1. The sum of two numbers is 72. If one number is 3 times the other, what is the largest number?

2. How many hours are there between 6:30am and 1:30pm on the same day?

3. Find the value of x

4. At $22.50 per metre, what is the price of 1 1/2 metres of cloth?

5. How many millilitres are there in half a litre? ​

A multiplying polynomials calculator is a tool used to multiply two or more polynomials together.

A multiplying polynomials calculator is a tool used to multiply two or more polynomials together. It can be helpful for simplifying algebraic expressions, solving equations, and performing various calculations in mathematics and engineering.

The calculator takes the coefficients of each polynomial as input and uses the distributive property to multiply the terms of each polynomial together. It then combines like terms and arranges the result in descending order of degrees. Multiplying polynomials can be a tedious and error-prone process, especially for large polynomials, so using a calculator can save time and reduce the chances of errors. The multiplying polynomials calculator is commonly used by students, teachers, engineers, and anyone working with algebraic expressions.

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Answer: x=15

Step-by-step explanation:

3x+5=50

3+5=50

Subtract the numbers

3x+5-5=50-5

3x/3=45/5

x=15

2.4 meter is approximately equal to 7.8740 feet ( rounded to four decimal places )

To convert 2.4 meter to feet, we can use the following formula:

1 meter = 3.28084 feet

The conversion is the process of changing the unit of one quantity to another units  

The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing

Therefore,

The length in feet = conversion factor × The length in meter

Substitute the values in the equation

2.4 m = 3.28084 × 2.4

Multiply the numbers

= 7.8740 feet ( rounded to four decimal places )

Therefore, 2.4 m is 7.8740 feet.

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Answer:

1.5

Step-by-step explanation:

Answer: 1.5

Step-by-step explanation:

300000 yen is approximately equal to 2233.38 USD  ( rounded to two decimal places )

The conversion factor to convert yen to USD is 0.0074

1 yen = 0.0074 USD

The conversion is the process of changing the unit of one quantity to another units  

The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing

The currency in USD = The currency in yen × conversion factor

Substitute the values in the equation

1 yen = 0.0074 USD

300000 =  300000 × 0.0074

Multiply the numbers

= 2233.38 USD ( rounded to two decimal places )

Therefore, 300000 yen is 2233.38 USD

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Answer:

B) 5

Step-by-step explanation:

   AB = 4 units

  BC = 3 units

Use Pythagorean theorem to find the length of AC,

                AC² = AB² + BC²

                      = 4² + 3²

                       = 16 + 9

                       = 25

                  [tex]AC = \sqrt{25}\\\\[/tex]

                 AC = 5 units

Answer:

x = 4

y = 8

Step-by-step explanation:

If y = 3x - 4 and y = -1/2x + 10, then

3x - 4 = -1/2x + 10

3.5x = 14

x = 14/3.5 = 4

y = 3(4) - 4 = 8

Usually there are 52 Sundays in a year approximately.

There are a total of 52 weeks in a year if we take a rough estimate.

Every week has one sunday in it. So, going by this logic, each year will have about 52 sundays in it.

Now, one thing that we should notice here is that is not certain that there will be definitely 52 sundays. This number of 52 can increase also by a number of one or two because it is possible that the year might not starting from sunday. Because when we do 365/7 we get 52.14 so, this decimal place might include one or two Sundays in it.

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1. The connection between exponential functions and geometric sequences is that the terms of a geometric sequence are generated by repeatedly multiplying the previous term by a constant ratio, which can be expressed using an exponential function.

2. Moore's Law is associated with the exponential function because it describes a growth pattern that is exponential in nature.

1. If  the first term of a geometric sequence is denoted by a_0 and the common ratio is denoted by r, then the nth term can be calculated using the formula a_n = a_0 * r^(n-1), which is equivalent to the exponential function f(n) = a_0 * r^n. Conversely, if we have an exponential function f(n) = a * r^n, then the sequence of its values for n = 1, 2, 3, ... forms a geometric sequence with first term a and common ratio r.

