Select the row of Pascal’s triangle that is used to expand the binomial expression (2x^3+3y^2)^7

Robinson's time is 25 minutes and Wrong' time is 40 minutes.

Equation of Time:

x + y = 65                  -------------------------- (1)

Total usage amount:

15x + 35y = 1775     -----------------------------(2)

There are several ways to answer this question. I will teach we how to create two equations from the given information. First we need to set some variables (or unknowns).  we need to set up a sprinkler time variable for each household. Let's call the time of the Robinson  family "x" and the time of the Wrong family "y". The total time used was 65, so the first formula is x + y = 65 ( Robinson's time plus Wrong's time gives total time).

Now,

We use the other hourly water information (remember we already have time variables for each family, x and y). We can set the following equation as 15x + 35y = 1775 (15 liters x the amount of time the Robinson's use water plus 35 liters x the amount of time the  use water gives equal to total usage).

Now,

We can solve for one of the variables (x or y). It doesn't matter which one we start with. Also, it doesn't matter which formula you start with. I used

x + y=65 . On the other hand, subtracting x gives y = 65 - x.

Now,

Replace y in the other formula. 15x + 35y = 1775 turns into

15x + 35(65-x) = 1775.

Distribute 35 to each term in brackets. By isolating the x variable: x=25

Recall that x means how long the Robinson's have been using sprinklers.

Now,

We can plug x into the other equation: 25 + y = 65

Therefore,

Subtract 25 on the other side to isolate y: y= 40

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The given equation has no solution. Option B is correct.

As mentioned, the solution of the equation 8.5m +8 = 8.5m is to be determined.

The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.

Here,
Given expression,
8.5m + 8 = 8.5m
Now,
8.5m - 8.5m = 8
0 ≠ 8

Thus, the given equation has no solution. Option B is correct.

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The two most vital body systems that are checked when performing the steps of checking the ABCs are the Circulatory and Respiratory Systems.

Blood veins in the circulatory system are responsible for moving blood away from and back toward the heart. Arteries carry blood out from the heart while veins carry it back. Oxygen, nutrients, and hormones are delivered to cells by the circulatory system, which also eliminates wastes like carbon dioxide.

The respiratory system refers to the network of tissues and organs in your body that facilitates breathing. It includes your lungs, blood vessels, and airways. The lungs' moving muscles are a part of the respiratory system. Together, these elements circulate oxygen throughout the body and remove waste gases like carbon dioxide.

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The value of the numerical expression (6 + 3)² + [10 - (15/3)] will be 86.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The expression is given below.

⇒ (6 + 3)² + [10 - (15/3)]

Simplify the expression, then we have

⇒ (6 + 3)² + [10 - (15/3)]

⇒ (9)² + [10 - 5]

⇒ 81 + 5

⇒ 86

The value of the numerical expression (6 + 3)² + [10 - (15/3)] will be 86.

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Answer:

If a scatter plot shows a linear association, then there is a line that describes the relationship between the two measured quantities reasonably well. This means that there is a clear pattern in the data, and that the data points tend to follow a straight line when plotted on a graph. This does not necessarily mean that there is a line that passes through all of the plotted data points or that there is a tendency for relatively high values for one measured quantity to be paired with relatively high values for the other measured quantity.

Step-by-step explanation:

Answer:

A scatter plot shows a linear association.

Step-by-step explanation:

Answer:

To calculate Nora's total annual interest on her $800 investment, we can use the following formula:

Interest = Principal x Rate x Time

In this case, the principal is $800, the rate is 6% per annum, and the time is 1 year. Plugging these values into the formula, we get:

Interest = $800 x 0.06 x 1

To convert the 6% rate to a decimal, we divide 6 by 100. This gives us 0.06. We then multiply the principal by the rate and the time to get the total annual interest. So the total annual interest on Nora's $800 investment is:

Interest = $800 x 0.06 x 1 = $48

Therefore, Nora will earn a total of $48 in interest on her $800 investment over the course of one year at a rate of 6% per annum.

