {(1 +\frac{r}{n})^{t*n} - 1}[/tex]

n= 12, 12 months in a year

So, monthly deposit= [tex]P= \frac{300000 \times \frac{0.05}{12}} {(1 +\frac{0.05}{12})^{25*12} - 1}[/tex]

                                 = 1250/2.4813

                                 = $503.77

So, monthly deposit= $503.77

To find interest:

Interest per year = 5%

Interest per month = 5/12 = 0.416 ≈0.42

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Answer: $503.77

Interest earned: $148,869

Step-by-step explanation:

Let A be the future amount.

Monthly Deposit= P=A*r/n÷ (1+r/n)^t*n-1

n=12 months in a year

P= (300,000*0.05/12)÷ [(1+0.05/12)^25*12]-1

P=1250/2.4813

P=$ 503.77

Interest earned.

$300,000-(503.77*12*25)

$300,000-151,131= $148,869

Answer:

Step-by-step explanation:

You want to find the maximum or minimum value and where it occurs for the function F(x)=-3x²+18x+3.

The vertex form of a quadratic is ...

  f(x) = a(x -h)² +k . . . . . . . vertex at (h, k)

The graph opens downward if a < 0, and opens upward for a > 0. When the graph opens downward, the function has a maximum at the vertex. When the graph opens upward, the function has a minimum at the vertex.

We can put the function in vertex form as follows:

  F(x) = -3(x² -6x) +3 . . . . . factor out the leading coefficient

  F(x) = -3(x² -6x +9) +3 +3(9) . . . . . . subtract and add 3(9)

  F(x) = -3(x -3)² +30 . . . . . . . . . simplify to vertex form

Comparing this equation to the form shown above, we see ...

  a = -3 < 0 . . . . . . . . . the function has a maximum

  (h, k) = (3, 30) . . . . . the maximum is 30 at x=3

__

Additional comment

The square of the binomial in parentheses is ...

  (x -p)² = x² -2px +p²

That is, to "complete the square", we add the square of half the x-coefficient. Here, that coefficient is -2p=-6, so we want to add p²=9 inside parentheses. To keep the expression the same, we need to add the opposite amount outside parentheses. We are effectively adding 0 in the form of -3(9) +3(9) = 0 so the expression can be put in vertex form.

A graphing calculator can quickly show you the minimum or maximum of the function.

The required measure of angle m ∠A  is 58.7° which is the correct answer would be an option (D).

The supplementary angles are defined as when pairing of angles addition to 180° then they are called supplementary angles.

Angles A and B are supplementary.

We have been given that m angle ∠B= 121.3°,

To determine the measure of angle A if the measure of angle B is 121.3°.

As per the property supplementary angles,

m∠A + m ∠B = 180°

m∠A + 121.3 ° = 180°

m ∠A = 180° - 121.3°

m ∠A = 58.7°

Therefore, the required measure of angle m ∠A  is 58.7°

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To fill the pool 3/4 full it will take 240 minutes

A rate is a ratio that compares two different quantities which have different units. For example, if we say John types 50 words in a minute, then his rate of typing is 50 words per minute. The word "per" gives a clue that we are dealing with a rate. The word "per" can be further replaced by the symbol "/" in mathematical problems.

3/4 of the volume the pool is 3/4×16000= 12000gallons

it takes 1 minutes to fill 50gallons

therefore to fill 12000 gallons it will take 12000×1/50 =240minutes

therefore the number of minutes it will take to fill 3/4 of the pool is 240minutes

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The smallest number from the sum of three consecutive even numbers is 14.

Given, The sum of three consecutive even numbers is 48.

we are asked to determine the smallest number of the numbers.

Let:

x= the 1st con.even number

x+2=the 2nd con.even number

x+4=the 3rd con.even number

Add the terms and equate it with the total, 48

x+(x+2)+(x+4) = 48

simplify

x+x+2+x+4=48

combine the like terms.

3x+6=48

3x = 48-6

3x=42

x=42/3

x=14

the three numbers are:

x = 14

x+2 = 14+2 = 16

x+4 = 14+4 = 18

smallest number of the three numbers = 14

Hence we get the smallest number as 14.

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The number that will go in between 0.438 and 44% in the thousandth place is 9 and the number is

This is found by converting all the given number to decimal

0.438

the thousandth place has number 8

44% = 0.440

The thousandth place has number 0

4/9 = 0.44444

this is greater than the two numbers and hence cannot go in between them

9/20 = 0.45

this is greater than the two numbers and hence cannot go in between them

checking the two numbers 0.438 and 0.440 the number that can go in between them is 0.439

9 in thousandth place is 0.009

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Step-by-step explanation:

3a + 3.8 is equal to what when a=1.5?

substitute in 1.5 for a:

3(1.5) + 3.8

3(1.5) + 3.8

4.5 + 3.8

= 8.3

The p-value in one-way anova table can be calculated using the following parameters

The anova table represents the analysis of variance.

To calculate the p value from the anove table, the following parameters are needed

df Treatment, df Error and F value

The representation of the above parameters are:

When these values are known, we look up to the df Treatment, df Error and F values on the anova table, and write out the corresponding p value

Take for instance:

The p-value for the above parameters is 0.1138

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Answer:

Line 1: slope is 1

Line 2: slope is -1

Lines are perpendicular

A division is a process of splitting a specific amount into equal parts. The unit rate for $12.50 for 5 ounces is $2.5

A division is a process of splitting a specific amount into equal parts.

Given,

$12.50 for 5 ounces

We need to find for a unit rate.

For this we need to use division. We have to split $12.50 among 5 ounces.

12.50 as Divisor and 5 as dividend.

Twelve point five zero divided by five

$12.50/5

2.5

Hence the unit rate for $12.50 for 5 ounces is $2.5

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