2. Moore's Law is a prediction made by Gordon Moore, co-founder of Intel, in 1965, that the number of transistors on a microchip would double every 18-24 months, while the cost per transistor would decrease. This has been interpreted to mean that the processing power of computers would double every 18-24 months, leading to exponential growth in computing power and an exponential decrease in the cost of computing.

Moore's Law is associated with the exponential function because it describes a growth pattern that is exponential in nature. The number of transistors on a microchip is growing at an exponential rate, which means that the rate of growth is proportional to the current number of transistors. This can be represented mathematically as an exponential function, such as y = a * e^(kx), where y is the number of transistors, x is time, a is the initial number of transistors, and k is the growth rate.

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If A be a matrix with linearly independent columns, then the statement that must be true is (A) The equation Az=b always has a solution for all b.

Since the columns of A are linearly independent, the matrix A has full column rank, i.e., its column space is the entire space R^n. Here are the implications of this fact for each statement:

A. The equation Az=b always has a solution for all b.

This is true, because for any b in R^n, we can write it as a linear combination of the columns of A, say b=c_1a_1+c_2a_2+...+c_na_n. Then, the solution to Az=b is simply z=[c_1,c_2,...,c_n]^T.

B. The equation Ab has a solution for all b precisely when it has more rows than columns.

This statement is false. The equation Ab=b is always solvable, regardless of the dimensions of A and b. The solution is simply b expressed in the basis of the column space of A.

C. There is no easy way to tell if Ax-b has a solution for all b.

This statement is also false. Since the columns of A are linearly independent, the equation Ax=b has at most one solution for each b. Therefore, Ax=b has a solution for all b if and only if the columns of A span the entire space R^n. This can be checked by computing the rank of A.

D. The equation Az-b has a solution for all b precisely when it has more columns than rows.

This statement is false. The equation Az=b is always solvable, regardless of the dimensions of A and b, as we have seen in (A).

E. The equation Ax-b never has a solution for all b.

This statement is false. The equation Ax=b has at most one solution for each b, and it is solvable for all b if and only if the columns of A span the entire space R^n, as we have seen in (C).

F. The equation Az-b has a solution for all b precisely when it is a square matrix.

This statement is false. The equation Az=b is always solvable, regardless of whether A is square or not, as we have seen in (A).

Therefore, the only true statement among the given options is (A) The equation Az=b always has a solution for all b.

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Answer:

Option 3: about 14 inches

Step-by-step explanation:

The notebook paper is in the form of a rectangle of length

[tex]l = 11[/tex] inches and width [tex]w = 8.5[/tex]  inches

The diagonal of such a rectangle is given by the Pythagorean formula
[tex]d = \sqrt{l^{2} + w^{2}}[/tex]

Substituting the values of [tex]l[/tex] and [tex]w[/tex]:

[tex]d = \sqrt{11^{2} + 8.5^{2}}\\\\d = \sqrt{121 + 72.25}\\\\d = \sqrt{193.25}\\\\d= 13.9014\;inches[/tex]

This corresponds to Option 3: about 14 inches

Answer:

Step-by-step explanation:

each dot in the following dot plot represents the number of players at one table in bev's bingo hall. a dot plot has a horizontal axis labeled number of players marked by 8 equidistant tick marks numbered from 0 to 7. dots are plotted above the following: 0, 1; 1, 2; 3, 3; 4, 1; 5, 1; 7, 1. a dot plot has a horizontal axis labeled number of players marked by 8 equidistant tick marks numbered from 0 to 7. dots are plotted above the following: 0, 1; 1, 2; 3, 3; 4, 1; 5, 1; 7, 1. find the interquartile range (iqr) of the data in the dot plot. players

The interquartile range (IQR) of the data in the dot plot is 3.5 players.