Step-by-step explanation:

Answer:

86

Step-by-step explanation:

The 64th term of the arithmetic sequence -3, -14 -25, will be - 696.

An arithmetic sequence is the sequence of numbers where each consecutive numbers have same difference.

Given that;

The arithmetic sequence is,

⇒ -3, -14 -25.

Now,

Since, We know that;

⇒ nth term = a + (n - 1)d

Where, 'a' is first term, 'd' is common difference.

Here, The arithmetic sequence is,

⇒ -3, -14 -25.

First term (a) = - 3

Common difference (d) = - 14 - (-3)

                                    = - 14 + 3

                                    = - 11

So, We get;

⇒ 64th term = - 3 + (64 - 1) (-11)

                    = - 3 + 63 × - 11

                    = - 3 - 693

                    = - 696

Thus, 64th term = - 696

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the number of arrangements if a and m come in a unit is 720.

What is the combination?

A combination is a choice made in mathematics from a group of different elements when the order of the choices is irrelevant (unlike permutations). For instance, if three fruits, such as an apple, an orange, and a pear, are supplied, there are three possible pairings of the two: an apple and a pear. Formally speaking, a k-combination of a set S is a subset of S's k unique components. In other words, two combinations are the same if and only if they have the same members. (It is not important how the individuals in each set are arranged.) The number of k-combinations for a set with n components

The word is the mailbox.

So it contains 7 words and the total number of arrangements will be 7! = 5040.

And if a and m comes in a unit then: the number of the arrangements will be 6! = 720.

Hence the number of arrangements if a and m come in a unit is 720.

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Answer:

Step-by-step explanation:

Answer: He will need 49 tiles.

Step-by-step explanation:

Given: The patio will measure 13.5 feet by 43 feet.

Area of patio = 13.5 feet x 43 feet [Area = length x width]

= 580.5 sq. feet

Since area of each concrete tile = 12 sq. inch

Number of concrete tiles required to cover patio = (Area of patio) ÷ (area of each concrete tile)

= 580.5 ÷ 12

= 48.375 sq. inch ≈49

The Proof for ABD is congruent to CBD is shown below.

The triangles are said to be congruent when two angles and a non-included side of one triangle match the corresponding angles and sides of another triangle.

Two triangles are congruent by side-side-side (SSS), side-angle-side (SAS), angle-side-angle (ASA), angle-angle-side (AAS) and right angle-hypotenuse-side (RHS).

Given:

AB || CD, <CBD = <ADB

In ΔABD and ΔCDB

<CBD = <ADB {Given}

BD= BD {Common}

<ABD = <CDB {Alternate Interior Angle}

So, By ASA Congruence Rule  ΔABD ≅ ΔCDB

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Answer:

Step-by-step explanation:

Rotation is the type of rigid transformation which is equivalent of two reflections across intersecting lines.

Define rigid transformation

A rigid  transformation is a transformation that persists the original size or shape of a given figure. Examples of rigid transformations are rotation, reflection etc;  

In mathematics a rigid transformation is also known as Euclidean Isometry or Euclidean transformation. Euclidean Isometry deals mainly with transformation of any figure. But, doesn't changes the length, shape or size of a given figure.

The concept of of two reflections across intersecting lines is equivalent to single rotation transformation of the original figure.  

Therefore the rigid transformation or Euclidean  isometry which is similar to two reflections across intersecting lines is rotation.  

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100 square centimeters are in the area of the largest possible inscribed triangle having one side as a diameter of circle.

What is the area?

A two-dimensional figure's area is the amount of space it takes up. In other terms, it is the amount that counts the number of unit squares that span a closed figure's surface. In general, square units such as square inches, square feet, etc. are used as the standard unit of area.