To find the interquartile range (IQR) of the data in the dot plot, we need to determine the values of the first quartile (Q1) and the third quartile (Q3).

The quartiles divide a dataset into four equal parts, where Q1 represents the 25th percentile and Q3 represents the 75th percentile.

Given the data points from the dot plot:

0, 1; 1, 2; 3, 3; 4, 1; 5, 1; 7, 1

First, arrange the data in ascending order:

0, 1, 1, 1, 3, 4, 5, 7

Next, find the median (Q2), which is the middle value of the data:

Median (Q2) = (3 + 4) / 2 = 3.5

Since there are 8 data points, we can calculate the position of Q1 and Q3 as follows:

Q1 position = (1/4) * (8 + 1) = 2.25

Q3 position = (3/4) * (8 + 1) = 6.75

Q1 is between the 2nd and 3rd data points: Q1 ≈ (1 + 1) / 2 = 1

Q3 is between the 6th and 7th data points: Q3 ≈ (4 + 5) / 2 = 4.5

Finally, calculate the IQR:

IQR = Q3 - Q1 = 4.5 - 1 = 3.5

So, the interquartile range (IQR) of the data in the dot plot is 3.5 players.

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Leslie used a total of 128 stones for the order.

Arithmetic operations is a branch of mathematics, that involves the study of numbers, the operation of numbers that are useful in all the other branches of mathematics.

It basically comprises operations such as Addition, Subtraction, Multiplication and Division.

The correct equation that represents how many stones were used for the order is:

total number of stones = number of bracelets x stones per bracelet

Let's use "s" to represent the total number of stones Leslie used for the order:

s = 8 x 16

s = 128

Hence, Leslie used a total of 128 stones for the order.

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The politician should obtain a sample of at least 602 voters to estimate the proportion of voters supporting her position on forced busing with a 90% level of confidence and a 4% margin of error.

What is the proportion?

A proportion is two ratios that have been set equal to each other; a proportion is an equation that can be solved. When I say that a proportion is two ratios that are equal to each other, I mean this in the sense of two fractions being equal to each other. For instance, 5/10 equals 1/2.

To determine the sample size needed to estimate the proportion of voters supporting a certain position within a certain margin of error and level of confidence, we can use the following formula:

n = (Z² * p * (1 - p)) / E²

where:

n is the sample size

Z is the z-score corresponding to the desired level of confidence (in this case, 90%, which corresponds to a z-score of 1.645)

p is the estimated proportion of voters supporting the politician's position (we don't have an estimate, so we'll use 0.5, which maximizes the sample size and provides the most conservative estimate)

E is the desired margin of error (in this case, 4%, which is equivalent to 0.04)

Substituting the values given, we get:

n = (1.645² * 0.5 * (1 - 0.5)) / 0.04²

n = 601.5625

We need to round up to the nearest whole number since we can't have a fractional sample size, so the minimum sample size needed is 602 voters.

Therefore, the politician should obtain a sample of at least 602 voters to estimate the proportion of voters supporting her position on forced busing with a 90% level of confidence and a 4% margin of error.

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Answer: The population three years ago was 156250.

Step-by-step explanation:

Let 3 years ago, the population of a city = P

Rate of growth (R) = 8% p.a.

Present population (P) = 1,96,830.

Therefore,

[tex]A=P(1+R100)n[/tex]

P = A÷(1 + 8/100)³

196830 ÷ (1+2/25)³

=156250.

3 years ago, the population of the city = 156250.

The length of the sides x and y of the right-angled triangle are both equal to 9m using the trigonometric ratio of sine and cosine of angle 45°

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.

The basic trigonometric ratios includes;

sine, cosine and tangent.

Considering the right-angled triangle, we shall calculate for the length x and y by application of the trigonometric ratio of sine and cosine for the angle 45°.

sin 45° = y/9√2 {opposite/hypotenuse}

by cross multiplication

y = 9√2 × sin 45°

recall that sin 45° = √2/2

y = 9√2 × √2/2

y = 9m

cos 45° = x/9√2 {adjacent/hypotenuse}

by cross multiplication

x = 9√2 × cos 45°

recall that cos 45° = √2/2

x = 9√2 × √2/2

x = 9m

Therefore, the length of the sides x and y of the right-angled triangle are both equal to 9m using the trigonometric ratio of sine and cosine of angle 45°.

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91.6 grams of a 100 gram sample will remain radioactive after 2 hours. The solution has been obtained by using the concept of radioactive decay.

What is Radioactive decay?

Radioactive decay is the spontaneous destruction of an atomic nucleus in a radioactive substance that causes the emission of radiation from the nucleus. A parent nuclide in a radioactive process is one that decays, and a daughter nuclide is one that is created in the radioactive process.

We are given that a radioactive substance has a decay rate of 0.044 per hour.

Using the radioactive decay formula,

N(t) = N₀ [tex]e^{-kt}[/tex]

Initially, N = 100

k = 0.044

t = 2

So,

⇒N(t) = 100 * e⁽⁻⁰°⁰⁴⁴ ˣ ²⁾

⇒N(t) = 91.5761

⇒N(t) = 91.6

Hence, 91.6 grams of a 100 gram sample will remain radioactive after 2 hours.

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Answer:

C

...................

The simple interest Samuel will have to pay will be 60 Rs.

What exactly is simple interest?

Simple Interest is a simple way for computing interest on a loan or principle amount. Simple interest is a concept that is employed in numerous industries, including banking, finance, and automobiles. When you make a loan payment, the monthly interest is deducted first, followed by the principle amount.

The simple interest formula is as follows:

SI=P*R*T/100

SI stands for simple interest.

P stands for principal.

R is the interest rate (in percentage)

T denotes the length of time (in years)

The following formula is used to compute the total amount:

Amount (A) = Principal (P) x Simple Interest (SI)

Now,

As given principle=1000

rate=12%

time=6 months=1/2 years,

Then interest in 6 months will be = 1000*12*1/2*100

=10*12/2

=10*6

=60

Hence,

           The simple interest Samuel will have to pay will be 60 Rs.

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The height of 164.8 centimeter after conversion to feet is equivalent to  5.41 feet .

The various measurements units that are used in measuring the height of an object are , centimeter (cm) , meter (m) , feet , inches .

We have to convert the height of 164.8 cm to feet ;

we know that , 1 centimeter is = 0.0328 feet ;

So , we multiply the units given in centimeter by 0.0328 ,

On multiplying 164.8 cm by 0.0328 ;

We get ;

⇒ 164.8 centimeter = 164.8 × 0.0328 ;

⇒ 164.8 centimeter = 5.40544 feet ≈ 5.41 feet ;

Therefore , 164.8 cm is approximately equal to 5.41 feet .

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Answer:

216

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High temp ≥ Low temp + difference

High temp ≥ -8°F + 35°F

High temp ≥ 27°F

An inequality is a relationship between two different quantities or expressions.

An inequality may be expressed by a mathematical sentence that uses the following symbols:

< is less than

> is greater than

≤ is less than or equal to

≥ is greater than or equal to

≠ is not equal to

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The length of the guy wire, to the nearest foot is 23 feet.

Based on the information provided, we can logically deduce that triangle ABE (ΔABE) is similar to triangle (ΔCDE) and the following parameters about the geometric figures;

Additionally, the corresponding sides of similar triangles are equal;

AB/CD = BE/DE

AB/6 = (9 + 4)/4

AB/6 = 13/4

AB = 19.5 feet.

By applying Pythagorean' theorem, side AE is given by:

AE = √(AB² + BE²)

AE = √(19.5² + 13²)

AE = 23.44 ≈ 23 feet.