Base = 2r = 2*10 = 20 cm

Height = r=  10 cm

Area =  1/2 * base * height

        =   1/2 * 20 * 10

        =   100 square centimeters

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Answer:

B

Step-by-step explanation:

Lines that are both perpendicular to a given line are parallel.

If the angle C is 15 degree and angle D is complementary then the measure of angle D is 75 degree .

In the question ,

it is given that ,

the measure of angle C is = 15 degree  ,

we have to find the measure of angle D in the question,

and the angle C and angle D are complementary ,

that means ; angle C + angle D = 90°

Substituting the values ,

we get ,

15° + ∠D = 90°

subtracting 15° from both the sides ,

we get ,

∠D = 90° - 15°

Simplifying  further ,

we get,

∠D = 75°

Therefore , the measure of angle D is = 75° .

The given question is incomplete , the complete question is

If Angle C = 15 degrees and Angle D is complementary to Angle C, what is the measure of Angle D ?

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Answer:

The equations 3x+y=-3 and 3x+y=-4 are both linear equations in the standard form. The standard form of a linear equation is ax+by=c, where a and b are coefficients, and c is the constant term.

Step-by-step explanation:

Answer:

180 cups of hot chocolate and 95 cups of coffee

Step-by-step explanation:

multiply the cups by the price and add them together and it adds up to the total sales they got

Examining the table showing number of students gaining certificates for outstanding achievements the modal number is 4

The most frequent number, or the one that appears the most frequently.

In a frequency table the frequency shows the number of times a the data measured appears

Looking at the table the number that has most frequency is 4. This means that the people that collected 4 certificates are more than any other set of people.

The next is two which have a frequency of two while the least the people that collected 6 certificates. they have a frequency of 2 which means they are only tow people

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The average length of DNA per gene would be 40,000 base pairs if the genome had 20,000 genes.

Average gene length: just 2.5% of the human genome codes for proteins. The remaining 97.5% are introns. The male nuclear diploid genome measures 205.00 centimeters (cm), is 6.27 Gigabase pairs (Gbp), and weighs 6.41 picograms (pg). 208.23 cm, 6.51 pg, and 6.37 Gbp are the female measurements. "The overall number of base pairs, which is the length of DNA per gene, will be roughly twice the number of genes present in the genome, in this example 40,000, for a 25% mammalian genome with 20,000 genes".

A DNA region from which an mRNA is transcribed is the de facto definition of a "gene" in mammalian genome annotation. Because one cannot deduce function from a genome sequence alone, the correct functional genetic definition of a gene—a segment of DNA that can complement a mutant phenotype—is lost.

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The graph of the function f(x) = [x² if x ≤ 2] [x + 4 if x > 2]

From the question, we have the following parameters that can be used in our computation:

f(x) = [x² if x ≤ 2] [x + 4 if x > 2]

The above function is a piecewise function, and it can be split as follows:

f(x) = [x² if x ≤ 2]

f(x) = [x + 4 if x > 2]

The domain x ≤ 2 in f(x) = [x² if x ≤ 2]  means that:

The x values stop at 2 (i.e. 2 inclusive)

The domain x > 2 in f(x) = [x + 4 if x > 2] means that:

The x values starts at a value greater than 2 (i.e. 2 exclusive)

This is represented by the graph (d) with the open and closed circles

Hence, the graph is graph d

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Answer:

70

Step-by-step explanation:

20+20

The required rate are the people moving apart 3 minutes after the woman starts walking is 2.36 ft/S.

The  rate of change of distance is speed ( not uprooting). Similar distance in different headings is alluded to as a similar distance.

Let x and y be the distance of the man and woman respectively.

We have,

dx/dt = 2 ft/s, dy/dt = 1 ft/s

Then, x = 2×6×60 = 720 ft

y = 1×5×60 = 300 ft

And in triangle which make by the locus of man and woman.  