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Answer:

360 degrees

Step-by-step explanation:

I remember learning this in Math class. The rhombus angle sum will make 360 degrees.

AC=3x-4 AB=62 BC=x-2, x = 17. This can be solved by using the concept of simplification.

A line is an endlessly long object without breadth, depth, or curvature in geometry. So, despite the fact that they can exist in two, three, or more dimensional environments, lines are one-dimensional things. The term "line" can also refer to a line segment that has two locations that serve as its endpoints in daily life.

The most clear and simple way to calculate depreciation is along a straight line. It is most beneficial when an asset's value declines slowly over time at a pace that is close to constant.

Given that,

AC=3x-4

AB=62

BC=x-2

As we can clearly see in line AB:

AC+BC= AB

=>(3x-4)+(x-2)= 62

=>4x -6 = 62

=>4x = 62+6

=>4x = 68

=>x = 68/4

=>x= 17

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The complete question is as follows:

The mean arterial pressure formula is MAP = CO x TPR or MAP = (SBP + 2DBP) / 3.

The mean arterial pressure (MAP) formula is:

MAP = CO x TPR

where:

CO is the cardiac output (how much blood is siphoned by the heart each moment)

TPR is the all-out peripheral resistance (the resistance from the bloodstream in the body's veins)

On the other hand, the mean arterial pressure can also be calculated using the following equation:

MAP = (SBP + 2DBP)/3

where:

SBP is the systolic blood pressure (the highest pressure in the arteries when the heart beats)

DBP is the diastolic blood pressure(the lowest pressure in the arteries when the heart is at rest between beats)

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The equation of the ellipse is equal to (x - 6)² / 49 + (y + 6)² / 36 = 1.

In this problem we must derive the equation of an ellipse based on information about the center, a vertex and a co-vertex thereof. The vertex represents the end of the major semiaxis that lies on the curve and co-vertex is the end of the minor semiaxis that lies on the curve. The major semiaxis is parallel with x-axis and the minor semiaxis is parallel with y-axis.

The standard form of the ellipse is shown below:

(x - h)² / a² + (y - k)² / b² = 1

Where:

Now we proceed to derive the equation of the ellipse:

Major semiaxis:

A = (13, - 6) - (6, - 6)

A = (7, 0)

a = 7

Minor semiaxis:

B = (6, 0) - (6, - 6)

B = (0, 6)

b = 6

Equation of the elipse:

(x - 6)² / 49 + (y + 6)² / 36 = 1

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The option range of a function is (-∞, ∞), x-intercept of (0.1, 0), and the vertical asymptote is x = 0.

What is a function?

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

As we can see in the picture, we have given a function:

We have a function:

g(x) = 4log(x) + 4

To find x-intercept plug g(x) = 0

0 = 4logx + 4

x = 0.1

(0.1, 0)

The vertical asymptote:

x = 0

The range of a function:

(-∞, ∞)

Thus, the option range of a function is (-∞, ∞), x-intercept of (0.1, 0), and the vertical asymptote is x = 0.

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The step by step process of making the  8 by 10 frame consists of gather materials, measure the size and cut and screw it.

The first step in making a frame is to gather your materials. You'll need wood or other materials to construct the frame, as well as some tools like a saw and a hammer or nail gun.

To calculate the size of your frame, you'll need to add some extra length and width to the dimensions of your photo.

Once you have your dimensions, you'll need to cut your wood or other materials to size. You'll need four pieces of wood to create the frame - two longer pieces for the sides, and two shorter pieces for the top and bottom.

Next, you'll need to assemble your frame using nails or screws. Make sure the corners are flush and that the frame is square. You can use a carpenter's square to check your angles and make sure everything is aligned correctly.

Finally, you'll need to finish your frame. This could involve painting or staining the wood, adding decorative elements like beads or embellishments, or simply leaving the wood as-is for a more natural look. Once your frame is complete, you can insert your photo or artwork and enjoy your new creation!

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