(x +y)^2 + (800)^2 = z^2

z = √(1020)^2+(800)^2

z = 1296.3 ft

So, people are 1296.3 ft apart,

Rate change

[tex]\frac{d}{dt}[/tex](x+y)^2 = [tex]\frac{d}{dt}[/tex]z^2

2(x+y)(dx/dt+dy/dt) = (2z)dz/dt

(720+300)+(2+1) = (1296.3)dz/dt

dz/dt = 3060/1296.3 = 2.36 ft/s

Thus, their moving rate is 2.36 ft/s

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The probability that a domino randomly selected from a set will be a double =  2  / 11

what is probability?

A thing's probability indicates how probable it is to happen. When we are uncertain about the result of a given event, we can talk about the probabilities of several outcomes—how likely they are. Statistics refers to the study of events that have a probability component.

When 'n' is the largest integer in the set, the total number of dominoes in the set is given by the following formula:

(n + 1) (n + 2) / 2

This means that (9 + 1) (9 + 2) / 2 =

(10)(11)/ 2  =    

110/2 =55

10 of these dominoes will be "doubles"

So....the probability that a domino randomly selected from a set will be a double =   10 / 55    =    2  / 11

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Answer:

Priya:  S=20w+50

Vanessa:  S=25w+20

6 weeks

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]

Define the variables:

Given that Priya starts with $50 in her bank account, the y-intercept of the linear equation modelling her savings will be 50.

If she then deposits $20 each week for 12 weeks, the slope will be 20.

Therefore, the linear equation that models Priya's savings is:

Given that Vanessa starts with $20 in her bank account, the y-intercept of the linear equation modelling her savings will be 20.

If she then deposits $25 each week for 12 weeks, the slope will be 25.

Therefore, the linear equation that models Vanessa's savings is:

Create a table for each linear equation from part a.

Priya                       Vanessa

[tex]\begin{array}{|c|c|}\cline{1-2} w & S \\\cline{1-2} 1&70 \\\cline{1-2} 2& 90\\\cline{1-2} 3&110 \\\cline{1-2} 4&130 \\\cline{1-2} 5& 150\\\cline{1-2} 6&170 \\\cline{1-2} 7&190 \\\cline{1-2} 8&210 \\\cline{1-2} 9&230 \\\cline{1-2} 10&250 \\\cline{1-2} 11& 270\\\cline{1-2} 12& 290\\\cline{1-2} \end{aligned}[/tex]               [tex]\begin{array}{|c|c|}\cline{1-2} w & S \\\cline{1-2} 1&45 \\\cline{1-2} 2& 70\\\cline{1-2} 3& 95\\\cline{1-2} 4& 120\\\cline{1-2} 5& 145\\\cline{1-2} 6& 170\\\cline{1-2} 7& 195\\\cline{1-2} 8& 220\\\cline{1-2} 9& 245\\\cline{1-2} 10& 270\\\cline{1-2} 11& 295\\\cline{1-2} 12&320 \\\cline{1-2} \end{aligned}[/tex]

Create a graph for each linear equation (see attachment).

The week in which Priya and Vanessa will have the same amount of savings is the week where the S-values in the tables are the same, and the point of intersection of the graphed lines.

Therefore, from inspection of the tables and graphs from part b, Priya and Vanessa will have the same amount of savings in week 6.

Answer:

sorry

Step-by-step explanation:

idrk

The height of the house is approximately 29.43 meters.

A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.

We can use the tangent function to solve this problem.

The tangent of an angle is equal to the opposite side (the height of the house) divided by the adjacent side (the distance between the house and the building). In this case, the angle is 30 degrees and the opposite side is the height of the house, so we can write the following equation:

tan(30°) = height of house / 25√3

We can use a calculator or look up the value of tangent 30° to find that tangent 30 is approximately 0.577. Therefore, the equation becomes:

0.577 = height of house / 25√3

Multiplying both sides of the equation by 25√3 gives us:

height of house = 0.577 × 25√3

Plugging in the values and simplifying, we get:

height of house = 29.43 m

Therefore, the house's height is approximately 29.43 meters.

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